sim needs faraday cage?

happyjack27 · Post by **happyjack27** » Sat Dec 24, 2011 4:05 am

my sims don't have a faraday cage - so perhaps recirculation is not being properly modeled.

unfortunately i can't actually model a faraday cage - the sim doesn't really model conductors effects on electric or magnetic fields.

i was thinking i could make a copy a larger copy of the coils and put them out at double the distance the faraday cage should be at, and then exactly half way inbetween the electric and magnetic field would be exactly neutralized, thus making for a virtual faraday cage.

then maybe i could run the sim with this and get a more accurate picture of recirculation.

does that sound right?

(i've upgraded my video card, so i might have to adjust my program to the new specs.)

erblo · Post by **erblo** » Sat Dec 24, 2011 8:56 pm

Sounds like a good idea, especially since you didn't see any recirculation at all. I think that image coils have already been discussed in the old thread, but just to check my understanding (for coils made from line segments):

The image coils are the same as the ordinary coils, but with radius r_I:

r_I=(r_0)^2/r

where r_0 is the radius of the V=0 sphere and r is the radius of the real coils.

The linear charge density on the image coils lambda_I:

lambda_I=(-r_0/r*lambda)*(r/r_I)=-r_0/r_I*lambda

where lambda is the linear charge density on the real coils. (The first parenthesis is the equation for a mirrored point charge and the second is to compensate for the bigger image coils changing the linear charge density).

If this is done using image coils with 0 current the result is a perfect conducting grounded (V=0) nonmagnetic spherical chamber/Faraday cage of radius r_0. I don't think you'd want to do the same for the magnetic field - wouldn't this mean that the chamber was superconducting? A nonmagnetic one feels closer to the real situation, but that might just be me

D Tibbets · Post by **D Tibbets** » Sat Dec 24, 2011 9:56 pm

Um, I'm in deep water here, but wouldant a Faraday cage only ensure that the charged particles and electric fields are playing in their own little universe without outaide interference. So long as you are inside the cage, nothing outside the cage or the cage itself would have any effect on what is going on inside, at least for electrical considerations, I'm not sure about magnetic. So, there would be no midway point where the fields balance.

If you cannot model conductors, then I wonder if the magrid can be modeled at all. If nothing else you would have to model the magrid surface as a ground (neutral potential). I think current trends is to use a high pos.potential on the conductive surface of the magrid, with low potential electron guns, but neutral magrid and high negative potential on the electron guns have a similar (but not identical?) effect.

If you are just injecting electrons and ions at set points with set energies and then watching what is happening, then I would not expect recirculation. You absolutely must have the positive charge on the surface of the magrid accounted for. If the sim does not allow this, the only work around would seem to be to substitute artificial calculations based on the radius of the electron. If the electron radius is outside the defined radius of the magrid, then apply an attractive potential to only those electrons (either towards the surface of the magrids surrounding the cusps, or assumed central attractive vector if you are not calculating the focusing effects of the magnetic fields). The repulsive space charge would still apply, but the attractive potential on the external electrons would be added to this. Of course distance- inverse square law considerations between the forces would need to be allowed for. If your sim is already allowing for Coulomb scattering, and the cusp confinement of the magnetic fields, the applied attractive potential on the escaping electrons should mimic the recirculating efficiency versus the KE of the electron, etc.

Another approach may be to assume a Faraday cage at the radius of the Magrid, then set up a seperate sim with the parameters of an attractive central potential. Account for the KE spread of the escaping electrons (entering electrons into this separate sim). Them merge the two ims results. Sum (or would it be subtract ?) the two sims.

Admittedly, this might demonstrate the recirculating effect, but you might have difficulty proving that this is what happens. Then again, it is all mathematical simulation, so the approach may not mean much so long as you can defend your formulas and reasoning.

Dan Tibbets

hanelyp · Post by **hanelyp** » Sat Dec 24, 2011 10:00 pm

I expect a Faraday cage around the system is less important than getting the charge distribution on the magrid right. Unfortunately, the same difficulties you have with a Faraday cage will apply to magrid charge distribution.

If you're not getting recirculation, check that the total charge of plasma + magrid is positive, producing a suitable potential between magrid and your desired boundary. Total charge should be just enough to bring an electron to a stop over the distance between the magrid radius and a selected turn-around radius.

happyjack27 · Post by **happyjack27** » Sun Dec 25, 2011 4:28 am

ah, that didn't occur to me, plasma charge + magrid charge > 0. duh.

the magrid surface is modeled as a charge source; though it doesn't conduct.

i wouldn't expect the charge of faraday cage to have a big effect on recirculation. if its grounded though, that might steepen the voltage gradient outside the magrid, so that could help recirculation. i would think matching the charge w/the image coils would simulate a grounded faraday cage.

i think its effect on the magnetic field will help. i expect it to make it turn the magnetic field around faster. though i'm not sure a real faraday cage would do that (they might do precisely the opposite), image coils certainly would.

happyjack27 · Post by **happyjack27** » Sun Dec 25, 2011 6:14 am

i looked it up, faradaqy cages don't affect static magnetic fields. so the only thing that would happen is the first thing i said about steeper voltage gradient. if i sim i'm going to do image coils w/inverse charge, no mag field, to simulated a grounded faraday cage. i would think faraday cage should be at 2x absolute center to coil midplane.

i'm pretty sure it would work beautifully w/a superconducting faraday cage. not as interested in that, actually. so ya, i think i'm gonna go w/waht erblo said. if i do it, that is. so if distance from coil to midplane is r, and charge density is c, and i want the faraday cage at 2r, then distance to image coils midplane is what? and linear charge density of image coils is what?

erblo · Post by **erblo** » Sun Dec 25, 2011 9:08 am

I agree that a check of total charge is the most relevant and simplest thing to do, as you said: duh (slaps palm to forehead).

As for a Faraday cage: Well, using the equations above (which I know work, if I just remember them correctly) you'd need the image coils to be at:

(2r)^2/r=4r

with the linear charge density (this is for line segments, not a surface...):

-(2r/4r)*c=-c/2

to get 0V at 2r. Looking forward to seeing the new sims!

KitemanSA · Post by **KitemanSA** » Sun Dec 25, 2011 2:57 pm

IMHO, you need two image grids, one for "ground state" outside and one to provide the image magnetic field due to the plasma inside. With that, you can actually mock up the wiffle-ball effect.

What if anythng can I do to help?

happyjack27 · Post by **happyjack27** » Sun Dec 25, 2011 3:21 pm

KitemanSA wrote:IMHO, you need two image grids, one for "ground state" outside and one to provide the image magnetic field due to the plasma inside. With that, you can actually mock up the wiffle-ball effect.

What if anythng can I do to help?

well i'd say only thing someone can do besides the programmer is make the segment list. but i had already made that too easy: the segment lists are broken up into sections, each one who's size, current density, and charge density can be independently scaled. so it seems all i have to do is copy the current segment list, and change 2 numbers.

as for 2nd pair of image coils to model the plasma's magnetic field, the sim already calculates the plasma's magnetic field. it uses the differential formula for the magnetic field produced from a moving point charge, with relativistic corrections. so that shouldn't be necessary. but if you want me to try it out, i suppose it'd be pretty easy to do. i'd just need the parameters you want to run.

for each set of coils: linear charge density, amp turns, center to midplane distance.
for plasma: net excess charge, total ion charge

if the inner image coil will be charged, you'll have to subtract that from the net excess plasma charge (and if it's positive, also the total ion charge)

as you can see from the videos, i can change the parameters globally while the sim is running with logarithmic (base10) sliders.

also, erblo, i was misleading when i said "magrid surface". the magrids are a collection of line segments, and linear charge density _is_ the parameter i need, as you presume. (if i enable electron loss to magrid, the electrons are lost when they reach a certain distance from any segment, so in that sense and that sense only the magrid is a surface / volume)

also, wb-6, doedec, or 32-gon?

wb-6: http://www.youtube.com/watch?v=XN9yr_5u ... hA&lf=plcp

doedec: http://www.youtube.com/watch?v=ULfi1fr3 ... ature=plcp

32-gon: http://www.youtube.com/watch?v=2xWQaJ-Q ... re=related

and do you think 2r is too close for the faraday cage? maybe 3r instead?
just don't want to let the voltage gradient run to infinity, as it does w/no faraday cage. i think that's impacting circulation. but i want to give room for the mag fields (which still _do_ go to infinity) to curve. from the picture here http://www.emc2fusion.org/ it looks about 3r. and it looks about ideal distance.

ladajo · Post by **ladajo** » Sun Dec 25, 2011 6:31 pm

It is intersting you are on this theme, and I am curious to see how it goes. I noted a while back that I thought this would be an issue for Famulus given his compact chamber.

erblo · Post by **erblo** » Sun Dec 25, 2011 11:45 pm

happyjack27 wrote: also, wb-6, doedec, or 32-gon?

...

and do you think 2r is too close for the faraday cage? maybe 3r instead?
just don't want to let the voltage gradient run to infinity, as it does w/no faraday cage. i think that's impacting circulation. but i want to give room for the mag fields (which still _do_ go to infinity) to curve. from the picture here http://www.emc2fusion.org/ it looks about 3r. and it looks about ideal distance.

I'd say start with wb-6, fewer cusps should make it easier to to see how the particles behave (more spiky cube and less hairy ball?). For the same reason I think a fairly large (3r) V=0 sphere would be a good starting point, it's easy enough to shrink it later... By testing different sizes you could (should?) see a larger portion of recirculation into different cusps - instead of just reversing back into the same one - for (very?) large chambers.

hanelyp · Post by **hanelyp** » Mon Dec 26, 2011 1:32 am

Happyjack, would it be possible in your software to have a population of charged particles with motion constrained to surfaces?

KitemanSA · Post by **KitemanSA** » Mon Dec 26, 2011 1:52 am

happyjack27 wrote:
KitemanSA wrote:IMHO, you need two image grids, one for "ground state" outside and one to provide the image magnetic field due to the plasma inside. With that, you can actually mock up the wiffle-ball effect.

What if anythng can I do to help?
well i'd say only thing someone can do besides the programmer is make the segment list. but i had already made that too easy: the segment lists are broken up into sections, each one who's size, current density, and charge density can be independently scaled. so it seems all i have to do is copy the current segment list, and change 2 numbers.

As I understand it (and I may not, the folks that were doing this before were Indrek and kcdodd, and I think icarus) the idea is to put a perfect scale replica of the main coil within with everything scaled by some value like 1/2 except the direction of current flow which is reversed. What this does (I think) is to zero out the magnetic field within the image coil and put an compressed field between the image and main coils that mocks up the wiffleball. This should make the "plasma" less quasi and more spherical.

As I understand the rational, a plasma acts like a superconductive surface which reflects a magnetic field... or something like that.

Anyone?

happyjack27 · Post by **happyjack27** » Mon Dec 26, 2011 2:04 am

hanelyp wrote:Happyjack, would it be possible in your software to have a population of charged particles with motion constrained to surfaces?

that would take some additional programming, me thinks. my first thought that is i could simply add some post-processing to a subset of the particle to remove the vector component (both position and velocity) normal to the surface. it would be a bit of an approximation, and it would take as much computation time as if one were applying the post-processing to _all_ of the particles, due to the nature of the processor (its a full data-parallel processor so branch divergence is not allowed, instead it's done by predicated instructions). so with those caveats... calculate as if it's position delta as if it wasn't constrained, remove the component of that that is normal to the surface, update the position w/that vector, then remove the component of the new position vector normal to the surface. it would be a lot of geometric calculations relative to what it accomplishes compares to the particle-to-particle interaction calculations (they're pretty streamlined). it might have a substantial impact on the overall framerate. then again, i believe i'm bandwidth-limited at this point, so a few extra calculations might not be a bad thing. i presume you're talking about simulating a conductor? (i read schaum's outline of electromagnetics, and i recall that due to the em fields w/in a conductor transferring charges almost instantaneously, all electromagnetodynamics actually lie on the _surface_ of the conductor, not the inside. never put the 2 together thou.

good idea!)

happyjack27 · Post by **happyjack27** » Mon Dec 26, 2011 2:14 am

KitemanSA wrote:
happyjack27 wrote:
KitemanSA wrote:IMHO, you need two image grids, one for "ground state" outside and one to provide the image magnetic field due to the plasma inside. With that, you can actually mock up the wiffle-ball effect.

What if anythng can I do to help?
well i'd say only thing someone can do besides the programmer is make the segment list. but i had already made that too easy: the segment lists are broken up into sections, each one who's size, current density, and charge density can be independently scaled. so it seems all i have to do is copy the current segment list, and change 2 numbers.
As I understand it (and I may not, the folks that were doing this before were Indrek and kcdodd, and I think icarus) the idea is to put a perfect scale replica of the main coil within with everything scaled by some value like 1/2 except the direction of current flow which is reversed. What this does (I think) is to zero out the magnetic field within the image coil and put an compressed field between the image and main coils that mocks up the wiffleball. This should make the "plasma" less quasi and more spherical.

As I understand the rational, a plasma acts like a superconductive surface which reflects a magnetic field... or something like that.

Anyone?

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?