The consequences of quasi-neutrality in the cusps

Discuss how polywell fusion works; share theoretical questions and answers.

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icarus
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Postby icarus » Sun Feb 08, 2009 10:32 pm

rnebel said:

3. Energy confinement on the WB-7 exceeds the classical predictions (wiffleball based on the electron gyro-radius) by a large factor.


Interesting, do I understand then that you are considering the wiffleball model as "classical"?

And a question I've been dying to ask for at least 6 months, how spherical does the wiffleball appear to be? (just by eyeball or fast-camera photos)

Of course, these questions are predicated on what you are and aren't allowed to talk about, which in itself would be nice to know so we don't waste energy on "inanswerable" requests for experimental information.
Last edited by icarus on Mon Feb 09, 2009 1:53 am, edited 1 time in total.

alexjrgreen
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Postby alexjrgreen » Sun Feb 08, 2009 10:44 pm

rnebel wrote:2. In one-D simulations the plasma edge (which corresponds to the cusp regions) is not quasi-neutral. Therefore, if the cusps are quasi-neutral it must be a multidimensional effect.

Why not do a 3D simulation?

Spacecraft Plasma Environment Analysis Via Large Scale 3D Plasma Particle Simulation
http://www.springerlink.com/content/ln7h412626722402/
Ars artis est celare artem.

TallDave
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Postby TallDave » Mon Feb 09, 2009 1:35 am

2. In one-D simulations the plasma edge (which corresponds to the cusp regions) is not quasi-neutral.


Aha! I thought so. How else is a non-ambipolar plasma going to shed the excess electrons? Hopefully, we'll get some direct experimental evidence of this.

Our conclusion is that both the wiffleball and the cusp recycle are working at a reasonable level.


Great to hear! Learning the details of exactly why will be interesting.

rnebel
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Postby rnebel » Mon Feb 09, 2009 5:32 am

Alex:

3-D Particle-in-cell is extremely expensive. Resolution goes like (N)**.5 where N is the number of particles. You have multiple timescales and multiple spatial scales to resolve. This means supercomputers.

Art Carlson
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Postby Art Carlson » Mon Feb 09, 2009 9:00 am

rnebel wrote:Here's what we know and what we don't know:

1. We don't have the spatial resolution of the density to see if the cusps are quasi-neutral on the WB-7

I'm willing to go out on a limb here and make a prediction: When you get those diagnostics, they won't show anything that isn't in agreement with Maxwell's equations.
rnebel wrote:2. In one-D simulations the plasma edge (which corresponds to the cusp regions) is not quasi-neutral. Therefore, if the cusps are quasi-neutral it must be a multidimensional effect.

In the 1-D model, you're talking about a violation of quasineutrality on the order of the Debye length, right? I agree that there is no reasonable way to treat both the extended surfaces and the cusp in a single, 1-D model.
rnebel wrote:3. Energy confinement on the WB-7 exceeds the classical predictions (wiffleball based on the electron gyro-radius) by a large factor.

Did I miss something, or is this your summary of not-yet-published data?

Art Carlson
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high-density quasi-neutral plasma from throat to wall

Postby Art Carlson » Mon Feb 09, 2009 9:30 am

Between the cusp and the wall we have need to drop a few tens of kV. What does the potential profile look like. I think most of us would expect it to be linear or at least a graceful arc. I have decided that can't be the case. You can apply my previous calculation almost unchanged, or you can just look at it this way: Since there is no perpendicular magnetic field, both species will react ballistically to any electric field. That is, one species will roll downhill, getting faster and less dense, the other will run uphill, getting slower and more dense. This would lead to a violation of quasi-neutrality and those MV fields that will spoil your day. If it were any other way, then confinement of a plasma for fusion would be easy.

No, I'm afraid both the electric potential and the plasma density in the flux tube of the cusp will have to be pretty much flat almost all the way out to the wall. You can have a magrid if you like, and it should (in principle) be able to keep the electrons from getting to the wall, but they will get most of the way there before bouncing off the Debye sheath.

This is my next claim: Not only does the cusp throat contain a high-density, quasi-neutral plasma, the entire cusp flux tube from the throat nearly to the wall does as well.

alexjrgreen
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Postby alexjrgreen » Mon Feb 09, 2009 10:23 am

rnebel wrote:3-D Particle-in-cell is extremely expensive. Resolution goes like (N)**.5 where N is the number of particles. You have multiple timescales and multiple spatial scales to resolve. This means supercomputers.

Rick,

Since you're already highly skilled in using supercomputers

http://www.cptc.wisc.edu/sovinec_research/talks/cray_wkshp2_03_sovinec.pdf

you should definitely ask if anyone out there has spare capacity.

The Institute for Plasma Research in Bhat, India has a Cray X1E. They might be willing to quote you a price...
Ars artis est celare artem.

Art Carlson
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Postby Art Carlson » Mon Feb 09, 2009 11:36 am

alexjrgreen wrote:you should definitely ask if anyone out there has spare capacity.

Usually getting computer time, even supercomputer time, is the easiest problem to solve. You also need a good code for the problem you're working on and somebody who understands both the code and the physics. He then needs the time to set up the problem properly and to understand what comes out. It's worth doing, but it will take a concerted effort.

alexjrgreen
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Postby alexjrgreen » Mon Feb 09, 2009 12:22 pm

Art Carlson wrote:It's worth doing, but it will take a concerted effort.

Definitely worth a PhD...
Ars artis est celare artem.

Skipjack
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Postby Skipjack » Mon Feb 09, 2009 1:53 pm

1. We don't have the spatial resolution of the density to see if the cusps are quasi-neutral on the WB-7
2. In one-D simulations the plasma edge (which corresponds to the cusp regions) is not quasi-neutral. Therefore, if the cusps are quasi-neutral it must be a multidimensional effect.
3. Energy confinement on the WB-7 exceeds the classical predictions (wiffleball based on the electron gyro-radius) by a large factor.


That are really good results Rick!
Makes me want more ;)
Thank you!

rnebel
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Postby rnebel » Mon Feb 09, 2009 5:14 pm

Art:

Real theories make quantitative predictions. How come you're scared to do that?

jmc
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Re: high-density quasi-neutral plasma from throat to wall

Postby jmc » Mon Feb 09, 2009 6:22 pm

Art Carlson wrote:Since there is no perpendicular magnetic field, both species will react ballistically to any electric field. That is, one species will roll downhill, getting faster and less dense, the other will run uphill, getting slower and more dense. This would lead to a violation of quasi-neutrality and those MV fields that will spoil your day. If it were any other way, then confinement of a plasma for fusion would be easy.


Not sure I agree with that, if electrons an ions are supplied independently of one another (i.e. cold electrons from the plate rushing in to neutralize the ions emerging from the cusps for example) then there is no need for the electrons emerging from the cusps to travel at the same speed as the ions to preserve quasineutrality.

jmc
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Postby jmc » Mon Feb 09, 2009 6:24 pm

rnebel wrote:Here's what we know and what we don't know:

1. We don't have the spatial resolution of the density to see if the cusps are quasi-neutral on the WB-7
2. In one-D simulations the plasma edge (which corresponds to the cusp regions) is not quasi-neutral. Therefore, if the cusps are quasi-neutral it must be a multidimensional effect.
3. Energy confinement on the WB-7 exceeds the classical predictions (wiffleball based on the electron gyro-radius) by a large factor.

Our conclusion is that both the wiffleball and the cusp recycle are working at a reasonable level.


This is quite exciting.

Just out of curiousity how were stored energy and confinement time meassured?

Art Carlson
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Re: high-density quasi-neutral plasma from throat to wall

Postby Art Carlson » Mon Feb 09, 2009 7:53 pm

jmc wrote:
Art Carlson wrote:Since there is no perpendicular magnetic field, both species will react ballistically to any electric field. That is, one species will roll downhill, getting faster and less dense, the other will run uphill, getting slower and more dense. This would lead to a violation of quasi-neutrality and those MV fields that will spoil your day. If it were any other way, then confinement of a plasma for fusion would be easy.

Not sure I agree with that, if electrons an ions are supplied independently of one another (i.e. cold electrons from the plate rushing in to neutralize the ions emerging from the cusps for example) then there is no need for the electrons emerging from the cusps to travel at the same speed as the ions to preserve quasineutrality.

My argument is quite general. It doesn't assume anything about the relative speed of the ions and electrons or even the direction of motion. It doesn't assume anything about the energy distributions either, except that trapped particles should be discussed separately, although they don't change the conclusion.

Art Carlson
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Postby Art Carlson » Mon Feb 09, 2009 8:18 pm

rnebel wrote:Art:

Real theories make quantitative predictions. How come you're scared to do that?

I realized later that I was being too timid. Maybe because taking the simple position that nobody else has a real theory is so unassailable.

Anyway, if a plasma can be formed that is near beta=1 in a substantial fraction of the coil volume, and the sheath thickness can be maintained small compared to the plasma radius, I predict:
  • The sheath will be everywhere at least an electron gyroradius thick.
  • The area of the cusp plasma will correspond to flux mapping from the sheath.
  • The main ball and the cusp plasma will both be quasineutral.
  • The density in the cusps will be within a moderate factor of the density in the main ball.
  • Ions and/or electrons will be lost through the cusps to the walls at a rate on the order of n*c_s*A.
  • Power will be lost through the cusps to the walls at a rate on the order of n*T*c_s*A.

If the electrons are remotely Maxwellian, which I do not predict but strongly suspect, then c_s = sqrt(T_e/m_i). Otherwise, T_e may be substitued with something close to the average energy, which will be closely realted to the voltages applied.


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