At 3:05 AM 12/4/4, Harry Veeder wrote:
>Since it is acceptable to question conservation laws on this forum,
>perhaps CF is possible because the charge on subatomic particles is not
>conserved in all contexts.
>
>Note: This is different from the concept of 'charge shielding'.
There are various concepts in which charge might not be conserved. Here is
an example I posted here a while back that indicates apparent charge moving
in a circle may vary depending the angle of observation.
Planar Circular Currents
BACKGROUND AND ASSUMPTIONS
It is well known that special relativity predicts changes in the observed
field of a particle due to the flattening of the field in the direction of
motion. This flattening is due to application of the Lorentz contraction
due to relative motion. This relativistic effect of flattening the
apparent field is called the "pancaking" of the Coulombic field. It is the
intent here to discuss the effects of pancaking with respect to planar
circular direct currents.
On p.492 of *The Electromagnetic Field*, Albert Shadowitz provides the
equation for relativistic (Coulombic) field pancaking as:
E = Q/(4 Pi e0 r^2) (1 - (v^2/c^2))/(1 - (v^2/c^2) sin^2 theta)^(3/2)
If we let b = v^2/c^2 then we can interpret apparent charge Q' to be:
Q' = Q (1 - b)/(1 - b sin^2 theta)^(3/2)
which can be interpreted to mean apparent charge is reduced to observers in
line with the charge velocity vector and increased as the viewing angle is
increased.
NOTE - it is not standard physics to interpret pancaking as a change in
apparent charge (standard relativity assumes charge is invariant with
velocity) but rather a change in observed field strength, but we should be
able to interpret the pancaking equation for Q' either way.
Consider the Bohr model of the atom where the electrons whiz around a
nucleus. Specific electrons present some degree of pancaking from any angle
viewed. In some directions apparent charge is increased and some
directions decreased. In a non-magnetic medium, the polar orientation of
atom orbitals is mixed in a uniform way due to the orientation of atoms
being mixed in a uniform way. Upon integration over 3D polar coordinates,
one finds that the average net charge change, according to the pancaking
equation, for randomly oriented atoms and orbitals, is zero. However, the
conditions examined here differ from those of an atom not in the presence
of ambient electronmagnetic fields, as do the resulting forces.
ANALYSIS OF THE RELATIVISTIC PANCAKING EFFECT
If some set of orbitals are aligned, say by a magnetic field, or if we have
the case of a planar circular current in a conductor, a neutral medium,
then the average apparent charge (as viewed from a long enough distance to
make the circle diameter insignificant) does not net out to zero, except at
a specific viewing angle. As viewed within the plane, pancaking reduces
the apparent charge of charges in motion, and increases the apparent charge
of charges in circular motion as viewed from the poles of the circular
motion.
The net apparent charge of a charge moving in a small circle relative to
the distance of the viewer comes from integrating to find the average value
of:
k(theta,v) = (1 - b)/(1 - b sin^2 theta)^(3/2)
for theta = 0 to 2Pi, where b = v^2/c^2, and then subtracting the average
value from one to obtain the net charge change factor K(v), because if v =
0 then the observed (apparent) charge Q' is the same as the charge Q:
Q' = Q * 1
If the average value of k(theta,v) is non-zero, when integrated over all
angles theta, for v not 0, then an average apparent net charge exists when
v not 0.
The average value f_avg of any function f(x) is given by:
f_avg(x) = 1/(b - a) [integral from a to b][ f(x) dx ]
so the value of net charge change factor K(v) = 1 - [average over theta of
k(theta,v)] is given by:
K(v) = 1 - 1/(2 Pi - 0) [integral from 0 to 2 Pi][ k(theta) d theta ]
which requires solving an elliptic integral of the second kind, and yields
a net charge:
Q_net = K(v) Q
where K(v) can be approximately based on the average speed of the electrons.
Note that in the 3D situation the averaging integral equivalent to the
above would be
[Integral from 0 to Pi] [k(theta) sin(theta) d theta]
because it is necessary to average over theta with a weight of sin(theta)
to account for the surface area involved. This integral evaluates to one,
thus K(v) evaluates to zero. However, in the planar version, K(v) does not
average to zero.
NUMERICAL APPROXIMATION OF THE PANCAKING EFFECT
The average values k_avg(v) of k(theta,v) for random planar orientations as
viewed from the plane were directly calculated by computer program, thus
producing the incremental force factor:
K(v) = 1 - k_avg(v)
over a complete circle, for theta = 0 to 2 Pi. Results for various values
of v/c are shown in Table 1:
v/c K(v)
.999999 0.363371045179493
.5 6.57845423323069D-02
.1 2.50470713873419D-03
.01 2.5000468772296D-05
.001 2.50000048662713D-07
.0001 2.50000153911856D-09
Table 1 - Direct numerical estimation of K(v)
These factors indicate the possibility of huge apparent net charges,
especially from electrons moving at the speed of k shell electrons (if such
could be made to move in a planar orbit.). The innermost electrons of Fe
have an ionization potential of 9277.69 eV, and Ni has 10775.40 eV. Using
half the ionization potential of Ni as electron kinetic energy we obtain:
1/2 m_e v^2 = (10775.4 eV)/2 = 8.63 J
v = 4.35x10^7 m/s
v = 0.145 c
so more than 0.25 percent of the total charge for such electrons would
appear as net apparent positive charge in the atom, if a sufficiently
strong magnetic field could be applied so as to make K shell orbitals
nearly flat (an astronomical magnitude magnetic field to be sure!)
ANALYTICAL SOLUTION USING MATHEMATICA
In order to obtain an exact form of the integral, Mathematica was used to
integrate the pancake function obtaining a finite integral. Unfortunately a
complete elliptic integral of the second kind appears in the solution.
The average value f_avg of any function f(x) is given by:
f_avg = 1/(b - a) [integral from a to b][ f(x) dx ]
so the value of net charge change factor K_incr(v) = 1 - k_avg is given by:
K_incr(v) = 1 - 1/(2 Pi - 0) [integral from 0 to 2 Pi][ k(theta) d theta ]
Mathematica says:
[integral from 0 to 2 Pi] [ (1 - b sin^2 theta)^(-3/2) d theta]
is given by:
-(EllipticE[x, b]/(-1 + b)) + (b*Sin[2*x])/(Sqrt[2]*(-1 + b)*
Sqrt[2 - b + b*Cos[2*x]])
which, when evaluated from 0 to 2 Pi, is
-4(EllipticE[b])/(b-1)
where EllipticE[b] is a complete elliptic integral of the second kind. So:
K(v) = 1 - 1/(2 Pi - 0) [integral from 0 to 2 Pi][ k(theta) d theta ]
= 1 - 1/(2 Pi) (1-b) [integral from 0 to 2 Pi]
[ (1 - b sin^2 theta)^(-3/2) d theta]
= 1 - 1/(2 Pi) (1-b) (-4(EllipticE[b])/(b-1))
= 1 - 4/(2 Pi) EllipticE[b]
K(v) = 1 - 2 Pi EllipticE[v^2/c^2]
or more appropriately:
K(v) = 1 - 2 Pi EllipticE[v^2/c^2]
Through use of Mathematica, the following confirming values of K(v) were
obtained:
Mathematica evaluation of K(v) =
v/c K(v) 1 - 2 EllipticE[(v/c)^2]/Pi
.999999 0.363371045179493 0.363375
.5 6.57845423323069D-02 0.0657845
.1 2.50470713873419D-03 0.00250471
.01 2.5000468772296D-05 0.0000250005
.001 2.50000048662713D-07 2.5e-7
.0001 2.50000153911856D-09 2.5e-9
Table 2
Thus it appears there is some evidence for a predicted net apparent charge,
when matter is viewed in a plane containing the matter and normal to the
magnetic field, in both neutral condensed matter and plasmas, or even
magnetron chambers, if a sufficient magnetic field is present. The fact
that apparent charge does not manifest in condensed matter might be
construed to confirm the QM view that the "electron is everywhere" in the
wave function, or that it has no specific location until sampled. There is
thus no radiation from atoms because the orbital electrons do not actually
"move."
Plasma electrons are not so constrained by the QM boundaries as electrons
in atoms though. The upper bound on the possible effect is less, due to
lower velocities, but still significant.
It should be noted that this speculation so far ignores the effects of
charge acceleration and general relativity effects.
Now, to evaluate the integral giving k(b) for b = (v/c)^2, b small. Given
the first few terms of EllipticE:
EllipticE[b] = Pi/2 - (Pi b^2)/8 - (3 Pi b^2)/128 + ...
we can evaluate the integral giving k(b) for b = (v/c)^2, b small:
K(v) = 1 - 2 EllipticE[b]/Pi
= 1 - 2 {1/2 - b/8 - 3 b^2/128}
K(v) = b/4 + (3/64) (b^2)
which is pretty good, and for many things
K(v) = b/4
works OK too, or the series
K(v) = (1/4) b + (3/64) (b^2) + (5/256) (b^3) + (175/16384) (b^4) + ...
can be used to compute the degree of accuracy desired.
It is interesting though, that:
EllipticE[1] = 1
so, a limit to the effect is provided by:
K(c) = 1 - 2 EllipticE[q]/Pi
= 1 - 2/Pi = 0.363380227632
EXAMINATION OF THE PANCAKING EFFECT
Let's assume uniform circular motion, i.e. DC current, in a charge balanced
medium. It is commonly assumed there is then no induction. However, it is
often stated that accelerating charges produce fields, so perhaps the
uniform acceleration of charges about the circle produce a field that
precisely cancels the pancake effect field computed above. This would be
a very unusual field that uniform charge acceleration about the circle must
produce if it exactly cancels the special relativistic (SR) Coulomb field
of a circle current, which is non-conservative. Given the SR Coulombic
field pancaking equation and b = v^2/c^2, we have:
k(theta) = (1 - b)/(1 - b sin^2 theta)^(3/2)
At theta = 90 deg we have:
k(Pi/2) = (1 - b)(1 - b)^(-3/2)
= (1 - b)^(-1/2) = gamma(v)
which represents an apparent charge increase for every charge as viewed
from a point on the major axis and distant from the circle. The charge
motion, from the polar vantage point, is viewed from the "side" at
approximately 90 degrees.
At theta = 0 deg. we have:
K(v) = b/2 + ...
which represents an apparent charge decrease. Using q' to designate the
apparent charge observed for an actual current bearing charge q, this gives
the following picture from the perspective of the velocity dependent SR
field component:
q' = q * gamma (q' > q)
(-)
N
|
|
(+) o | x (+) q' = q * K(v) (q' < q)
|
|
S
Magnetic
Poles
(-)
o - current out of page (electrons into page)
x - current into page (electrons out of page)
(+) - positive net apparent charge
(-) - negative net apparent charge
Fig. 1 - Diagram of SR based Coulombic field
Note that, because the proposed current is carried by electrons moving
within a positive medium, that the field is positive to the sides. If the
current were carried by positive charge, the SR Coulombic field would be
reversed.
EFFECTS OF CHARGE ACCELERATION
Next, it is necessary to consider the special relativistic effects of
acceleration. In *Classical Electromagnetism via Relativity,* Plenum
Press, 1968, W. G. V. Rosser develops (p. 272 ff) a proof that the field
from a closed circuit, ignoring radiation fields, is zero. Rosser
utilizes the following SR based equations for his proof:
E = Ev + Ea
Ev = q/(4 Pi e0 s^3) [r - r u/c][1 - v^2/c^2]
Ea = q/(4 Pi e0 s^3 c^2) {r x ([r - r u/c] x [a])}
s = [r - (r dot u)/c]
where r, u, and a are vectors.
Earlier in the text (p. 252) Rosser credits the above equations to Frisch
and Wilets (Amer. J. Phys. 24(1956) p.574.) The above equations are not
approximations and are consistent with the Maxwell-Heaviside equations.
Rosser only actually proves his case for a specific circuit which has sharp
bends, but assumes the bends are not significant because the accelerations
involved are not large (apparently due to the fact the electron velocity is
slow in wires ) This seems to be a flawed approach and also as immaterial
to high velocity situations, like those found in stars. Further, Rosser's
proof has the glaring limitation that it only shows a netting to zero in
the plane of his special circuit, which consists of two (radial from the
point of observation) straight lines and two arcs centered on the point of
observation.
Even if Rosser's proof is assumed to be correct in general, to the level
of accuracy he produces, and even if the apparent charge is assumed to net
to zero in the plane of the circuit, a non-conservative field appears when
we look at the ramifications of the Ea equation in the polar regions of
Fig. 1.
Rosser shows (p. 276) that the formula for Ea implies:
Ea ~= -q/(4 Pi e0 c^2) [a_perp]/[r]
where [a_perp] is the component vector of vector [a] that is perpendicular
to vector [r]. Using scalar centripital acceleration
a = v^2/r
to estimate the Coulombic field at points on the central polar axis distant
from the current ring, we obtain:
Ea ~= -q/(4 Pi e0 c^2) (v^2/r)/(r)
= -q/(4 Pi e0 r^2) (v^2/c^2)
and we obtain an apparent charge factor of -v^2/c^2 = -b due to the
acceleration component of the polar Coulombic field. Now, clearly , -b
does not exactly, at every v, offset the charge factor:
gamma(v) = (1-b)^(-1/2)
obtained using the standard SR field pancaking equation. We are left with
an apparent net charge at the poles of:
q' = q [(1-b)^(-1/2) - b]
If this is true, then a field is predicted which is not energy
conservative. A path from the polar region to a distant point on the plane
of the circular current, to a near point on the plane, and back to the
polar region, gains a fixed increment of energy.
Call [(1-b)^(-1/2) - b] the net relativistic polar apparent charge factor
Fp(v). Table 1 provides a quick look at various evaluations of Fp(v).
b gamma(v) Fp(v) Incr., 1-Fp(v)
v/c (v/c)^2 1/(1-b)^.5 1/(1-b)^.5-b 1-1/(1-b)^.5+b
0.0000 0 1 1 0
0.0001 0.00000001 1 0.99999999 1E-08
0.0010 0.000001 1 0.999999 9.99999E-07
0.0100 0.0001 1.000000005 0.999900005 9.9995E-05
0.1000 0.01 1.000050004 0.990050004 0.009949996
0.2000 0.04 1.000800961 0.960800961 0.039199039
0.5000 0.25 1.032795559 0.782795559 0.217204441
0.6000 0.36 1.071866157 0.711866157 0.288133843
0.7000 0.49 1.147154143 0.657154143 0.342845857
0.9000 0.81 1.70523372 0.89523372 0.10476628
0.9900 0.9801 5.037672145 4.057572145 -3.057572145
0.9990 0.998001 15.82325228 14.82525128 -13.82525128
0.9999 0.99980001 50.00375017 49.00395016 -48.00395016
Table 1 - Tabulation of Polar Apparent Charge Factors
Note that the slope of Fp(b) near b=0, is given by:
d/db Fp(b) = 1/(2(1-b)^(3/2)) - 1
which for b very small evaluates to roughly -1/2. Therefore, the
incremental charge Q'(b) in a neutral planar circular conductor, for b very
small is roughly:
Q'(b) = b/2 Q
= Q [v^2/(2c^2)]
= [Q/(2c^2)] v^2.
This addition of an apparent charge, proportional to v^2, to a neutral
circular planar conductor, implies that if that neutral conductor is spun
about its major axis in the direction of current flow, that the net polar
apparent charge will increase. If the drift velocity is v_drift and the
rim velocity is v, then the two current net polar charge factor will be:
F_net(v,v_drift) = [1/(2c^2)] (v+v_drift)^2 - [Q/(2c^2)] (v)^2
F_net(v,v_drift) = [2 v v_drift + v_drift^2]/(2c^2)
and since v_drift is typically under 1 mm/sec, and v can be many meters per
second, a gain in the polar charge of at least 4 orders of magnitude can
obtained by rotating the current carrier about its axis.
SOME POTENTIAL CONSEQUENCES
It might be conjectured at this point that the Podkletnov antigravity
experiment that NASA has been replicating, which uses a current carrying
levitated spinning superconducting ring, does not show any artificial
gravity because NASA is using a sensitive gravitometer. The field
predicted looking at the pancake effect is electrostatic. Such a field
might achieve the effect Podkletnov first noticed, namely that smoke rose
above the spinning superconducting disk. It may be that the smoke
particles were somewhat ionized. However, all the antigravity effects
reported by Podkletnov can not be justified by the means discussed here,
because the suggested electrostatic field would induce attracting charges
on neutral objects. It is of interest that, due to the Faraday ice pail
effect, shielding for the suggested force, which is electrostatic in
nature, can not be easily achieved.
The numbers can be significant for current carrying masses spinning at very
high velocities, and in cases where very strong magnetic fields are
involved and thus affecting atomic structure and alignment, and might
provide an explanation for polar jets observed for fast spinning
astronomical objects. In addition, a net anti-gravitational force from flat
galaxies, or more specifically from aligned spinning structures within
them, is predicted by the proposed theory. It is of further interest that
if the proposed potential exists then conservation of energy is violated,
free energy devices can be made.
A SMALL TEST CASE
Let's First look at a specific and mundane case readily tested by amateur means.
Copper density is 8.96 g/cm^3 at 300 K, and atomic weight is 63.546.
Avogadro's number is 6.0221x10^23 atoms/mole. There is thus 8.96 *
6.0221x10^23 /63.546 = 8.49x10^22 atoms per cm^3 of copper. This is also
the approximately number of conduction band electrons per cm^3.
If we assume a 7 cm radius disk spinning at 1800 rpm, or 30 rps, we obtain
about a 13.2 m/s rim velocity. Assume the perimeter of the disk is wrapped
with 140 turns, or 6160 cm of 0.02846 in, 0.0723 cm dia., No. 21 copper
wire, carrying 1 amp DC. This wire has a cross sectional area of 0.0164
cm^2, or 1.64 mm^2. Total wire volume is (0.0164 cm^2)(6160 cm) = 101
cm^3. This wire has 13.05 ohms per 100 ft., or .428 ohms/meter. Total
resistance is thus estimated at (.428 ohms/meter)(6160 cm) = 26.3 ohms,
thus the wire is driven at 26.3 volts to achieve the 1 amp current.
The 101 cm^3 of wire has a total (8.49x10^22 atoms per cm^3)(101 cm^3) =
8.57x10^24 conduction band electrons. There are thus (8.57x10^24
electrons)/(6160 cm) = 1.39x10^21 electrons/cm of wire.
We have a current of 1.0 amps in the wire, or 1.0 coulomb/second. There is
1/q_e = 6.2415x10^18 electrons/coulomb, giving 6.2415x10^19 electrons/sec
flowing in the wire. The electrons thus move at (6.24x10^19
electrons/sec)/{1.39x10^21 electrons/cm) = 0.0449 cm/sec, so:
v_drift = 4.49x10^-4 m/sec
We have about 8.57x10^24 conduction band electrons carrying the current so
at 6.24x10^18 electrons/coulomb we have:
Q = 1.37 x 10^6 coulombs
carrying the current, so since:
F_net(v,v_drift) = [2 v v_drift + v_drift^2]/(2c^2)
Q' = Q [2 v v_drift + v_drift^2]/(2c^2)
Q' = (1.37x10^6 coul.) [ 2 (13.2 m/s) (4.49x10^-4 m/sec) +
(4.49x10^-4 m/sec)^2]/(1.8x10^17 m^2/s^2) ]
= (1.37x10^6 coul.)(6.59x10^-20)
Q' = 2.71x10^-14 coul.
If we had a test charge of 1 coul. at a distance of 1 m from the spinning
coil, and lying on its axis, we would have a force:
F = [1/(4 Pi epsilon_0)] Q1 Q2/r^2
= [1/(4 Pi (8.85x10^12 F/m)](1 coul.)(2.71x10^-14 coul.)/(1 m)^2
F = 2.44x10^-4 N
giving a field strength of:
E = 2.44x10^-4 N/coul.
= 2.44x10^-4 volts/meter
which might be barely usable, but would be readily detected by use of a
very low resistance loop.
In that the field is non-conservative, it may be of sufficient magnitude to
be of some utility if used with a superconducting current loop, or big
cross section copper loop, wrapped about a magnetic core, but the back emf
of the magnetic field building in the conductor would prohibit much power
from being extracted. The power to drive the device is about 26 watts,
plus maybe another 20-180 watts to drive the motor. However, a spinning
superconductor could be used for the primary, and that would take almost no
power except cooling.
Suppose we could get 2 mV out of a 2 m triangular secondary current loop
(the potential gain is higher near the rotating primary loop) and we have a
copper conductor with a cross section of 144 cm^2, or 22.3 in^2. Copper
has a conductivity of 4.01x10^6 ohm^-1 cm^-1, so the conductor has
conductivity of (144 cm^2)(4.01x10^6 ohm^-1 cm^-1) = 5.77x10^8 cm ohm^1, or
a resistance of 1.73x10^-9 ohm/cm. Using 600 cm for a length we have a
total resistance of (1.73x10^-9 ohm/cm)(600 cm) = 1.03x10^-6 ohm. We would
thus have a current I = E/R of (.002 V)/(1.03x10^-6 ohm) = 1940 amps, which
is of course readily detectable. The heat output would be a mere (0.002
V)(1940 amps) = 3.88 watts.
A practical device might be made by using very high speed rotating
superconductor(s) carrying lots of current. If a 2000 amp carrying
superconductor rotating at 18000 rpm is used, then the power output jumps
to 388 watts.
A variation is to drive the primary with A/C. The secondary would then be
driven at (0.002 V) (1940 amps) = 3.88 watts A/C. It could be used to
drive a transformer primary in order to drive a secondary at 3.88 watts and
the voltage desired. Upping the rpms to 18,000 would produce about 38.8
watts, which would be above theoretical break-even if frictionless brushes
and low friction bearings were used.
SCALING UP
By using supercooled aluminum wire, the conductivity can be increased by a
factor of 10^5. This means the current can be increased by a factor of
10^(5/2) = 316 and still maintain the same I^2 R heat dissipation, and
electron drift velocity v_drift can also be increased by a factor of 316.
The drift velocity could be about (4.49x10^-4 m/s)(316) = 0.1419 m/s.
Assuming a rim velocity of (60 rps)(1m)(Pi) = 188 m/s, the performance per
turn can be compared to the small proof of concept experiment by:
perf = F_net(188 m/s,0.1419 m/s) / F_net(188 m/s,4.49x10^-4 m/s)
= [2 (188 m/s) (0.1419 m/s) + (0.1419 m/s)^2] /
[2 (13.2 m/s) (4.49x10^-4 m/sec) + (4.49x10^-4 m/s)^2]
= (53.4 m^2/s^2) / (.1186 m^2/s^2)
= 450
The coil cross section can be increased from about 1 in^2 to about 100
in^2, thus giving another 100 fold increase in number of turns, and a total
ampere-turns multiplier of 100*316 = 31600. The computed field strength of
about 2.44x10^-4 volts/meter for the experiment then becomes (2.44x10^-4
v/m) * 31600 * 450 = 347 v/m, spread out over an area of about 3 m^2. A
special triangular coil of cross section 3 m can length 3m to a side can
then gain about (347 + 1/4 (347) + 1/9(347)) V/turn = 472 volts/turn.
Assuming 100 turns that is 47.2 kV output, with a conductor cross section
of 3 m^2/100 = 300 cm^2. Assuming the secondary is driven at a mere 1000
A/cm^2, with half the cross section taken up by winding space and
insulation, that is (300 cm^2)*(1000 A/cm^2) = 30 kamps at 47.2 kV, or
1.42 GW.
This indicates a very practical output. This is by far the most commercial
idea, if proven feasible experimentally, even if it disappointingly does
not result in the hoped for inertial drive.
The proof of principle experiment was to take 140 turns of 1 amp. The
proposed practical device armature has 14000 turns at 316 A/turn,
therefore has total amp turns of (14000 turns)(316 amps/turn) = 4.42
mega-amp-turns in a coil of radius 1 m, and a 10 inch by 10 inch cross
section, or 25.4 cm square cross section. It may not be feasible to hold
this together. However, major offsetting gains in performance can be had
by supercooling the secondary coil, and by increasing the area of the
rotating coil, which then permits a much larger secondary coil, both in
area and acceleration length, and reduces the magnetic pressure on the
rotating coil. The coil cross section can be made thinner and wider, so
structural support can be beefed up around it. The coil would actually
consist of a series of concentric coils with structural support and cooling
conduits interlaced between them.
Using a seat of the pants number of about .7 N for 1000 amps. for the 1m
radius coil hoop force, that force is increased by the square of the ratio
of the amperages, (4.42x10^6/10^3)^2 or about 1.954x10^7, giving a force of
8.37x10^7 N, or 1.882x10^7 lbf, or about 9410 tons force between two halves
of the proposed coil. Too much. At a 1m radius, or 6.28 m, that is about
75 inches perimeter giving a lateral force of about 213 tons/inch.
Centrifugal force has to be added to that too.
An FEA simulation of the 1 m diameter coil (to the conductor cross section
midline) with 23.4 cm square conductor carrying 4,420,000 amps was run.
The half hoop force was 1.267x10^7 N, or 2.85x10^6 lbs, or 1424 tons. The
field strength at the conductor midline was a modest 1.27 T, seemingly not
out of the ordinary to contain, even rotating. However, the iLB force of
1.426 N/inch, or 32,000 lbs/in. This is difficult considering the need for
cooling and the fact the coil also needs to rotate. There is considerable
room for design adjustment, and at the anticipated power output, much
leeway in cost.
Earlier, for the proof of principle experiment, it was assumed a secondary
coil would reside only on one side of the rotating primary. However, a
duplicate secondary (stator coil) can be placed on the other side of the
rotating primary, thus doubling the output. Also, by adding another meter
to the radius, the current and thus the power output of the secondary is
quadrupled, or the primary current can be correspondingly reduced.
If feasible, superconducting wire would be useful for the spinning primary
coil from a couple aspects. One is cooling would not be a function of
current, and another would be that the insulation is actually metal, and
thus much more resistant to stress than plastic or rubber at cryogenic
temperatures. There is no apparent way that a back e.m.f can be generated,
but superconducting wire must be tested to see if a back e.m.f. somehow is
generated. Unfortunately, a couple meter diameter superconducting coil
would cost fairly big dollars, but nothing like a nuclear plant.
Unless there is a significant mistake, and provided the basic principle
stands the experimental test, it should be feasible to put a GW plant in a
box about 10 meters to a side.
TEST RESULTS
A test using copper conductors was conducted by Frank Stenger in 2001. The
results were negative. It is my belief that the formula changes applied
due to acceleration are incorrect. A thorough test of principle, however,
requires use of a superconducting secondary coil. In such a case a
spontaneously increasing magnetic field in the superconductor would be
evidence for the expected field.
Regards,
Horace Heffner
