Expert: Philip A. Stahl - 3/6/2009

Question
Can the Hall current exist in solar conditions? Can it trigger solar flare? If so, how? Thanks.

Answer
Hello,

Yes the Hall current has been proposed to account for some solar flares. The first mention in connection to incepting flares was probably by Sen and White ('A Physical Mechanism for the Production of Solar Flares') in Solar Physics, Vo. 23, p. 146, 1972.


If you think of a sunspot as a circular area, then Sen & White envisaged the vertical magnetic field B coming out vertically on either side of the umbra of the spot, and an electric charge separation field E( directed inward to the center of the umbra) while a velocity V is directed outwards. In other words, E and V are anti-parallel.

As a result of the Hall effect, where J(H) = V x B(z), one gets a Hall current (actually current density) which acts in a circuital direction (clockwise) around the periphery of the umbra. Thus, in their model, the Hall current forms a complete circuit. (they suggest it could be responsible for facular brightening, but this remains open)

At the end of their paper (Sec. 5) Sen and White try to show how the Hall current plays a major role in triggering a flare. Their proposal was that a "two stream instability" (see the previous questions and answers on this ) occurs when the electron drift velocity associated with J(H) exceeds the ion thermal velocity.

Basically, in terms of the actual physical principles this isn't terribly mysterious.

For example, we can also write the Hall current density in terms of the Hall conductivity k(H):

J(H) =  k(H)E

where E is the electric field.

If one looks at the actual (complicated) function expressing k(H) one will see not only the appearance of the electron and ion plasma frequencies, but also the electron and ion COLLISION frequencies. So the higher either or both of these, the higher k(H) will be and the higher J(H) will be. (The electron and ion number densities also factor in)

Thus, any heating which also increases collisions, will increase J(H) and hence the likelihood of a flare.

If a "two-hump" electron distribution function f(v) develops, where one has the condition df(v)/dv > 0 (exactly opposite of what we refer to as "Landau damping"), then we will get a two-stream or beam instability and the way is paved for k(H) to be enhanced and the triggering of a flare via much higher J(H).

Hope this helps!