sim needs faraday cage?

[KitemanSA]

no expert here but sounds like what i've head. so then i'd just use formulas from erblo for inner mirror coils, depending on where i want the wb radius to be. and the mirror coils would thus supply the net electrostatic plasma pressure to reach b=1, so the remaining plasma (simulated by point particles) should actually be exactly neutral?

Ummm, I think what you are getting with the image coil is the massive number of electrons and ions that result in the basic neutral plasma. Is that what you said?

Anyway, it allows you to calculate the response of a MUCH smaller number of ACTUAL particls while having them act like they were among the actual quasi-neutral whole. (Neutral image coils + non-neutral particles = quasi-neutral...)

I'd LOVE to see one of your sims with a β=1 wiffleball shape.

[D Tibbets]

A Faraday cage outside of the electrons position would have zero effect. Provided the frequency considerations, a Faraday cage ( or diverter or direct conversion grid) would have an effect only if thwe particle has passed it (greater radius) or hits it. This is Gauss's law in action. This is why 'venition blinds' direct converters are discussed. The charged particle must pass it before it will be diverted or slowed. So long as there is a roughly spherical geometry, Gauss's law applies. That is why a faraday cage works. the near inner portions of the grid pull on the particle the same as all of the surface on the opposite side. (it also shields outside electric fields) so that the net influence on the charged particle is zero. The magrid itself itself acts as a (efficient ?) faraday cage to the ions and electrons within it. The accelerating/ recirculating effects are only present once the charged particle is outside the magrid.

The method of placing one magnetic field inside another served to demonstrate the formation of the Wiffleball effect. It served to defuse A. Carlson's skepticism of the wiffleball possibility.
I don't think it had anything to do with the possibility of recirculation.

Dan Tibbets

[happyjack27]

alright, so i have a neutral inner image coil, who's radius and amp-turns i still have to calculate as a function of the magrid coils.

and an outer mirror coil with, conversely, an e field but no m field, to simulate a faraday cage at 3r.

lets say r=0.5 meters center-to-midplane on a wb-6 configuration.
i can calculate the outer mirrors coil charge from erblo's formula. that leaves:

magrid linear charge density
magrid amp-turns
inner mirror coil amp-turns
inner mirror coil center-to-midplane distance
net plasma excess charge (s/b less than total magrid charge)
total ion charge ( i.e. neutral plasma density)

i think it would be easier just to put the net excess charge on inner mirror coils, as then i could just use erblo's formulas to match the charge neutral surface to the magnetic neutral surface and thus have b=1. then all the rest of the plasma -- the plasma simulated w/point charges -- would just be neutral. then i could even model the particles at a 1:1 representation ratio.

so i suppose:

*what is the target wiffleball radius at 0.5m center to midplane? 0.25m?
*then what's a reasonable amount of amp turns on the magrid?
*and linear charge density on the magrid?

from that, the inner and outer coil parameters can be calculated, and the point charges would be net neutral, and i can run them at 1:1. so we're down to just 3 variables.

[happyjack27]

btw, when/if i do the outer mirror coils, i'm going to set the chamber loss radius to match the faraday cage radius. i figure if a negatively charged particle outside the magrid has enough kinetic energy to reach V<0, well, then it has too much. besides, in a real situation, outside the faraday cage v=0 anyways, so it would be lost to the chamber. (unless the chamber itself has a negative charge, but then it'd be bleeding off electrons at high PE just to have the few that don't go to the grounded faraday cage go right through the entire contraption, and that's just a waste -- or worse, impart high energy to cold electrons in the center, calling them to spill out and maybe even pop the wiffleball. also that gets to another point, once an electron hits a real faraday cage, even from the inside, it's just as likely to go to ground as it is to fall back down the well) long story short, i figure any electron that hits the virtual faraday cage is lost - SHOULD BE lost. so it's a perfect place to set the chamber loss radius.

also, come to think of it, that elucidates a reason why electrostatic "reflectors" can be a bad idea: they keep particles in that s/b removed. if they should stay in, they WILL stay in if you just give them enough space to reach v=0. if their ke is such that exceed v=0, well then they shouldn't stay in. so then the thing to do is put a grounded faraday cage out a large distance, with a shape conformal to a constant pe from the wiffleball surface. simply put, that's the surface where v would be constant in the absence of a faraday cage (and the presence of a stable wb).

well i'm guessing that wouldn't be exactly a sphere - it would be sort of a bumpy/curvy quasi-sphere. but for my sims, a sphere will have to do, as that's my only choice when using mirror coils to create virtual conductors.

then your electron guns could be placed right on the surface of faraday cage, and release at 0 KE. i suppose you couldn't get them to release at exactly 0 KE so you'd probably have to place them just inside the cage.

[happyjack27]

where's indrek/icarus when u need him? icarus, what does a charge iso-surface look like at about 3r w/a fully formed wiffleball? (i'm guessing the grid on emc2fusion site is a pretty good approximation. probably just like image coils wrapped tightly in a mesh)

[D Tibbets]

Remember that the magnetic fields loop around, so if an upscattered electron is fast enough to avoid reversing near the Magrid, and if it stays trapped on a field line it will loop around and be accelerated into another cusp. This would add KE to the electron- retained energy when it reached the furthest point on the field line + Magrid potential. That is why the 2008 patent application mentioned as pecific distance outside the magrid where the upscattered electrons have to ground (wall, 'scrapper', etc).

Dan Tibbets

[kcdodd]

D Tibbets I don't quite understand your statement that a "Faraday cage" (which I assume just means a conductor of fixed voltage surrounding the coils) would have no effect. The electric fields would most certainly depend on the shape of the surrounding conductors which would change the plasma dynamics.

[happyjack27]

D Tibbets I don't quite understand your statement that a "Faraday cage" (which I assume just means a conductor of fixed voltage surrounding the coils) would have no effect. The electric fields would most certainly depend on the shape of the surrounding conductors which would change the plasma dynamics.

agreed. esp. if its grounded. it seems like you're saying that there is no voltage gradient between a grounded conductor and a charged conductor (in this case, the faraday cage and the magrid, respectively), and that's just absurd. then there'd be no such thing as electricity, and fusors certainly wouldn't work.

the whole point of me wanting to put a faraday cage in my sim is so that the electric potential energy of an electron reaches its peak before hitting the chamber wall (namely, V=0), thus presumably its KE would reach its minimum - 0 - and it would turn around before being lost. (and again, if it didn't reach its minimum by then, then it's too high energy and we _want_ to remove it from the chamber.) so then of course it has to be grounded.

i'm constraining the v=0 isosurface to a finite volume. the sim doesn't really have any chamber walls - just an electron loss region. so its like my chamber walls are ungrounded and any voltage gradient outside the magrid goes to infinity. if it helps, instead off thinking it as a faraday cage, just think of it as grounding the vacuum chamber walls.

are you saying that w/a grounded faraday cage, it's not going to increase the voltage gradient between the magrid and cage, the voltage will just drop suddenly and discontinuously to 0 at the cage?

but then what if you put a small negative charge on the cage? would that not then push back against the positive charge gradient, such that the space charge (err, voltage) would go continuously from the magrid charge to the cage charge?

[KitemanSA]

Please note he said "outside the electrons position" which I take to mean effectively outside the ground state. You all are using the Faraday cage to create a ground state. Placing one outside yours will have no effect.

[kcdodd]

What is a ground state, and what do you mean outside a ground state?

[D Tibbets]

D Tibbets I don't quite understand your statement that a "Faraday cage" (which I assume just means a conductor of fixed voltage surrounding the coils) would have no effect. The electric fields would most certainly depend on the shape of the surrounding conductors which would change the plasma dynamics.

I could answer your question with some brilliant logic and prose.... or it might be better if you watch this lecture video. It is the third lecture in a series (they are all excellent). At ~ 19:53 he draws a graph of the electric field inside and outsiade a conductive sphere.

http://ocw.mit.edu/courses/physics/8-02 ... ausss-law/

This is the third lecture and the parent page is here:

http://ocw.mit.edu/courses/physics/8-02 ... -lectures/

Note that spherical symetry is not essential, it just becomes much more difficult to explain the effect. There was a thread on Talk Polywell where this was hashed out to my satisfaction. I was initially a disbeliever, but was converted to the idea that the shape can be irregular, and there can be holes (or a wire mesh). While the effect may not be absolute, it is close enough (just as in the demo near the end of the lecture) untill the holes become too large. There is a demo in anoter of these lectures where the professor steps inside a wire mesh Faraday cage, and it blocks the high voltage from a Van De Graph from reaching him. He also shows that the mesh size blocks AM radio signals, but not FM radio signals. DC electric fields are most easily blocked, and as the ossilating frequence increases the holes/ mesh need to be smaller.


Dan Tibbets

[kcdodd]

Hmm. A uniformly charged sphere is not the same as a sphere of uniform voltage (a conductor). A sphere of uniform charge would indeed have no field inside. But a sphere of uniform voltage may not be of uniform charge. If you bring a charge close to the surface of the conductor a charge will be induced in the conductor surface to keep the same voltage. The induced charge would then indeed distort the fields inside the sphere since it breaks spherical symmetry.

[D Tibbets]

Hmm. A uniformly charged sphere is not the same as a sphere of uniform voltage (a conductor). A sphere of uniform charge would indeed have no field inside. But a sphere of uniform voltage may not be of uniform charge. If you bring a charge close to the surface of the conductor a charge will be induced in the conductor surface to keep the same voltage. The induced charge would then indeed distort the fields inside the sphere since it breaks spherical symmetry.

Provided the sphere is conductive like a metel, the charge will be evenly distributed over it's surface irregardless of it's shape (there may be some inductive differences between the inside of a metal sphere, and outside, but this is irrelavent. On that surface (inside of outside) this charge would be the same, or very close to it due to conductivity. And induced charges on the inside and outside surfaces of a conductor is a static condition. In a dynamic system where there is current flow with a constant potential source (power supply) inductance would be very limited. If you take a surface that is not very conductive- like cat fur, then there can be uneven charge distribution, but not in a normal conductive metal. If the magrid was coated with a good insulating ceramic, then things could change, but not with exposed metal surfaces. Remember M. Simon's comments about having insulated standoffs between the magrid magnets and the wall. The electrons that hit them or collect around them if they have some magnetic shielding, could produce a local charge that could repell further electrons. The key here is the insulating layer. If conductive, any charges that hit the surface will very quickly transfer the charge throughout the metal to the power supply circuit, and so long as the power supply was robust enough, there would be no voltage change globally, and of course none locally due to the conductivity. Note that this is more complex if you are talking about pulses that are so short that the current cannot travel far in the metal in that time frame. This would depend on the electron speed through the metal.

Dan Tibbets

[kcdodd]

I just don't think that is true. One of the first things you learn in undergrad E&M is the method of image charges to solve voltage boundary conditions. The simplest is an infinite conducting plane held at zero volts. Bring a charge of +q within a distance of l. One can put an image charge of -q at distance -l. However, there is not really a charge at -l, it is just a tool. What that represents is surface charge density on the conductors surface induced by bringing the other charge close. The same thing will happen inside the vacuum chamber surface. However, the method of image charges doesn't always work for arbitrary shapes, though I think it has already been suggested by putting image coils to get a similar effect.

[KitemanSA]

alright, so i have a neutral inner image coil, who's radius and amp-turns i still have to calculate as a function of the magrid coils.

and an outer mirror coil with, conversely, an e field but no m field, to simulate a faraday cage at 3r.

lets say r=0.5 meters center-to-midplane on a wb-6 configuration.
i can calculate the outer mirrors coil charge from erblo's formula. that leaves:

magrid linear charge density <<This should not be linear. It should vary to make a uniform voltage. Maybe something more like [(1+cos(2θ))/2] so that the charge density would be 1/2 where the coils are closest, and 1 at the 45degree point.>>
magrid amp-turns
...