A Funel analogy instead of a Wiffleball analogy

[D Tibbets]

Instead of using Bussard's analogy of marbles bouncing around in a Wiffle Ball, I wonder if the following analogy would hold water.
Imagine a funnel with a collection cone 10 inches wide and a central hole 1 inch wide. Set it up on the floor with the cone up and drop a marble towards it. The chances are good that the marble will rattle around in the collection cone and drop through the hole. Now cut off almost all of the cone. The central hole is still there- it hasn't changed in size. Now try dropping a marble and see how likely it is to hit the hole.
I have often mentioned that the cusps are pinched almost closed, but I wonder if this is misleading. The cusp (the near parrellel opposing magnetic field lines with a field null between them) is not changed. But the curving geometry of the cusp throat (collection cone) is flattened (almost) in a manner similar to cutting off the collection cone of a funnel.
In the example the collection area was decreased from ~ 100 square inches to 1 square inch- a 'Wiffleball Trapping Factor' of 100, [EDIT] or perhaps I should say - the FunnelLESS Trapping Factor as suggested by KitemanSA below.

Dan Tibbets

[KitemanSA]

I think you may have the analogy backward. The funnel isn't the hole, it is the cone. The hole is just a cylinder or a hose. It doesn't become a funnel until you add the cone. And when you postulate cutting the cone off (I think flatten it out is a better description) you increase the funnelless trapping factor or decrease the funnel collecting factor.

[icarus]

And then think about the ExB velocity component causing the 'marbles' to swirl, in bulk, circumferentially around the axis of the funnel on the flatter part of the surface, resembling an 'inverted' spherical surface, at a speeds that are not an insignificant fraction of that of light, and you are getting there for the point cusps at least.

[D Tibbets]

I like this analogy, but have a question.
Since the fuel ions are charged, near and being impinged on by the magnetic field, they are also spiraling in the direction of the flux. The marble in the funnel is spiraling towards the exit, but there are other ways it can spin as it heads that direction right. not only clockwise and counter clockwise ?

So are you approximating the flux direction is like gravity on the marble?

Yes- the flux lines flow parallel to the Wiffleball surface, so in this simple model I imagine the electrons bounce like a ball off a floor (or inside a "Wiffle Ball"). There is not any spiral or angular momentum introduced by the ball bouncing around the throat of a cusp. In reality, the picture is more complex. The direction of the poles (North or South) are unimportant so long as they are the same direction.
I've wondered if having the polarity arranged so that the electron completes its' 1/2 gyro radius spiral around the border field line in a direction that tends to throw it back more towards the center, rather than the opposite side of the cusp throat might help. I have never seen mention of this, so I guess it is not significant. If the local coulomb collisions in these throat (funnel) areas dominate the the effect would be damped out. And, if most electrons are trapped on the field lines ,and before escape, oscillate back and forth on it then this back and forth motion for thousands (100,000 ?) of times makes the significance of the direction of the first magnetic deflection unimportant. Also, in this multicusp system, if the magnetic flux traped electron is avoiding (for its' first oscillation) one cusp, it would only be thrown towards another cusp.

In the DPF, there is apparently a considerable significance to the spiralling (angular momentum introduced by a background magnetic field as weak as the Earth's field) of the charged particles helping to form a tight ..um.. focus. I don't know whether this would have any significance in a Polywell system.

Then, add possible spinning plasmas, pulsating conditions, electrostatic interactions of the charged particles within the cusp and cusp throats, etc. and the picture can only become even more murky. I guess that is why people do experiments.

Dan Tibbets

[WizWom]

I like this analogy, but have a question.
Since the fuel ions are charged, near and being impinged on by the magnetic field, they are also spiraling in the direction of the flux. The marble in the funnel is spiraling towards the exit, but there are other ways it can spin as it heads that direction right. not only clockwise and counter clockwise ?

So are you approximating the flux direction is like gravity on the marble?

Yes- the flux lines flow parallel to the Wiffleball surface, so in this simple model I imagine the electrons bounce like a ball off a floor (or inside a "Wiffle Ball"). There is not any spiral or angular momentum introduced by the ball bouncing around the throat of a cusp. In reality, the picture is more complex. The direction of the poles (North or South) are unimportant so long as they are the same direction.

The electric flux will be "out" from the anode to the cathode.
The magnetic flux will be around the wires. The design of WB-6 and WB7 is not using toroidal coils, but solenoid style multiple loops. The magnetic flux will be from the center of the loop, then around the loop of wire, and back to the center of the loop. And because of the multiple loops, these lines will twist in interesting ways, and will NOT maintain a constant distance from the loops of wire. The direction of the poles is VERY important, because it decides the WB trapping factor - where the magnetic flux overpowers the electrix, and where it works to twist the electrons just enough to keep them from the cathode.

[D Tibbets]

I like this analogy, but have a question.
Since the fuel ions are charged, near and being impinged on by the magnetic field, they are also spiraling in the direction of the flux. The marble in the funnel is spiraling towards the exit, but there are other ways it can spin as it heads that direction right. not only clockwise and counter clockwise ?

So are you approximating the flux direction is like gravity on the marble?

Yes- the flux lines flow parallel to the Wiffleball surface, so in this simple model I imagine the electrons bounce like a ball off a floor (or inside a "Wiffle Ball"). There is not any spiral or angular momentum introduced by the ball bouncing around the throat of a cusp. In reality, the picture is more complex. The direction of the poles (North or South) are unimportant so long as they are the same direction.

The electric flux will be "out" from the anode to the cathode.
The magnetic flux will be around the wires. The design of WB-6 and WB7 is not using toroidal coils, but solenoid style multiple loops. The magnetic flux will be from the center of the loop, then around the loop of wire, and back to the center of the loop. And because of the multiple loops, these lines will twist in interesting ways, and will NOT maintain a constant distance from the loops of wire. The direction of the poles is VERY important, because it decides the WB trapping factor - where the magnetic flux overpowers the electrix, and where it works to twist the electrons just enough to keep them from the cathode.

All right, flux is a poor choice of words. The magnetic field lines will be parallel to the Wiffleball surface. Keep in mind that the Wiffleball as I'm using it here is the actual surface with the curvatures into the cusps, not an imaginary perfect sphere with holes in it. Any charged particle approaching from near machine center will adiabatically reflect from this surface after completing ~ one half of a gyro radius orbit about the field line, or with the right geometry/ energy/ magnetic field gradient,etc it will be trapped on a field line and oscillate back and forth on that field line till it is knocked off or otherwise affected by several transport mechanisms.

As far as N-S orientation, The direction the electron takes as it spirals around a field line is dependent of the pole. But who cares which way it goes. The face and edge cusps are similar in how they handle an electron, so the system is symmetrical. If the electron bounces off the magnetic field it will take a path that would average out to be the same within this porcupine quasi spherical surface. If the electron is trapped on a field line it will start in one direction, but most would reverse and oscillate back an forth, probably thousands of times before some series of electrostatic collisions, or magnetic transport mechanisms removes it from the system. If my assumption of the number of oscillations off of, or along a magnetic field line is correct, I could see the original direction contributing perhaps 1 part in thousands (100,000?) to the chance of the electron escaping This would be completely irrelevant. Where is my reasoning off? I also seem to recall Bussard saying which pole faced in was unimportant, so long as all the magnets had this orientation. But I cannot find this source now.

Dan Tibbets