Dynamics of a cloud of fast electrons travelling through the plasma

Numerical analysis of quasi-linear relaxation has been made for four models of electron beam with a finite length travelling through the plasma. In Model 4, a model atmosphere of the corona is adopted and also an increase in the cross-section of the electron beam is taken into account. The electron velocity distribution generally becomes a quasi-plateau form in limited velocity and time ranges. If, however, collisional decay of the fast electrons is too strong and the initial beam density is not high enough, the plateau does not appear. Collisional damping of plasma waves cannot be neglected, since the growth rate of the waves is strongly suppressed by the appearance of the quasi-plateau.An approximate formula for the velocity distribution of the solar electrons passing through the corona has been derived analytically taking into account not only the interaction with plasma waves, but also the collisional damping of the plasma waves and collisions with thermal particles. By the use of this formula, we can easily compute the time profile of the plasma waves caused by these solar electrons at any given place in the interplanetary space. The validity of this semi-analytical approach is checked by the numerical analysis of Model 4, showing a satisfactory fit between the numerical and semi-analytical results.The direct application of this method to the problems of type III radio bursts is left to a later paper.