Confinement of Thermalized plasmas: Why not E instead B?

In summary, the density limit for thermalized plasmas (as in Tokamaks) is likely much higher than the current magnetic field techniques.
  • #1
mheslep
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I'm pondering the density limits realizable in thermalized plasmas (as in Tokamaks) and it seems that confinement by a rotating electric field (something like a Paul trap) would theoretically allow much higher densities than the current magnetic field techniques. No doubt I'm missing something but I hope Ill be excused for thinking out loud. Here's the reasoning:

Magnetic Limit ----------------------------------------------------------
The confinement limit for a mag. field is the Brillouin density:
[tex]\eta=\frac{\epsilon_{0}B^2}{2Mion}[/tex] in ions per M^3
For deuterons and assuming the highest achievable(?) steady state field:
B=20 Tesla (ITER is 13T last I looked)
Mion=2*AMU in Kg

Gives:
[tex]\eta=10^{12}[/tex]
ions per cm^3

E Field Limit(?) -------------------------------------------------------
Here I'm considering the force to be overcome is the de-focusing effect of the space charge and neglecting and self confining mag. field. To keep it simple I'm using a cylindrical geometry of a non-neutral plasma. In that case the radial E field created by the space charge is found from Poisson:
[tex]\nabla E=\rho / \epsilon_{0}[/tex]
solving in gauss's law form:
[tex]Er = r\eta q_{e} / (2 \epsilon_{0})[/tex]

Then using the density found for the mag limit above at 1M:
Er @ d=1e12cm-3 = 8millivolt / cm
a trivial field. So a confining field producing 8mV/cm at the outside edge is needed to hold a cold(?) plasma. A rotating E-field would be required that produced a time averaged potential well with that Er, something like a Paul trap.
http://en.wikipedia.org/wiki/Paul_trap
I'm guessing that Er could be increased by ~10^8 before running into equipment limits.

Observations:
-The mass variable in the Brillouin limit makes mag. fields a lousy way to contain ions in particular; electrons
would get 2*3600x more density than deuterons, hence Bussard and the Polywell.
-E fields are orders of magnitude better at confinement. So why isn't electric
field confinement of plasma under more investigation?
 
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  • #2
Have I posted in an inappropriate section? Apologies if so, please advise and off I'll go.
 
  • #3
It's rather a specialised topic. Maybe High energy section ?
 
  • #4
mheslep said:
Have I posted in an inappropriate section? Apologies if so, please advise and off I'll go.

The most appropriate section would be classical physics, but here is not a bad place either. (I will remove the post in the high energy section, that has nothing to do with it).
 
  • #5
I would PM ZapperZ if I were you. He is an expert in things of this nature and I'd be very surprised if he did not know the answer to this.

If that does not work, go to the ITER website, find a experimenter's e-mail and write a succinct question. Most professionals will help you if you keep your e-mail short.
 
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  • #6
Chaos' lil bro Order said:
I would PM ZapperZ if I were you. He is an expert in things of this nature and I'd be very surprised if he did not know the answer to this.

If that does not work, go to the ITER website, find a experimenter's e-mail and write a succinct question. Most professionals will help you if you keep your e-mail short.

Yes, I have to say that I'm not knowledgeable enough to give a good answer. I know of electrostatic confinement, (which is used: look up "fusor" systems), but the problem with that - as I understand it - is that the plasma will always be in contact with an electrode which defines the field. I vaguely know of a theorem which forbids "electrostatic confinements", but I'm not very into all this...
 
  • #7
vanesch said:
I vaguely know of a theorem which forbids "electrostatic confinements", but I'm not very into all this...

Is that Earnshaw's theorem?

"A collection of point charges cannot be maintained in an equilibrium configuration solely by the electrostatic interaction of the charges."

scienceworld.wolfram.com/physics/EarnshawsTheorem.html
 
  • #8
siddharth said:
Is that Earnshaw's theorem?

"A collection of point charges cannot be maintained in an equilibrium configuration solely by the electrostatic interaction of the charges."


Yes, that's what I had in mind. But I don't know up to what point this is a problem for plasma confinement.
 
  • #9
Electrostatic repulsion would require a plasma to be surrounded by a surface of the same charge - and the plasma itself would require some net - (surplus of electrons) or + (deficiency of electrons). This would be difficult if not impossible (see siddharth's post).

I think the charge density would be prohibitive, and would introduce the problem of repulsion in the plasma (and potentially large local instabilities), which would be in addition to its thermal pressure (nkT). Then there is the matter of discharge.
 
  • #10
-Electrostatics: Yes 3D electrostatic confinement from an external field is impossible (Earnshaw, or otherwise trying to get local minimums from Laplace's equation). As per my OP I am suggesting a rotating field, ala a Paul trap, for which confinement is clearly possible. The question then: what's the density limit?

-Charge Density prohibitive. Yes I'm proposing a non-neutral, nuclei only plasma. But per the numbers I showed in the OP, its not prohibitive. The field from a plasma space charge at ITER densities is small, millivolts/cm. (At least from my derivation, am hoping you guys will any find holes in that). And so the confinement field is small.
 
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  • #11
mheslep said:
-Charge Density prohibitive. Yes I'm proposing a non-neutral, nuclei only plasma. But per the numbers I showed in the OP, its non prohibitive. The field from a plasma space charge at ITER densities is small, millivolts/cm. (At least from my derivation, am hoping you guys will any find holes in that). And so the confinement field is small.

Looking at your numbers, there's something strange. A charge density of 10^12 elementary charges per cm^3 gives us 10^18 elementary charges per m^3 which means about 0.1 Coulomb per m^3.
Now, a charge density of 0.1 Coulomb per m^3 gives me:
div E = 10^10 V/m^2 if I fill in Gauss' law.

I don't quickly see emerging your mV/cm field...

Am I wrong somewhere ?
 
  • #12
Arg! No you are not wrong. I bungled the cm^3 to M^3 conversion (wrong way) Apologies all 'round for the trouble. Ill double check next time before posting.

Then, with the density per _meter_ ^3 of 10^18, using even only a plasma volume of 1x10-6 _meter_ ^3 the field at the edge w/ r~0.01 _meter_ is still Er=90 MegaVolts/Meter. That takes us beyond in your garage fusion plasma confinement.
 

1. What is the difference between E and B in thermalized plasmas?

The E and B fields refer to the electric and magnetic fields, respectively, in a plasma. In thermalized plasmas, both E and B fields are present, but they have different properties. The E field is responsible for the acceleration and heating of particles, while the B field helps to confine and stabilize the plasma.

2. Why is E field not used for confinement in thermalized plasmas?

The E field is not used for confinement in thermalized plasmas because it tends to cause instabilities and disrupt the plasma. This is due to the fact that the E field can easily interact with and accelerate the charged particles in the plasma, causing them to collide and lose their energy. This results in an unstable and unconfined plasma.

3. What are the advantages of using B field for confinement in thermalized plasmas?

The B field is preferred for confinement in thermalized plasmas because it does not interact directly with the charged particles, making it more stable. Additionally, the B field can be manipulated and controlled to contain the plasma in a specific region, allowing for better confinement and control of the plasma.

4. Can E field be used in combination with B field for confinement in thermalized plasmas?

Yes, in some cases, both E and B fields can be used together for confinement in thermalized plasmas. This is known as magnetic confinement, where the B field is used to contain the plasma while the E field is used to heat and accelerate the particles. However, careful control and manipulation of both fields is necessary to avoid instabilities and maintain plasma stability.

5. Are there any other methods for confining thermalized plasmas besides E and B fields?

Yes, there are other methods for confining thermalized plasmas, such as inertial confinement and laser confinement. In inertial confinement, high-intensity lasers or particle beams are used to compress and heat the plasma, resulting in fusion reactions. In laser confinement, the plasma is confined and heated using laser beams. However, these methods are still in the early stages of development and have their own challenges and limitations.

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