Return current

2.3 Return current

Figure 11:

Spectra of the three sources shown in Figure 10

as observed by RHESSI at peak time. Left and middle: Spectra of footpoints. A power-law was fitted in energy between the dotted lines. Right: Spectrum of the coronal source. A power-law and a thermal population was fit between the dashed lines (from Battaglia and Benz, 2007

It is unlikely that the fluxes of high-energy electrons and ions precipitating to the chromosphere balance out. Thus a beam current results. In a conducting plasma, a beam current cannot induce appreciable magnetic fields, and in static state the electric charge cannot separate along the field line. Thus a return current builds up to conserve charge and current neutrality (Spicer and Sudan, 1984 ; van den Oord, 1990 ; Benz, 2002 ). The current is most likely driven by a dominant electron flux in the precipitating particles. Thus the return current direction is downward in the loop. It is composed mostly of thermal electrons moving freely upward along field lines.

As the return current consist of thermal particles, collisions play a much bigger role than for the beam particles (see Equation 8 ). Collisions cause electric resistance. Ohm’s law then requires an electric field in downward direction, slowing down the beam electrons. The return current and its associated electric field are inevitable consequences of the standard flare model.

Some observational features have been interpreted as the effect of an upward pointing electric field. Figure 11 displays spectra of the two footpoints observed in hard X-rays. They do not show a trace of thermal emission in the RHESSI range of energies. Their non-thermal power-law indices are identically 2.7 $±$ 0.1. The power-law of the coronal non-thermal emission (Figure 11 , right) is 5.6 $±$ 0.1. The difference larger than 2 can be interpreted as an effect of the return current’s electric field flattening the spectra of the footpoints. The return current may also leave an observational signature in the shape of the non-thermal X-ray spectrum in the form of a kink (Zharkova et al., 1995 ).

Return currents solves what has been referred to as the flare particle number problem: as the number of precipitating electrons inferred from hard X-rays is very large, the coronal acceleration region would soon be evacuated if not replenished. If only electrons escape from the acceleration region, the return current keeps its density constant. If also ions escape, the acceleration region is evacuated. This may be avoided by a pressure driven flow of neutral plasma. None of the observational signatures, however, for both neutral flow and return current are fully established, and their existence still needs corroboration.