Beta/magnetic pressure - the equations with real numbers in.

[chrismb]

Can someone with more taught plasma knowledge than me just fix up my understanding of the magnitude of magnetic pressure in the devices we often discuss?:

magnetic pressure is = B^2/2u[o]

and 'gas pressure' is = n.k.T

So if we have a tokamak or Polywell with, say, 5T and it has a volume with n=1e19 (well, this is ~how much a tok runs with, so I understand) then we get a magnetic pressure of 5^2/2.(1.26e-6) = 10MPa, which is 100atm!?

Is that right? Seems an awfully high figure to me in a vacuum chamber?!

And if we put it into the gass pressure eqn with n=1e19, then we get a T of 70GK (6.5MeV).

So shouldn't a 5T field be enough to contain a 6.5MeV plasma? If those magnitudes are correct for magnetic pressure I don't see how a measley 10keV plasma is remotely poorly confined! [What] am I missing [/something] here?

[93143]

I thought big tokamaks ran about 1e20.

For JET (3.45 T toroidal) I get 4.7 MPa. At beta=0.05, the plasma pressure would be about 237 kPa.

Using 10 keV (116045050 K), this yields a density of... 1.5e20.

Not too bad...

[chrismb]

If that's a reasonable beta then I guess it's in the ball park. (The tok shot plots usually show n as units of 1e19, rather than over 1e20, though)

I thought beta was higher... hmmm...

[MSimon]

If that's a reasonable beta then I guess it's in the ball park. (The tok shot plots usually show n as units of 1e19, rather than over 1e20, though)

I thought beta was higher... hmmm...

I have seen betas as high as .1 quoted for toks. I'm not sure if that was actuals or some time real soon now.

[D Tibbets]

Can someone with more taught plasma knowledge than me just fix up my understanding of the magnitude of magnetic pressure in the devices we often discuss?:

magnetic pressure is = B^2/2u[o]

and 'gas pressure' is = n.k.T

So if we have a tokamak or Polywell with, say, 5T and it has a volume with n=1e19 (well, this is ~how much a tok runs with, so I understand) then we get a magnetic pressure of 5^2/2.(1.26e-6) = 10MPa, which is 100atm!?

Is that right? Seems an awfully high figure to me in a vacuum chamber?!

And if we put it into the gass pressure eqn with n=1e19, then we get a T of 70GK (6.5MeV).

So shouldn't a 5T field be enough to contain a 6.5MeV plasma? If those magnitudes are correct for magnetic pressure I don't see how a measley 10keV plasma is remotely poorly confined! [What] am I missing [/something] here?

Noted the high quoted pressure. It occurs to me that comparing pressure with density is missleading. The density of air (one atmosphere ) is standardized at a set temperature. One mole of air= 22.4 liters at STP conditions. A mole of gas at a Maxwellian temperature of ~ 5000 eV (550,000,000 degrees C) would exert a proportionatly higher pressure (I'm too lazy to look it up and calculate it), but I suspect the pressure would be huge. So it may not be surprizing that a very hot gas, despite a low density, would generate a high pressure at high temperatures. If a strong perminate magnet of perhaps a few hundred Gauss can suport weights of many pounds, the lifting (or pushing) power of a magnet of several Tesla could resist a considerable gas pressure (pounds/ sq. inch).

Dan Tibbets

[KitemanSA]

Noted the high quoted pressure. It occurs to me that comparing pressure with density is missleading. The density of air (one atmosphere ) is standardized at a set temperature. One mole of air= 22.4 liters at STP conditions. A mole of gas at a Maxwellian temperature of ~ 5000 eV (550,000,000 degrees C) would exert a proportionatly higher pressure (I'm too lazy to look it up and calculate it), but I suspect the pressure would be huge. So it may not be surprizing that a very hot gas, despite a low density, would generate a high pressure at high temperatures. If a strong perminate magnet of perhaps a few hundred Gauss can suport weights of many pounds, the lifting (or pushing) power of a magnet of several Tesla could resist a considerable gas pressure (pounds/ sq. inch).

Assuming ideal gas law, which DOESN'T apply, but let us look at it anyway:

Pv=nRT (or some such varient). Given everthing the same except the T,
P = X*T where X represents evcerything else
T@5000eV ~2,000,000 times T@STP ((500,000,000/250)

Thus, P ~2E6 bar. As you say... HUGE, but not real