Info

including the initial and boundary conditions determined by a particular problem of CR propagation. In Eq. 2.12.1 $(r,R,Ze,t) is the source function; Ja are the components of particle flux in terms of r and R. It will be taken into account that in the case of anisotropic diffusion the spatial flux is where Kik is the tensor diffusion coefficient and udTii is the drift velocity of CR in space arising from regular motions of magnetized plasma and from the presence of inhomogeneous magnetic fields and CR density gradients. Substituting Eq. 2.I2.2 in Eq. 2.12.1 we obtain the general equation describing a propagation of CR in the approximation of anisotropic diffusion.

2.12.2. The case of propagation in a galactic arm

For the first approximation the regular magnetic field component in an arm of the Galaxy can be considered as uniform field Ho. Let the x-axis is directed along Ho . Then in a rectangular coordinate system x, y, z we obtain where Ko = vA/3 is the coefficient of particle diffusion in the absence of a regular magnetic field (A is the transport path for scattering). Here t = A/v is the mean time between collisions, mL = ZeHo/Mc is the Larmor frequency of the motion of a scale field Ho. Including that A depends on a particle rigidity R = cp/Ze and curvature-radius in the magnetic field Ho is rL = R/300Ho (if R is expressed in volts, Ho is in gauss, then rL is expressed in cm), and we obtain

particle with a charge Ze and a relativistic mass M = Amc2 (l - v2jc2) ^ in a large colT = A/rL = 300A(r)ho/r ,

i.e. colt is a function only of R and is independent of a particle charge Ze and of its velocity v. Substituting Eq. 2.12.4 in Eq. 2.12.3 we have

Was this article helpful?

0 0

Post a comment