等离子体物理Chapter 5.pdfVIP

Chapter 5 Distribution function of charged particles in electric field 5.1 Method for solving kinetic equation The directed velocity is usually much lower than the random because of the small losses of electron energy in collision with heavy particles. Therefore the anisotropy of the electron velocity distribution remains low. Owing to this, when solving the kinetic equation one can use an expansion of the distribution function in parameters characterizing its anisotropy. The rapid convergence of the series permits us to restrict ourselves to a small number of terms and find rather easily both the anisotropy and the symmetric part of the distribution function. Let us consider in more detail the case where a homogeneous electric field E is the source of disequilibrium. The electron velocity distribution function may depend only on the velocity υ and the angle Θ between the directions of velocity υ and field E . Therefore it is natural to represent this dependence as an expansion in orthogonal Legendre polynomials P (cos Θ) n ∞ f (υ) ∑f n (υ)Pn (cos Θ) (5-1) n 0 The first two terms of the sum in (5-1) contain the polynomials P 1 0 and P cos Θ. With small anisotropy we can restrict ourselves to 1 these terms in solving many problems. Then we have 1 υ z (5-2) f (υ) f 0 (υ) =+cosΘf 1 (υ) f 0 (υ) =+ f 1(υ) υ where we have assumed that the OZ