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United States Patent 6,417,597
Baker, Jr. July 9, 2002
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Gravitational wave generator
Abstract
A gravitational wave generation device comprising an ensemble
of energizable elements involving magnetic, electrical and electromechanical
functions that are under the control of a computer and attendant
computer software system. The magnetic and electrical force elements,
when energized as directed by the computer, operate in concert
to produce a rapid third-time-derivative motion of a mass. This
action causes the generation of high-frequency gravitational waves
that can be modulated and shaped in order to be utilized for communication,
propulsion, and various physics experiments. The energizable elements
can be very small coils or coil sets encased in a computer chip,
current-carrying conductors, or small electromechanical devices.
The mass acted upon by the coil elements can be a permanent magnet
or magnets, or electromagnets. In the electromechanical-element
configuration the device can be used both for the generation of
gravitational waves and their detection.
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Inventors: Baker, Jr.; Robert M. L. (8123 Tuscany Ave., Playa
del Rey, CA 90293)
Assignee: Baker, Jr.; Robert M. L. (); Baker; Bonnie (Playa Del
Rey, CA)
Appl. No.: 616683
Filed: July 14, 2000
Current
U.S. Class: 310/300; 310/311; 700/286; 976/DIG.403; 976/DIG.405
Intern'l Class: G21H 003/00; G21H 001/00
Field of Search: 310/300,311 700/286 976/DIG. 403,DIG. 405 376/153
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References
Cited [Referenced By]
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U.S.
Patent Documents
2719944 Oct., 1955 Brailsford 318/254.
2814769 Nov., 1957 Williams 318/171.
3612630 Oct., 1971 Rosensweig 308/10.
3667019 May., 1972 Elliott et al. 318/254.
3722288 Mar., 1973 Weber 73/382.
3903463 Sep., 1975 Kanamori 318/138.
3959700 May., 1976 Sugiura et al. 318/138.
4035658 Jul., 1977 Diggs 290/55.
4052134 Oct., 1977 Rumsey 416/119.
4086505 Apr., 1978 McDonald 310/74.
4546264 Oct., 1985 Pinson 290/54.
4874942 Oct., 1989 Clauser 250/251.
5398571 Mar., 1995 Lewis 74/572.
5446018 Aug., 1995 Takahata et al. 310/90.
5495515 Feb., 1996 Imasaki 378/119.
5513530 May., 1996 Ney et al. 73/382.
5514923 May., 1996 Gossler et al. 310/74.
5646728 Jul., 1997 Coutsomitros 356/352.
5721461 Feb., 1998 Taylor 310/268.
5831362 Nov., 1998 Chu et al. 310/90.
5929579 Jul., 1999 Hsu 318/439.
Foreign Patent Documents
1333343 Oct., 1973 GB .
Other
References
Chakrabarty, "Gravitational Waves: An Introduction,"
Aug. 21, 1999, Physics, pp. 1-21.*
J. Weber, "Gravitational Waves" in Gravitation and Relativity,
Chapter 5, pp. 90-105 (W.A. Benjamin, Inc., New York, 1964).
J. Weber, "Detection and Generation of Gravitational Waves",
Physical Review, (1960) vol. 117, No. 1, pp. 306-313.
J. Weber, "Gravitational Radiation from the Pulsars",
Physical Review Letters, (1968) vol. 21, No. 6, pp. 395-396.
Robert L. Forward and Larry R. Miller "Generation and Detection
of Dynamic Gravitational-Gradient Fields", Hughes Research
Laboratories, Aug. 5, 1966, pp. 512-518.
F. Romero B., et al., Generation of Gravitational Radiation in
the Laboratory, Fakultat fur Physik der Universitat Konstanz,
Z. Naturforsch 36a, 948-955 (1981).
Richard, Jean-Paul, Recent developments in the measurement of
space time curvature, Acta Astronautica, vol. 5, pp. 63-76. Pergamon
Press 1978.
Primary
Examiner: Mullins; Burton S.
Attorney, Agent or Firm: Christie, Parker & Hale, LLP
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Parent
Case Text
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REFERENCE TO RELATED INVENTION
The
present application is a continuation-in-part of application Ser.
No. 09/443,527, filed Nov. 19, 1999, now U.S. Pat. No. 6,160,336
entitled Peak Power Energy Storage Device and Gravitational Wave
Generator which is incorporated herein by reference.
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Claims
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What is claimed is:
1.
A gravitational wave generator utilizing a computer controlled
logic system to produce gravitational waves by imparting a third
time derivative to the motion of a mass or a system of masses.
2.
A gravitational wave generation device comprising:
a
plurality of energizable elements;
a
plurality of electronic switches connected to the elements;
a
computer-controlled logic system operatively connected to a power
source for selectively energizing the elements; and
a
transmitter operatively connected to the elements for selectively
connecting the elements to an information processing device in
a predetermined time sequence to generate gravitational waves.
3.
A device according to claim 2 wherein the electronic switches
are semiconductor based.
4.
A device according to claim 2 wherein the plurality of elements
are piezoelectric crystals.
5.
A device according to claim 2 wherein the plurality of elements
are silicon semiconductors.
6.
A device according to claim 2 wherein the plurality of elements
are thin-film piezoelectric resonators.
7.
A device according to claim 2 wherein the plurality of energizable
elements are piezoelectric polymers.
8.
A device according to claim 2 wherein the plurality of elements
are of a submillimeter size and incorporated into a semiconductor
chip.
9.
A device according to claim 2 wherein the plurality of energizable
elements are of a submillimeter size and integrated with polymer-based
devices.
10.
A device according to claim 2 wherein a subset of the energizable
elements are arranged in a line of such elements such that when
energized by a train of current pulses, the duration of which
allows the pulses to traverse a subsequent energizable element
completely, and reaches the next energizable element in the line
with time delays between the elements to ensure that the pulses
can reach each of the elements in the line at an appropriate time
to generate gravitational waves as the train of pulses progresses
down the line.
11.
A device according to claim 2 wherein the plurality of elements
are of a submillimeter size and integrated with polymer-based
devices.
12.
A device according to claim 2 wherein the plurality of elements
are nanomachines.
13.
A device according to claim 12 wherein the nanomachines are piston
actuators.
14.
A device according to claim 12 wherein the nanomachines are motors.
15.
A device according to claim 12 wherein the nanomachines are vibrators.
16.
A device according to claim 12 wherein the nanomachines are pumps.
17.
A device according to claim 2 wherein a mass or masses are is
set in motion by the elements and exhibits a third-time-derivative
motion of the mass or masses to produce a gravitational wave.
18.
A device according to claim 17 wherein the mass or masses are
a plurality of electromagnets.
19.
A device according to claim 18 wherein a cylindrically shaped
magnetic core mass is provided, surrounded by a sheath composed
of a plurality of very small coils or coil sets, each individually
controlled by computer means.
20.
A device according to claim 17 wherein the mass or masses are
a plurality of permanent magnets located around the rim of a spindle.
21.
A device according to claim 20 wherein to a plurality of conductive
wire coils or coil sets adjacent to the spindle rim are segmented
into one or more separate, juxtaposed sectors.
22.
A device according to claim 20 wherein the plurality of magnets
located around the periphery of the spindle rim are separated
into one or more separate, juxtaposed magnets.
23.
A device according to claim 2 wherein the plurality of elements
are electrically energizable elements.
24.
A device according to claim 23 wherein the plurality of electrically
energizable elements are capacitors.
25.
A device according to claim 23 wherein the plurality of electrically
energizable elements are dielectric resonators.
26.
A device according to claim 2 wherein the plurality of elements
are small conductive wire coils or coil sets.
27.
A device according to claim 23 wherein the plurality of conductive
wire coils or coil sets are microscopic in size and integrated
with polymer-based devices.
28.
A device according to claim 26 wherein the plurality of small
conductive coils or coil sets are individually sequenced radially
outward by current pulses to generate gravitational waves resulting
from a third-time-derivative motion or jerk of a time-variable
moment of inertia or mass distribution of a magnetic mass.
29.
A device according to claim 26 wherein the plurality of coils
or coil sets along a predetermined line of such coils or coil
sets are energized by a train of current pulses, the duration
of which is controlled by computer means to cause the pulse to
traverse a subsequent coil or coil set completely and reaches
the coil set in the line via the same single conductor wire with
predetermined time delays between the coils or coil sets to ensure
that the pulses reach each of the coils or coil sets in the line
at an appropriate time to generate gravitational waves as the
train of pulses progresses down the line.
30.
A device according to claim 23 wherein the plurality of conductive
wire coils or coil sets are of a very small size and encased in
or imprinted on a semiconductor chip.
31.
A device according to claim 30 wherein the semiconductor chip,
containing the plurality of very small coils or coil sets, is
layered with circuit elements sequenced to launch a magnetic-field
pulse of very brief duration which interacts almost simultaneously
with the electromagnetic field of a magnetic mass to cause a sufficient
third-time-derivative motion or jerk of the magnetic mass to generate
gravitational waves.
32.
A device according to claim 31 wherein the magnetic mass is a
single magnet acted upon by the plurality of coils or coil sets
adjacent to it.
33.
A device according to claim 2 wherein the plurality of elements
are electromagnetic-force elements.
34.
A device according to claim 33 wherein the plurality of electromagnetic-force
elements are solenoids.
35.
A device according to claim 33 herein the electromagnetic force
elements are coil sets that are flattened out into one or more
parallel conductor pairs situated close to one another and are
pulsed with a current by computer controlled switches to produce
a gravitational wave.
36.
A device according to claim 35 wherein the plurality of parallel
conductor pairs are arranged in a mosaic pattern or in multiple
layers of a mosaic pattern.
37.
A device according to claim 35 wherein the plurality of parallel
conductor pairs are of microscopic size and encased in or imprinted
on a semiconductor chip or integrated with a polymer-based device.
38.
A device according to claim 35 wherein the plurality of parallel
conductor pairs along a predetermined line of such parallel conductor
pairs are energized by a train of current pulses the duration
of which is controlled by computer means to cause the pulse to
traverse a subsequent pair of parallel conductors completely and
reaches the parallel conductors in the line via the same single
conductor wire with predetermined time delays between the pairs
of parallel conductors to ensure that the pulses reach each of
the pairs of parallel conductors in the line at an appropriate
time to generate gravitational waves as the train of pulses progresses
down the line.
39.
A gravitational wave detection device comprising:
a
plurality of collector elements;
a
plurality of electronic switches connected to the elements;
a
computer-controlled logic system operatively connected to an information
processing device for selectively connecting the elements in a
predetermined time sequence; and
a
receiver operatively connected to the information processing device
to indicate the detection of gravitational waves.
40.
A device according to claim 39 wherein the plurality of elements
are piezoelectric crystals.
41.
A device according to claim 39 wherein the plurality of elements
are silicon semiconductors.
42.
A device according to claim 39 wherein the plurality of elements
are thin-film piezoelectric resonators.
43.
A device according to claim 39 wherein the plurality of elements
are piezoelectric polymers.
44.
A device according to claim 39 wherein the plurality of elements
are capacitors.
45.
A device according to claim 39 wherein the plurality of elements
are of a submillimeter size and incorporated into a semiconductor
chip.
46.
A device according to claim 39 wherein the plurality of elements
are nanomachines.
47.
A device according to claim 46 wherein the nanomachines are piston
actuators.
48.
A device according to claim 46 wherein the nanomachines are generators.
49.
A device according to claim 46 wherein the nanomachines are electrical
transducers.
50.
A device according to claim 46 wherein the nanomachines are pressure
transducers.
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Description
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BACKGROUND OF THE INVENTION
This
invention relates to the generation of high-frequency gravitational
waves that can be modulated and utilized for communication, propulsion
and for the purpose of testing new physical theories, concepts,
and conjectures. More particularly this invention relates to a
combination of small energizable elements operatively connected
to a computer working in concert to produce a third-time-derivative
motion of a nearby mass or electromechanical elements that generates
a high-frequency gravitational wave. The invention also relates
to the detection of gravitational waves.
DESCRIPTION
OF THE PRIOR ART
Albert
Einstein in his General Theory of Relativity predicted gravitational
waves (GW). Such waves have never been detected, but an extra-terrestrial
source of low-frequency GW, namely a neutron double star pair,
has been observed to coalesce at a rate exactly as predicted if
it radiated GW. The production of GW having a high frequency and
generated by relatively strong magnetic, electrical and electromechanical
forces acting on relatively small masses rather than by the relatively
weak gravitational forces acting on large celestial masses is
not known.
The
prior art indicates that gravitational-wave generators are theorized
although not reduced to practice. Joseph Weber in "Detection
and Generation of Gravitational Waves", Physical Review,
Volume 117, Number 1, January, 1960, p. 313 has proposed electromechanical-force-produced
GW by use of piezoelectric crystals: "Waves one meter long
could be radiated by a crystal with dimensions about fifty centimeters
on a side. If it is driven just below the breaking point, each
crystal would radiate .apprxeq.10.sup.-20 [watts], assuming P.sub.max
to be its static published value." No one has, however, put
such a device in practice.
According
to Robert L. Forward a gravitational-wave generator could be constructed
by means of a tube in which very dense Newtonium (element 127)
is caused to move up-and-down the tube at high-speed (not really
a dipole since as Joseph Weber indicated {"Gravitational
Waves" in Gravitation and Relativity, Chapter 5,W. A. Benjamin,
Inc., New York, 1964, p. 91} the lowest order of gravitational
radiation from a system cannot be a dipole, but must be a quadrupole).
However no drawings or other descriptions of such a generator
are known that are sufficiently specific to enable a person skilled
in the art to practice the generator.
As
described in the parent patent, there is considerable prior art
in the detection of gravitational waves including U.S. Pat. No.
5,646,728, which involves a very low amplitude interferometer
instrument suitable for detecting gravitational waves. This prior
art involves only the detection of low-frequency (below a MHz)
gravitational waves generated by natural processes, such as astrophysical
or celestial events. It is believed that there is no prior art
in the detection of high-frequency gravitational waves that are
artificially generated for communication or other purposes.
SUMMARY
OF THE INVENTION
The
present invention relies upon the fact that the rapid movement
or "jerk" of a mass or the rapid change or "jerk"
in angular momentum with time, over a period of time such as a
picosecond caused by the operation of the present invention, will
produce a quadrupole moment and generate a sequence or train of
useful high-frequency, for example Tera Hertz (THz), gravitational
waves (GW). The device described will accomplish this GW generation
in several alternative ways based upon the device's rotating and
non-rotating, symmetrical and non-symmetrical masses acted upon
by means of relatively strong magnetic, electrical and electromechanical
forces. Such forces are produced by an ensemble of very small,
sub-millimeter, energizable elements operating in concert under
the control of the device's computer. As noted, this process is
substantially different from the extra-terrestrial generation
of low-frequency GW by very large rotating and non-rotating celestial
masses acted upon by relatively weak gravitational forces.
Gravitational
waves are absorbed differently and propagate differently through
matter and space than do electromagnetic waves. Thus gravitational
waves may offer advantages over electromagnetic waves in that
they can be transmitted through material opaque to electromagnetic
waves and their intensity may fall off less rapidly with distance
than electromagnetic waves. Up to now man-made machines in use
do not generate significant or measurable GW.
BRIEF
DESCRIPTION OF THE DRAWINGS
The
foregoing features and advantages of the present invention will
be more fully understood by reference to the following detailed
description of the invention when considered in connection with
the accompanying drawings in which:
FIG.
1A and FIG. 1B are schematic views of coil sets 56 embedded in
or imprinted on a silicon chip 57 and connected to transistors
or ultra-fast switches 58 in order to generate current pulses
59 in the magnetic field of the permanent magnets 60;
FIG.
2 is a schematic view of a single-sector or linear-motor embodiment
of a gravitational-wave-generator device. The sector refers to
the sector of the annulus of the plan view of the rim of the spindle
device shown in the parent patent, U.S. Pat. No. 6,160,336 and
is, therefore, a single, isolated segment of the rim. A sheath
68 of coils, embedded in semiconductor chips 57 individually or
collectively connected to computer controlled transistor or ultra-fast
switches, surrounds a central magnetic-mass composed of magnetic
sites 57 incorporated with core, piston, or barrel 63;
FIG.
3 is a schematic view of infinite-radius coils evolved into parallel
plate conductors 66, which may have ballast 67 attached in order
to vary their masses, connected to fast switches 58 in order to
generate current pulses 59 acting in concert to generate a train
of gravitational waves 29 (which propagate in both directions
from the jerk since there is a square associated with the kernel
of the quadrupole equation (3)--so there is no preferred direction
along the axis of the jerk); and
FIG.
4 is a schematic view of the utilization of electromechanical
elements 65 that act in concert to generate and detect gravitational
waves 29.
ANALYSIS
OF BINARY PULSAR PSR 1913+16
Since
the observation of the binary pulsar PSR 1913+16 represents the
only experimental confirmation of GW, the features and advantages
of the present invention will be better understood by the analyses
of such a double-star system. This pair of neutron stars will
coalesce in 3.5.times.10.sup.8 years due to GW radiation and produce
a rather continuous GW until that time. According to J. H. Taylor,
Jr. in "Binary pulsars and relativistic gravity", Reviews
of Modern Physics, Volume 66, Number 3, July, 1994, pp. 711-719,
the period of their mutual rotation is 7.75 hours (or 2.79.times.10.sup.4
[sec]), periastron is 1.1 solar radii (one solar radius is 6.965.times.10.sup.8
[m]), and apastron is 4.8 solar radii. It's radius of gyration
is essentially the semi-major axis=(1.1+4.8)/2=2.95 solar radii=(2.95)
(6.965.times.10.sup.8)=2.05.times.10.sup.9 [m]. The neutron stars
exhibit a mass of about 1.4 solar masses so that together their
mass is (2) (1.4) (1.987.times.10.sup.30)=5.56.times.10.sup.30
[kg]. Thus the moment of inertia of the binary-pulsar system is
approximately (5.56.times.10.sup.30) (2.05.times.10.sup.9).sup.2
=2.34.times.10.sup.49 [kg-m.sup.2 ]. The current angular rate
of the system=2.pi./2.79.times.10.sup.4 =2.25.times.10.sup.-4
[radians/sec]. Thus the angular momentum of the system is currently,
I.omega.=(2.34.times.10.sup.49) (2.25.times.10.sup.-4)=5.27.times.10.sup.45
[kg-m.sup.2 /sec]. According to a perusal of binary-star catalogs
by John Mosley of the Griffith Observatory, the binary pulsar
PSR 1913+16 is at a distance from our Sun of 23,300 light years.
If there was little or no GW diffraction, then the reference area
is a circular ribbon or strip having a width of the diameter of
a neutron star, 3.times.10.sup.4 [m]. Thus the reference area
equals (3.times.10.sup.4) (2.pi.) (2.33.times.10.sup.4) (9.5.times.10.sup.15
meters per light year)=4.17.times.10.sup.25 [m.sup.2 ].
In
the case of a binary star pair such as PSR 1913+16 the GW power,
P, is computed from the quadrupole moment, which for two masses
on orbit about one another is given, for example, by an equation
on p. 356 of L. D. Landau and E. M. Lifshitz, The Classical Theory
of Fields, Forth Revised English Edition, Pergamon Press, 1975.
They give the time-variable factor in P as a function of the true
anomaly, v, and orbital eccentricity, e, as
(1+e
cos v).sup.4 ([1+{e/12}cos v].sup.2 +e.sup.2 sin.sup.2 v)/(a[1-e.sup.2
]).sup.5. (1)
In
conventional astrodynamic/celestial-mechanics notation this factor
is
p/r.sup.6
+(dr/d.tau.).sup.2 /12.mu.r.sup.4, (2)
where
p is the orbital "parameter" or semilatus rectum [AU],
r is the radial distance between the two masses [AU], .tau. is
the characteristic time measured in k.sub.s days or in units of
5.0022.times.10.sup.6 [s] for heliocentric-unit systems, and .mu.
is the sum of the two masses [solar masses]. Note that one AU
(astronomical unit)=1.496.times.10.sup.11 [m] and one solar mass=1.987.times.10.sup.30
[kg]. The dr/d.tau. term is related to dI/d.tau. (=2 .mu.r[dr/d.tau.]),
d.sup.3 I/d.tau..sup.3 (=-2 .mu..sup.2 [dr/d.tau.]/r.sup.2) ,
d.sup.2 v/d.tau..sup.2 (=-.mu.p[dr/d.tau.]/r.sup.3), and d.sup.3
v/d.tau..sup.3 (=-2 .mu. .mu.p[1/r-1/a-4{dr/d.tau.}.sup.2 /.mu.]/r.sup.4),
where a=the semi-major axis of the orbit [AU] and for a circular
orbit dr/d.tau.=0. These time derivatives are directly related
to the embodiments of the invention.
The
GW power radiated, P, which causes a perturbation in the semi-major
axis, a, (and an attendant secular decrease in the orbital period)
is obtained by integrating the time-variable factor, Eq. (2),
over the orbital period using the mean anomaly, M, which is directly
proportional to the time (that is, M=n [t-T], where n is the mean
motion [=.omega. in Landau and Lifshitz's {ibid, p. 357} notation]
and T is the time of periastron passage). The value of the average
GW power, P, is computed from observations that define the eccentricity
(based primarily upon Doppler-shift determination of the range
rate at periastron and apastron), semi-major axis, and orbital
orientation angles of PSR 1913+16. The error in the computed value
of P is related to the observational error leading to the determination
of the orbital elements as well as the determination of the masses
of the pair of neutron stars, .mu.=m.sub.1 +m.sub.2 =1.4+1.4=2.8
[solar masses]. For example, a 0.1 percent change in the measurement
of range rate at periastron results in a 0.28 percent change in
GW power, P, and a 0.1 percent change in the mass of the stars
results in a 0.33 percent change in GW power.
The
observed accumulated shift in the times of periastron passage,
T, caused by the secular shortening of the orbital period of PSR
1913+16, compares closely, within observational error, to that
predicted by General Relativity and confirms the existence of
GW radiation. Likewise is confirmed the existence of a dr/d.tau.
component, which is related to d.sup.2.omega./dt.sup.2 (.apprxeq.d.sup.3
v/d.tau..sup.3) and d.sup.3 I/dt.sup.3, that are involved in the
GW-generator embodiments of the invention
The
average GW power, P, established by Landau and Lifshitz (ibid,
p. 357) by analytically integrating and given as a function of
eccentricity, e, is for e=0.641, 9.28.times.10.sup.24 [watts]
so for the disk reference area the GW flux at the Sun's distance=9.28.times.10.sup.24
/4.17.times.10.sup.25 =0.222 [watts/m.sup.2 ]. If the GW is totally
diffracted and the propagation is spherically isotropic, then
the GW flux at the Sun's distance=9.28.times.10.sup.24 /(4.pi.[2.33.times.10.sup.4.times.9.5.times.10.sup.15
].sup.2)=1.51.times.10.sup.-17 [watts/m.sup.2 ]. By numerically
integrating (see, for example, an algorithm found in R. L. M.
Baker, Jr., Astrodynamics, Applications and Advanced Topics, Academic
Press, New York , 1967, pp. 263-272) over the mean anomaly (directly
proportional to time) the average GW power, P, is 9.296.times.10.sup.24
[watts]. The peak GW power, 1.73.times.10.sup.26 [watts] occurs
at the time of periastron passage (every 7.75 hours) and at the
Sun's distance would result in a GW flux of 1.73.times.10.sup.26
/(4.pi.[2.33.times.10.sup.4.times.9.5.times.10.sup.15 ].sup.2)=2.81.times.10.sup.-16
[watts/m.sup.2 ] if the GW were totally diffracted and the propagation
were spherically isotropic. If GW detectors were sensitive enough
to detect such an intensity and they did not, then it would lend
credence to the disk-like propagation of GW waves or at least
to diffraction of GW less than 45 degrees from the orbit plane
of PSR 1913+16 at the Sun's distance.
Individual
Independently Programmable Coil System (IIPCS)
Of
fundamental importance to the operation of the present invention
is the Individual Independently Programmable Coil System (IIPCS)
described and illustrated in parent patent U.S. Pat. No. 6,160,336.
This system, is enabled by a computer and associated computer
software, to control a system of either transistors or of ultra-fast
switches. The switches rapidly turn off or on a myriad of sub-millimeter
coils, current-carrying conductors and/or electromechanical elements
and generate magnetic (or electromechanical) force to produce
a third time derivative or "jerk" or, alternatively,
a harmonic oscillation of a mass or masses.
For
a very large number of ultra-small, sub-millimeter coil elements
involved in some of the embodiments of this invention a miniaturized
integrated circuit can be utilized. They are embedded in or imprinted
on a silicon chip, organic material, or in connection with polymer-based
devices. They consist of multiple layers, with appropriate sequencing
time delays to ensure near simultaneity of the magnetic field's
interaction with individual elements, as in FIG. 1A, or as the
direct-current train of approximately one-picosecond pulses, which
traverse each coil set on the chip levels, as in FIG. 1B and possibly
integrated in the chip with the ultra-fast switches or transistors
or other semi-conductors. Although switches or transistors having
picosecond capability are utilized in the various numerical examples,
much slower switches or transistors could be utilized to successfully
practice the invention. A preferred embodiment utilizes conventional
computer chips, containing the IIPCS circuit elements about 18
micrometers or less apart, synchronizing clock, input/output ports,
and sub-millimeter coils on 50 to 100 micrometer centers. The
chips are about 6 mm to 9 mm square and are obtained from silicon
wafers. These chips are sewn into a circuit-board roll with an
approximately 25-micrometer-diameter gold thread. Several layers
of this roll (for example, 25) are connected in a fixed location
or band adjacent to the moving spindle's rim and form the IIPCS
in the spindle rim's magnetic field. Such rolls are routinely
fabricated by French-owned Oberthur Card Systems (plant in Rancho
Dominguez, Calif.), French-based Gemplus, Schlumberger (Paris
and New York), and California-based Frost & Sullivan.
In
the miniaturized integrated circuit situation, as exhibited in
FIG. 1A, there will be a very large number of small, sub-millimeter
coil sets or elements 56 embedded in or imprinted upon a silicon
chip 57 in multiple layers. Ultra-fast switches or transistors
of the IIPCS 58 will launch a series of current pulses 59 of approximately
picosecond duration moving at the electron's mobility speed, c,
that will be timed to reach the individual coil sets or elements
almost simultaneously along several individual wire conductors,
as in FIG. 1A, or one single wire conductor per line, as in FIG.
1B, and thereby interact with the magnetic field 60 in concert.
This interaction will result in a third-time-derivative motion
or jerk of the magnetic mass to generate a train of gravitational
waves. The ultra-fast switches are preferably semiconductor-based,
such as a semiconductor optical amplifier (SOA) or a semiconductor
nonlinear interferometer such as a nonlinear Sagnac interferometer
on a phosphide semiconductor chip, etc. (see, for example, D.
Cotter, et al, "Non-linear Optics for High-speed Digital
Information Processing", Science, Volume 286, Nov. 19, 1999,
pp. 1523-1528). In FIG. 1B, the IIPCS and its array of ultra-fast
switches is programmed to launch a train of current pulses or
intervals of approximately a picosecond duration 59 such that
each member of the pulse train will reach each of the coils or
coil sets at the same time. The pulse train can consist of stretches
of constant or zero current. The duration of the pulses will be
such to completely energize any given coil set as it passes through
it in order to produce a magnetic field interaction. The interaction
will result in a third-time-derivative lateral motion or jerk
of a cylindrical, central magnetic core 63 shown in FIG. 2 and,
as will be discussed, generate a GW train 29, which propagates
both in the direction of and opposite to the direction of the
jerk as illustrated in FIGS. 8A and 8B of U.S. Pat. No. 6,160,336.
This core, piston, or barrel 63 is surrounded by and immediately
adjacent to a sheath 68 of IIPCS-controlled coil sets 64. In the
case of the current-pulse train on a single conductor wire interconnecting
a line of coils or coil sets, there will be a build up of impulses
to full value as the current-impulse train progresses down the
line of coil sets. Use of a single conductor wire for each line
of coils or coil sets reduces the resistive power loss. In order
to transmit information, all pulses in the train may not be present
or they may be at different amplitude thereby modulating the GW.
Portions or stretches of the pulse train could also be intervals
of constant current. In each line of coils set in series along
one conductor wire 61 there will be time delays 62 between coil
sets to ensure simultaneity of the current pulses reaching any
given coil set.
In
FIG. 3, ultra-fast switches or transistors of the IIPCS 58 will
launch a series of current pulses acting in either direction 59
of approximately picosecond duration moving at the electron's
mobility speed, c, along individual conductors or single interconnecting
conductor wires in order to produce current pulses 59, acting
in concert to generate a modulated gravitational wave 29. The
current pulses will be timed to reach individual parallel-plate
conductors 66, which may have different masses or may have ballast
67 attached and/or carry different current and/or have different
modulus of elasticity and/or are constructed differently in their
mounting for the purpose of exhibiting high-frequency asymmetrical
mass displacements.
In
FIG. 4, ultra-fast switches or transistors of the IIPCS 58 will
launch a series of current pulses 59 of approximately picosecond
duration moving at the electron's mobility speed, c, along individual
conductors or single interconnecting conductor wires that will
be times to reach individual, sub-millimeter electrical or electromechanical-force
elements 55 in sequence to reinforce the build up or modulation
of a GW beam 29. The ensemble of electrical or electromagnetic
force elements will be embedded in or imprinted on a silicon chip
57 in multiple layers.
Quadrupole
Moment
Although
the specific relationship for GW generation will be an outcome
of the experimental use of the invention; as an example of that
relationship consider the standard GW quadrupole Eq. (110.16),
p. 355 of L. D. Landau and E. M. Lifshitz (opcit) or Eq. (1),
p. 463 of J. P. Ostriker, ("Astrophysical Sources of Gravitational
Radiation" in Sources of Gravitational Radiation, Edited
by L. L. Smarr, Cambridge University Press, 1979) which gives
the GW radiated power [watts] as
P=-dE/dt=-(G/45c.sup.5)
(d.sup.3 D.sub..alpha..beta. /dt.sup.3).sup.2 [watts] (3)
where
E=energy
[joules],
t=time
[s],
G=6.67423.times.10.sup.-11
[m.sup.3 /kg-s.sup.2 ] (universal gravitational constant),
c=3.times.10.sup.8
[m/s] (the speed of light, approximately the electron's mobility
speed in the conductor), and
D.sub..alpha..beta.
[kg-m.sup.2 ] is the quadrupole moment-of-inertia tensor of the
mass of the device, and the
.alpha.
and .beta. subscripts signify the tensor components and directions.
Note
especially the third time derivative in the squared term or kernel
(that is, (d.sup.3 D.sub..alpha..beta./dt.sup.3).sup.2) of Eq.
)3). Such a time-rate-of-change of the second derivative ("acceleration")
is often referred to as a "jerk". Because the factor
of this kernel is so small, 1.76.times.10.sup.-52, the kernel
and hence the jerk must be very large. In the following examples
of GW generation by various devices, we shall often cite astrophysical
analyses of the same GW formulation. It should be recognized,
however, that although kernels are analogous in the invention
and in the celestial astrophysical systems (or events) their operation
is quite different. In most cases the astrophysically generated
GW rely on rather slow-moving, low-frequency events (a fraction
of a Hertz to possibly a MHz) and weak gravitational forces. On
the other hand, the various embodiments of the invention rely
on vary fast-moving, high-frequency events (in the THz range)
and relatively strong magnetic, electrical or electromechanical
forces.
DETAILED
DESCRIPTION OF THE PREFERRED EMBODIMENTS
In
order to understand the various embodiments of the invention it
is useful to refer to the historical roots of GW generation. From
Eq. (1), p. 90 of Joseph Weber (opcit, 1964) one has for Einstein's
original formulation of the gravitational-wave (GW) radiated power
of a rod spinning about an axis through its midpoint, having a
time-constant moment of inertia, I [kg-m.sup.2 ], and an angular
rate, .omega. [radians/s]:
P=-(G/45c.sup.5)
([{2.times.12}][I.omega..sup.3 ]).sup.2=-G(I.omega..sup.3).sup.2
/5(c/2).sup.5 [watts]. (4)
Equation
(4) is an approximation and is, strictly speaking, only valid
for lengths very much less than the GW wavelength and speeds of
the rod's rotation less than c.
This
is the same equation as that given for two bodies on a circular
orbit (also exhibiting a time-constant moment of inertia) on p.
356 of Landau and Lifshitz, opcit (I=.mu.r.sup.2 in their notation)
where .omega.=n, the orbital mean motion, and similar to all of
the equations associated with the various embodiments of the invention.
Although Eqs. (3) and (4) result from relativistic mechanics,
classical mechanics (such as the use of the conventional moment
of inertia in Eq. (4)) will be utilized herein to provide useful
results.
Spindle-Device
GW Generation Embodiment
It
is reasonable (by appealing to simplicity, that is, by Ockham's
Razor) to suggest that for the spin up/down of a spindle device,
as referred to in the parent application, (referred to herein
as the "(Id.sup.2.omega./dt.sup.2).sup.2 formulation or component"):
P=-G
.kappa..sub.I.omega.2dot (Id.sup.2.omega./dt.sup.2).sup.2 /5(c/2).sup.5
[watts] (5)
where
.kappa..sub.I.omega.2dot
=a dimensionless constant or function to be established by experiment
and
d.sup.2.omega./dt.sup.2
=second time derivative of the spindle's angular velocity, .omega.,
or third time derivative of it's angle, termed, a "jerk".
In fact, as noted by M. S. Turner and R. V. Wagoner "Gravitational
Radiation from Slowly Rotating `Supernova` Preliminary Results,"
in Sources of Gravitational Radiation, Edited by L. L. Smarr,
Cambridge University Press , 1979, p. 383 that "If the angular
velocity .omega. . . . is non-uniform, octupole (post-Newtonian)
radiation is generated (in addition to the quadrupole (Newtonian)
radiation . . . " (emphasis added) and on p. 385 they state
"This radiation is generated not by non-spherical distribution
of matter . . . , but by internal motions."
This
third derivative, d.sup.2.omega./dt.sup.2, is computed by introducing
the equation of motion for a rotating body
Id.omega./dt=rf
(6)
where
r=radius
of the spindle's rim [m] and
f=force
tangential to the rim [N].
The
derivative is approximated by
Id.sup.2.omega./dt.sup.2.congruent..DELTA.(Id.omega./dt)/
.DELTA.t=.DELTA.(rf)/.DELTA.t=r.DELTA.f/.DELTA.t; (7)
in
which .DELTA.f is the nearly instantaneous increase in the force
tangential to the rim or jerk caused by the magnetic field when
it is turned on or turned off or pulsed by the transistors or
ultra-fast switches of the Individual Independently Programmable
Coil System (IIPCS), that is, a tangential jerk. Thus
P=-1.76.times.10.sup.-52
(.kappa..sub.I.omega.2dot r.DELTA.f/.DELTA.t).sup.2 [watts]. (8)
(1)
Numerical Example
As
a numerical example, (for a spindle GW-generation device slightly
different from the exemplar spindle shown in U.S. Pat. No. 6,160,336)
set .kappa..sub.I.omega.2dot =1 (subject to experimental determination
later), r=1000 [m], .DELTA.f=1.8.times.10.sup.7 [N], and .DELTA.t=10.sup.-12
[s]. These numbers arise as follows: The rim is a thin (approximately
one cm thick) band of Alnico 5 permanent magnets (or electromagnets)
facing radially outward. In general, permanent magnets exhibit
irregular magnetic fields and associated forces. As a rule of
thumb such a band of juxtaposed magnets will produce in excess
of 30 pounds per 1.75 inches (or 206 pounds per foot) of tangential
rim force. Each 1.75-inch magnet has a flux density, B, of about
2,600 gauss or 0.26 [Tesla] developed every 4.4 cm. The kilometer-radius
rim is a large hoop connected to a central spindle/hub as described
in the parent patent. The IIPCS coil sets at the rim's periphery,
when switched on generate a 0.26 [Tesla] flux density every 0.044
[m] and produce in excess of a 200 pound per foot or 3000 [N/m],
which is defined as .DELTA.f/.DELTA.l, or impulse of tangential
force every meter on the rim (that is, a force built-up almost
to full value during spin up in approximately a picosecond and
a similar build up of retarding force during spin down) . Since
the rim's circumference is 2.pi. (1000) (3.28 feet per meter)=20,600
feet, the tangential rim force produced when the coils are fully
energized is 4.1.times.10.sup.6 pounds or 1.8.times.10.sup.7 [N].
The 10.sup.-12 [s] intervals, with the coils turned turn on and
then off, will generate a train of direct-current, approximately
one-picosecond pulses. In each line of coils there will be an
ultra-fast switch (such switches could be located near to the
coils and each one energizing a large number of coil sets or else
co-located with a central IIPCS control computer).
Inserting
the numbers in Eq. (8) for the spindle's gravitational-wave (GW)
power for the tangential jerk yields
P=-1.76.times.10.sup.-52
(2.times.10.sup.3.times.1.8.times.10.sup.7 /10.sup.-12).sup.2
=-2.3.times.10.sup.-7 [watts]. (9)
The
reference area of the 1 cm thick rim is (0.01) 2.pi.(1000)=63
[m.sup.2 ], so that the GW energy flux is 3.times.10.sup.-9 [watts/m.sup.2
]. For a time-constant value of I there may be a somewhat less
simple, .kappa..sub.I.omega.dot.omega. ([d.omega./dt].omega.).sup.2,
formulation or component of the GW power for spin up/down, but
as will be seen, for most applications it is expected to result
in a smaller power than the larger of the .kappa..sub.I.omega.2dot
(Id.sup.2.omega./dt.sup.2).sup.2 or (I.omega..sup.3).sup.2 formulations
or components.
Note
that the coil sets must be very close together. In order for the
coils fields to interact with the whole rim's magnetic field and
impart the mechanical impulse or jerk, they must be spaced no
more than 0.3 mm or 300 [micrometers] apart (the distance light
and, hence, the magnetic field and resulting impulse on the permanent
magnets, travels in a picosecond). If all coil sets in a line
of coil sets are connected in series by the same conductor, then
each member of the pulse train traverses a 300-micrometer-length
coil set, separated from the next coil set by a time delay circuit.
Such a time-delay circuit could be simply a 300-micrometer-long
jumper (see 62 in FIG. 1B) between coil sets. In this connection
it is noted that if each coil set is connected by its own unique
conductors as in FIG. 1A, instead of one single conductor wire
along each line of coils, then the communications lines or conductors
to all of the coil switches from the logic circuits of the control
computer must be equal to better than 0.01 mm or 10 [micrometers]
in order to ensure near simultaneity or proper timing. That is,
the electrons must reach all of the coils sets at the appropriate
time in less than approximately a fraction of a picosecond of
time difference.
(2)
Magnetic Field Build Up and Heat Loss
Although
of little concern in most applications, the length of time to
"build-up" the magnetic field of the coils is important
here. The electrons must complete sufficient coil turns (moving
at the electron's mobility speed or about light speed) in approximately
a picosecond to "launch" most of the magnetic field
that produces the impulsive force, "hammer blow" or
jerk when it interacts with the static magnetic field of the permanent
or electromagnets carried around by the rim or other magnetic
mass. Thus, they must be very tightly wound with each coil "set"
having a total length of less than 0.3 mm (0.0003[m] or 300 micrometers).
If each of the ultra-small, sub-millimeter coil sets consist of
two coils or turns, as exhibited in FIGS. 7A, 7B, 7C, 7D, 7E,
7F, 7G, and 7F, of the parent patent, then their diameters are
on the order of d=0.3/2.pi.=0.05[mm]=50 [micrometers] or less.
The coil wire could be made of gold having about a 0.015-mm or
15-micrometer diameter. The resistance for such wire at room temperature
is about 135 [ohms/m]--high-temperature superconducting material
would be useful here. In the spin-up mode the IIPCS will need
to build up 0.26 [Tesla] flux density every 0.044 [m] (the requirements
for the spin-down mode are essentially the same, but reversed).
Thus
B=.mu..sub.o
ni/l[Tesla] (10)
where
.mu..sub.o =4.pi..times.10.sup.-7 (permeability of free space),
n is the number of coil turns, i is the current through the coils
[amps], and l is the length of the coil conductors [m]. The double
coil sets will be placed on 50 to 100 [micrometer] centers, so
that there will be about 2.times.100.times.100=2.times.10.sup.4
coil turns on each square-centimeter level of the stack of 25
coil levels or layers. With l=0.044 [m] and B=0.26 [Tesla], ni=9.1.times.10.sup.3
[amp turns]. For n=25.times.2.times.10.sup.4 =5.times.10.sup.5,
i=9.1.times.10.sup.3 /5.times.10.sup.5 =0.018 [amps] or 18 milliamperes.
The total length of 15-micrometer-diameter gold wire across any
given layer or level is 100(rows).times.100(coil & jumper/time-delays).times.(600
micrometers)=6 [m]. For the 25 layers or levels there will 150
[m] of wire with a resistance of 150[m].times.135[ohms/m]=2.025.times.10.sup.4
[ohms]. Since on average every other pulse or current interval
across a conductor wire will carry no current, since in order
to modulate the GW some pulses or current intervals in the train
will be missing, the heat loss per centimeter of chip stack or
semi-conductor layers is
(1/2)i.sup.2
R=3.28[watts]. (11)
This
heat loss can be reduced by 32% by using 25-micrometer-diameter
wires for the time-delay jumpers, but high-temperature superconductors
for this purpose are contemplated. In addition there may be some
energy loss or resistance occasioned by electromagnetic radiation
(EM) generated during the GW generation process. Such a loss can
be reduced by the design of the energizing, for example coil,
elements and controlling the direction of current pulses by the
IIPCS. By the way, EM radiation can be easily screened out by
means of interposing a conductor in the GW path, which is opaque
to EM radiation but transparent to GW.
The
spin-up/down of the entire rim is not instantaneous and is anticipated
to progress at the speed of light in the rim from the juxtaposed
permanent-magnet sites on the rim acted upon by the coil-magnetic
fields. (Spin up/down does not progress at the local speed of
sound, but rather it is expected to progress at the speed of light
like a signal being transmitted by pushing a frictionless rod.
That is, all of the ferromagnetic molecules comprising the magnets
on the periphery of the rim move in concert, as the GW crest moves
through the magnets at light speed, impelled by their magnetic
fields. On the other hand, impulsive stresses in the spindle or
dumbbell device are propagated inwardly at the speed of sound
in the material of the device rather than at the speed of light.)
Thus, for example, at a one picosecond cycle or switching rate
an in-rim light speed of 3.times.10.sup.8 [m/s] some (10.sup.-12)
(3.times.10.sup.8)=0.0003 [m] or 0.3 [mm] or 300 micrometers of
the rim on each side of the juxtaposed coil/magnet activity sites
will respond (spin up or down) during each picosecond after coil
activation. This process, in the case of a dumbbell-shaped rim,
will generate an ever widening fan of gravitational waves, 51
as exhibited in FIG. 8B of the parent patent. Many more than the
4,290 coil sites of the exemplar device of the parent patent could
be distributed around the rim (perhaps over only a single sector
or selected sectors adjacent to the rim; thereby greatly reducing
the required number of coils and "focusing" the GW).
A large number of ultra-fast switches, preferably semiconductor
based, would be activated simultaneously by the IIPCS coil-control
computer, with communication lines of nearly equal length to all
switches.
(3)
Rim Material Accelerations
A
random series of positive and negative jerks tend to build up
a positive acceleration over time by random walk. Consider an
extreme case, however, in which the maximum jerk builds up rim
acceleration (spin up, or deceleration, spin down) continuously
over a length of time, .delta.t=10.sup.-7 [s] or 100 nanoseconds.
The mass per unit length of the magnetic mass of the rim for the
exemplar device of the parent application is .DELTA.mass/.DELTA.l=3.83
[kg/m]. The jerk is
da/dt=d.sup.3
S/dt.sup.3 =([.DELTA.f/.DELTA.l]/[.DELTA.mass/.DELTA.l]/.DELTA.t=(3000[N/m]/3.8[kg/
m]/10.sup.-12 =7.89.times.10.sup.14 [m/s.sup.3 ], (12)
where
S is the displacement. Therefore, in .delta.t=100 nanoseconds
(10.sup.-7 [s]) of continuous and constant jerk, da/dt, the acceleration,
a, would build up to
a(t)=.intg..sub.o.sup..delta.t
(da/dt)dt=(7.89.times.10.sup.14) (10.sup.-7)=7.89.times.10.sup.7
[m/s.sup.2 ], (13)
(of
course, control of the jerks by the IIPCS would never allow such
a high build up of acceleration) the speed would build up to
dS/dt=.intg..sub.o.sup..delta.t
(da/dt)dt=(da/dt).delta.t.sup.2 /2=(7.89/2).times.10.sup.14.times.(10.sup.-7).sup.2
=3.9[m/s], (14)
and
the displacement would build up to
S=.intg..sub.o.sup..delta.t
(ds/dt)dt=(da/dt).delta.t.sup.3 /6=(7.86/6).times.10.sup.14.times.(10.sup.-7).sup.3
=1.315.times.10.sup.-7 [m]. (15)
The
angular rate build up over 100 nanoseconds is 3.9[m/s]/1000[m]=3.9.times.10.sup.-3
[radians/s] versus, for example, the mean motion of double star
PSR1913+16 of 2.25.times.10.sup.-4 [radians/s]. Thus there is
considerable "motion" in the magnetic mass, but essentially
the mass goes only a very short distance. In this regard, as already
noted, the IIPCS can be programmed to ensure that there is not
a secular increase or accumulation of magnetic-mass displacement
beyond a certain prescribed limiting value. For example, if the
jerk were reversed every two seconds (reciprocating) then the
acceleration would build up to less than 200 [g's]. The stress
moves away from the magnetic mass at sound speed (for example,
5000 [m/s]) or about 500 micrometers in 100 nanoseconds. They
represent microscopic shock waves that will dissipate.
Radial-Jerk
GW Generation Embodiment
In
the case of the radially directed pulses or displacements of the
rim or rim sector or sectors, they result in a time-variable value
of the moment of inertia, I. These displacements are built up
in the radial direction by the sequential activation of radial
arcs of coils in a given, single wedge-shaped sector or juxtaposed
sectors of the rim or dumbbell. Under the control of the IIPCS,
radially oriented strips of the aforementioned circuit-board or
computer-chip rolls are sequentially activated to build up or
generate a (d.sup.3 I/dt.sup.3).sup.2 formulation or GW component
as the GW moves outward at light speed. The radial displacements
should be asymmetrical (as controlled by the IIPCS) in order to
produce a quadrupole moment or so that the GW will not cancel
out. The astrophysical analogy here is a vibrating white dwarf
star emitting GW (see, for example, D. H. Douglas, p.491, of L.
L. Smarr, opcit).
As
is well known and noted in specifics by Geoff Burdge, Deputy Director
for Technology and Systems of the National Security Agency (written
communication dated Jan. 19, 2000) "Because of symmetry,
the quadrupole moment can be related to a principal moment of
inertia, I, of a three-dimensional tensor of the system and .
. . can be approximated by
-dE/dt.apprxeq.G/5c.sup.5
(d.sup.3 I/dt.sup.3).sup.2 =5.5.times.10.sup.-54 (d.sup.3 I/dt.sup.3).sup.2."
(16)
In
which k in Burdge's notation is G and the units are in the MKS
system [watts] not the cgs. In this case
P=-G.kappa..sub.I3dot
(d.sup.3 I/dt.sup.3).sup.2 /5c.sup.5 [watts] (17)
where
I=.delta.m r.sup.2 [kg-m.sup.2 ],
.delta.m=mass
of an individual rim sector or a number of sectors (or dumbbell)
[kg], and
r=half
of the distance between opposing .delta.m [m]. Thus
d.sup.3
I/dt.sup.3 =.delta.m d.sup.3 r.sup.2 /dt.sup.3 =2r.delta.m d.sup.3
r/dt.sup.3 + . . . (18)
and
d.sup.3 r/dt.sup.3 is computed by noting that
2r.delta.m
d.sup.2 r/dt.sup.2 =2rf.sub.r [N-m] (19)
where
f.sub.r =radial force on a single rim sector, rim sectors, or
dumbbell. (This single-sector embodiment of the invention can
also be visualized as a linear motor.)
The
derivative is approximated by
d.sup.3
I/dt.sup.3 =2r.DELTA.f.sub.r /.DELTA.t, (20)
in
which .DELTA.f.sub.r is the nearly instantaneous increase in the
radial force on the rim caused by the magnetic field when it is
turned on and off or pulsed by the transistors or ultra-fast switches
of the IIPCS, that is, a radial jerk. In this regard the coils
are sequenced radially outward by the IIPCS (at the speed of light)
in order to generate or build up the high-frequency gravitational
waves. Thus
P=-5.5.times.10.sup.-54.kappa..sub.I3dot
(2r.DELTA.f.sub.r /.DELTA.t).sup.2 [watts]. (21)
Again,
.kappa..sub.I3dot will be a function determined experimentally
to account for the fact that r may not be less than the GW wavelength
for most high-frequency GW of interest.
As
a numerical example, for a spindle similar to the one mentioned
in the prior numerical example, but with a one-meter wide apron
of peripheral magnets and IIPCS coil sets both top and bottom
(thus 2.times.100 cm/m=200 times more force per meter along the
rim's periphery), .kappa..sub.I3dot =32, .DELTA.f=3.6.times.10.sup.9
[N], r=1000 [m] and .DELTA.t=10.sup.-12 [s], so that (pending
experimental verification)
P=-1.76.times.10.sup.-52
(2.times.1000.times.3.6.times.10.sup.9 /10.sup.-12).sup.2 =-9.12.times.10.sup.-3
[watts] (22)
Again
the reference area is 63 [m.sup.2 ], so that the GW energy flux
near the device is about 1.45.times.10.sup.-4 [watts/m.sup.2 ].
Single-Sector
or Linear-Motor, Tangential-Jerk GW Generation Embodiment
The
single-sector or linear-motor embodiment of the invention (sometimes
referred to as a linear induction motor or LIM) is the most preferred
embodiment of the invention. It can be visualized to involve a
single sector of the rim with the impulsive forces being tangential
rather than radial. Alternatively, it can be conceptualized as
the rim magnets and adjacent coils being peeled off from the rim
and laid out flat. In this case an exemplar device would be 2000
[m] in length and 3 [m] in diameter. The approximately one-centimeter-wide
chip rolls would be placed longitudinally along the sides of central,
cylindrical, permanent- (or electro-) magnetic core, piston, or
barrel as shown in FIG. 2. Each meter-long segment of the roll
would produce about 3000 [N] of longitudinal force, f.sub.l, and
all together they form a sheath of sub-millimeter coils surrounding
the central magnetic core, piston, or barrel consisting of magnetic
sites. Note that in this case the motion of the magnetic mass
is asymmetrical (either "in" or "out") so
that there is a quadrupole and the GW do not cancel and become
null. The IIPCS controlled current can proceed in either direction
and in the single-interconnecting-line-of-coils embodiment of
the invention alternative coil lines can be energized by pulse
trains moving in opposite directions to vibrate the magnetic mass.
The magnetic mass itself can be composed of electromagnets, with
or without cores, that can be controlled by the IIPCS to augment
the GW generation.
(1)
Numerical Example
As
a numerical example, there would be about one roll or 25-layer
strip of chips spaced around and adjacent to the barrel in a longitudinal
direction (parallel to the barrel axis) every 2 centimeters forming
the sheath. Thus there would be .pi..times.3[m].times.100[cm/m]/2[cm]=471
strips, 2000 [m] long or
.DELTA.f.sub.l
=(471) (2000[m]) (3000[N/m])=2.83.times.10.sup.9 [N] (23)
and
with .kappa..sub.mr3dot =32 (to be established experimentally),
P=-1.76.times.10.sup.-52
(2.times.2000.times.2.83.times.10.sup.9 /10.sup.-12).sup.2 =-2.26.times.10.sup.-2
[watts]. (24)
Thus,
with the reference area of the two 3 [m] diameter ends, 2.pi.(1.5).sup.2
=14 [m.sup.2 ], (GW propagating in both directions) the generated
GW flux is about 1.6.times.10.sup.-3 [watts/m.sup.2 ].
(2)
Sector-Material Accelerations
In
this case the jerk is obtained from
(da/dt).sub.per
unit area =(.DELTA.f/.DELTA.t)/(.DELTA.mass/.DELTA.A) (25)
where
.DELTA.f=.DELTA.f.sub.i [N]/(2000[m].times.3[m].pi.)=2.83.times.10.sup.9
/1.885.times.10.sup.4 =1.5.times.10.sup.5 [N/m.sup.2 ], so that
.DELTA.f/.DELTA.t=1.5.times.10.sup.5
/10.sup.-12 =1.5.times.10.sup.17 [N/m.sup.2 -s] and (26)
.DELTA.mass/.DELTA.A=mass
per area (3.8 [kg/m] of strip) (471 strips per meter)=1.79.times.10.sup.3
[kg/m.sup.2 ], so that da/dt=1.5.times.10.sup.17 /1.79.times.10.sup.3
=8.38.times.10.sup.13 [m/s.sup.3 ]. Therefore, in 100 nanoseconds
of continuous jerk the acceleration would build up to
a=d.sup.2
S/dt.sup.2 =(da/dt).delta.t=(8.38.times.10.sup.13) (10.sup.-7)=8.38.times.10.sup.6
[m/s.sup.2 ]. (27)
As
already noted, the IIPCS would be programmed so that accelerations
would never approach this value! As an example, for a one THz
alternating jerk the acceleration would only build up to (8.38.times.10.sup.13)
(10.sup.-12)=83.8 [m/s.sup.2 ]=8.6 [g's] (alternating or reciprocating
"hammer blows" acting on a single mass or masses (such
as magnetic sites); not harmonic oscillation of two masses). In
the extreme case of 100 nanoseconds of continuous jerk in the
same direction, the speed would build up to
dS/dt=(da/dt).delta.t.sup.2
/2=(8.38.times.10.sup.13).times.10.sup.-14 =0.42[m/s] (28)
and
the displacement of the magnetic mass (magnetic surface of single
sector, piston, or barrel) is
S=(da/dt).delta.t.sup.3
/6=(8.38.times.10.sup.13 /6).times.10.sup.-12 =1.40.times.10.sup.-8
[m]. (29)
Again
there is considerable "motion" of the magnetic mass,
but it goes a very small distance before the IIPCS reverses the
built-up acceleration, speed, and displacement.
Infinite-radius
Coil GW Generation Embodiment
For
comparison with the foregoing embodiments of the invention, consider
the evolution of coil pairs or coil sets into flattened-out pairs
of parallel wires (that is, infinite-radius coils) situated very
close to each other and carrying a large current in the same direction
(and, therefore, attracting each other). This current, which can
go either way, is to be pulsed by a large number of ultra-fast
switches or transistors 58 (FIG. 3) about every picosecond by
the IIPCS to produce pulses of electrical current through the
wires. For simplicity, as an example consider the wires to be
flat, one-meter square plates (therefore a one-square-meter GW
reference area or smaller (e.g., in order to achieve r<<.lambda..sub.GW)
down to a current-pulse wavelength across or made larger by constructing
a mosaic of individual plate pairs) as exhibited schematically
in FIG. 3. As a numerical example, let each plate carry a one-thousand
ampere current and the plates in the pairs are situated one-micrometer
(10.sup.-6 [m]) apart and the pairs are separated at a greater
distance, say, 0.1 [mm]. In order to achieve asymmetrical mass
displacement (to produce a quadrupole moment) one plate of each
pair or of each "coil set" could be considerably more
massive than the other, that is, exhibit a considerably larger
cross section or be joined to a ballast 67 in FIG. 3 or carry
a much larger current than the other or have different modulus
of elasticity or be constrained differently in their mountings.
If the IIPCS pulsed these conducting plates with picosecond-duration
pulses, then during each cycle the attractive, impulsive force
(lateral jerk) for each coil pair or set of coil pairs would be
.DELTA.f=(.mu..sub.o
/2.pi.) (1000[amps].times.[1000[amps])/10.sup.-6 [m]=2.times.10.sup.5
[N]. (30)
The
IIPCS-controlled switches 58 in FIG. 3, will sequence the current
pulses 59 moving approximately at light speed, c, to build up
a gravitational wave 29.
Let
GW-radiated power be given by
P=G(md.sup.3
r.sup.2 /dt.sup.3).sup.2 /5(c/2).sup.5.varies.G(.DELTA.f/.DELTA.t).sup.2
/5(c/2).sup.5 =1.76.times.10.sup.-52 (.DELTA.f/.DELTA.t).sup.2
[watts], (31)
where
.DELTA.f/.DELTA.t=2.times.10.sup.5 /10.sup.-12 =2.times.10.sup.17
[N/s]. Thus, pending experimental verification:
P.varies.1.76.times.10.sup.-52
(2.times.10.sup.17).sup.2 =7.04.times.10.sup.-18 [watts] (32)
and
since the reference area is two square meters (GW propagates into
and out of the plates) the GW flux=3.5.times.10.sup.-18 [watts/m.sup.2
]. The product of the amperage of, say, two plates would need
to go up by a factor of about 10.sup.5 (to about one-million amperes)
or the distance between the plates reduced by the same factor
(to ten picometers or 10.sup.-11 [m]), or the number of plate
pairs increased by a factor of a thousand, or a mosaic of many
plate pairs per level (and multiple levels), or some combination
thereof in order to approach the GW-flux values for the other
embodiments of the invention. Such a current is, however, exceeded
by the eighteen-million-ampere current passed through the Sandia
Laboratory Z-pinch machine (A. Wilson, "Z Mimics X-rays from
Neutron Stars", Science, Volume 286, Dec. 10, 1999, p. 2059).
The current-produced jerk of this machine would be expected to
generate a GW pulse as its tungsten wires collapse on each other,
if they do so in an asymmetrical manner.
Electromechanical-force
GW Generation Embodiment
At
one THz the GW wavelength is 3.times.10.sup.-4 [m] or 300 micrometers
so that the half wavelength and the optimum crystal dimension
according to Joseph Weber, p. 313, 1960 opcit, is 150 micrometers
and, of course, even smaller for the approximate quadrupole equation
to hold. If the ensemble of electromechanical elements, for example,
piezoelectric crystals, were controlled by the IIPCS and replaced
the coils, and were on 160 micrometer centers in the chips, then
there would be about 60.times.60=3.6.times.10.sup.3 per square
centimeter. If there were 25 chip levels or layers, then there
would be about 25.times.3.6.times.10.sup.3 =9.times.10.sup.4 crystals
per square centimeter or 9.times.10.sup.9 per [m.sup.2 ] as shown
schematically in FIG. 4. The energy would be 10.sup.-20 [watts]
per crystal (if each driven just below its breaking point as enhanced
by low-temperature and high-frequency operation) multiplied by
9.times.10.sup.9 (crystals).congruent.10.sup.-11 [watts] (subject
to experimental verification) . With the crystals properly oriented
and programmed by the IIPCS to propagate GW radiation out of the
side of the centimeter-thick, one-meter-square crystal array (whose
area is about one centimeter by one meter, that is a reference
area of 2.times.10.sup.-2 [m.sup.2 ]) the GW flux would be 1/2.times.10.sup.-11
/10.sup.-2 =5.times.10.sup.-1C [watts/m.sup.2 ]. As noted by Joseph
Weber (ibid), such a system could be employed " . . . to
generate and detect gravitational radiation." (Emphasis added.)
With regard to detection, the crystals would represent very small
resonators whose natural frequencies were in the terahertz range.
Alternatives to the preferred embodiment of the invention using
piezoelectric crystals (or piezoelectric polycrystalline ceramics),
include, but are not limited to either P or N processed strain-gage
silicon semiconductors, thin-film piezoelectric resonators, electromechanical
nanomachines, capacitors, dielectric resonators, solenoids and
piezoelectric polymers. Electromechanical nanomachines are such
devices as piston actuators, motors, vibrators and pumps. For
specific design details either G. L. Wojcik, et al, "Electromechanical
Modeling Using Explicit Time-Domain Finite Elements", IEEE
1993 Ultrasonics Symposium Proceedings, Volume 2, pp. 1107-1112
or Jan Kocback's "Finite-Element-Modeling Analysis of Piezoelectric
Disks,--Method and Testing", Master of Science Thesis, Department
of Physics, University of Bergen, Bergen, Norway, can be utilized.
As
discussed in detail in the 1960 and 1964 Joseph Weber articles
referred to above, the passage of a gravitational wave deforms
an object or set of objects as it passes through them. For example,
a piezoelectric polymer, a silicon semiconductor, a thin-film
piezoelectric resonator, a piezoelectric-crystal functioning as
a collector element is deformed by a GW and produces a small electrical
current. Likewise, the plates of a capacitor functioning as a
collector element are slightly moved relative to each other and
thereby produces a signal. In fact, these elements are both energizable
and generate GW and also are collectors and detect GW through
the same conductors. The nanomachine collectors operate in a similar
fashion. A nanomachine is a microscopic or molecular sized machine,
for example, a microscopic version of the dumbbell motor/generator
of the parent patent. As a GW passes through the collector, the
dumbbell moves slightly and submicroscopic coils respond to this
motion and generate a small current. Likewise, energizing the
microscopic coils in the motor mode will generate GW due to dumbbell
motion. Electrical transducer or micro strain gauge nanomachines
respond to the deformation occasioned by the passage of a GW in
exactly the same fashion as it does to a mechanically induced
strain and thereby function as a GW collector. The nanomachine
pressure transducer collector element responds to a slight change
in pressure of a set of particles comprising a fluid as the GW
passes through it. The location of the collector elements and
their connection with ultra-fast switches or transistors is identical
to the location of the energizer elements, shown in FIG. 4 and,
as already noted may be one and the same element acting as either
an energizer or a collector.
Communication
Utilizing GW
As
an approximate numerical example related to a possible gravitational-wave
detector for a train of high-frequency, THz, gravitational waves,
consider the absorption cross section, a [m.sup.2 ], for such
antennas as given by Joseph Weber (opcit, 1964, p.99)
.sigma.=15.pi.GIQ.beta..sup.2
N.sup.2 /8.omega.c[m.sup.2 ] (33)
where
G=6.67423.times.10.sup.-11 [m.sup.3 /kg-s.sup.2 ] (universal gravitational
constant),
I=moment
of inertia or quadrupole moment of the detector element(s) [kg-m.sup.2
],
Q=.pi.
times the number of oscillations a free oscillator undergoes before
its amplitude decays by a factor of e,
.beta.=2.pi./.lambda.
[1/m] (propagation constant),
.lambda.=c/.nu.
[m] (gravitational-wave wavelength),
N=the
number of quadrupoles coupled together in the antenna (see Eq.
(2.9A), p.62, of Gravitational Radiation and Relativity, Edited
by J. Weber and T. M. Karade, World Scientific Publishing Co.,
Singapore, 1986),
c=3.times.10.sup.8
[m/s] (the speed of light),
.nu.=frequency
of gravitational radiation [1/s or Hz], and
.omega.=angular
frequency (or mean motion) [1/s].
For
Q=10.sup.6 (as noted by Joseph Weber opcit, 1960, p. 308, "A
practical antenna might be expected to have Q.apprxeq.10.sup.6."
A large Q implies that a long time is required for the quadrupole
element to reach thermal equilibrium. Also, the detection devices
that Weber had in mind were large isolated aluminum cylinders,
suspended and well isolated from the environment. The collector
elements for the present device will probably be contained on
a chip with damping constraints and a much smaller Q is likely).
.nu.=10.sup.12
[Hz] or one [THz], and
.beta.=2.pi.v/c=2.09.times.10.sup.4
[1/m], and
.omega.=.nu./2=5.times.10.sup.11
[1/s]; see Weber, 1964, opcit p. 90, we have
.sigma.=1.15.times.10.sup.-15
IN.sup.2 [m.sup.2 ].
This
value, depending upon I and the number of quadrupoles (with masses
and characteristics nearly identical) coupled together in the
antenna, N, compares favorably with .sigma.=10.sup.-20 [m.sup.2
] of the Weber Bar given on p. 102 of Weber , ibid.
An
approximate estimate of what bandwidth a gravitational-wave (GW)
communication system might achieve is obtained as follows: Suppose
that the distance between the GW generating or transmitting device
and the receiver or detector is about one Earth's radius, 7,000
[km] or 7000 rim radii. Also, suppose that we are transmitting
through the Earth's mantle and that 10 percent of the GW energy
gets through. Thus, for the tangential-jerk situation the "signal"
obtained by modulating the current pulses by the IIPCS (some pulses
missing and some forming a longer-duration pulse or pulses of
different amplitudes) is using the power near the spindle device
given by Eq. (9) and the average power flux of 2.times.10.sup.-9
[watts/m.sup.2 ] there
S=(2.times.10.sup.-9)
(0.1)/7000=2.8.times.10.sup.-14 [watts/m.sup.2 ] (34)
at
the receiver or detector (assuming that the GW propagates in a
single plane with little or no diffraction). For the radial-jerk
spindle situation using the power near the device given by Eq.
(22) and the average power flux of 1.times.10.sup.-4 [watts/m.sup.2
] there
S=(1.times.10.sup.-4)
(0.1)/7000=1.4.times.10.sup.-9 [watts/m.sup.2 ]. (35)
For
the longitudinal-jerk, linear-motor situation with average power
from Eq. (24) (if there were a fall off with range in "rim"
radii), with a 2000 [m] length or radius of gyration and a resulting
average power of 1.times.10.sup.-3 [watts/m.sup.2 ] we have,
S=(1.times.10.sup.-3)
(0.1)/7000=1.4.times.10.sup.-8 [watts/m.sup.2 ]. (36)
Let
us estimate the "noise" N=10.sup.-20 [watts/m.sup.2
] in the THz band(probably not many GW sources there, but Brownian
motion, thermal and quantum fluctuations, etc. may result in much
more noise than this) and that the GW detector exhibits a sensitivity
on this same order. It should be recognized, however, that the
bandwidth of the long-base-line, interferometric GW detectors
now under construction are at most about a few kHz and they are
not designed for THz detection. Furthermore, a six to ten order-of-magnitude
improvement of the sensitivity of the single-crystal detectors
considered by Joseph Weber 42 years ago might need to be accomplished
(sensitivity of about 10.sup.-10 [watts] as given on p. 313 of
Weber opcit, 1960). More recently, however, Weber has speculated
optimistically (opcit, 1986, p. 30) that there is " . . .
no limit to the theoretical sensitivity of a (elastic solid) gravitational
radiation antenna, and perhaps no limit to the number of novel
methods for improving the sensitivity of existing antennas."
Using
Shannon's classical equation (C. B. Shannon, Bell Systems Technical
Journal, Volume 27, Number 379, p. 623, 1948), the maximum rate
of information transfer, C, for the spindle's tangential-jerk
GW embodiment is given by
C=Blog.sub.2
(1+2.8.times.10.sup.-14 /10.sup.-20).congruent.(10.sup.12) (20)=2.times.10.sup.13
[bps], (37)
for
the radial-jerk GW embodiment
C=Blog.sub.2
(1+1.4.times.10.sup.-9 /10.sup.-20).congruent.(10.sup.12) (30)=3.times.10.sup.13
[bps] (38)
and
for the longitudinal-jerk (linear-motor) GW preferred embodiment
C=Blog.sub.2
(1+1.4.times.10.sup.-8 /10.sup.-20).congruent.(10.sup.12) (40)=4.times.10.sup.13
[bps]. (39)
In
each embodiment the bandwidth, B, is taken to be the IIPCS switch
on-off or "chop" rate of about 10.sup.12 reciprocating
"hammer blows" or jerks per second (one THz and multiple
GW generators or "transmitters" could increase the bandwidth
further).
There
exists a useful figure-of-merit or trade-off function for the
longitudinal-jerk (single-sector or linear-motor) preferred embodiment
of the invention that relates to the received signal:
S.varies.([2.pi.rl{l.DELTA.f.sub.l
/.DELTA.A}/.DELTA.t].sup.2 /[.pi.r.sup.2 ]).alpha. (40)
.varies.(l.sup.2
[.DELTA.f.sub.l /.DELTA.A]/.DELTA.t).sup.2.alpha. (41)
(note
that the radius of the single-sector cylindrical magnetic core,
piston, or barrel, cancels out) where
S=signal
at the detector (receiver) [watts/m.sup.2 ],
r=radius
of the single-sector magnetic core, piston, or barrel [m],
l=radius
of the single-sector or length at magnetic core, piston, or barrel
[m],
.DELTA.f.sub.l
/.DELTA.A=longitudinal force per unit area acting on the single-sector
magnetic core, piston, or barrel [N/m.sup.2 ],
.DELTA.t=impulse
time [s],
.alpha.=attenuation
due to intervening material between the GW generator (transmitter)
and detector (receiver) [dimensionless],and assume that for the
single-sector or linear-motor preferred embodiment of the invention,
if there is little or no GW diffraction, then there is no range,
.rho. dependence (to be tested experimentally).
As
a numerical example, consider the solution for the length, l,
l=.sup.4
(S/.alpha.).times.(.DELTA.t/[.DELTA.f.sub.l /.DELTA.A]).sup.2
(42)
where
S=4.5.times.10.sup.-4
multiplied by the nominal=(4.5.times.10.sup.-4) (1.4.times.10.sup.-8)=6.26.times.10.sup.-12
[watts/m.sup.2 ] (assume a {1/4.5}.times.10.sup.4 more sensitive
detector or receiver),
.alpha.=10
multiplied by the nominal=(10) (0.1)=1 [dimensionless] (assume
no attenuation),
.DELTA.t=10.sup.-1
multiplied by the nominal=10.sup.-13 [s] (occasioned by the possible
design of a 100 femtosecond ultra-fast switch and pulse duration),
and
.DELTA.f.sub.l
/.DELTA.A=100 multiplied by the nominal=(100) (5.64.times.10.sup.9
/[2000.times.3.pi.])=(100)(3.0.times.10.sup.5)=3.0.times.10.sup.7
[N/m.sup.2 ] (assume increased magnet efficiencies due to, for
example, use of high-temperature super conductors and electromagnets).
Thus,
in this case the length of the GW generator would be (with the
factor of 7000 rim radii removed; thus the factor of 10.sup.-3
/7)
l=.sup.4
([6.26.times.10.sup.-12 /10][10.sup.-3 /7]/[100/0.1].sup.2) (2000)=6.15.times.10.sup.-3
[m]=6.15[mm]. (43)
Equation
(41) can be utilized by a person with average skill in the art
to practice the inventions utilizing fast or ultra-fast switches
or transistors having different capabilities, that is different
.DELTA.t, different detection capabilities, S, different forces,
.DELTA.f, and different lengths, l including lengths significantly
smaller than GW wavelength.
Propulsion
No
doubt high-frequency GW experiments will reveal many applications
of GW to propel spacecraft by means of remote GW generators. In
this regard, on p. 349 of Landau and Lifshitz (opcit), they comment:
"Since it has a definite energy, the GW is itself the source
of some additional gravitational field. Like the energy producing
it, this field is a second-order effect in the h.sub.ik (tensor
describing a weak perturbation of the galilean metric). But in
the case of high-frequency gravitational waves the effect is significantly
strengthened . . . " (Emphasis added.)
The
axis of rotation of a spindle GW-generation device defines a preferred,
single, unique direction in space and also a preferred, single,
unique plane. The axis of the single-sector, linear-motor GW generator
device defines a preferred, unique direction in space as well.
Thus there is an asphericity or pattern to the gravitational radiation,
an anisotropy or focusing, that is analogous to a radio-antenna
pattern of field strength. The concept that, as a part of this
pattern, the gravitational waves are constrained to the "preferred"
plane of the rim, or axis of the linear-motor's "preferred"
line in space, without diffraction, will also be tested. These
concepts have potential application to spacecraft propulsion either
by remote "gravitational force field" generation or
by placing anisotropic GW generators on board a spacecraft--a
"Relativistic Rocket".
* * * * *
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