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

In summary, the conversation discusses the transport of energy by radiation in a spherical region of the sun, as well as the temperature, gravitational acceleration, and density of matter in this region. It also mentions the electric polarization in the sun, which is described by the function P(T(R), g_sun(R), rho_sun(R)), and its small value at radius R. The problem at hand involves finding a way to calculate this polarization and the average outward radial movement of light in the sun.
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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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FAQ: Back of the envelope estimate, energy flow in a box of plasma

1. What is a "back of the envelope estimate" for energy flow in a box of plasma?

A back of the envelope estimate is a rough calculation or estimation done quickly and informally, usually on the back of an envelope or scrap piece of paper. In the context of energy flow in a box of plasma, it refers to a quick and approximate calculation of the amount of energy flowing through the box at any given time.

2. How is energy flow in a box of plasma measured?

Energy flow in a box of plasma can be measured through various methods, such as using probes to measure the electric and magnetic fields, or using spectroscopy to measure the radiation emitted by the plasma.

3. What factors affect the energy flow in a box of plasma?

The energy flow in a box of plasma is affected by several factors, including the temperature and density of the plasma, the strength of the magnetic field, and the presence of any external forces or sources of energy.

4. How does energy flow in a box of plasma relate to plasma confinement and stability?

The energy flow in a box of plasma is closely related to plasma confinement and stability. If the energy flow is too high, it can cause instabilities and disrupt the confinement of the plasma. On the other hand, if the energy flow is too low, it may not be enough to sustain the plasma and keep it stable.

5. Can back of the envelope estimates for energy flow in a box of plasma be accurate?

While back of the envelope estimates can provide a rough idea of the energy flow in a box of plasma, they are not always accurate. These estimates do not take into account all the complex variables and interactions within the plasma, so they should be used as a quick approximation rather than a precise measurement.

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