Electron acceleration by stochastic wave packets

An analytical theory for the time evolution of the distribution function, energy and current of an assembly of electrons submitted to a quasi-sinusoidal stochastic field is given. To the first order, energy and current are obtained using Sturrock's stochastic acceleration theory. The calculation of the transition probability enables us to get the distortion of the distribution function, and to recover the preceding first order results. To the second order, collisions are taken into account, in the framework of the two dimensional theory. The turn-on time for the current is evaluated. The obtained results are compared with the numerical results of Karney and Fisch