Effect of a strong external magnetic field on the plasma wake field

In the linear approximation, the effect of the strong external constant longitudinal magnetic field B-0 on the wake waves in a cold plasma, where ions are assumed to be immobile, is studied. A comparison is made between the processes occurring in the plasma in the absence, B-0 = 0, and in the presence, B-0 not equal 0, of this field for two cases: the case of a slab geometry of the driving electron bunch with a uniform charge distribution and the case of a cylindrical geometry of the driving bunch with a nonuniform charge distribution, which is assumed to be Gaussian and parabolic in the longitudinal and transverse directions, respectively. It is shown that the presence of the external field B-0 not equal 0 gives rise to qualitatively new features of the bunch-produced fields in the plasma. In particular, for Bo is 0, the dependence of these fields on the Lorentz-factor of the bunch becomes weaker for the Coulomb component of the field and stronger for the wake component; and the field screening is absent. Also, it is shown that the magnetic field in the wake vanishes when B-0 = 0, and, when B-0 not equal 0, this field is not equal to zero and is inversely proportional to the distance from the bunch.