Substituting this relation into the first equation of the set Eq. 2.2.16 we find the equation for the function F(r, p, t):

^ + Lo jF(r,p,t) = dJdt'{xp[-Lo(t-f)]/?((,t;r,t)F(r,p,t)=r .(2.2.19)

On the right hand side of this equation t1 = t was set, according to the first equation of the set Eq. 2.2.16, and it is necessary to keep in mind that we should put r = r after the action of the operator exp[- Lo(t -t')]. For further analysis Eq. 2.2.19 it is necessary to concretize a dependence of the correlation tensor Bap (r, t;r1, t1) on the coordinates and time. The most general form of the correlation tensor Bap fitting the experiment and the Maxwell equation is

(J?+ Lo]f(r,p,t) = Da\dT{exp(-L0T)BaP(r -r-ujDpF(r,p,t-t)} =r (2.2.21)

The right hand side of the Eq. 2.2.21 differs from zero in time intervals of the order of the correlation time of a random field. If the correlation time of a random field is small compared to the characteristic time of the distribution function variation, i.e. t >> t , then it is possible to write

(J? + Lo jF(r'p,t) = Da0dT{exp(-L0r)Bap(rx,r -r-u0z)DpF(r,p,t)) =r (2.2.22)

2.3. Kinetic equation in the case of weak regular and isotropic random fields

If the momentum of a particle is varied weakly at distances of the order of the correlation radius of a random field, one can set the variation of a particle momentum as Ap(t)= 0 and the variation of its radius-vector as Ar(T) = vt for the action of the operator exp(- Lot) Then dt



If a random magnetic field is statistically isotropic the correlation tensor Bag (r, x)

has the following form:


2lc2 xll>

Here 8ap is the unit tensor and T(x/lc) is a dimensionless function, which is assumed to be known from observations. Usually it is suitable to choose the function W(x/lc) in the form

Here K^(x) is the McDonald function, v is the index of the inhomogeneities spectrum of the interplanetary magnetic field (usually v> 1). Direct measurements of the magnetic field in the interplanetary space give for v the values 1 < v < 3.8 . Fourier-image of the function T(x/lc) corresponds to a power spectrum decreasing in the region of small scales of inhomogeneities

Substituting Eq. 2.3.3 - 2.3.6 into Eq. 2.3.1, we obtain dF + v dF = HoDF + ylc(ff 12 (r ) D|v _ Uo| _1DF,

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