The Alfven-Carlquist double-layer theory of solar flares

The Vlasov equations for ions and electrons are used to develop a theory of a double layer in which there are both free and trapped electrons and ions. The equations which replace the Langmuir condition and the Bohm conditions are found, and by numerically solving the resultant differential equation the authors find for particular choices of distribution functions the potential distribution in the layer. The applicability of this theory to solar flares is discussed, and it is shown that conditions in solar flares may be such that double layers can exist for which the free particles have a power-law energy distribution. These particles will be accelerated in a double layer and may in this way account for the production of high-energy particles during the impulsive phase of solar flares. (Auth.)