I Back of the envelope estimate, energy flow in a box of plasma

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The discussion centers on estimating electric polarization in a spherical region of the sun where energy is transported by radiation. It considers the temperature, gravitational acceleration, and density of matter at a specific radius, R. The Klein-Nishina formula suggests that light's interaction with charged particles results in a slight outward force, particularly affecting electrons more than protons. Calculations show that radiation pressure at the sun's surface is significant, but the resulting electric field needed to balance this pressure is extremely small, potentially less than a nanovolt per meter. The conclusion indicates that while electric polarization exists, its magnitude is minimal.
Spinnor
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Say we look at a spherical region of the sun where energy is mainly transported by radiation. Say this happens between some particular radius R and R + dr. Let the temperature at R be giving by T(r). At this particular radius let the gravitational acceleration be a reasonably well know function of r, g_sun(r). Assume the temperatures are so high that nearly all matter in this region is ionized. Assume the density of matter at and near R is given by another good function of r, rho_sun(r).

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Given the information above show there is, or is not, also a function of all the factors above (might be missing some) that gives the electric polarization in the sun at R given by P(T(R), g_sun(R), rho_sun(R)), however small its value might be at R.

How should I break down the above problem to come up with a back of the envelope answer. The Klein-Nishina formula tells us that even if small, the average outward radial movement of light in the interior of the sun should give a bit of an outward "kick" to charged matter? Because the interaction cross-section of light and matter goes as 1/m^2, the electrons get "kicked" by light more then protons? This is where I get stuck analyzing this problem.

Thanks for any help suggestions moving this problem forward.
 
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At the surface of the sun the flux of radiation is ## L / 4\pi R^2 = 6.28 × 10^{7} {\rm W m^{-2}} ##. Dividing by the speed of light I get a radiation pressure of ## 0.21 {\rm N m^{-2}} ##. Multiply that by the Thomson(!) cross section to get ## 1.4 × 10^{-29} \rm N ## for the force on an electron. Or ## 8.7 × 10^{-11} \rm eV/m ##. In the interior of the sun this value would be even smaller. It seems you need only an extremely small electric field of less than a nanovolt per meter to balance the radiation pressure.

Spinnor said:
the electric polarization in the sun [...], however small its value might be
Is this the quantity you had in mind? It is small indeed, unless I have miscalculated!
 
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