Radiated power of electron in fusion device?

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SUMMARY

The discussion centers on the radiated power of electrons in fusion devices, specifically referencing Trubnikov's argument against the feasibility of magnetic fusion due to excessive radiated power. The Larmor formula is highlighted for calculating the power radiated by accelerated electrons, with the discussion focusing on the ITER fusion device's parameters: a major radius of 6m, minor radius of 2m, a magnetic field of 5T, an electron density of 1020/m3, and an electron temperature of 10KeV. Participants emphasize the need to calculate the acceleration of electrons in a magnetic field to derive total radiated power and fusion power.

PREREQUISITES
  • Understanding of the Larmor formula for radiated power
  • Familiarity with Trubnikov's formula and its application
  • Knowledge of plasma physics, specifically magnetic confinement
  • Basic principles of thermodynamics related to electron temperature
NEXT STEPS
  • Calculate radiated power using the Larmor formula for ITER parameters
  • Study Trubnikov's formula in detail for its implications on fusion power
  • Explore the relationship between plasma volume and electron density in fusion devices
  • Investigate the effects of magnetic fields on electron acceleration in plasma
USEFUL FOR

Physicists, engineers, and researchers involved in fusion energy development, particularly those focusing on magnetic confinement and plasma behavior in devices like ITER.

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Homework Statement


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?

Homework 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

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?
 
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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.
 

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