trying to understand Solar Flares

[Widdekind]

By dimensional analysis, the (total) energy, in the magnetic field, generated by a mass of plasma, of characteristic size-scale L, carrying a characteristic current I, is

[math]B \approx \frac{\mu_0 I}{L}[/math]

[math]E \approx \frac{B^2}{\mu_0} L^3 \approx \mu_0 I^2 L[/math]

Now, when two opposing magnetic fields are juxtaposed, the opposing parts vanish (e.g. x-direction), and the parallel parts remain (e.g. y-direction). So, the total field energy, after reconnection, is reduced by about half [math]\left( <B>^2 + <B>^2 \; \rightarrow \; <B>^2 \right)[/math].

So, in order-of-magnitude approximation,

[math]B \approx \sqrt{\frac{\mu_0 E}{L^3}}[/math]

[math]I \approx \sqrt{\frac{E}{\mu_0 L}}[/math]

The brightest Solar Flares release [math]\approx 6 \times 10^{25} J[/math] of energy, and span [math]\approx 10^5 km[/math]. So,

[math]B \approx 1 Gauss[/math]

[math]I \approx 1 T Amp[/math]

The ratio of magnetic-field energy density, to particle thermal energy density, is

[math]\frac{\frac{B^2}{\mu_0}}{n K_B T} \approx 10^{-9.5}[/math]

if the density (in the photospheric "feet" of the prominence) is nearly 1024 per m3, and the Flare temperature is millions of K. So, nearly none of the thermal energy is organized, into coherent currents. (Out in the corona, above the sun's surface, the density is a trillion times lower, so magnetic energy densities may dominate, perhaps explaining why most corona plasma remains confined near the sun, most of the time.)

If open field lines allow plasma particles to stream away from the sun's surface, out to space; then why wouldn't open field lines allow charged particles, to well up from the sun's deep interior, to its surface? The "feet" of solar prominences are millions of K, comparable to the sun's deep interior. Perhaps when field lines open out, through the sun's surface, super-hot plasma from the deep interior can stream along those lines, straight up to the surface, and then out along the field lines looping through the prominence? And then, if those field lines open out to space, then the plasma can stream away to space, too? Inexpertly, the "feet" of solar prominences look like plasma from the sun's deep interior, welling up to the sun's surface:

 

 

Speculating, there seems to be a "catch-22" with trying to employ EM fields, to contain fusing plasma, for hypothetical controlled fusion reactors. For, stars require the immense gravity, of enormous amounts of matter, to gravitationally contain their runaway fusing plasma reactions. (Evidently, stars' magnetic fields also do contain plasma particles, except where the field lines occasionally reconnect, and open up "coronal holes" in the field, releasing puffs of plasma particles.) (Stars contain plasma, with other plasma, "plasma confined plasma".) Now, EM forces are "40 orders of magnitude stronger than gravity". But, to exploit EM fields, requires first establishing them. And, to establish EM fields, requires fighting against those very EM forces. So, you'd have to go against EM forces first, to then exploit those EM forces to contain fusing plasma. Unless you could establish an EM field once-and-for-all, and then gradually recoup start-up costs, then perhaps 'tis impossible to break even? Conversely, pushing space gas into a pile, and letting gravity do the rest, generates a star, which releases enormous amounts of energy, with nearly no start-up costs. So, perhaps 'tis practically impossible, to be more energy efficient, than a natural stellar fusion reactor (possibly employing some "stellar engineering" techniques, to steward the star; but probably not even). If so, then even hypothetical advanced Aliens would still exploit stars, building "lots & lots of solar panels". And, inter-stellar space-travel might be impossible, without fusion power plants -- except on "battery power", i.e. energy, harvested from stars, could be converted into anti-matter, and then used as fuel on ships. But, if it is impossible to contain plasma at fusion temperatures; then would it not be (even more) impossible to contain plasma heated by antimatter reactions? What other mechanism, besides plasma, could "catch" the photons, from pair-annihilation reactions? Practically, photons do not react with EM fields, only other charged particles (which one wouldn't want to be parts of their own space-craft). So, perhaps the only practical form of inter-stellar propulsion would be anti-matter bombs, in "anti-matter pulse propulsion" pusher-plate space-craft? If only natural stars can, practically & economically, generate fusion energy; and if massive stars cannot be incorporated into maneuverable space-craft; then only energy converted from stars, into transportable "batteries" or "bombs", could be employed in space-craft.

 

In swift summary, perhaps improving upon natural stars, as energy sources, is impractical (if not impossible).