From: johncobb@ut-emx.cc.utexas.edu (John W. Cobb)
Newsgroups: sci.physics.fusion
Subject: Re: electrostatic fusion
Date: 6 Jan 93 22:19:40 GMT
Reply-To: johncobb@ut-emx.cc.utexas.edu (John W. Cobb)
Organization: The University of Texas at Austin

In article <C0CIoo.Iun@efi.com>, chrisp@efi.com (Chris Phoenix) writes:
|>In article <1992Dec31.055118.11523@asl.dl.nec.com>
terry@asl.dl.nec.com writes:
...
|>>The thing to remember about these field emission effects is that while they
|>>do permit electrons to stream off in a decidedly non-classical fashion from
|>>a cold needle, the total acceleration provided by the effect is no higher
|>>than it would be for the same voltage differential without the sharp points.
|>>
|>>Why?  Because the region of extremely high field gradient is also very, very
|>>short.  It has to be -- a voltage difference is a voltage difference is a
|>>voltage difference, and if you "use up" most of the gradient in a very short
|>>distance, the rest of the gradient will just be very shallow.  E.g.:
|>
|>OK, I'll stick my neck out again.  According to this analysis, if you
|>put the same number of electrons on a big sphere or a small sphere, a
|>proton at the surface of either sphere has the same potential energy
|>relative to a distance of infinity from the sphere.  This seems
|>correct to me.
|>

chop, thump, bump, roll, roll. Sorry Chris, welcome to Decaps anonymous
(Ann Bolelyn Pres. Ichabod Crane Secy.). The last statement is incorrect.
Given a fixed charge (number of electrons) on the surface of a sphere, the
electric potential at the surface of the sphere does depend on the radius.
If you halve the radius, the potential will be 4 times as large.

|>The point about the points (sorry) is that they allow you to cram a
|>lot of electrons into a small space.  Imagine a sphere with a cone
|>stuck onto it.  (Call it a "construct".)  Put some number of electrons
|>onto the sphere.  Now the "voltage" at the surface of the sphere
|>opposite the cone is X.  But the "voltage" at the tip of the cone may
|>be 20X.  (I put voltage in quotes because I'm not sure if I should say
|>"potential" or "apparent gradient" or...)  I agree that if you put the
|>same number of electrons on this construct as on the above spheres,
|>the potential energy of a proton at any point on its surface is the
|>same as it was above.
|>

I think the wording of your message is confusing. The electric field is what
provides the force (i.e. how hard the field pulls the particles).
Mathematically,
the electric field is the gradient of the potential. The physics comes
into play
when you ask whether the problem at hand depends of the field or on the
potential.

There are really two distinct problems here (actually many more). First
consider
a sphere inside a box. Assume the box is attached to a grounded wire and that
the ball inside the box is attached to another wire that is held at a given
potential V. This is the case that Terry is referring to. Here you can magnify
the electric field if the ball is replaced by a needle. Near the point of the 
needle the field can be very strong. In fact for a small arrangement, moderate
voltages can cause "mini-lightning bolts" from electric fields that exceed the
breakdown voltage. However, each of the electrons that leave the needle whether
by breakdown at the needle's point of thermal excitation off of the midshaft
will strike wall with an energy per unit charge of V volts. No matter its path,
the electron will have gone through a voltage drop of V volts going from
needle to wall. This is what Terry means by "a voltage drop is a voltage
drop is a
voltage drop".

Now consider another arrangement. Given the sample ball in the miidle of a 
grounded box. Now instead of attaching it to a given reference voltage, give
it a fixed charge and electrically insulate it. Now suppose that the ball is
malleable and can change its size. For example, let's let the ball be a balloon
attached to a air hose and pump. If, while the balloon is inflated to a radius
d a single electron "sneaks" off the ball and is accelerated to the wall, it
will acquire and energy of eV where V is the instantaneous voltage drop between
the balloon and the wall (ground). Now deflate the balloon until its radius is
d/2. Now when an electron "sneaks" off the smaller surface, it will fall
through
a larger electrostatic potential (about 4V if the box is large). The difference
is that the ball is not held at a fixed potential but rather at a fixed charge.
It's potential can fluctuate. Well this seems like something for nothing until
you realize that you must do electrical work to deflate the balloon.
Thus you are
trading stored elastic energy in the balloon's surface tension for electrical
potential energy. It is not a free lunch, it is more of an amplification scheme
in the same sense that a simple lever (or pulley) allows one to lift
heavy object
with a small force. A similar mechanism may be responsible for the phenomena
associated with sonoluminescence where a multitude of particles at low energy
can act collectively to create a small number of particles at high energy. In
fact there the amplification in energy can be about 10 orders of
magnitude, truly
enormous.

Now if you want to talk about fusion applications, you need to specify
what your
setup is etc. before you can intelligently answer whether it can have an
effect and what that effect is.

|>If you disagree with the above two paragraphs, read this restatement:
|>The voltage of the current source is a red herring--ignore it.  The
|>only question is how many electrons will end up on the "construct".

That's one approach (equivalent to my econd example).

|>Terry's analysis implicitly assumes a fixed number of electrons:
Nope: he assumes a fixed potential.

|>charge a sphere, then deform it into a cone.  This is not the setup
|>the CF people are using.  After reading other discussion on this
|>group, it sounds like it is unknown how to compute the integral
|>mentioned in the previous paragraph, so there is no way to know how
|>many electrons will end up on the construct.

Well not really. It is just that no one has done it yet, but it is quite
doable, certainly numerically.

Let me suggest another scheme. Take a ball of charge and squeeze it
into a cigar shape and then further into a needle. Now you get both
advantages. 
The potential goes way up just from solving poisson's equation since the charge
now occupies a much smaller volume and the field gradient is even more
accentuated at the two ends because of the "sharp corners" effect. Hmmm,
something to think about. How you get it to cause fusions is not so clear to
me.

However this looks remarkable similar to something which has recently grabbed
my attention. It is a novel small-scale fusion idea with single component 
plasmas. The citation is:

 "Non-neutral plasma compression to ultrahigh density"
by Dan Barnes and Leaf Turner in Physics of Fluid B Vol. 4 p. 3890 December
1992.
Briefly the idea is to take a single component plasma  in a penning trap and 
cool it thermodynamically to cyrogenic temperautes. Pick your magnetic field
such that the EXB drift causes a spin at just the right frequency. Then you
can do the math and find that in the rotating frame the dynamics of the
plasma is that of motion in a spherically symmetric potential with a weird
shape. Because it is a potential, you can solve for the nonlinear langmuir
oscillation. The pertrubation can be either spherical, cigar or pancake -like.
Because of the nature of the "potential" you can get hugh density
multpilications.
The idea is that this might form a small (a few watts) fusion device if we are
really lucky and if it can't achieve that goal, it might be a great compact 
intense neutron source.

you gotta love the idea if for no other reason than the novelty of the
approach.


john w. cobb



Newsgroups: sci.physics.fusion