Full MHD Version — Particle Acceleration and Collimation

Abstract

In this chapter, we discuss the analytical solutions obtained for cylindrical jets, quasimonopole outflows, and the black hole magnetosphere. It is demonstrated that the self-consistent analysis makes it possible to determine the main characteristics of the outgoing wind, including the determination of the total energy loss and the poloidal magnetic field structure. The conditions of the effective energy transformation from the electromagnetic flux to the particle flux are given as well. For cylindrical jets both the relativistic and nonrelativistic versions are discussed. It is shown that taking into account the finite ambient pressure, one can determine the magnetic flux within the central core. For nonrelativistic flows, which are magnetically dominated near the origin, the solution can be constructed only in the presence of an oblique shock near the jet base, where additional heating is to take place. The analytical solutions obtained for quasimonopole and parabolic magnetic fields illustrated the general property that the efficient particle acceleration can take place only for the strongly collimated outflows. Two toy solutions for the black hole magnetosphere support the physical nature of the Blandford–Znajek process. Finally, the results obtained by the self–similar approach and in the numerical simulation are briefly discussed. It is demonstrated that there is now a lot of numerical data that confirms the analytical results obtained by the Grad–Shafranov equation method.