Equilibrium of high-current electron beam in hybrid coaxial magnetostatic undulator

摘要

In some analogy to works of Reiser and others, in the continuous media approach, we estimate self-electric and self-magnetic fields of an annular high-current electron beam propagating in an ideally conducting grounded coaxial drift-tube without assumptions of uniform density profile and rigid rotator. Then, in the approximation of constant beam density and “rigid rotor” type of rotation, we derive analytically equilibrium equations for the initial internal and external radii of the beam and study numerically its steady-state propagation in combined finite longitudinal homogeneous (guide) and periodic undulator (realistic) magnetostatic fields. It is shown that the values of the equilibrium radii of the electron beam in a coaxial drift-tube can be controlled by choosing the cathode radii and value of the longitudinal homogeneous (guide) magnetic field so that the beam can be transported in any suitable position and amplify efficiently a chosen mode of the coaxial drift-tube. However, it is also found that the possible transmitted currents are an order of magnitude smaller (cf. also Fig. 7) than those predicted for the electron beam in strong (infinite) guide magnetic field alone. It seems that measurements of the possible transmitted current of the Strathclyde hybrid coaxial free-electron laser/maser are much closer to the former estimate.