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D efense 
Intelligence 
R eference 
D ocument
j^^^^^^JJ A cquisition Threat Support
6 April 2010
IC OD: 1 December 2009
DIA-08-1004-005
High-Frequency Gravitational 
W ave Communications
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High-Frequency Gravitational W ave Communications
Prepared by:
Acquisition Support D ivision (D W O-3)
D efense W arning Office
D irectorate for Analysis
D efense Intelligence Agency
Author:
AAP Person 77
Administrative Note
COPYRIGHT W ARNING: Further dissemination of the photographs in this publication is not authorized.
This product is one in a series of advanced technology reports produced in FY 2009 
under the Defense Intelligence Agency, Defense Warning Office's Advanced Aerospace 
Weapon System Applications (AAWSA) Program. C omments or questions pertaining to 
this document should be addressed to|AAP Person 1 | AAWSA Program
Manager, Defense Intelligence Agency, ATTN: C LAR/DWO-3, Bldg 6000, Washington, 
DC  20340-5100.
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Contents
Summary...............................................................................      v
1 .0 Introduction.............................................................................................  1
1.1 Introduction.....................................................................................................  1
1.2 D efinition of High-Frequency Gravitational W aves............................................1
2 .0 HFGW Communications...........................................................................................2
2.1 HFGW Generators (T ransmitters)...........................................  2
2.1.1 HFGW Generator Concepts................................................................    2
2.1.2 Alternative Approaches..................................................................................6
2.1.3 Piezoelectric Approach...................................................................................6
2.1.4 Infrared-Excited M olecules Approach..........................................................7
2.2 HFGW D etectors (R eceivers)..............................................  12
2.2.1 Alternative Approaches..........................................................................  12
2.2.2 Concept (Li-Effect).......................................................................................14
2.2.3 Quantum B ack-Action Limit.........................................................................16
2.2.4 Li-B aker HFGW D etector..............................................................................20
3 .0 Operational Concerns............................................................................................22
3.1 Link B udget...........................................................................................................22
3.1.1 Signal-to-Noise R atio...................................................................................22
3.1.2 Link B udget Considerations.........................................................................23
3.2 B andwidth........................................................................  25
3.3 Frequency and T ime Standard............................................................................25
3.3.1 Improvements Accruing from a HFGW  T ime Standard............................27
3.3.2 Search Space Improvement Accruing From HFGW FT S...............  28
3.3.3 T he Impact of Phase Noise Improvements on Phase Shift Encoding ... 29
3.3.4 T he Impact of Frequency Noise Improvements on FD M A and FHSS.....30
3.4 Possible Future Upgrades to the FT S D evices..................................................30
3.4.1 Propagating Signals From Optical Lattice Clocks for T iming..................31
3.4.2 In Navigating and M apping Interplanetary Geoids..................................31
4 .0 Future Potential....................................................................................  32
4.1 D evelopmental R oadmap.....................................................................................32
4.2 HFGW Communications Predictions to 20 50 .....................................................33
4.3 Interplanetary Navigation and Geoid M apping to 20 50 ..................................34
4.4 Other Possible HFGW Applications....................................................................36
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4.5 20 50 and B eyond............................................................................................  37
5 .0 Acknowledgements......................................................................    37
6 .0 R eferences..................................................................................    37
Appendix A: Nomenclature....................................................        44
Appendix B : Li-B aker HFGW D etector...........................................................................45
Appendix C: Perturbative Photon Fluxes Generated B y High-Frequency 
Gravitational W aves and T heir Physical Effects...................  52
Figures
Figure 1. Communication Link B lock D iagram...............................................................2
Figure 2. Change in Centrifugal Force of Orbiting M asses, AfCf, R eplaced by Change 
in T angential Force, Aft, to Achieve HFGW R adiation...................3
Figure 3. Circular R esonator Geometry Using Infrared Excitation.............................8
Figure 4. R adiation Pattern Calculated by Landau and Lifshitz (1975)......................8
Figure 5. GW Flux Growth Analogous to Stack of N Orbital Planes............................9
Figure 6. Stack of Circular-W ave-Guide Plates W ith T ypical M olecule Jerks, Af's... 9
Figure 7. Omni-D irectional Nature of the HFGW R adiation Pattern..........................10
Figure 8. Predicted R elic GW Energy D ensity as a Function of Frequency.............11
Figure 9. B irmingham University HFGW D etector......................................  13
Figure 10 . INFN Genoa HFGW D etector...................................  13
Figure 11. T he National Astronomical Observatory of Japan 10 0 M Hz D etector ... 14
Figure 12. D etection Photons Sent to Locations that are Less Affected by Noise.. 15
Figure 13. Quantum B ack Action as a M echanism for Creating the Standard 
Quantum Limit.............................................................................17
Figure 14. Schematic of Ultra-Sensitive HFGW D etector............................................21
Figure 15. Fractal M embrane Component of Li-B aker D etector Exhibited in Planar 
Form......................................................................    21
Figure 16. Conceptual SNR  Fill Factors: Signal and Noise Components..................23
Figure 17. A B lock D iagram of a T ypical Link B udget.................................................24
Figure 18. A Proposed Near Earth D istribution of Frequency T ime Standard..........26
Figure 19. HFGW Supplemented R emote T erminal D esign.........................................27
Figure 20 . Acquisition Search Space Improvement Accruing From HFGW FT S.......28
Figure 21. T he Impact of Phase Noise Improvements on Phase Shift Encoding ... 29
Figure 22. T he Impact of Frequency Noise Improvements on FD M A and FHSS......30
Figure 23. T he Earth's Associated Lagrangian Points................................................31
Figure 24. HFGW Com Space Application D evelopment R oadmap, Estimated 
T imeline.......................................................................................32
Figure 25. A GW Pair on Earth as Used by a Lunar M ission.......................................34
Figure 26. A GW Pair on Earth and on the M oon, as Used by a M ission to M ars .... 35
Figure 27. A GW Pair on Earth and on M ars for an Outer Planetary R eference 
Pair.........................................................................  35
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High-Frequency Gravitational W ave Communications
Summary
• Fourteen laboratory high-frequency gravitational wave (HFGW ) generators 
(or transmitters) have been proposed in the past 45 years in peer-reviewed 
journal articles.
• T he most promising laboratory HFGW  generators are those that utilize very 
large numbers of sub-microscopic radiation elements.
• T he Piezoelectric Approach to HFGW  generation is best for the proof-of- 
concept test and the proposed IR -excited M olecules Approach is best for an 
operational communications HFGW  transmitter.
• T en different HFGW  detectors (or receivers) have been proposed since 
1978 and reported in peer-reviewed journal articles.
• Several different HFGW receivers can be utilized for communication, but the 
proposed Li-B aker detector (plans & specification development in Appendix 
B ) shows the most promise (underlying concept in Appendix C). T he Li- 
effect, upon which the Li-B aker detector is based, is not so new that it is 
untested in the literature. At least nine peer-reviewed research publications 
concerning the theory have appeared following the initial peer-reviewed 
article by Li, T ang and Zhao (1992).
• B ecause HFGW  communications are carried on an extremely narrow beam 
directly through the Earth, there is a very low probability of interception.
• T heoretical results confirm that the Li-B aker detector is photon-signal 
limited, not quantum-noise limited—that is, the Standard Quantum Limit is 
so low that a properly designed Li-B aker detector can have sufficient 
sensitivity to observe HFGW s of amplitude A « 10 32 m/m.
• Utilizing the IR -excited M olecules HFGW generator approach and the Li- 
B aker detector, the theoretical information-transfer rate over 7,0 0 0 km of 
distance, beamed directly through the Earth, is about 1.9 x 10 6 bits per 
second.
• A means of propagating a Frequency T ime Standard may be one viable 
early low-bandwidth application for HFGW communications.
• HFGW sources on the Earth, the M oon, and M ars may act as reference 
standards for interplanetary navigation, with the advantage that they 
cannot be shielded or shadowed by planetary masses. Plasma interference 
seen at planetary entry would be eliminated, and precise charting of 
Lagrangian points would be possible.
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1 .0 Introduction
1.1 INT R OD UCT ION
Of the applications of high-frequency gravitational waves (HFG Ws), communication 
appears to be the most important and most immediate. G ravitational waves have a 
very low cross section for absorption by normal matter, so high-frequency waves could, 
in principle, carry significant information content with effectively no absorption unlike 
electromagnetic (EM) waves. Multi-channel HFG W communications can be both point- 
to-point (for example, to deeply submerged submarines) and point-to-multipoint, like 
cell phones. HFG Ws pass through all ordinary material things without attenuation and 
represent the ultimate wireless system. One could communicate directly through the 
Earth from Moscow in Russia to C aracas in Venezuela—without the need for fiber optic 
cables, microwave relays, or satellite transponders. Antennas, cables, and phone lines 
would be things of the past. A timing standard alone, provided by HFG W stations 
around the globe, could result in a multi-billion dollar savings in conventional telecom 
systems over ten years, according to the recent analysis of Harper and Stephenson 
(2007). The communication and navigation needs of future magneto hydrodynamic 
(MHD) aerospace vehicles, such as the MHD aerodyne (www.mhdprospects.com), which 
is high in electromagnetic interference, similar to plasma interference seen at reentry, 
would be another possible applications area for HFG W communications.
1.2 D EFINIT ION OF HIGH-FR EQUENCY GR AV IT AT IONAL W AV ES
Visualize the luffing of a sail as a sailboat comes about or tacks. The waves in the sail's 
fabric are similar in many ways to gravitational waves (G Ws), but instead of sailcloth 
fabric, gravitational waves move through a "fabric" of space. Einstein called this fabric 
the "space-time continuum" in his 1915 work known as G eneral Relativity (G R). 
Although his theory is very sophisticated, the concept is relatively simple. This fabric is 
four-dimensional: it has the three usual dimensions of space—east-west, north-south, 
and up-down—plus the fourth dimension of time. Here is an example: we define a 
location on this "fabric" (Einstein, 1916) as 5th Street and Third Avenue on the fourth 
floor at 9 AM. No one can see this "fabric," just as no one can see wind, sound, or 
gravity. Nevertheless, those elements are real, and so is this "fabric." If one could 
generate ripples in this space-time fabric, many applications would become available. 
Much like radio waves can be used to transmit information through space, gravitational 
waves could be used to perform analogous functions. G ravitational waves are the 
subject of extensive current research, which so far has focused on low frequencies. 
High-frequency gravitational waves, as defined by physicists Douglass and Braginsky 
(1979), are gravitational waves having frequencies higher than 100 kHz. Low-frequency 
gravitational waves (LFG Ws), such as those detectable by interferometric G W detectors 
(for example, the Laser Interferometer G ravitational Observatory, or LIG O) are not 
applicable to communications due to their very long wavelengths, often thousands of 
kilometers in length and, even more importantly, the inability to generate them 
effectively in the laboratory. Furthermore LFG W detectors cannot detect HFG Ws 
(Shawhan, P. S., 2004).
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2 .0 HFGW Communications
C onsider the case of a single point-to-point two station full duplex communication 
system, as is represented in Figure 1. Such a system is often characterized as a single 
data link, and requires two transmitters, one at each end, and two receivers, one at 
each end. To avoid self-interference the link in one direction often uses a frequency of 
radiation different than the link in the opposite direction.
F ull D uplex Communication Link
U sing G ravitational W ave G enerators and S ensors
S tation 1 S tation 2
Figure 1. Communication Link B lock D iagram
If one were to apply the emerging technology of gravitational wave control to such a 
link, one would use G W generators for the transmitters on each end, and G W sensors 
for the receivers at each end (Stephenson, 2009a). In the example shown in Figure 1, 
station 1 would have a G W generator transmitting at a frequency of an and a G W 
sensor sensitive to a frequency of ©2, without being sensitive to a frequency of ©i. 
Likewise, station 2 would have a G W generator transmitting at a frequency of 02 and a 
G W sensor sensitive to a frequency of wi, without being sensitive to a frequency of ©2. 
This is the minimum functionality required to constitute a communication link. Signal 
strengths of the respective G W generators would need to be sufficient to overcome link 
loss, coupling losses, and noises sources. Signal to noise considerations and link 
budgets are covered in further detail in Section 3.1.
2.1 HFGW GENER AT OR S (T R ANSM IT T ER S)
2.1.1 HFGW Generator Concepts
Several sources for HFG Ws or means for their generation exist. The first generation 
means is the same for gravitational waves (G Ws) of all frequencies and is based upon 
the quadrupole equation first derived by Einstein in 1918. A formulation of the 
quadrupole that is easily related to the orbital motion of binary stars or black holes,
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rotating rods, laboratory HFG W generation, and so forth is based upon the "jerk" or 
shake of mass (time rate of change of acceleration) and is derived by Baker (2006) as
P = 1.76X10'52 (2rAf/At)2 W (1)
where P is the power of the G Ws, W; r is the distance between two masses, m; Af is a 
change in force, N; over the time interval At, s; that is, the jerk or shake of the two 
masses, such as the change in centrifugal force vector with time; for example, as 
masses move around each other on a circular orbit. Figure 2 describes that situation. 
Please recognize, however, that Af need NOT be a gravitational force (see Einstein, 
1918; Infeld quoted by Weber 1964, p. 97; G rishchuk 1974). Electromagnetic forces 
are more than 1035 larger than gravitational forces and should be employed in 
laboratory G W generation. As Weber (1964, p. 97) points out: "The non-gravitational 
forces play a decisive role in methods for detection and generation of gravitational 
waves ..." Equation (1) is also termed "quadrupole formalism" and holds in weak 
gravitational fields (well over 100 g's), for speeds of the generator "components" less 
than the speed of light and for r less than the G W wavelength. This last restriction may 
not really apply. C ertainly there would be G W generated for r greater than the G W 
wavelength, but the quadrupole formalism might not apply exactly. For very small At, 
the G W wavelength, Ag w = cAt (where c ~ 3x io8 ms-1, the speed of light) is very small 
and the G W frequency vg w is high. As a numerical example, r is choosen to be 10 m 
(convenient laboratory size, though usually greater than Ag w), Af = 4xio8 N; for 
example, the force produced by a large number of piezoelectric resonators and At = 
2xlO'10 s; equivalent to about a vg w = 5 G Hz jerk or shake frequency so that Ag w = 6 
cm and P = 2.8xi0’13 W or 0.28 picowatts. C learly a very small HFG W power is 
generated.
Figure 2. Change in Centrifugal Force of Orbiting M asses, Afd; R eplaced by Change in T angential Force, 
Aft, to Achieve HFGW R adiation
One of the first suggested means for the laboratory generation of HFG Ws was the so- 
called gaser analogous to the laser for light. Simply described (Halpern and Laurent,
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1964), the gaser consists of a long rod of a material and microscopic parts of which can 
be excited by a means, such as electromagnetic (EM) radiation, to emit HFG Ws. They 
utilize linearized theory to treat the interaction of a gravitational field with matter: 
"Application is made to the emission ... of gravitons by microscopic systems such as 
molecules and nuclei." G rishchuk and Sazhin in early 1974 discussed the emission of 
gravitational waves by an electromagnetic cavity. In August of 1974 C hapline, Nuckolls 
and Woods suggested the generation of HFG Ws by nuclear explosions. In this same 
regard Fontana suggested that the problem of efficient generation of HFG Ws and pulses 
of gravitational radiation might find a reasonably simple solution by employing nuclear 
matter (Fontana and Baker, 2006; Fontana and Binder, 2009), especially isomers. A 
fissioning isomer not only rotates at extremely high frequency (~ 3.03xl024 s-1) 
according to the aforementioned references, but is also highly deformed in the first 
stages of fission (the nucleus is rotating and made asymmetric "before" fission). Thus 
one achieves significant impulsive forces (for example, 3.67xl08 N) acting over 
extremely short time spans (for example, 3.3xlO'22 s). Alternatively, a pulsed particle 
beam, which could include antimatter, could trigger nuclear reactions and build up a 
coherent G W as the particles move through a target mass. The usual difficulty with 
HFG Ws generated by nuclear reactions is the small dimensions of their nuclear-reaction 
volumes—that is, the small moment of inertia and submicroscopic radii of gyration (for 
example, IO-16 m) of the nuclear-mass system. Such a difficulty is overcome by utilizing 
small clusters of nuclear material, whose nuclear reactions are in synchronization; for 
example, through the use of a computer controlled logic system. Such nuclear- 
energized HFG W generators are currently very theoretical. Braginsky and Rudenko 
(1978) discussed the generation of gravitational waves in the laboratory and proposed 
a means utilizing small particles In 1981 Romero and Dehnen analyzed the generation 
of gravitational radiation in the laboratory also utilizing a linear array of piezoelectric 
crystals that will be analyzed in more detail in Section 2.1.3. In 1988 Pinto and Rotoli 
presented a paper on the laboratory generation of gravitational waves at the Italian 
Conference on General Relativity and Gravitational Physics. Another Italian, G iorgio 
Fontana (1998), suggested that the possibility of emission of high frequency 
gravitational radiation from junction between d-wave and s-wave superconductors.
Kraus (1991) proposed that gravitational-wave communication might be possible in the 
IEEE A ntennas & Propagation magazine. At the first HFG W Working G roup C onference 
at the MITRE C orporation in 2003, G rishchuk analyzed electromagnetic generators and 
detectors of gravitational waves. At that same C onference Valentin Rudenko presented 
a paper on the optimization of parameters of a coupled generator-receiver for a HFG W 
Hertz experiment. At the second HFG W Working G roup C onference in Austin, Texas, in 
2007, Kolosnitsyn and Rudenko presented another paper on the generation and 
detection of the high-frequency gravitational radiation in a strong magnetic field. In 
2007, and more recently this year, a new type of HFG W generator/detector and mirror 
system based on thin, type I superconducting films was proposed by R. C hiao, S. 
Minter, and K. Wegter-McNelly (2007; 2009a,b). Therefore it is evident that a number 
of devices for the laboratory generation of HFG Ws have been proposed including the 
aforementioned gaser (as has been mentioned, was first proposed by Halpren and 
Laurent in 1964, some 45 years ago) discussed by Fontana and Baker (2003); as well 
as an actual laser generator of HFG Ws as discussed by Li and Li (2006). Finally a rather 
practical laboratory HFG W generator, which may be appropriate for the initial proof-of- 
concept test, is one utilizing off-the-shelf components such as magnetron energized 
piezoelectric crystals or Film Bulk Acoustic Resonators or FBARs has been analyzed in 
Woods and Baker, (2005) and Baker, Woods and Li (2006).
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The figure of merit for a HFG W generator is given explicitly by Baker, Woods and Li 
(2006). This Figure of merit can be extended by considering other effects since in the 
laboratory the force change could not even approach those of the celestial sources. It 
would seem that the magnitude of any laboratory generated G Ws could be best 
increased (1) by utilizing electromagnetic forces rather than gravitational, (2) by 
increasing the distance between the gravitational radiators, (3) by increasing the G W 
frequency (that is, reducing At) and especially (4) by developing a large number of in­
phase system elements. This last effect enters as the square of the number of 
elements, N , as proved using G eneral Relativity analyses by Dehnen and Romero- 
Borja's analyses (Romero and Dehnen, 1981; Dehnen and Romero, 2003). Such N2 
dependence also may be the key to successful laboratory generation of G Ws, especially 
HFG Ws. In that regard, recent proposal by Woods (Woods and Baker, 2009; Black and 
Baker, 2009)) propose the use of infrared-energized atomic nuclei, electrons and or 
molecules, which have a very large N, contained in a stack of N waveguide rings 
(Patents Pending). The distance between G W radiators may be proportional to the G W 
wavelength in that it may have a limit that is less than or equal to a G W wavelength. 
The wavelength is inversely proportional to the G W frequency. Thus given some value 
for the proportional constant, say unity or the distance between radiators equal to one 
G W wavelength, the G W frequency cancels out. As already noted it is important to take 
advantage of square of the number of in phase elements for useful laboratory HFG W 
generation. If the elements are sliced in one dimension (the dimension along the axis of 
HFG W generation) in order to increase the number of elements, then the change in 
force per element will be inversely proportional to the number of elements. For 
example, if the elements are sliced into one hundred separate pieces, then each piece 
will have one hundredth of the force of the unsliced element. Essentially, f = ma and it 
is assumed that the acceleration of the element was the same after the split as before. 
This result also follows Equation (8), page 17 in Baker, Stephenson and Li (2008b) and 
if there were 100 splits of an FBAR, then the power to an individual slice, P and its 
mass, m would be both one hundredth of their un-split value and the square root of 
their product would again be one hundredth. The frequency of the split elements may 
be a higher value — but the attendant increase in G W power proportional to the square 
of the higher frequency and the decrease in power due to a smaller distance between 
tracks (assuming that the distance between tracks is one G W wavelength, which would 
be smaller) would cancel and there would be no net effect on HFG W amplitude. It is 
concluded, therefore, that in this particular special situation the amplitude of the 
generated HFG Ws is proportional to the number of in-phase elements, A/ (not the 
square). In any event a large number of elements for a given HFG W-generator length 
can be best realized by reducing the size of the individual elements to submicroscopic 
size (as discussed in U. S. Patent Number 6,784,591).
In the case of HFG W generation for communications applications, it is important to 
relate the amplitude of a G W, A, with the power, P, or more exactly with the G W flux, 
Fg w, in Wm'2. For a viable communications link, the HFG W amplitude, A, must be large 
enough to be detected at the HFG W receiver. From Appendix B of Baker, Woods and Li 
(2006),
A = 1.28xio18 ( Fg w/vg w)’a m/m (2)
where A has the dimensionless value of spacetime strain or m/m and vg w is the G W 
frequency s'1. Following the proceeding numerical example we will concentrate the 
HFG W on a diffraction-limited area of 4xl0‘3 m2 or 0.004 m2 for a HFG W flux of
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(2.8x10 13)/(4xl0‘3) = 7xl0‘u Wm’2. Thus A = 2xl0’33. It is an extremely small 
HFG W amplitude, but possibly a detectable signal.
2.1.2 Alternative Approaches
There are several alternative approaches to the laboratory generation of HFG Ws 
developed over the past 45 years as discussed in the preceding Section 2.1.1. They can 
be categorized as EM-cavity generated, nuclear-energy generated, superconductor­
generated, laser-impact generated and energized microscopic & submicroscopic-particle 
generated HFG Ws. Of these categories the last category appears to be the most 
promising for early deployment in HFG W communications systems. Furthermore, one 
embodiment of that category: the Magnetron-energized FBARs generator, utilizing off- 
the-shelf equipment, would seem the most useful for proof-of-concept tests. For a 
practical, operational communications system HFG W generator (transmitter) the strong 
dependence of HFG W generator's power on the number of radiating elements, N, 
recommends a system utilizing molecular elements as suggested by Braginsky and 
Rudenko (1978) or using Infrared (IR)-energized pentane molecules in a stack of 
circular waveguides as proposed by Woods and Baker (2009). The Magnetron-energized 
FBARs and the IR-energized pentane will be considered in the next-following sections.
2.1.3 Piezoelectric Approach
Let us consider the 1.8xio8 cell-phone film bulk acoustic resonators or FBARs, 10,000 
Microwave-Magnetron, proof-of-concept laboratory HFG W generator. Assuming a 10 pm 
distance or margin between the 100 pm square conventional FBARs, the overall length 
of the laboratory generator will be 110 x (10-6 m) x (1.8x10s elements) = 19.8 km. It 
will have a total HFG W power of 0.066 W and for a distance out from the last in-line, in­
phase FBAR element of one HFG W wavelength (6.1 cm) it will have a flux of 3.53 Wm’2, 
yielding a HFG W amplitude there of A = 4.9x 102S m/m. By the way, the inline set of 
FBAR elements also produces a more needlelike radiation pattern of HFG Ws so that the 
flux and resulting A may even be larger. Although the frequencies may be different 
analyses (2003), one can extrapolate approximately from the results of Dehnen and 
Romero-Borja's analyses in which the angle of the needle-like radiation pattern is 
inversely proportional to the square root of the product of the distance between the 
radiators (the width between FBAR bands or tracks) and N. The distance for the system 
discussed here is 6.1 cm and for Dehnen's system 0.00001 m, for a factor of 6,100 and 
N differs by (1.8xl08)/(5xl07) = 3.6 for a product of 2.2xl04and the inverse of the 
square root is 6.7xlO'3. Using the result from Dehnen's paper (Equation (4.51), page 
12) of a needle half angle of 1.7 degrees we would extrapolate to 0.0115 degrees or 
very approximately 2xl0’4 radians. Since there is no longer the constraint to the use of 
rudimentary off-the-shelf components as there was for the proof-of-concept apparatus, 
the specially designed submicroscopic elements can be manipulated. First, they will be 
staggered into two bands or tracks of 100 rows each or 110 x 100 pm = 1.1 cm wide 
bands of FBARs a wavelength or 6.1 cm apart. The rows will be staggered by displacing 
adjacent rows in the bands by 1.1 pm. Thus the overall length will be reduced to 198 
m. Second, the 100 pm length of each FBAR element can be sliced, along the direction 
of travel of the HFG W build up, into one-hundred 1 pm wide slices (exhibiting 0.1 pm 
margins). The staggered row displacements are now reduced to 11 nm. The overall 
length will be reduced to about 198 cm. C oncentrating the 10 MW power to each of 
these 1.1 cm wide bands may prove to be difficult. Thus, as an example, the 
continuous-wave Magnetrons will be replaced by a pulsed microwave source having
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one-microsecond-long pulses one second apart. The required average power for each 
FBAR band will now be 10 W. As a practical nanotechnology limit, the slice width can be 
reduced by two orders of magnitude to 10 nm. This would also require that the row 
displacements would be 110 pm (we are now into atomic if not sub-atomic dimensional 
changes). The overall length could be reduced to about 2 cm or the amplitude of the 
HFG Ws could be increased to A = 4.9xl0‘26. In this latter case the average energizing 
microwave power applied to each band would need to be increased to 1 kW. A preferred 
compromise in this apparent nano-technology limit might be to reduce the HFG Ws 
generator's length to about 20 cm and increase the HFG W amplitude A to 4xi0’27 m/m.
The complementary approach to optimizing a practical HFG W generator is to increase 
the force produced by each element without increasing the required power (that is, 
increasing element efficiency). This was initially done using the modern light-weight 
piezoelectric FBARs rather than the heavy 10-gram crystals considered by Dehnen and 
Romero-Borja that were of 1981 vintage. Special designs of FBAR-like elements for 
optimum force-generation efficiency will improve the HFG W generator performance 
beyond that for the usual cell-phone FBAR designs. Another approach to element design 
is to utilize nano-size lasers whose targets are the force-generating elements (Li and Li, 
2006). Utilization of myriads of nano-size lasers would generate high-frequency HFG W 
pulses as noted in U. S. Patent Number 6,784,591. Thus there are a number of 
opportunities to enhance HFG W generation performance, utilizing special element 
designs, either by reducing the generator size or increasing the generated HFG W 
amplitude or both.
2.1.4 Infra red-Exci ted M olecules Approach
The very theoretical IR-generated HFG Ws suggested by Woods and Baker (2009) have 
significant promise. If one has a standing wave in a waveguide ring and excites it 
properly, then one will have a G W source at its center, as shown in Figure 3. The G W 
flux produced at its center is proportional to the n submicroscopic particle pairs (in this 
case pentane molecule pairs) in each ring. There is no n2 buildup, but there is an n 
buildup. If one has a stack of N plates of rings, which are excited in sequence at light 
speed as a generated, growing as a G W passes by, then one has an nN2 buildup in G W 
flux.
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IR monomode waveguide 
formed by active material
High power IR source
Figure 3. Circular R esonator Geometry Using Infrared Excitation
Analogous to Figure 2, we see in Figure 4 the radiation pattern for a pair of orbiting 
masses.
T
GW
Figure 4. R adiation Pattern Calculated by Landau and Lifshitz (1975)
Next consider a number N of such orbit planes stacked one on top of another with the 
gravitational-wave (G W) radiation growing flux (Wm*2) proportional to N2 as the G W 
moves up the axis of the Af orbit planes as in Figure 5.
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The stack of orbital planes are no replaced by a stack of N plates each containing n 
molecules in each waveguide ring as exhibited in Figure 6. Now there is a HFG W wave 
moving up the axis of the rings (or normal to the waveguide plates) and increasing in 
strength according to the product nN2.
Figure 6. Stack of Circular-W ave-Guide Plates 
W ith T ypical M olecule Jerks, AFs
One should consider the IR rings in more detail. As calculated, the IR wavelength is 
about 2.5x10 6 m. The IR waveguide has a cross-sectional area radius of M4 in order 
for it to be a monomode (lowest order mode) so that the phase doesn't change across 
the waveguide. Thus the cross-sectional area of each IR ring is n x (2.5xl0-6 m/4)2 = 
1.23x 10 12 m2 and its diameter is l,25xl0 6 m. The volume of each 100-m radius nano­
size toroidal ring is 2n x (100) x (1.23xio12) = 7.7x 10"12 m3. The mass density of 
pentane is divided by its molecular mass and that gives the density of jerkable masses 
of 6.3xl028 m 3. Thus the number of jerkable mass pairs, n, in a 100 m radius circular 
wave guide 2n = (6.3xl028) x ( 7.7xl0*12) = 4.85X1017 submicroscopic "particles" or 
potentially jerkable masses or n = 2.45x 1017 mass pairs. According to Table 1 of 
Woods and Baker (2009) for pentane Pi = 4.62xi016 W. Thus the flux at one meter 
distance for all of the mass pairs in a single ring from Equation (8) of Black and Baker 
(2009) is n x (0.01146) x p, = 1.29 Wm 2. It should be recognized that the axes of the 
opposite pentane molecules jerk (in response to the EM wave) may not be anti-parallel 
and tangential to the circular waveguides. On the other hand, the radiation pattern for 
the HFG W exhibits some omni-directional form, as shown in Figure 7, so significant 
HFG W radiation will be directed along the axis of the stack of circular waveguides 
(normal to the plates) and the HFG W will build up.
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Figure 7. Omni-D irectional Nature of the HFGW R adiation Pattern
Next consider a more convenient laboratory arrangement for the rings. The ring radius 
is reduced to one meter, but set up 100 rings, concentrically (side by side concentric 
rings in the same plane or plate) with an average radius of the one meter. The reduced 
radius drops the Pi by (100)2 to 4.62x 10’20, but because of the 100 concentric rings the 
n = 4.85x1017/2 remains the same. Thus the flux for a single "plate" of concentric rings 
is only reduced by IO4 to 1.29xl0'4 Wm-2. Now stack some IO6 of these 1.25xl0'6m 
thick plates on top of one another. Thus a 1.25 m high stack, barrel or cylinder as 
described in Baker (2001) is created. In this case, as shown in Figure 6, W = 106 and 
the N2 law can be applied. Thus a HFG W total flux of 1.29X108 Wm'2 in a very narrow 
beam will be generated by the stack. Of course (as pointed out in Woods and Baker 
(2009)) caution needs to be taken on how much power is fed to each ring. One possible 
arrangement is to feed the output of one ring to the input of the next. The problem 
here is that the source won't have a long enough coherence length, even if the 
attenuation of the IR doesn't kill the power after a ring or two. To avoid this, from one 
source the available energizing power could be divided equally between all the rings 
and fed to them up the stack or cylinder at the speed of light. The practical difficulties 
would be how to drive them all in correct phase, but it is a challenge for future research 
in the IR-ring approach.
Foran operational 50,000A infrared (IR.), 12.5 meter long, 10-meter radius (104 
concentric rings per plate so Pi = 1.29xl02 Wm 2 and 107 plates) cylindrical HFG W 
generator (Woods and Baker, 2009), the flux at a one-meter distance from the 
generator is, according to Table 1 of Black and Baker (2009) for A/ = 107, (1.146x 1012) 
x (1.29X102) = 1.48X1014 Wm'2 (very large, but with a very narrow 2.3xl0'4 radian 
half-power-point needle beam). The required generator power can be reduced by 
utilizing pulsed HFG Ws. Suppose that the distance between the generating or 
transmitting device and the detecting or receiving device is a little more than an Earth's 
equatorial radius, or ~ 7x 10s meters. At this distance, 7,000 km, the flux of the
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received signal, S, is (1.48xl014)/(7xl06)2 = 3 Wm-2, more than adequate for an 
effective communication system.
With this configuration, the width of the needle-like, narrow HFG W beam at the receive 
end is (2.3xi0'4) x (7xio6) = 1.6 km, and multiple HFG W carrier frequencies can be 
used, so the signal is very difficult to intercept, and is therefore useful as a low- 
probability-of-intercept (LPI) signal, even with widespread adoption of the technology. 
From Equation (2) the amplitude A of the HFG W at 7,000 km with the HFG W frequency 
(twice the IR frequency of vg w = 1.2xl014 s’1) given by: A  = 1.28xl0‘18 (S/vg w )'a = 
1.8xW32 (in dimensionless units or m/m), which would be detectable by the currently 
designed Li-Baker HFG W detector. Since the exact frequency and phase of the HFG W 
signal is known (unlike the stochastic relic HFG Ws, for which the Li-Baker detector was 
designed), a much more sensitive, optimized HFG W detector will likely be developed.
As shown in Figure 8, from G rishchuk (2008), there will be negligible relic HFG W noise 
at the IR HFG W generator's frequency of 1.2xl014 s1 and no other cosmic sources at 
these frequencies are currently hypothesized. Prior to the proof-of-concept test, one 
can assume a noise figure at the Li-Baker detector of 10'8 Wm’2.
Figure 8. Predicted R elic GW Energy D ensity as a Function of Frequency
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2.2 HFGW D ET ECT OR S (R ECEIV ER S)
2.2.1 Alternative Approaches
One of the first suggested means for the detection of HFG Ws concerns electromagnetic 
detectors (Braginsky, et al. 1974 and Braginsky and Rudenko, V, 1978). Then 
Pegoraro, et al. (1978) suggested the use of tuned resonant chamber HFG W detectors. 
Rudenko and Sazhin in 1980 proposed a Laser interferometer as a gravitational wave 
detector (somewhat similar to the current Japanese approach). In 1995 Tobar 
characterized multi-mode resonant-mass HFG W detectors and three years later in 1998 
(Ottaway, et al.) proposed a compact injection-locked Nd:YAG laser for HFG W 
detection. And in 1999 Tobar suggested, microwave parametric transducers for the 
next generation of resonant-mass gravitational wave HFG W detectors.
In the past few years, HFG W detectors have been fabricated at Birmingham University, 
England, INFN Genoa, Italy and in Japan. These types of detectors may be promising 
for the detection of the HFG Ws in the G Hz band (MHz band for the Japanese) in the 
future, but currently, their sensitivities are orders of magnitude less than what is 
required for the detection of high-frequency relic gravitational waves (HFRG Ws) from 
the big bang. Such a detection capability is to be expected, utilizing the Li-Baker 
detector (please see Appendix B for Plans & Specifications development). Nevertheless, 
all four candidate detectors; plus, possibly, the use of superconductors (Li and Baker, 
2007) should be analyzed for possible military applications. The Li-Baker HFG W 
detector was invented by R. M L Baker, Jr. of Transportation Sciences C orporation, 
C alifornia and patented in P. R. C hina (Baker, 2001). Based upon the theory of Li, Tang 
and Zhao (1992) termed the Li-effect, the detector was proposed by Baker during the 
period 1999-2000, a patent for it was filed in 2001, subsequently granted (Baker, 
2001), and preliminary details were published later by Baker, Stephenson and Li 
(2008a). This detector was conceived to be sensitive to relic HFG Ws (HFRG Ws) having 
amplitudes as small as 10'32 to IO’30.
The Birmingham University HFG W detector measures changes in the polarization state 
of a microwave beam (indicating the presence of a G W) moving in a waveguide about 
one meter across (see Figure 9). Also see C ruise (2000), Ingley and C ruise (2001) and 
C ruise and Ingley (2005). It is expected to be sensitive to HFG Ws having spacetime 
strains of A ~ 2 x 10'13 (Hz)',/2, where Hz is the G W frequency, and as usual A is a 
measure of the strain or fractional deformation in the spacetime continuum 
(dimensionless m/m).
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Figure 9. B irmingham University HFGW D etector
The INFN Genoa HFG W resonant antenna consists of two coupled, superconducting, 
spherical, harmonic oscillators a few centimeters in diameter (see Figure 10). The 
oscillators are designed to have (when uncoupled) almost equal resonant frequencies. 
In theory, the system is expected to have a sensitivity to HFG Ws with size (fractional 
deformations) of about ~ 2xl0'17 (Hz)^ with an expectation to reach a sensitivity of ~ 
2x 10-20 (Hz)_fe (Bernard, G emme, Parodi, and Picasso (2001); C hincarini and G emme. 
(2003)). As of this date, however, there is no further development of the INFN G enoa 
HFG W detector.
Figure 10 . INFN Genoa HFGW D etector
The Kawamura 100 MHz HFG W detector has been built by the A stronomical 
Observatory of Japan. It consists of two synchronous interferometers exhibiting an 
arms length of 75 cm. Please see Figure 11. Its sensitivity is now about 10'16 (Hz)'V!
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According to C ruise (2008) of Birmingham University its frequency is limited to 100 MHz 
and at higher frequencies its sensitivity diminishes. In the case of the Infrared-excited 
molecules approach, on might employ a variant of the Robinson G ravitational Wave 
Background Telescope for the receiver or detector (Yoon, et al., 2006). It is a 
bolometric large angular scale C osmic Microwave Background (C MB) polarimeter, but 
might possibly be modifiable for direct HFG W detection.
UNIVERSITY™  
BIRM INGHAM
D evelopment of 10 0 MH z G W  detectors 
at N ational Astronomical O bservatory of
Synchronous recycling Interferometer (Concept: Drever 1983)
Figure 11. T he National Astronomical Observatory of Japan 10 0 M Hz D etector
2.2.2 Concept (Li-Effect)
The Li-Effect was first published in 1992 and subsequently, some nine peer-reviewed 
papers have been published concerning it including a capstone paper, Li, et ai. (2008) 
included as Appendix C . The Li-Effect is very different from the classical (inverse) 
G ertsenshtein-Effect. With the Li-Effect, a gravitational wave transfers energy to a 
separately generated electromagnetic (EM) wave in the presence of a static magnetic 
field. That EM wave has the same frequency as the G W and moves in the same 
direction. This is the "synchro-resonance condition," in which the EM and G W waves are 
synchronized (move in the same direction and have the same frequency) and is unlike 
the G ertsenshtein- Effect.
The result of the intersection of the parallel and superimposed EM and G W beams, 
according to the Li-Effect, is new EM  photons moving off in a direction perpendicular to 
the beams and the magnetic field directions. Thus, these new photons occupy a 
separate region of space (see Figure 12) that can be made essentially noise-free and 
the synchro-resonance EM beam itself (in this case a G aussian beam) is not sensed 
there, so it does not interfere with detection of the photons. This Li-Effect was utilized 
by Baker (2001) in the design of the Li-Baker HFG W detector and C hinese Patent 
(Baker, 2000) of a device to detect HFG Ws, the innovative Li-Baker HFG W Detector.
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Signal (PPF) and Noise (BPF) 
have very different physical behavior 
PPF > BPF at this end of x-axis
s
*
+
Signal (PPF) and Noise (BPF) 
have very different physical behavior 
PPF > BPF at this end of x-axis
A
4
GW & EM
Synchro-Resonant
Figure 12. D etection Photons Sent to Locations T hat are Less Affected by Noise
The synchro-resonance solution of Einstein's field equations [Li et al. (2008), pp. 411 to 
413] is radically different from the G ertsenshtein (1962) effect. The newer Li-Effect 
solution utilizes a coupling between EM and gravitational waves (Li, Tang and Zhao, 
1992) that arises according to the theory of relativity. And a strong static magnetic field 
in the /-direction, 8, is superimposed upon a G W propagating in the z-direction, as in 
the inverse G ertsenshtein effect. However, with the Li-Effect, there is an additional 
focused microwave beam ("G aussian beam") at the expected frequency, phase and 
bandwidth of the HFG Ws in the same direction (z) as the G W (as shown in Figure 12).
Unlike the Gertsenshtein effect, a first-order perturbative photon flux (PPF), comprising 
the detection photons, will be generated in the x-direction. Since there is a 90 degree 
shift in direction, there is little crosstalk between the PPF and the superimposed EM 
wave (G aussian beam), so the PPF signal can be isolated and distinguished from the 
effects of the G aussian beam, enabling detection of the G W.
Here's how it works:
The perturbative photon flux (PPF), which signals the detection of a passing 
gravitational wave (G W), is generated when the two waves (EM and G W) have the
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same frequency, direction and phase. This situation is termed "synchro-resonance." 
These PPF detection photons a are generated as the EM wave propagates along its z- 
axis path, which is also the path of the G Ws, as shown in Figure 12.
The magnetic field is in the y-direction. According to the Li-Effect, the PPF detection 
photon flux (also called the "Poynting Vector") moves out along the x-axis in both 
directions.
The signal (the PPF) and the noise, or background photon flux (BPF) from the G aussian 
beam have very different physical behaviors. The BPF (background noise photons) are 
from the synchro-resonant EM G aussian beam and move in the z-direction, whereas the 
PPF (signal photons) move out in the x-direction along the x-axis.
The PPF signal can be intercepted by electromagnetic-interference-shielded microwave 
receivers located on the x-axis (isolated from the synchro-resonance G aussian EM field, 
which is along the z-axis). In addition, isolation is further improved by cooling the 
microwave receiver apparatus to greatly reduce thermal noise background (Baker, 
Stephenson and Li, 2008a).
The resultant efficiency of detection of HFG Ws is very much greater than from the 
inverse G ertsenshtein effect, which has been exploited in some previously proposed 
HFG W detectors and found to have insufficient sensitivity to HFG Ws (Eardley, et al., 
2008). The amplitude of the PPF has space accumulation dependence—that is, it is 
proportional to the length of the wave overlap. This is because the G Ws (gravitons) and 
EM waves (photons) have identical propagation velocities, so that the two waves 
overlap synchronously and coherently throughout and their interaction is cumulative 
(Boccaletti et al., 1970; DeLogi and Mickelson, 1977). This is the synchro-resonant 
condition or Li-effect. This means that for maximum signal, the interaction overlap 
coupling must be as long as possible. It should be noted that the identification of this 
coupling or Li-effect, upon which the Li-Baker HFG W detector is based, is not so new 
that it is untested in the literature. At least nine peer-reviewed research publications 
concerning the theory have appeared following Li, Tang and Zhao (1992), including 
those by Li and Tang (1997), Li et al. (2000), Li, Tang and Shi (2003), Li and Yang 
(2004), Li and Li (2006), Li and Baker (2007), Li, Baker and Fang (2007), Baker, 
Stephenson and Li (2008a), and Li et al. (2008).
2.2.3 Quantum B ack-Action Limit
The Standard Q uantum Limit (SQ L) will be introduced and reviewed in this section 
(Stephenson, 2009b), and design of the Li-Baker HFG W Detection System will also be 
reviewed to understand how the SQ L might limit the sensitivity of this new type of G W 
detector.
Review of the Standard Q uantum Limit
The Standard Q uantum Limit (SQ L) is often defined as "The limit on measurement 
accuracy at quantum scales due to back-action effects." But what is "back-action"? (See 
Kippenberg and Vahala, 2008.) From C lerk (2008) the Heisenberg Uncertainty Principle 
is
(dx) x (dp) > h/2 (3)
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where /lx is the position uncertainty, A p is the momentum uncertainty, and ft is 
Planck's reduced constant. Thus measuring x disturbs p, which in turn disturbs future 
measurements of x
A x(dt) = 4x(0) + dt[A p(O)/m] (4)
where zlx(O) is the initial position uncertainty is, Jp(O) is the initial momentum 
uncertainty, dt is the time of the future measurement, and m is the mass of the system 
under measurement. E/c2 may be substituted for mass in an energy only system. This 
is depicted in Figure 13.
To summarize, the quantum effects of measurements on future measurements is 
quantum back action. Therefore the Standard Q uantum Limit defines the lower 
sensitivity limit for all measurement instruments, including gravitational-wave 
detectors, according to the Heisenberg uncertainty principle. Detectors cannot avoid 
quantum back action, however the use of higher energies in the detection process can 
change the relative scale and impact of back action, and the use of squeezed states can 
shift the relative distribution of back action into states not involved in measurement.
Figure 13. Quantum B ack Action as a M echanism for Creating the Standard Quantum Limit
C alculating the Standard Q uantum Limit (SQ L)
A method for calculating the Standard Q uantum Limit (SQ L) is introduced in this 
section. The calculation of coherent versus stochastic SQ L is compared and contrasted. 
Important terms of the SQ L calculation are described, including the impact of contained 
energy levels within the detector on SQ L, and the sources of Q uality Factor and its 
effect on SQ L. C alculating the Standard Q uantum Limit (SQ L)
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C oherent Versus Stochastic SQ L
The question under consideration in this paper is whether or not the Li-Baker detector, 
Figure 14, is quantum-limited when detecting relic HFG W. In other words, does the 
standard quantum limit (SQ L) interfere with the sensitivity of the Li-Baker detector 
design? The answer will be negative if the SQ L is less than 10‘32 m/m. G rishchuk (1977, 
2007) has calculated the SQ L for G W detectors in general, which for a coherent G W is
hdet = (1/Q)(h^/E)1/2
and for a stochastic G W is:
hdet = (1/Qf\hfd/E)1/2,
(5)
(6)
where hdet is the metric (strain) detection limit in m/m, a is the frequency of sensed 
gravitational waves (typically around 10 G Hz in the Li-Baker detector), E is the effective 
energy contained within the detector cavity summed over the detection averaging time, 
and Q  is the quality factor or selectivity of the signal over noise.
The SQ L depends on the values of these parameters. For the remainder of this paper, 
we will consider the SQ L of only the stochastic signal detection case. In the following 
subsections the best possible value of the SQ L using current technology will be 
estimated to determine the fundamental limitations of the Li-Baker detector as now 
envisioned.
Impact of C ontained Energy Levels on SQ L
First attempt to estimate a realistic best case for the energy contained within the 
detection process, E. Typically it is expected that for a refrigerated microwave resonant 
cavity the best possible electrical quality factor will be around 2kx105. Assuming a "best 
efforts" value of 1000 W for the power of the G aussian beam in a laboratory 
installation, the effective total RF energy stored in the microwave resonant cavity of the 
Li-Baker detector, summed over the system averaging time, is estimated to be given by 
(G rishchuk, 2007):
Erf = (103 W) x (1000s) x (2kx105/2tt) = 10nJ (7)
over a typical 1000 s averaging time. Both the Li-Baker detector and a detector using 
the G ertsenshtein effect use a large static magnetic field B. For the present suggested 
outline design for the Li-Baker detector, the nominal value of 8 = 3 T, so that the 
magnetic energy density is given by
Eb = (VaJB^tprpo) = 3.6xl06 Jm-3 ■ (8)
The interaction volume in a practical laboratory-based detector is likely to be a 
maximum of around 1 m3. So, the effective total stored energy from the G aussian
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beam is much greater than the stored magnetic field energy, and it follows that E - Erf 
= 1011 J to a reasonable approximation.
Sources of Q uality Factor and Effect on SQ L
To calculate the SQ L, hdet, we also need the value of the detector quality factor Q (not 
the same as the cavity quality factor). Anything that concentrates or enhances the 
signal preferentially over noise, in any measurement dimension, can be considered a 
contributor to the quality factor Q . The quality factor can therefore be understood as 
the "signal selectivity" in each dimension, so that
Qtot = (Qspatial)(Qt) = QrQsolid angleQt . (9)
The temporal quality factor in the Li-Baker detector arises from averaging the signal 
over time, so that at 10 G Hz, Qt = Hhnt = (10x 109 Hz) x 1000s = 1013.
There is a contribution to Q arising from the fractal membranes that focus and 
concentrate the signal photon energy - but not the background photons - along the 
radial dimension. The radial selectivity arising from the general relativity solution, in 
conjunction with fractal membranes, is calculated by Li et al. (2008). Their table III 
gives Qr = SNR(r=37cm)/SNR(r=3.5cm) — 3.4xl021.
This is mostly due to the effective Q contribution arising from the synchro-resonance 
solution to the Einstein field equations that limit the PPF signal to a radiation pattern in 
certain directions, whereas noise is distributed uniformly. By utilizing directional 
antennas, the Li-Baker detector can capitalize upon this gain due to the focusing power 
of fractal membranes as a contribution to Q in angular space as well. This is calculated 
in detail, octant by octant, by Li et al. (2008). Page 24 of Li etal. summarizes this in 
terms of angular concentration onto the detector. A non-directional antenna 
corresponds roughly to solid angle 2^-steradians (one hemisphere), so that the effective 
antenna gain is estimated as (Qsoiid angle) = 2^ sr/10 4sr = 6.3xl04. Therefore, the 
predicted maximum quality factor will be Qtotai = QrQsoiid angieQt = 2.1xl039. This finally 
gives the Standard Q uantum Limit (SQ L) for stochastic G W detection at 10 G Hz:
hdet = (l/Q)1/2(hfO/E)1/2 = 1.8xl0*37 m/m . (10)
C omparison of SQ L With Predicted Sensitivity
As noted in the previous section, hdet = 1.8x1 O'37 m/m represents the lowest possible 
G W amplitude detectable by each RF receiver in the Li-Baker HFG W detector, limited by 
quantum back-action. An additional (l/>'2) factor applies if the separate outputs from 
the two RF receivers are averaged, rather than used independently for false alarm 
reduction, resulting in a minimum hdet = 1.2xl0'37. Since the predicted best sensitivity 
of the Li-Baker detector in its currently proposed configuration is A = 10'32 m/m, these 
results confirm that the Li-Baker Detector is photon-signal limited, not quantum noise 
limited; that is, the Standard Q uantum Limit is so low that a properly designed Li-Baker 
detector can have sufficient sensitivity to observe HFRG W of amplitude A * 10‘32 m/m.
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2.2.4 Li-B aker HFGW D etector
The detector, shown in Figure 14, has five major components:
1. A G aussian (focused, with minimal side lobes) microwave beam (G B) is aimed along 
the + z-axis at the same frequency as the intended HFG W signal to be detected (Yariv, 
1975), typically in the G Hz band, and also aligned in the same direction as the HFG W to 
be detected. The microwave transmitter's horn antenna is not shown, but would be 
located on the -z-axis.
2. A static magnetic field B, generated by two powerful magnets, typically using 
powerful superconductor magnets such as those found in a conventional MRI medical 
body scanner, is directed along the y-axis.
3. Two paraboloid-shaped reflectors, which are formed from "fractal membranes" (Wen 
et al., 2002; Zhou etal., 2003; Hou etal., 2005), are located in the y-z plane at the 
origin of the coordinate system to aim and focus the detection photons at diffraction­
limited spot antennas connected to two microwave receivers. These reflectors, shown in 
planer form in Figure 15, are segmented (similar to a Fresnel lens) and located back-to- 
back in the y-z plane. They are thin enough (less than a centimeter thick in the x- 
direction) to not block the z-directed G aussian beam. These microwave reflectors reflect 
the x-directed detection photons (PPF) and reject the z-directed G aussian-beam 
photons, which move parallel to the surface of the reflectors in the y-z plane.
4. High-sensitivity shielded microwave receivers are located at each end of the x-axis 
each about one meter distant from the origin.
5. Interior noise from thermal photon generation is eliminated by cooling the Li-Baker 
detection apparatus to below ~ 48 mK (0.048 Kelvin). Thus there are effectively no 
thermal photons at 10 G Hz. Noise from the interior background photon flux (BPF) from 
the EM G aussian beam is reduced to a negligible level by moving the receivers out to 
the side about a meter away from the EM beam and by a series of superconductor or 
microwave absorbent baffles to "shade" the receivers. Stray EM resulting from 
scattering of particulate matter near the apparatus and possible dielectric dissipation 
can be effectively suppressed by evacuating the apparatus to about 7.5x 10‘7 Torr (a 
rather high vacuum). External noise is eliminated by the use of a steel and titanium 
cryogenic containment vessel surrounding the low-temperature Li-Baker detection 
apparatus.
In summary, several different HFG W receivers can be utilized for communication; but 
the proposed Li-Baker detector (plans & specification development in Appendix B) 
shows the most promise (detailed underlying concept is derived in the paper included 
as Appendix C ).
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z
Stainless Steel & Titanium Vacuum / 
Cryogenic Containment Vessel and 
Faraday Cage (7.5(10)A-7 Torr, <480m K>
Figure 14. Schematic of Ultra-Sensitive HFGW D etector
Figure 15. Fractal M embrane Component of Li-B aker D etector Exhibited in Planar Form
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3 .0 Operational Concerns
3.1 LINK B UD GET
3.1.1 Signal-to-Noise R atio
Signal-to-noise ratio (SNR) is an important figure of merit in communication systems 
because it is an indicator of whether or not a transmitted signal will be useful upon 
arrive at its destination, the receiver. Without processing gain an SNR > 1 will be 
required to maintain a link budget. On the transmitter's end, the signal to noise is 
determined by the useful signal that is produced by the transmitter after it is already in 
its transmission mode, such as the G W power at the output of the G W generator 
antenna, divided by the RSS (Root Sum Square) of the uncorrelated noise sources 
referred to the same spot in the signal chain—that is, output referred noise equivalent 
power (NEP). This signal to noise ratio is represented by the left hand column in Figure 
16.
The components of the transmitter's noise equivalent power may be sorted by the 
source of the noise. First, before the signal is converted to G W it is in the realm of EM 
or photon radiation. Photons themselves make noise, and this component goes as the 
square root of the total number of photons. Then there is thermal noise—that is, the 
photons generated by blackbody radiation of the transmitter components themselves. 
Other electronic and semiconductor components providing the source signal generate 
their own photon noise due to carrier activity. All these noise sources are carried along 
with the original EM signal and may be converted just as faithfully as if they were 
signals should they fall within the transmission bandwidth. All of this is just for the EM 
noise component.
The generation process itself may also be a source of noise, and will vary widely 
depending upon the generator method used. For example, the generation process noise 
created in the G ASER would be significantly different than that created in a tuned 
resonant EM toroid cavity. This of course would be an important consideration in 
selecting a generator type.
Finally, it is expected that there are a variety of G W noise sources. Background sources 
from space are predicted, in low levels, across the entire frequency spectrum. Also, in a 
G W generator situation, parasitic vibrations may also have quadrupole moments, such 
as the walls of a generation cavity for instance, or an unwanted vibration within a slab 
of SC , and these could also generate G W noise.
Then there is link loss to contend with. While it is expected that the attenuation of G W 
due to absorption and scatter will be quite low, geometry alone will dictate that a 
spherically uniform radiating source will fall off as 1/R2. This link loss will affect both the 
transmitted signal and the transmitted noise.
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Signal to noise ratios (SNR ’s) at the transmitter and at the receiver 
must be calculated to support a communications link design.
GW
Link 
Loss
Predicted SNR 
Components at 
the Receiver
Signal
Noise
Source 
Noise
EM to GW
Conversion 
Noise
Predicted SNR 
Components at 
the Transmitter
Noise
GW Antenna
& Receiver 
, Noise
GW  to EM 
Conversion 
Noise
Figure 16. Conceptual SNR  Fill Factors: Signal and Noise Components
In the receiver all these same noise sources are duplicated in reverse, as shown on the 
right had side of Figure 16. Referring power now to the input, there will be a received 
power, and the created by the receiver that was not created at the transmitter, also G W 
to EM conversion noise, and EM receiver noise of the same types as received 
propagated transmit noise. Added to this will be G W noise admitted or outlined for 
transmitters. When all these noise components are referred the input of the receiver, 
the total NEP, which is the RSS of all the noise components, must be less than the 
signal present at the input of the receiver to qualify as a useful link.
A few comments are in order regarding the "Q -factor" of the receiver. One way to 
increase Q  is to narrow bandwidth. However, this has limited value. At some point, 
shrinking the bandwidth will shrink the signal received as quickly as the noise received, 
and some receiver noise components remain constant, resulting in a net drop in SNR. 
Another way to increase Q  is to arbitrary increase sample times of the signal. This 
technique will, relatively speaking, shrink receiver end noise components as referred to 
the input of the receiver, but it will not have any impact of the noise generated at the 
transmitter. Therefore in this case the SNR will approach a constant. However, both of 
these approaches for improving sensitivity will have an adverse effect on the 
information capacity of the channel, which is important for a communication 
application.
3.1.2 Link B udget Considerations
Now consider the signal side of the communication challenge. The central question is, 
How do we close the link? That is, how much signal is necessary at the input of a 
communication channel to have a useful signal at the other end? These questions may 
be answered, qualitatively in this case, by considering the terms of the expression in
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Figure 17. In general, an EM signal Si will be used to actuate some type of G W 
generation device, and this device will have a conversion efficiency of peg, which 
represents the ratio of power of the EM input signal to power of the G W signal 
generated. Not all of the G W generated will be constructively used to radiate in the 
desired direction; some of the G W power will be lost to destructive interference, and 
some will not be radiated through the antenna aperture. Thus the transmitter will have 
a less than unity radiated power efficiency, Rx.
An end-to-end power link budget from the transmitter to the receiver 
must be also calculated to support a communications link design.
Figure 17. A B lock D iagram of a T ypical Link B udget
Then there will be propagation link loss, or transmission loss, T, which will be the 
antenna pattern integrated across the solid angle of the receiver antenna aperture as 
seen from the source. The receiver may have an G W antenna that aids in focusing an 
otherwise wider solid angle into a narrower detection aperture, and if this is true, then 
there will be an efficiency associated with this receiver antenna, designated here as Rr.
At the receiver's detector, there is another conversion factor to account for, the 
conversion efficiency of G W signal power to EM signal power pge, which would be much 
less than unity, except that the Q  factor enters the equation as a component of pge. Of 
course Q  may also impact the bandwidth range over which the signal is collected, LI to 
L2. There is also a hidden integral here which occurs over the sample time, which is 
understood.
All of these terms will have to be defined and well understood before a communication 
system can be successfully designed. Many of these parameters have been predicted 
for the components reviewed in prior sections, however, they will not be verified until a 
successful experiment can be performed.
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3.2 B AND W ID T H
An estimate of the bandwidth that a HFG W transglobal communication system might 
achieve, after a proof-of-concept test is successfully completed, based on a technical 
paper by Black and Baker (2009), is as follows: for a 50,000& infrared (IR), 12.5 meter 
long,10-meter radius (104 concentric rings per plate so Pi = 1.29xl02 Wm-2 and 107 
plates) cylindrical HFG W generator (Woods and Baker, 2009), the flux at a one-meter 
distance from the generator is, according to Table 1 for /V = 107, (1.146xl012) x 
(1.29xio2) = 1.48x io14 Wm-2 (very large, and with a very narrow 2.3x 10*4 radian 
half-power point needle beam). The required generator power can be reduced by 
utilizing pulsed HFG Ws. Suppose that the distance between the generating or 
transmitting device and the detecting or receiving device is a little more than an Earth's 
equatorial radius, or ~ 7xl06 meters. At this distance, 7000 km, the flux of the 
received signal, S, is (1.48xi014)/(7xi06)2 = 3 Wm-2, more than adequate for an 
effective communication system.
With this configuration, the width of the needle-like, narrow HFG W beam at the receive 
end is (2.3xl0‘4) x (7xl06) = 1.6 km, and multiple HFG W carrier frequencies can be 
used, so the signal is very difficult to intercept, and is therefore useful as a low- 
probability-of-intercept (LPI) signal, even with widespread adoption of the technology. 
From Equation (2), derived in the Appendix of Baker, Stephenson and Li (2008a), the 
amplitude A of the HFG W at 7,000 km with the HFG W frequency (twice the IR 
frequency of vg w = 1.2x 1014 s'1) given by: A = 1.28x 10"18 S,77vg w = 1.8xl0‘32 (in 
dimensionless units or m/m), which would be detectable by the currently designed Li- 
Baker HFG W detector. Since the exact frequency and phase of the HFG W signal is 
known (unlike big-bang relic HFG Ws, for which the detector was designed), a much 
more sensitive, optimized HFG W detector will likely be developed.
G rishchuk (2008) indicates that there will be negligible relic HFG W noise at the IR 
HFG W generator's frequency of 1.2xl014 s-1 and no other cosmic sources at these 
frequencies are currently hypothesized. Prior to the proof-of-concept test, we will 
assume a noise figure at the Li-Baker detector of 10’8 War2.
Using C .E. Shannon's classical equation (1948), the maximum rate of information 
transfer, C , is given by:
C = Blog2(l+ S/N) (3A)
C = Blog2(l+ 3.0/10-8) ~ 1.9X106 bps (3B)
The bandwidth, B, here is arbitrarily taken to be 100 kHz for a future advanced system. 
The necessity for large temporal Q factors, (Q t ~109), currently precludes bandwidths 
larger than a few Hz for early systems, but the use of coherent signals will represent an 
easing of sensitivity requirements significantly, improving bandwidth. Note that it is 
based on a single carrier chopping frequency, whereas in practice, one can spread the 
information over an entire band of HFG W frequencies.
3.3 FR EQUENCY AND  T IM E ST AND AR D
The first application of HFG W to the distribution of frequency and time standard (FTS) 
data would be to assist otherwise conventional communications equipment. A typical 
near-Earth distribution system could conceivably result in a number and configuration
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of the ground stations, shown in Figure 18 where their latitude and longitude are given 
in parentheses.
Figure 18. A Proposed Near-Earth D istribution of Frequency T ime Standard
The large transmitter ground stations would provide the signals used as both the 
frequency and time standards. All FTS ground stations would be synchronized such that 
they emit signals exactly in phase with each other, all tied to a common frequency time 
source, such as the US Naval Observatory. Each station would use a different frequency 
such that the remote terminal (RT) user set could easily differentiate signals, and any 
phase or time difference observed would be due to either the relative position of the 
remote terminal with respect to each ground station, or the relative velocity of the 
remote terminal with respect to each ground station. Each ground station would 
transmit both a carrier wave (C W) signal for a frequency reference and a periodic pulse 
signal (PPS) for a time reference. At least 3 ground stations would be needed for self­
triangulation by the remote terminals, at least 4 with redundancy. HFG Ws will 
propagate through the Earth with little modification, but very slight HFG W phase 
modification may be observed in surveillance applications (Baker, 2007.)
The counterpart to the fixed ground infrastructure would be the remote terminal side or 
user side of the FTS infrastructure. Each remote terminal would need to be equipped 
with a small HFG W receiver, which could pickup all 3 or 4 ground stations 
simultaneously. The arrival times of the received PPS signals could be compared via 
time difference of arrival, or TDOA, and used to develop a position estimate. The C W 
signal phases could be compared to determine the Doppler velocity of the remote 
terminal with respect to an Earth C entered Inertial (EC I) coordinate system. Thus, the 
HFG W FTS system could be used as a navigational aid, akin to the G PS system. This 
end of the infrastructure would be receive only and could therefore be a very low power
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device. Therefore mobile devices, such as portable remote spaceborne terminals could 
be typical users of such a navigational service. An example is depicted in Figure 19.
Figure 19. HFGW Supplemented R emote T erminal D esign
The navigational sensitivity of the HFG W receiver would depend on the frequencies 
used in the HFG W FTS system, as the received C W HFG W signal would act as the 
remote terminal's "built-in" frequency standard, replacing the need for internal crystal 
oscillators or C esium or Rubidium standards. An HFG W FTS carrier wave with a 
frequency of 300 G Hz with a wavelength of 1 mm would result in 3 pico-second type 
time accuracy. The use of TDOA with these accuracies would allow for arbitrarily small 
navigational errors.
3.3.1 Improvements Accruing from a HFGW  T ime Standard
The cost of the FTS infrastructure must be more than balanced by the benefit resulting 
from that infrastructure if the cost is to be justified. G iven that the G PS already 
provides adequate navigation services for most applications, navigational benefits alone 
would not justify the cost of an HFG W FTS system. However, in the case of a universal 
HFG W FTS, there are additional benefits associated with applying the frequency and 
time standards to standard telecommunications problems. The universal nature of the 
HFG W frequency and time standards are especially helpful. The following 
telecommunication benefits of an HFG W FTS system will be described in this section: 
improvement in acquisition time from search space improvements, improvements in 
modulation and coding efficiency from phase noise improvements, and improvements in 
bandwidth efficiency from frequency noise improvements.
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3.3.2 Search Space Improvement Accruing From HFGW FT S
The following points are relevant with respect to the universal use of HFG W FTS among 
all remote terminals (including for instance cell phone handsets and their associated 
cellular towers):
• During signal acquisition the receiving terminal must perform a search of the search 
space of frequency, phase, and code to acquire the transmitting terminal signal.
• If there is less noise in these parameters the search space is reduced, speeding 
acquisition.
• Ultra-fast acquisition allows more efficient TDMA, or Time Domain Multiple Access 
style operations, such as transmit on demand, that use bandwidth more efficiently.
The smaller resultant search space is depicted graphically in Figure 20.
S earch space 
U sing freq &
S earch space 
W ithout using 
freq & time 
standards
time standards
Figure 20 . Acquisition Search Space Improvement Accruing from HFGW FT S
An equation for acquisition search space time is presented in Equation (12)
Tacq — Nphase*Nfreq*Ncode*(ta) (12)
where Nphase = number of phase space cases to check for acquisition,
Nfreq = number of frequency cases to check for acquisition,
Ncode = number of code sync possibilities to check and
ta = acquisition test time, per test case.
In a typical example, if 30 MHz chipping is used with a 5 psec error, there will be 150 
code sync possibilities to check. If a case where a frequency error of 1 Hz is used within 
the acquisition window would cause a missed acquisition, and the worst case frequency 
error is 150 Hz, then the number of frequencies that must be checked is also 150. 
Finally, we must check each possible phase possibility, say 16 different options for 16- 
PSK. PSK stands for Phase Shift Keying and is the encoding of data bits using 
incremental phase modulation. These acronyms are specified in the nomenclature
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section below. For a 5 psec acquire test time, the result is Tacq = 150 x 150 x 16 x 5 
^isec =1.8 seconds acquisition time.
However, with effectively perfect knowledge of time, frequency, and hence also phase, 
there will only be one case to check, so result is Tacq = lxlxlx5 psec = 5 psec 
acquisition time. This is essentially instantaneous for applications such as TC P/IP or 
VoIP. This will favorably impact the overall TDMA efficiency in that it speeds the 
claiming process to the point where an "always on" link can be replaced by a "link on 
demand." This is a savings of 25 to 50 percent in channel usage for VoIP and TC P/IP 
sessions over "always on."
3.3.3 T he Impact of Phase Noise Improvements on Phase Shift 
Encoding
The use of a universal HFG W FTS would also benefit the relative phase noise of all 
terminals, allowing for finer phase encoding. Phase noise limits the type of modulation 
and manner of encoding that can be performed in phase space, commonly used for 
over the air telecommunication systems. An HFG W FTS system could reduce phase 
noise by providing a frequency reference with outstanding stability. For example, 
moving from Q PSK to 8PSK or 16-PSK improves bandwidth efficiency by a factor of 2 to 
4. The phase space improvement is summarized in Figure 21.
Figure 21. T he Impact of Phase Noise Improvements on Phase Shift Encoding
In the example of Figure 21 nominal performance allows only Q PSK, but improved 
phase noise would allow higher density phase encoding. Data rate will scale linearly 
with encoding efficiency as shown in Equation (13):
Data Rate = (BW/2) x (C oding Efficiency) x (FEC  Rate) / (PN Spreading Factor) (13)
C oding efficiency will be a factor of 2 better when moving from Q PSK to 8PSK, or a 
factor of 4 better when moving from Q PSK to 16-PSK. This will translate directly into a 
linear increase in the allowable data rate that a given bandwidth can support. Put 
another way, a universal frequency time standard could quadruple over the air 
bandwidth efficiencies just by improving phase noise alone. Phase noise improvements 
would be limited only by the slight variations induced in the HFG W signal passing 
through the earth as described in Baker (2007).
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3.3.4 T he Impact of Frequency Noise Improvements on FD M A and 
FHSS
The very low noise frequency standard that would be supplied by an HFG W FTS system 
would allow for much more efficient use of reserved frequency bandwidth. Frequency 
noise limits the type of modulation and manner of encoding that can be performed in 
frequency space, such as Frequency Division Multiple Access (FDMA) or Frequency 
Hopping Spread Spectrum (FHSS). HFG W can reduce frequency noise by providing a 
frequency reference with outstanding stability. For example, guard bands can be shrunk 
in FDMA, and frequency slices can be smaller and more stable in FHSS.
A frequency space representation of the FDMA and FHSS noise improvements are 
depicted in Figure 22.
Figure 22. T he Impact of Frequency Noise Improvements on FD M A and FHSS
Frequency Hop Spread Spectrum.
Efficiencies in guard-band structure can be defined as in Equation (14).
G uard band BW Efficiency = (Total Bandwidth -{Sum of G uard BW})/Total Bandwidth 
(14)
G uard bands often consume 30 to 50 percent of assigned frequency space. While guard 
bands would still be required to allow for the side lobes of signals, the frequency error 
component would be eliminated. Similar efficiencies may be gained in the FHSS 
approach. A better knowledge of absolute frequency allows better frequency coding 
efficiencies, as seen in Equation (13) and depicted in Figure 21.
3.4 POSSIB LE FUT UR E UPGR AD ES T O T HE FT S D EV ICES
Per the 9 Feb 2009 issue of New Scientist, optical lattice clocks are under development 
that will lead to a dramatic improvement over the current standard C esium atomic 
oscillation clocks that now provide frequency time standard references. Optical lattice 
clocks vibrate at optical frequencies rather than microwave frequencies, with the 
reference frequency mixed down via frequency combs to allow measurements back 
down in the microwave regime. Strontium lattice clock are already operating with 
measurement precisions of 1 part in 1016, and theoretical performance approaches 1 
part in 1018. At this precision one could measure the time delay caused by changing 
once centimeter in height in the Earth's gravitational field.
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3.4.1 Propagating Signals From Optical Lattice Clocks for T iming
The 1 part in 1018 measurement precision of optical lattice clocks will be affected by 
general relativity effects, in other words propagation delays due to gravitational field 
gradients will be readily measureable. "It will make us think a little harder about what 
we really mean by time," Kleppner (2008). In effect, measuring the propagation delays 
at this level allows very fine measurement of the "geoids," or surfaces of constant 
gravity, surrounding planets and inhabiting interplanetary and interstellar space. The 
delay experienced by RF waves could therefore be precisely compared with the 
propagation delay experienced by gravitational waves, which are not as strongly 
affected by the presence of mass. Such a differential propagation delay comparison 
(between RF & G W) could lead to an important new technology in the mapping of 
geoids, which could for instance be applied to the problem of mapping the positions of 
the Lagrangian points, which vary slightly over time.
3.4.2 In Navigating and M apping Interplanetary Geoids
The importance of locating and navigating to Lagrangian points is well established 
(Baker, 1967). See Figure 23 for a depiction of the Earth's Lagrangian points and their 
uses.
Gravity holes
The E arth and sun's gravitational fields balance at five Lagrangian points, LI to LS , Later this year the S TE R E O  A and B 
spacecraft will explore the L4 and L5 regions for the first time
E AR TH  O R BIT
L3: H ighly unstable 
due to gravitational 
pull of other planets
G R AVITATIO N AL
F IE LD  CO N TO U R S
S TE R E O  A O R BIT
(D ue to reach L4 S eptember 20 0 9)
L4: S table May contain 
dust and rocks from the 
early solar system
D IR E CTIO N
O F MO TIO N
LI: 15 million km 
from E anh ideal location 
for monitoring the sun H ome 
w N AS A's ACE , S O H O  and 
W IN D  satellites
LS : S table May contain 
dust and rocks from the
early solar system
L2:15 million km from E arth. 
I Permanently shielded from the 
sun. H ome to N AS A's W MAP 
satellite, The Planck satellite. 
H erschel and James W ebb space 
telescopes will all sit here
S TE R E O  B O R BIT
(D ue to reach LS  O ctober 20 0 9)
Figure 23. T he Earth's Associated Lagrangian Points [New Scientist, 9FebO9 and Baker (1967), p.128, Figure 
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LI is an ideal location for solar monitoring, whereas L2 is permanently shielded from 
the sun.
4 .0 Future Potential
4.1 D EV ELOPM ENT AL R OAD M AP
A development roadmap is suggested here for the application of High Frequency 
G ravitational Waves (HFG Ws) in the field of communications. The development 
roadmap should be twofold:
• Theoretical work should continue on HFG W transmitters (generators) and receivers 
(detectors).
• Experimental devices should be built and tested in the laboratory and then 
transitioned over to a practical communications system.
A suggested developmental roadmap schedule and phasing timeline is included as 
Figure 24. Theoretical research is always an ongoing enterprise, but it is especially 
important to encourage work in the development of experimental approaches aimed at 
demonstrating laboratory generation and sensing of gravitational waves for the next 
few years. This is the kind of academic work that is best done in a research university 
setting, at least for the next ten years or so, until laboratory experiments can verify 
laboratory generation. Without early confirmation the technology will not gain 
widespread acceptance and move forward.
Figure 24. HFGW Com Space Application D evelopment R oadmap, Estimated T imeline
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The most benefit would come from a coordinated effort spread over a number of 
different universities. Wherever possible, pre-existing assets should be utilized to 
stretch funding as far as possible. For example, if synchrotron light is needed to verify 
the G ertsenshtein effect and the Li-effect, a survey of existing national synchrotron 
light facilities should be part of the funded effort to find an appropriate host facility. The 
funding activity—that is, the National Science Foundation—would have the overall 
responsibility to coordinate this activity in an ongoing manner, through proposal review, 
contract awards, and progress reviews, and the approach should be flexible enough to 
allow the redirection of funding should a particularly promising new technology or 
invention move to the forefront.
Assuming that positive laboratory results can be achieved and peer reviewed in a 10 to 
12 year timeframe, the next step would call for a period of prototype development, in 
which the device physics and engineering needed to support the technology could be 
matured. As prototypes show promise they could be transitioned to device 
development, the first time that industry would likely enter the field. Once the 
individual devices required to support G W communication technology—for example, G W 
generators and G W sensors—are in place, at that point it will be possible to begin full­
scale development of systems applications. This is a conservative timeline, based on 
scaling from the development of previous technologies. If breakthroughs materialize, or 
if the pace of technological development quickens, progress may certainly occur more 
quickly than this.
4.2 HFGW COM M UNICAT IONS PR ED ICT IONS T O 20 50
In what follows, with an eye to the future, extrapolations are made concerning the 
development of a HFG W communications technology into the far future (for example, 
2050 and beyond). It is difficult to predict even ten years in advance to the time when 
we expect to have the results of the proof-of-concept test (or "Bell-Watson" 
experiment) are available and the immediate applications to HFG W communications 
completed. Speculation beyond that time will be contingent upon advanced 
development of FBAR crystals, new materials within the toroidal waveguides, and so 
forth, or even entirely new approaches such as those proposed by G . Fontana, V. 
Rudenko, R. C hiao, et al. No doubt the Li-Baker detector performance can also be 
greatly improved with stronger magnetic fields, more intense G aussian beams, and 
better baffles as well as new detector designs yet to be developed possibly based upon 
theories developed at Birmingham University, INFN G enoa and The National 
Astronomical Observatory of Japan. Optimum designs of communication channels, 
bands and modulation are also be anticipated. Many of these advanced concepts were 
discussed at the 3rd HFG W Workshop in Huntsville in February 2009. Nanotechnology 
advances will allow for the fabrication of smaller and smaller HFG W transceivers having 
millimeter dimensions and milliwatt power requirements by 2050 and "Radio ID" or 
rather "HFG W ID" nanochip tags may be ubiquitous. G ravitational wave transmissions 
would also have the advantage of being able to pierce the protective plasma shielding 
that may in the future be routinely used to protect the crew aboard manned vessels— 
that is, communications through artificial magnetospherics, a technological limit of RF 
communications.
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4.3 INT ER PLANET AR Y NAV IGAT ION AND  GEOID  M APPING T O 20 50
While there is no doubt that stellar tracking will remain the primary source of 
navigation for space missions in the foreseeable future, as introduced in Section 3.4.2, 
HFG W may also prove useful in conjunction with RF in providing a navigation aid for 
interplanetary missions (with no planetary shielding) by mapping geoids in 
interplanetary space via long baseline navigation. For instance, if there were one G W 
source on Earth, and one G W source on the Moon, such a pair of G W sources would 
provide relative beacons for missions to Mars that could serve multiple roles as 
navigation beacons, communication relays, and in conjunction with RF signals, map 
geoids via relative time difference of arrival signals. Very Long Baseline Navigation 
could be achieved by placing a source on Earth and one G W source on Mars for a 
baseline that would most often be very widely spread with respect to the outer planets, 
for outer planetary missions. See Figures 25-27 for a number of different navigation 
beacon pair options.
Moon
R , = 6378 km x2 = diameter 
R l0 = 384,40 0 km = .0 0 257 AU
max ~ 2R e / R |0 rad 
’2 degrees
Figure 25. A GW Pair on Earth as Used by a Lunar M ission
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Mars
Rem = Earth to Mars Max range 1AU + 1.5 AU = 2.5 AU 
R|o = 384,400 km = .00257 AU
®fhax ~ Rlo ^ Rem f®d 
- 60 mdeg
R ei
GW ,
Moon Sun
blo
Earth
GW
Figure 26. A GW Pair on Earth and on the M oon, as Used by a M ission to M ars
Saturn
Range to Jupiter 5.2AU + /- 1.5AU
Range to Saturn 9.6AU + /- 1.5 AU Jupiter
(Rem / 2% ) rad 
- 28 deg
GW
Sun
Mars ■
Figure 27. A GW Pair on Earth and on M ars for an Outer Planetary R eference Pair
Earth
(/ em ^ Rsat) ^^
-15 deg
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4.4 OT HER  POSSIB LE HFGW APPLICAT IONS
The most stunning advances in HFG W applications will probably not be in 
communications, but in the remotely HFG W-generated nuclear fusion, HFG W propulsion 
and HFG W surveillance. If an ultra-high-intensity HFG W flux impinges on a nucleus, it is 
possible that it could initiate nuclear fusion at a remote location, or mass disruption. 
Also it may be possible to create radioactive waste-free nuclear reactions and energy 
reactions (Fontana, G . and Baker, R. M L, Jr. 2007). As they suggest: "At high 
amplitudes, G R (G ravitational Radiation) is nonlinear, thus we might expect a departure 
from geometric optics. Fortunately, the problem has been already theoretically 
examined and the resulting effects are found to be advantageous. Nonlinearity 
improves the focusing process and h goes to one in finite time, producing a singularity 
"regardless" of the starting, non-focused amplitude of the impinging gravitational wave 
(C orkill and Stewart, 1983; Ferrari, 1988a; Ferrari 1988b; Ferrari, Pendenza and 
Veneziano, 1988; Veneziano, 1987; Szekeres, 1992). The effect of a \h = 0.995 pulse 
of HFG Ws on the couple formed by a deuterium nucleus and its electron is the reduction 
of their relative distance by a factor of 200. If this distance reduction is effective for a 
few picoseconds, then the two nuclei of a deuterium molecule can fuse and give an He 
atom plus energy, which is the usual nuclear-fusion process in a star."
HFG Ws could theoretically be used for propulsion and control of the motion of objects 
such as missiles, missile warheads, spacecraft, and asteroids, and remote control of 
clouds of hazardous vapors. G ravitational field changes by one or more HFG W 
generators could urge a spacecraft in a given direction, causing a lower static 
gravitational field in front of a vehicle (it "falls" forward) and a higher one behind 
(providing a "push"). The concept is that the mass essentially "rolls" down a "hill" 
produced by the static g-field; that is, potential energy increase of a mass is provided 
by the energetic HFG Ws. The magnitude of the static g-field is proportional to the 
square of the HFG W frequency (Landau and Lifshitz, 1975, section 108, page 349). 
Specifically:
"Since it has definite energy, the gravitational wave is itself is the source of some 
additional gravitational field (static g-field). Like the energy producing it, this field is a 
second-order effect in the hik. But in the case of high-frequency gravitational waves the 
effect is significantly strengthened: the fact that the pseudotensor t‘k is quadratic in the 
derivatives of the hik introduces the large factor A"2. In such a case we may say that the 
wave itself produces the background field (static g-field) on which it propagates. This 
[static g] field is conveniently treated by carrying out the averaging described above 
over regions of four-space with dimensions large compared to A. Such an averaging 
smooths out the short-wave "ripple" and leaves the slowly varying background metric 
(static g-field)." (Brackets and underline added for clarity and emphasis.)
Such an application must also await the future development of very high-intensity 
HFG W generators.
A novel means of imaging or HFG W surveillance might be developed in future to 
establish a system to allow for observing activities and materials in three dimensions, 
within and below structures and within the Earth and its oceans. G ravitational waves, 
including HFG Ws, pass through most material with little or no attenuation; but although 
they are not absorbed, their polarization (Li and Nan, 2009), phase velocity (causing
36
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refraction or bending of gravitational rays), backscatter, and/or other characteristics 
can be modified by a material object's texture and internal structure. For example, the 
change in polarization of a G W passing through a material object is discussed in Misner, 
Thorne, and Wheeler (1973): "In the real universe there are spacetime curvatures due 
not only to the energy of gravitational waves, but also more importantly to the material 
[objects and structures] content of the universe ... its wavelength changes [based on 
gravitational red shift] and [the gravitational wave] backscatters off the curvature to 
some extent. If the wave is a pulse, then the backscatter will cause its shape and 
polarization...." It is difficult to theoretically establish the actual magnitude of the 
changes, especially at very high frequencies (1014 Hz and higher) and to quantify them 
prior to HFG W generation/detection laboratory experiments.
4.5 20 50 AND  B EYOND
The phases of human space exploration may be divided into the following phases:
• Epoch 1 - Interplanetary Exploration
• Epoch 2 - Interstellar Exploration
• Epoch 3 - Intergalactic Exploration
• Epoch 4 - Universal Exploration
Each phase will have its own challenges and opportunities, but one can certainly 
speculate that the human need for connectedness and communication knows no 
bounds. So any scope of expansion beyond Epoch 1 will have enormous challenges in 
the area of communication. The vast distances involved will require some form of 
communication that entails faster-than-light (FTL) propagation. While this is a highly 
speculative area, such schemes have been proposed for FTL HFG W. Both Fontana and 
Meholic (unpublished reports) have proposed models of the universe, such as the 
trispace model, in which subluminal or luminal gravitational waves may couple into a 
super-luminal "parallel universe" inside which FTL speeds are possible. Such as scheme 
would be required to communicate between star systems and galaxies if humankind is 
to maintain any type of cohesive civilization. Without communications we have a history 
of fractured civilization, and we slip into becoming our own worst enemy. Universal 
communication holds the lofty promise of universal peace.
5 .0 Acknowledgements
The research published in technical papers authored by G ary Stephenson, chief 
investigator for Seculine C onsulting, (Stephenson, 2009a, Harper Stephenson (2007) 
and Stephenson (2009b)) were crucial in the preparation of this study and is gratefully 
acknowledged.
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Appendix A: Nomenclature
A amplitude of gravitational wave, metric strain in spacetime, m/m
B bandwidth, s4
B magnetic field strength, Tesla
c speed of light in vacuum (2.998 x 108 ms-1)
C maximum rate of information transfer, bits per second (bps), s 1
dt time of future measurement, s
E effective energy contained within the detector cavity summed over the detection 
averaging time, J
Fg w gravitational-wave flux, Wm 2
h strain, m/m
hdet (strain) detection limit, m/m
h Planck's reduced constant 1.055 x 10 34 Js
N noise, Wm-2
N number of linearly arranged G W radiation elements, integer
Nphase number of phase space cases to check for acquisition, integer
Nfreq number of frequency cases to check for acquisition, integer
Ncode number of code sync possibilities to check, integer
n number of pairs of oppositely jerking at one-time mass elements, integer
P power of the generated gravitational waves, W
Q  temporal quality factor or selectivity of the signal-to-noise ratio, dimensionless
R range, m
Rcvri receiver 1
Rcvr2 receiver 2
Rr receiver antenna power efficiency, dimensionless
Rx. radiated power efficiency, dimensionless
S signal strength, Wm-2
Si input signal strength, Wm-2
So output signal power, W
r distance between two jerking-mass, gravitational-wave radiation elements, m
T propagation or transmission-factor losses, dimensionless
ta acquisition test time per test case, s
tint integration or signal averaging time, s
Xmiti transmitter 1
Xmit2 transmitter 2
Af change in force of a jerking-mass, gravitational-wave radiation element, N
Ap momentum uncertainty, kg-ms 1
At time interval, s
Ax initial position uncertainty, m
peg conversion efficiency (ratio of power of the EM input signal to power of the G W 
signal generated), dimensionless
pge conversion efficiency (ratio of power of the G W input signal to power of the EM 
signal generated), dimensionless
A wavelength, m
vg w gravitational-wave frequency, s 1
a frequency of sensed gravitational waves, s-1
coi transmitting frequency, s-1
<02 receiver-sensitivity frequency, s-1
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Appendix B : Li-B aker HFGW D etector
Appendix B describes a joint academia/industry project to design the ultra-high 
sensitivity Li-Baker detector for high-frequency gravitational waves (HFG Ws). The 
partnership consists of Louisiana State University (LSU) and Transportation Sciences 
C orporation (TSC ) in C alifornia. The Li-Baker HFG W detector exploits a solution of field 
equations that couples photons and G W in first order, and the sensitivity of the detector 
will be much better than previously-proposed HFG W detectors. The outcome of this 
study will be an engineering-ready design for the HFG W detection system, to be 
developed under continued funding. Future construction of this detector will broaden 
the search spectrum of the existing LIG O low frequency G W detection system; it will be 
used to detect and characterize the relic HFG W cosmological background radiation, 
contributing to clarifying the origins of the universe. This offers the first and best hope 
of G W detection in a completely new G W frequency regime around 10G Hz, near the 
cutoff of what is cosmically generated and a proof of the capability of the detector to 
sense the HFG W emissions of the HFG W generator discussed in Sections 4.4, 4.5 and 
4.6.
This first activity is to develop designs, plans and specifications for the Li-Baker 
configuration for ultra-high sensitivity detection of relic high-frequency gravitational 
waves (HFRG Ws) in the laboratory. The first goal will be to develop the design to a 
stage where the likely performance can be evaluated in detail. Following a future 
proposal, the Li-Baker detector will subsequently be built and used for the basic-science 
purposes of sensing HFRG Ws having their origin related to the "big bang," as well as for 
detecting laboratory-generated HFG Ws (Romero and Dehnen, 1981; Baker, 1999, 
2000; Woods and Baker, 2005, 2009). As discussed in Sections 4.4, 4.5 and 4.6 .Use 
will primarily be made of "off-the-shelf" components, and components described in the 
open scientific literature and in the various patents issued to Project Scientist R obert M  
L B aker, Jr. (Baker, 1999, 2000, 2001, and Patents Pending) who is the inventor of 
the Li-Baker HFG W Detector (Baker, 2001). Other components will be designed by the 
project participants during the Detector Design (DD) process. The project plan and 
timing are described below under separate headings for each component of the work.
DD1.1 Containment Vessel
Design of the cryogenic containment vessel and vacuum system: D r. R .C. W oods 
(LSU) + graduate student, G.V . Stephenson (T SC), D r. R . M L B aker (T SC). This 
will be divided into four subtasks:
D D 1.1.1 Selection of material for the containment vessel: this choice will be 
made in light of the vessel's approximate size and shape, initially anticipated to be 
cylindrical, overall approximately 2m diameter and 3m length. Manufacturing ultra-high 
vacuum chambers requires fabrication that ensures leak-free performance. For 
example, Meyer Tool & Manufacturing, Inc. (Oak Lawn, Illinois) supplies custom 
chambers for ultra-high vacuum (UHV) applications. C ompanies such as Meyer will be 
consulted and/or visited to evaluate their manufacturing capability. The final selection 
from the expected short-list of titanium, stainless steel and/or aluminum containment 
vessels will be made based upon manufacturer recommendation and evaluation of test 
data.
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D D 1.1.2 D etailed design of brackets and fixtures for the internal equipment, 
wiring, piping and through-wall connections: the general principles demonstrated 
by existing Magnetic Resonance Imaging (MRI) system designs (for example, from 
Siemens MRI, G E Healthcare, and others) will be followed to determine the most 
compatible design of the internal equipment, wiring, piping and through-wall 
connections for the HFG W detector. A cryostat or cryogenic containment vessel 
supported inside the vacuum vessel will house the superconducting magnet assembly 
necessary for the Li-Baker detector. Through-wall fittings and seals for copper leads 
supplying the magnet and other internal apparatus will be needed. Design of brackets, 
wiring, and piping of detector equipment will also be based upon input from the other 
tasks.
D D 1.1.3 D esign of vacuum system: there are a large number of "off-the shelf" 
Ultra-High Vacuum (UHV) equipment providers such as: Varian, Inc. (Lexington, 
Massachusetts), Kimball Physics, Inc. (Wilton, New Hampshire), and Edwards High 
Vacuum Ltd. (UK), amongst others. Those with capability for producing a system able 
to evacuate the chamber to about 10’7Torr for the HFRG W detector will be approached 
to undertake a detailed specification.
D D 1.1.4 D etailed design of size and shape of containment vessel: determination 
of the containment vessel's precise dimensions will be based upon the final designs of 
the equipment determined by the other tasks and will integrate all the specific sub-task 
designs, resolving any conflicts between units.
DD1.2 Signal Processing,
Design of the recording apparatus hardware and software development that will be 
needed to handle merging the two receiver inputs over an averaging period of up to 
1,000s: D r. R . M L B aker (T SC), G.V . Stephenson (T SC). This will require the 
conceptual design of digitizing hardware and software to handle the data gathered, 
including the combination of multiple receiver signals, the use of delay histograms, 
statistical filtering techniques, and the study of false alarm pitfalls in non-linear signal 
processing. There is much overlap with this area and DD1.5, the design of the detection 
receivers. The expected G W signal structure must be characterized to optimize the 
matched filtering needed. The definition of a detection event is the foremost 
consideration, and will be studied both in terms of the threshold level and in terms of 
the statistics of exceeding that level. Expected signal to noise enhancements 
("processing gain”) will be investigated for various filtering and processing options, and 
the effect of the Q -factor inherent in the detection apparatus will be included in this 
area of the investigation. Linear processing techniques such as multiple receiver 
combination and delay histogram searches will be studied, and nonlinear signal 
processing will also be considered, including its effect on detectability, as well as its 
effect on false alarm generation. This task includes the selection of the best computing 
and digitizing recorder platforms for the signal-processing needed. Also under this task 
is an investigation of whether magnetic field modulation can be used to advantage in 
this detector. Any scattered BPF does not depend upon the applied magnetic field or on 
the G W. Therefore, the wanted PPF can be "labeled" by varying the applied (nominally 
static) magnetic field in some way. A common technique in magnetic resonance 
experiments is to use field modulation coils that superimpose upon the constant applied 
magnetic field a time-varying component at low frequency (for example, around 50Hz 
but asynchronous with the commercial power supply frequency). As a result, the PPF is
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"labeled" as whatever is recovered from the receivers at the same frequency as (and 
indeed phase-locked to) the modulation, so therefore the PPF can be distinguished from 
scattered BPF very easily. Typically a lock-in amplifier (referenced to the field 
modulation) is used to recover the signal in such an arrangement, which provides 
significant noise rejection by effectively reducing the detection bandwidth.
DD1.3 Microwave Transmitter (Gaussian beam},
Design of the microwave transmitter for the G aussian beam, directed towards the 
central fractal membranes: D r. R .C. W oods (LSU) + graduate student, D r. R . M L 
B aker (T SC), G.V . Stephenson (T SC). This is expected to require 10 to possibly 
10,000W (l,000W nominal) at around 10G Hz, with an associated power supply and 
appropriate safety interlocks. Possible technologies include solid-state, magnetron, 
traveling-wave tube (TWT), or high-power klystron, and specifications will be developed 
under this component of the work. These are all mature technologies and commercial 
units will suffice. Possible suppliers include: Microwave Power Inc. (Santa C lara, 
C alifornia; solid-state, up to 500W); ETM Electromatic Inc. (Newark, C alifornia; TWT or 
klystron, up to lOkW); and Toshiba Electron Tube and Devices C o., Ltd. (Japan; TWT or 
klystron, over lOkW). G enerally speaking, wideband solid-state amplifiers produce less 
output power than medium bandwidth models or narrow-band tube designs, so that the 
compromise here will be to decide whether to accept lower power in favor of wide 
tunability. Also required is a suitably matched transmit antenna. Again, commercial 
designs will suffice, such as those from Rozendal Associates Inc. (Santee, C alifornia), 
ETS-Lindgren (C edar Park, Texas), or Orban Microwave Products (El Paso, Texas). The 
compromise that must be worked out in the antenna design is that a high-gain antenna 
is needed to constrain the G B to be within the resonance cavity or interaction volume 
(so that microwave input power is not wasted), but a high-gain antenna is less tunable 
than a broadband low-gain antenna. As in other work areas of this proposal, the 
complete design will need to establish the cost-performance tradeoff issues surrounding 
the various approaches.
DD1.4 Fractal Membranes and Microwave Absorbers
Design of the fractal membranes as microwave reflectors/absorbers at select 
frequencies (Wen et al., 2002; Zhou etal., 2003) and other high-performance 
microwave absorbers: D r. R . M L B aker (T SC), G.V . Stephenson (T SC).
D D 1.4.1 Design of the fractal membrane (FM ) reflectors at the waist of the 
G aussian beam including their paraboloidal form. An analysis will be completed to 
determine the optimal material of the FMs (copper, stainless steel, or aluminum are the 
obvious leading candidates). A paraboloidal surface will be designed that can be 
fabricated from the FM to focus the PPF at the planned locations of the microwave 
receivers. Hong Kong University of Science and Technology can fabricate the fractal 
membranes out of these metals in almost any form.
D D 1.4.2 The interior of the containment vessel (except for an opening at the 
G aussian-beam transmitter end) must be treated to eliminate exterior sources of noise. 
Either a Faraday C age (using a mosaic of HTSC  tiles; for example, YBC O) or fractal 
membranes are possibilities. Both will be examined in detail to determine the optimal 
approach. A design compatible with the containment vessel shape (DD1.1.4) and 
placement of interior detector elements will be developed.
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D D 1.4.3 Selection of appropriate microwave absorbing material at around 10G Hz; 
design of the interior baffles around the G aussian beam, and a "tunnel" between 
fractal-membrane reflectors and receivers (Baker, Stephenson and Li, 2008). A 
computer program for ray tracing of the PPF and the BFF will be developed and utilized 
for the baffle design. An analysis will be made of the latest technology reported by 
C han et al. (2006), Landy et al. (2008), and Yang et al. (2008), and these will be 
compared with those available from established suppliers of current technology high 
performance microwave absorbing materials including ARC  Technologies, Inc. (San 
Diego, C alifornia), Millimeter Wave Technology Inc. (Passaic, New Jersey), C uming 
Microwave (Avon, Massachusetts), and many others.
DD1.5 Detection Receivers
Design of the microwave receivers (for the PPF) at each end of the detector 
containment vessel, tunable around 10G Hz: G.V . Stephenson (T SC), D r. R .C. W oods 
(LSU) + graduate student. D r. R . M L B aker (T SC). Three possibilities have already 
been identified for the technology to be used here, and specifications will be developed 
for each option found suitable for use in the final design so as to enable a final choice to 
be made.
D D 1.5.1 Off-the-shelf microwave horn plus HEM T receiver: if tens to hundreds of 
photons per sample are available then standard microwave horns may be used, coupled 
to high electron mobility transistor (HEMT) amplifiers. This task will include a sensitivity 
analysis of this receiver type to determine the suitability of this approach, and a 
conceptual design will be developed using off-the-shelf components. Now highly 
developed, HEMT technology has previously been found reliable enough to use in the 
receivers for differential microwave radiometers (DMRs) flown in the NASA C Osmic 
Background Explorer (C OBE) satellite mission.
D D 1.5.2 R ydberg-Cavity R eceiver as developed at Kyoto University (Yamamoto et 
al., 2000): Rydberg atoms are excited atoms with one or more electrons that have a 
much higher principal quantum number than ground state, usually conditioned via laser 
pumping. The low binding energy of the excited electrons leads to very low 
photoionization energy; therefore, Rydberg atoms are sensitive to low-energy 
microwave photons, and allow a microwave device somewhat analogous to a 
conventional photomultiplier tube to be constructed. When a microwave photon strikes 
a high cross-section Rydberg atom, it causes the electron to be ejected and the atom is 
ionized. If a large electric field is established within the container, the electron is 
accelerated, causing cascading impact ionization. The advantage of this receiver is that 
it is sensitive to low-energy single-photon events, and has very good time resolution. 
The disadvantage is its cost and complexity. This task will include a conceptual design 
of an alternative Rydberg atom receiver apparatus suitable for the PPF arising from 
HFRG W, and will also include a sensitivity calculation of the proposed apparatus.
D D 1.5.3 Circuit QED  microwave receiver as developed at Yale University (Schuster 
et al.,2007): a third option will also be explored, the C ircuit Q ED microwave photon 
receiver. A resonant co-planar waveguide, containing a C ooper Pair Box (C PB) in the 
center and delineated by Josephson junctions, define a photo-sensitive area in the 
center of the cavity. The cavity qubit energy levels shift when the cavity encounters a 
microwave photon. The advantage of this type of receiver is that it is very sensitive to 
individual photons and can integrate multiple photons over time. It has the
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disadvantage that this device is of a unique design that is currently available only from 
Yale University, and is likely not to be exportable. This task will include developing a 
conceptual design using this alternative type of receiver for the PPF arising from 
HFRG W.
DD1.6 Cryogenic System
Specification and design of the cryogenic system refrigeration unit, required for low- 
temperature operation to obtain the best possible reduction in intrinsic thermal noise: 
D r. R .C. W oods (LSU) + graduate student. D r. R . M L B aker (T SC), G.V .
Stephenson (T SC). The required criterion is that the temperature Tsatisfies kBT << 
hen (where kB is Boltzmann's constant); that is, T << h^/kB s 480mK for detection at 
10G Hz. This condition is satisfied by the target temperature for the interaction volume 
T < 48mK, which can be obtained using a common helium-dilution refrigerator. Then, 
the signal PPF will be significantly greater than the thermal photon flux.
C ost/performance tradeoffs may also be important in this design, so that other possible 
economic solutions to receiver cooling will also be considered before finalizing the 
design.
D D 1.6.1 Off-the-shelf cryogenic systems: a number of companies have developed 
ultra-low temperature systems (mK range) for a variety of applications. A common 
application is refrigeration of receivers as needed in the Li-Baker HFRG W detector. One 
possibility is the Oxford Instruments' KelvinoxMX range (see summary data attached) 
that appears to suit the present requirements subject to further evaluation of each 
model in the range. Other manufacturers to be investigated include Scientific Magnetics 
(UK), and C ryofab Inc. (Kenilworth, New Jersey).
D D 1.6.2 Specifications for system best suited to the detector: specifications will 
be established for the selected cryogenic system. This will include cryogen level 
monitoring devices (for example, Oxford Instruments Intelligent Level Meter ILM200) 
for warning if the cooling fails.
DD1.7 Electromagnet
Development of the electromagnet specification needed to produce the required static 
magnetic field (up to 35T, ~3T nominal): D r. R .C. W oods (LSU) + graduate 
student, D r. R . M L B aker (T SC), G.V . Stephenson (T SC). It is expected that a 
commercial design can be identified for this task. The chosen design will be capable of 
providing the requisite magnetic field at least over the interaction cavity volume in the 
containment vessel. Exceptional field-uniformity is not a particularly important issue in 
this application, though the G W interaction volume or cavity (roughly cylindrical, 6cm 
diameter and 30cm long) plus extra volume for the surrounding apparatus is somewhat 
larger than many other experimental applications require, and the required field is 
perpendicular to the cylindrical axis. Hence, one solution is that the final solenoid 
design must completely surround the cylindrical axis of the interaction volume 
perpendicular to the applied field. An alternative approach is to use two solenoids, one 
each side of the interaction volume, similar to the popular Helmholtz coil configuration. 
In a development of this, a number of small (~6cm diameter) solenoids could be 
stacked along the length of the interaction volume, with their Helmholtz-like opposite 
paired solenoids the other side of the interaction volume. In the latter cases, since the 
paired solenoids are not perfect ring coils, the resultant field would be non-uniform. A
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quantitative estimate would be needed to ensure that the non-uniformity is not serious 
in the present application, but this is not expected to be a problem since field non­
uniformity just produces non-uniform PPF generation in the interaction volume. The 
fractal membrane reflectors would still focus all the PPF at the receivers. The design 
tradeoff will be whether one or two large magnets are more cost-effective than a larger 
number of smaller magnets. The design effort will be divided into two major sub-tasks: 
off-the-shelf electromagnets currently available, and emerging-technology proposed 
magnets that may become available during the construction phase of the HFG W 
detector.
D D 1.7.1 Off-the-shelf hardware: Excepting major installations, iron-core magnets 
are limited to around 2T over small volumes so that superconducting magnets are 
expected to be used here. C ryogen-free (more accurately, the cryogen is completely 
enclosed and re-cycled each time the magnet is cooled for use) superconducting 
magnets producing fields up to 16T are available commercially from a number of 
manufacturers including Scientific Magnetics, Oxford Instruments, and C ryogenic Ltd. 
(all UK). As examples, Oxford Instruments can supply magnets producing 9T in a 20cm 
bore, and 5T in a lm bore. Typically, cooling is provided by an integral G ifford- 
McMahon cryo-cooler at 4.2K. Use of a cryogen-free "dry" magnet means that there are 
no cold seals to be a source of leaks.
D D 1.7.2 Emerging technology: Since the detection PPF signal is directly proportional 
to the static magnetic field value, the detector sensitivity will be increased by using 
larger fields than currently-available commercial designs permit. To this end we will 
investigate the feasibility of co-developing with a third-party (for example, National 
High Magnetic Field Laboratory, Tallahassee, Florida) a custom-made high-field design 
capable of up to 35T (Bird, 2004), which may be realizable during the construction 
phase of the Li-Baker detector. If successful, achieving this value of magnetic field 
would improve the sensitivity of the Li-Baker detector by an order of magnitude. In this 
case, if a separate refrigeration system is required, the specification would include 
cryogen level-monitoring to ensure safe auto-rundown of the superconducting magnet if 
the helium level falls below a pre-set value, to reduce the danger associated with 
cryogenic-system related magnet failure. .1
Systems Engineering, Tasks
Following the completion of the Li-Baker detector development tasks, plans and 
specifications will be drawn up by LSU in collaboration with T SC. Since overlap of tasks 
is possible, approximately 18 months will be allowed for the detector design, and 
approximately 8 months for the preparation of plans and specifications. With 
approximately two months overlap of the major tasks, a total of two years will be 
scheduled for the detector's design and development of the plans and specifications. 
Fig. 4.1a shows a G annt chart for scheduling the project. For any large engineering 
project, coordination among investigators is important for the development of a 
coherent, unified design. This is the role of systems engineering tasks, depicted at the 
top of Fig. 4.1a. In the present case, the development of the detector will demand the 
close coordination of the detection link budget very early on, in order to carefully guide 
the component design for each of the component areas, and to ensure that the 
sensitivity goals can be met. This task culminates in a review of the predicted signal-to- 
noise ratio. A follow-on to this task is the development of key component requirements 
Interface requirements development is the next level of detail in systems engineering
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task area, resulting in interface control documentation/drawing review prior to the 
critical design reviews of the component equipment areas. Finally, the systems 
engineering activity concludes with the development of test plans that will detail 
integration activities and reduce integration risk in subsequent phases. These activities 
are standard level-of-effort tasks that are rolled into other task bids as a background 
activity.
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Appendix C: Perturbative Photon Fluxes Generated B y 
High-Frequency Gravitational W aves and T heir Physical 
Effects
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