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				Beta/magnetic pressure - the equations with real numbers in.
				Posted: Sun Feb 14, 2010 7:15 pm
				by 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?
			 
			
					
				
				Posted: Tue Feb 16, 2010 10:23 pm
				by 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...
			 
			
					
				
				Posted: Tue Feb 16, 2010 11:31 pm
				by 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...
			 
			
					
				
				Posted: Wed Feb 17, 2010 12:09 am
				by MSimon
				chrismb wrote: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.
 
			 
			
					
				Re: Beta/magnetic pressure - the equations with real numbers
				Posted: Wed Apr 21, 2010 12:33 am
				by D Tibbets
				chrismb wrote: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 
			 
			
					
				Re: Beta/magnetic pressure - the equations with real numbers
				Posted: Wed Apr 21, 2010 12:44 am
				by KitemanSA
				D Tibbets wrote: 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     
