Using Eq. 2.4.21 we derive from Eq. 2.4.20 the equation for the function

^+ Lo^F(r,p, t) = La0dt exp(- Lo(t -1'))/(p, t;ri,Pi, t)L/F(r,p, t) .(2.4.22)

We have returned here to the previous notations |x}^|r,p} and have omitted the index o in Fo . On the right hand side of Eq. 2.4.22 according to Eq. 2.4.20 and Eq. 2.4.21 t1 = t was set and one should keep in mind that after the action of the operator exp(- Lo (t -1')) it is necessary to set r1 = r and p1 = p .

For further analysis of Eq. 2.4.22 one should concretize a dependence of the correlation tensor on the coordinate axes and time. If a magnetic field is completely frozen in plasma the most general form of the correlation tensor Da/ compatible with the experimental data and satisfying Maxwell's equations will be as follows

A stochastic magnetic field which is described by the tensor Eq. 2.4.23 corresponds to the case in which turbulence presents an aggregate of regions with the scales of the order of the correlation radius of the stochastic field. Inside every one of these regions the turbulence is uniform; however, the total intensity of turbulent pulsations of magnetic field varies slowly at a transition from one to another of turbulent regions. Corresponding to this the first argument in the right hand side of Eq. 2.4.23 describes a smooth variation of the intensity of turbulent pulsations at a transition from one turbulent region to another and reflects the fact that the pulsation intensity varies considerably only with the variation of p by the value of the order of the correlation radius lc of a stochastic field. The second argument describes a local structure of turbulence which is a universal parameter inside a region with the characteristic scales of the order of lc. Notation of the second argument in the form of r - ucT implies that one can neglect the proper motion of magnetic field inhomogeneities and consider that all space time variations of a stochastic magnetic field are connected with a transfer of stochastic inhomogeneities with the velocity uc . If turbulence is not only uniform but also statistically isotropic, the correlation tensor of the second rank of a stochastic magnetic field will have the following form (Monin and Yaglom, M1965, M1967; Dolginov and Toptygin, 1968):

Da (p, r ) = BaA(p,r ) = i^2 (p)){^(r/lc )Ol -^(r/lc , (2.4.24)


r o and ^(r/lc) is a scalar function, which is assumed to be known from observation; ^Hj2 (p) is the mean square of a stochastic magnetic field.

Including Eq. 2.4.23 and setting t -1' = t we shall write Eq. 2.4.22 in the form d j 1 — + L0 J F (r, p, t) = LaJ dt'exp(- ZGr)

xBaA(^^'Pi;ri - r - "qTPjLAF(r,p,t- t). (2.4.26)

The right hand side of Eq. 2.4.26 differs from zero in the time intervals of the order of the correlation periods of a stochastic field. Assuming that the correlation period is small as compared with the characteristic time of variation of the average distribution function F we can write

+ Lo jF(r,p,t) = La JdTexp(-Lo^Bd^1 ,Pi;ri - r-u0T,pjLXF(r,p,t). (2.4.27)

If the momentum of a particle in the regular magnetic field H0 varies weakly at distances of the order of the correlation radius of a stochastic field one will be able to set Ar(r) = v(t) and Ap(t) at the action of operator exp(- L0t) . Then

+ Lo j F (r, p, t) = La BaA (r, p )F (r, p, t), (2.4.28)


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