I have started applying my code to polywell concept.This code is fully kinetic.
Only two coils can be used since it has to be axisymmetric, but some basic concepts can be tested.
http://www.youtube.com/watch?v=avHqD8zrpr4
I simply started the simulation with a slightly higher electron concentration to ions. Electron density and electric field directions are plotted here. As can be seen, the electrons are quickly pushed out destroying the inner well. The electrons are started out in thermal distribution, so will do some additional work to test non-thermal effects.
Initial Polywell Simulation
Initial Polywell Simulation
Carter
I'd be interested in learning the reasoning for that.hanelyp wrote:Looks like your initial plasma pressure exceeded your magnetic pressure. I'd have likes to see how it settles down after the initial blowout. Also, you might try adjusting the coil spacing so that the area between the coils matches the sum of areas on the coil faces.
In theory there is no difference between theory and practice, but in practice there is.
This is at kT = 600keV, n = 1e17, and potential at 600kV.
What happens is the electrons quickly leave the initial plasma configuration because of their low mass. Without the external electric field most would blow off leaving the ions exposed, which would then undergo a coulomb explosion. Instead the efield keeps them confined to the immediate area. However, the ions are still exposed internally and are exploding, just more slowly.The movie is only about a nanosecond long in sim time.
I think hanelyp's intention is to try and match the B field strength in both areas. Since flux must be conserved, naively matching the areas should match flux density (aka B field strength). I have matched the B field, but it is not quite this naive ratio of areas because of non-uniformity.
What happens is the electrons quickly leave the initial plasma configuration because of their low mass. Without the external electric field most would blow off leaving the ions exposed, which would then undergo a coulomb explosion. Instead the efield keeps them confined to the immediate area. However, the ions are still exposed internally and are exploding, just more slowly.The movie is only about a nanosecond long in sim time.
I think hanelyp's intention is to try and match the B field strength in both areas. Since flux must be conserved, naively matching the areas should match flux density (aka B field strength). I have matched the B field, but it is not quite this naive ratio of areas because of non-uniformity.
Last edited by kcdodd on Sat Jun 05, 2010 4:17 am, edited 1 time in total.
Carter
Pressure? It looked like the plasma was pushing the magnetic field out of that way, then the magnetic field pushing back after some plasma escaped.BenTC wrote:I'd be interested in learning the reasoning for that.hanelyp wrote:Looks like your initial plasma pressure exceeded your magnetic pressure. I'd have likes to see how it settles down after the initial blowout. Also, you might try adjusting the coil spacing so that the area between the coils matches the sum of areas on the coil faces.
The spacing? Closer to equal magnetic field at equator and poles. If I'm correct that the equatorial plain of the simulation was on the left edge of the movie, the weaker equatorial magnetic field would account for the plasma billowing out more there.
After quite a bit of fiddling, I have gotten the simulation to settle into what appears to be a "wifflball" trapping type configuration at beta=1. The trapping factor I can get so far seems to be about 2:1.
This figure depicts the density profile and magnetic field surfaces. Again, this is axisymmetric about the left side.
This figure depicts the density profile and magnetic field surfaces. Again, this is axisymmetric about the left side.
Carter
kcdodd:
Very interesting. What parameters did it seem most sensitive to, i.e. the ones that you 'fiddling' with most? Coil spacing, voltage potential, etc?
Does beta=1 mean that you were keeping mag. coil strength, electron energy and density all constant?
Also how are you defining trapping factor here? I.e does 2:1 mean twice as good as no 'wiffleball-trapping effect trapping?
Very interesting. What parameters did it seem most sensitive to, i.e. the ones that you 'fiddling' with most? Coil spacing, voltage potential, etc?
Does beta=1 mean that you were keeping mag. coil strength, electron energy and density all constant?
Also how are you defining trapping factor here? I.e does 2:1 mean twice as good as no 'wiffleball-trapping effect trapping?
In terms of physically, the plasma needs to be rather small (like 1/3 or 1/4) compared to coil radius/spacing. What that means is the bfield pressure has to be much higher then the plasma pressure inside the cusp or the plasma will simply push itself out and the flat top density will continue all the way out through the cusp.
Of course beta=1 is a bit fuzzy in the type of situation since there is already a point of B=0 in the center even without plasma. What I mean is once the plasma pressure is pushed to the order of magnitude that it begins to create a volume of B=0. Once there increasing plasma pressure can increase the size of the plasma all the way to the coils dimensions in one power of ten. Talking about going from say 10^20 to 10^21 is the range in this simulation.
If you look at the plot I posted, there is a large region of nearly flat density (red area) which sharply drops off when |B| > 0. This is about twice the density in the cusp where the bfield surfaces join. That is what I mean by 2:1. I don't post specific dimensions and parameters since they are not really relevant yet.
Basically the fiddling involved a process of changing initial plasma size and pressure (they have to match) and periodically re-randomizing the velocity distribution to simulate long term equilibrium, since I can only do about 30ns sim-time per day on my pc, while collision time-scale is between micro and millisecond scale.
There are no electric fields involved here. I had to turn them off for stability at these densities.
Of course beta=1 is a bit fuzzy in the type of situation since there is already a point of B=0 in the center even without plasma. What I mean is once the plasma pressure is pushed to the order of magnitude that it begins to create a volume of B=0. Once there increasing plasma pressure can increase the size of the plasma all the way to the coils dimensions in one power of ten. Talking about going from say 10^20 to 10^21 is the range in this simulation.
If you look at the plot I posted, there is a large region of nearly flat density (red area) which sharply drops off when |B| > 0. This is about twice the density in the cusp where the bfield surfaces join. That is what I mean by 2:1. I don't post specific dimensions and parameters since they are not really relevant yet.
Basically the fiddling involved a process of changing initial plasma size and pressure (they have to match) and periodically re-randomizing the velocity distribution to simulate long term equilibrium, since I can only do about 30ns sim-time per day on my pc, while collision time-scale is between micro and millisecond scale.
There are no electric fields involved here. I had to turn them off for stability at these densities.
Carter
kcdodd:
thanks.
So I notice right at the tip of the high density region as it meets the cusp that the field lines have quite sharp directional changes there (not smooth like elsewhere), is the numerical solution struggling in that region or do you think that might be physical? Also as the high density region pushes out, this increases the mag field in this region correct? This would be the stabilising mechanism that the wiffleball-arguments are based on in this tiny region.
thanks.
Like driving a wedge, the inclined plane leverage of Archimedes.What that means is the bfield pressure has to be much higher then the plasma pressure inside the cusp or the plasma will simply push itself out
So I notice right at the tip of the high density region as it meets the cusp that the field lines have quite sharp directional changes there (not smooth like elsewhere), is the numerical solution struggling in that region or do you think that might be physical? Also as the high density region pushes out, this increases the mag field in this region correct? This would be the stabilising mechanism that the wiffleball-arguments are based on in this tiny region.
Unfortunately the visualization software I am using has trouble drawing smooth streamlines and it is very annoying. Here is the raw magnetic vector field. You might also see what looks like some magnetic turbulence in the center. I am not really sure how real it is, but it is interesting.
[edit:] sorry, could you expand on what "tiny region" you are talking about?
[edit:] sorry, could you expand on what "tiny region" you are talking about?
Carter
Yes, I see eddy currents in the magnetic fields.kcdodd wrote:Unfortunately the visualization software I am using has trouble drawing smooth streamlines and it is very annoying. Here is the raw magnetic vector field. You might also see what looks like some magnetic turbulence in the center. I am not really sure how real it is, but it is interesting.
[edit:] sorry, could you expand on what "tiny region" you are talking about?
But without the secondary magnetic fields of the moving charge carriers, I'm afraid it really is sort of pointless.
Wandering Kernel of Happiness
Thanks for the arrow plot, it shows what I was looking for even better.
kcdodd:
http://img51.imageshack.us/img51/63/visit0008a.png
It seems like the 'nose' has formed a smooth, stable interface with concave curvature, i.e. opposite curvature to the whole of the rest of the interface. If this can happen, it is what will cause the pinching off and stop the plasma pushing out all the way along the cusp. If you were going to do multiple-scale analysis, singular perturbations, etc this would be the singular point you would expand around to determine if wiffle ball was going to work . The higher order effects determine behavior here because the first orders are in balance and cancel out. It kind of demonstrates that there must be some small interfacial tension effect present ... I wonder where that arises from ...
kcdodd:
Essentially it is the only point on the arrow plot where you have two arrows pointing nose-to-nose towards each other, i.e. the stagnation point, singularity (actually a line, ring, since this is axisymmetric). At the right most extent of the high-density region as it meets the magnetic field boundary, see the circled region in the image.could you expand on what "tiny region" you are talking about?
http://img51.imageshack.us/img51/63/visit0008a.png
It seems like the 'nose' has formed a smooth, stable interface with concave curvature, i.e. opposite curvature to the whole of the rest of the interface. If this can happen, it is what will cause the pinching off and stop the plasma pushing out all the way along the cusp. If you were going to do multiple-scale analysis, singular perturbations, etc this would be the singular point you would expand around to determine if wiffle ball was going to work . The higher order effects determine behavior here because the first orders are in balance and cancel out. It kind of demonstrates that there must be some small interfacial tension effect present ... I wonder where that arises from ...
Do you have more details of your code avaliable anywhere? What language is it in? Any plans to post the code? What are the equations you're solving?
If your code is slow I may be able to give you some tips if it's in MATLAB or C/C++.
However, absent any of that information I will provide you with some helpful pure speculation:
The vortex-like constructs on the left hand side of your image looks like the kind of thing you would get if you're taking too large of steps in your integrator. The transitions between the two main regions looks "correct" to me, however.
Depending on what your doing one good check that your taking small enough steps is to look at the total energy of your system and make sure it's decreasing with time (after subtracting any input energy).
If your code is slow I may be able to give you some tips if it's in MATLAB or C/C++.
However, absent any of that information I will provide you with some helpful pure speculation:
The vortex-like constructs on the left hand side of your image looks like the kind of thing you would get if you're taking too large of steps in your integrator. The transitions between the two main regions looks "correct" to me, however.
Depending on what your doing one good check that your taking small enough steps is to look at the total energy of your system and make sure it's decreasing with time (after subtracting any input energy).