Problem with plasma temperature calculus

It may be difficult to separate "theory" from "application," but let''s see if this helps facilitate the discussion.
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Javier Lopez
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Problem with plasma temperature calculus

Post by Javier Lopez »

I am on trouble when obtaining plasma temperature from plasma output energy (measured using Photodiode sensors and Pulsotron-2)

I calculated using Stefan Boltzmann:

W=A*s*T^4

s=Stefan Boltzmann constant 5.67e-8 W/m2/K4
A=plasma area (m2)
T= temperature in ºK
W=watts
http://hyperphysics.phy-astr.gsu.edu/hb ... tefan.html
http://es.wikipedia.org/wiki/Ley_de_Stefan-Boltzmann

Using ITER data:
A=490m2
W=50MW
I obtained 1150ºK (good for ITER Steel) that is only 0.1 eV, very far from promised 20keV
http://www.iter.org/newsline/122/182

Using same formula for Sun: 67MW/m2 I obtain 5770ºK close to real 5800ºK
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Chris Bradley
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Re: Problem with plasma temperature calculus

Post by Chris Bradley »

ITER is actually aiming/designed for 500MW, not 50MW.

This is not the power pouring into the chamber walls. Quite the opposite. The whole idea is that the energy in the 10's of keV plasma is being held *without* the heat being dissipated to the walls. The whole objective of the tokamak is that the power being lost is low whilst the energy in the plasma is high. The ratio, contained-energy/lost-power, is called the 'energy confinement time' and this needs to be as long as possible. (This is the 'tau' in the Lawson Criterion.)

In tokamak, energy confinement is done by 'magnetic confinement'. The magnetic fields do not strictly 'confine' the plasma, but the plasma conforms to the magnetic surfaces of the field and meet the chamber in only a small limited area, either a 'limiter' or a 'divertor'. (The outer 'edge' of the plasma is called the 'scrape off layer' (SOL) because the plasma in that edge flow down the magnetic fields into the divertor plates where they strike it, cool and are evacuated.)

Therefore, the things you need to look at for the whole energy balance is; energy in the plasma, confinement time, divertor power (many MW/m²), and finally the 'rated fusion power' which for ITER is designed to be 500MW of fusion output consisting of 400MW of neutrons (that will end up in the thermal jacket around the chamber) and 100MW of alpha particles (that stay in the plasma and heat it, making up for the power losses from it).

The whole idea is that at some operating size/plasma energy, the alpha particles will be able to drive enough power into the plasma to make up for all the losses (without needing external power inputs), whilst the neutron power is turned into useful energy.

I do not doubt that the ITER design is capable of generating 400MW of neutrons. But this will still be in the form of 'a pulse' (albeit 400s long), so it will not be possible to prove indefinite plasma stability needed for the design to make commercial sense. Nor will it be able to demonstrate reuse of tritium bred in the jacket, nor will any power acutally be captured from the thermal jacket to deomonstrate 'useful energy'. That would have to come in yet another later, and larger, tokamak.
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Carl Willis
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Re: Problem with plasma temperature calculus

Post by Carl Willis »

Putting numbers into a formula is easy. The "hard" part, or at least the part that requires thought and some physical understanding, is ensuring that the underlying assumptions are any good and that the quantities being used are accurate and precise enough to motivate conclusions.

Is it a good assumption that the gas discharge in a tokamak is a black body? No. (For the Sun, on the other hand, it's reasonable).

Is it a good assumption that the surface area of the heated volume is well-defined and is 490 m^2? I have no idea where you got that number...perhaps you could explain its physical basis. In any case I seriously doubt it's applicable to this kind of calculation.

-Carl
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Javier Lopez
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Re: Problem with plasma temperature calculus

Post by Javier Lopez »

I obtained from http://www-fusion-magnetique.cea.fr/gb/iter/iter02.htm: 2pi*2.0m * 2pi*6.21m = 490 m2.
From Chris data we would use divertor's plasma temperature and divertor's W/m2.
Accordingly http://www-fusion-magnetique.cea.fr/etn ... %20f4e.pdf Divertor works at 3000ºC and power must be 150MW (plus 15MW from neutrons) so it has to be a reasonable effective area of about 30m2.
Plasma pressure is 20 atmospheres so convection must be powerful. Can 14 teslas separate 20keV (232 Mega ºK) plasma temperature from 3000ºC divertors walls?
Accordingly Pulsotron test data when plasma is entering in the eV range it radiates all its power at the same rate it receives. In only a fews microseconds. Can the 14 teslas magnetic field shields light radiation?

I think I have so big formula error or Stefan Boltzmann law does not work or it will be impossible to heat plasma beyond 100 eV with Tokamaks
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Carl Willis
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Re: Problem with plasma temperature calculus

Post by Carl Willis »

The error(s) are not in your Stefan's Law formula, but in your use of it.

This formula relates the thermal radiation power from a black body to the temperature of the black body. It does not relate the total power output of a fusion reactor to the temperature of a plasma inside, which apparently is your interest. Again: Is such a plasma--basically a low-density gas--black to thermal radiation? No, that's probably a very poor assumption. Does a lot of power leave a fusion reactor through forms other than thermal radiation? Yes, there may be a lot of mass transport of heat for example: convection of background gas, emission of neutrons and other particles from the volume of interest, etc.

Your "Pulsotron-2" project is going to continue to get short shrift on this board as long as you avoid explaining its construction and operation in an actionable sense. When you last talked about it in 2009 and posted photos of stuff exploding, I asked for details. Other people asked for details. You promised details. And we never heard from you again. Jog your memory:

viewtopic.php?f=15&t=7218#p49090

I'm of the mind that this is where you need to pick up the ball, rather than trying to seek another round of free Physics 101 tutoring. Let's make the rest of this thread about the details of your project. If that can't happen, we may just have to close the thread and move on. Thank you...

-Carl
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Javier Lopez
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Re: Problem with plasma temperature calculus

Post by Javier Lopez »

I am very sorry because I can not give the details because signed contracts

About low density plasma is not inside ITER that will work at 7 atmospheres pressure
http://www.psfc.mit.edu/library1/catalo ... cowley.pdf

What is ITER plasma emissivity, 3e-19?

I measured about 0.3 in high temperature plasmas at high pressures
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Carl Willis
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Re: Problem with plasma temperature calculus

Post by Carl Willis »

>I am very sorry because I can not give the details because signed contracts

Then according to forum guidelines you simply can't solicit help with it or continue to discuss it here. We're "open source" as our name says.

-Carl
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