# Radiated power of electron in fusion device?

1. Mar 18, 2015

### 1a2

1. The problem statement, all variables and given/known data
Some time ago, an (in)famous paper by Trubnikov argued that magnetic fusion would be impossible because the power radiated by electrons would exceed any likely fusion power. He provided a very elaborate calculation, but the result was not greatly diffferent from the simple Larmor formula for the power radiated by an accelereated electron for v<<c. As an illustration, consider the large new fusion device ITER, under construction in France. Estimate the radiated power for a major radius of 6m, minor radius 2m, a field of 5T, density of 10^20/m^3 and 10KeV electron temperature. Is this result useful?

2. Relevant equations
P = \frac{q^2 a^2}{6\pi\epsilon_{0}c^3} (Larmor formula)

For Trubnikov's formula, I think it is equation (1) in the link below?
http://www-naweb.iaea.org/napc/phys...oceedings 1958/papers Vol31/Paper12_Vol31.pdf

3. The attempt at a solution
I'm not sure if the problem wants me to calculate the answer using Larmor's formula or Trubnikov's formula. Since the acceleration is not given, I don't think I can use Larmor's formula. I also don't see how the major and minor radius values matter for either formula. Do I just plug-in the other values into equation (1) in that link?

2. Mar 18, 2015

### phyzguy

I'm not familiar with Trubnikov's formula, but you can certainly use Larmor's formula. You know the electron temperature, so you should be able to calculate the velocity. Since there is a magnetic field, you should be able to calculate the acceleration as they spiral around the magnetic field. You need the major and minor radii, since you need to know the plasma volume in order to calculate the total number of electrons, the total radiated power, and the total expected fusion power.