Propagation of a wide ion beam into a magnetic barrier

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Abstract
A fully relativistic and self‐consistent Vlasov equilibrium model is presented and solved for the general problem of the motion of a neutralized ion beam in a transverse magnetic field. The radius of the beam is taken to be much larger than any characteristic length of the system so that the model is, in effect, one‐dimensional. The beam has density n0 and velocity v0 and enters a vacuous region with an externally applied transverse magnetic field B0. It is found that the distance that the ions penetrate into the barrier is determined primarily by the longitudinal electric field produced by the electrons, so that their penetration length is much less than the ion gyroradius. In the case v20/c2≪m/M−B20/16πn0Mc2 the model equations can be solved analytically. In this case the injected plasma is quasi‐neutral and the ions closely follow the electrons. The penetration length of the plasma is then the geometric mean of the electron and ion gyroradii due to the magnetic field Bc= (B20+16πn0Mv02)1/2. A discussion of the numerical results is included.