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I'm learning about plasma physics and I've seen a number of papers which state something like 'soft x-ray pictures reveal the magnetic field lines', and it is common to use a soft x-ray image of the sun to demonstrate the magnetic field lines of a flare. Here's an example: https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.82.603

In the earth's magnetosphere it is chalked up to charge exchange, eg: https://arxiv.org/abs/1107.0680

However, in the sun is charge exchange still a good explanation? Isn't everything ionized already?

I can't figure out why this bandwidth in particular reveals B field lines, and I haven't been able to find a citation which explains this assumption. Either it's something quite obvious or it's an empirical observation. I found this paper which delineates the empirical observation: https://iopscience.iop.org/article/10.1086/378944/, but I haven't been able to find a physical explanation for this emission on the sun.

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The X-rays come from charged particles (ions and electrons), both continuum (bremsstrahlung) and discrete transitions contribute (i.e. continuum radiation from free-free and free-bound processes, and emission lines that arise from electronic reconfigurations in the inner shells of incompletely ionised metal ions).

The charged particles are constrained to move in helical paths along the magnetic field lines. The gyroradius is given by $$ r_{\rm gyro} = \frac{mv_{\perp}}{|q| B}$$ and is largest for electrons.

For $kT \sim 10^{6}$ K (soft X-ray emitting plasma) then $v_{\perp} \sim \sqrt{kT/m} = 4 \times 10^{6}$ m/s and if B-fields are of order $10^{-7}$ T (reasonable for the solar corona), then $r_{\rm gyro} \sim 200$ m. This small gyroradius is why the charged particles, and hence the X-ray emission, trace the B-field lines - they spiral around the field lines on radii that are much too small to be resolvable with X-ray telescopes.

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    $\begingroup$ It may help to clarify that the effective spatial resolution of the best space-based solar telescopes are still upwards of ~100 km and that the coronal arcs can be 10s of thousands of km above the photosphere for contrast. If the gyroradii were comparable to the arc size or length, the situation would be different and the images effectively blurred (not arguing this is physically possible, just trying to think about why the gyroradii matters from a student point of view... hopefully I still haven't lost that ability...). $\endgroup$ – honeste_vivere Mar 25 at 20:24
  • $\begingroup$ Thank you! For discrete transitions do you mean that ions become excited through collisions? I had always assumed the positive ions would be fully ionized in the solar plasma, but if the discrete transitions were form ion relaxation then my assumption that all species are fully ionized is clearly wrong. If that is not what you refer to, could you please elaborate on the discrete transitions? $\endgroup$ – SabrinaChoice Mar 26 at 2:54
  • $\begingroup$ I think charge recombination can't happen between the ions and the electrons, because the plasma is so hot that seems to preclude a bound state for the electrons in the ion's potential. $\endgroup$ – SabrinaChoice Mar 26 at 3:15
  • $\begingroup$ @sabrinachoice Obviously the hydrogen is, but the optically thin coronal plasma exhibits a host of emission lines in electronic rearrangements of highly (but not completely) ionised ions. The Wikipedia page is quite accurate as a summary. en.m.wikipedia.org/wiki/Coronal_radiative_losses $\endgroup$ – Rob Jeffries Mar 26 at 6:57
  • $\begingroup$ @RobJeffries thank you! In my googling I hadn't run across that page, I think I was missing several key words. $\endgroup$ – SabrinaChoice Mar 27 at 22:43

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