  Using a so-called hemispherical model we derive a general transport equation
for cosmic ray and thermal particles scattered in pitch angle by magnetic
inhomogeneities in a moving collisionless plasma. The weak scattering through
90 degrees results in isotropic particle distributions in each hemisphere. The
consideration is not limited by small anisotropies and by the condition that
particle velocities are higher than characteristic flow velocity differences.
For high velocities and small anisotropies the standard cosmic ray transport
equation is recovered. We apply the equations derived for investigation of
injection and acceleration of particles by collisionless shocks.
