Relativistic Dynamics of a Charged Particle in Crossed Magnetic and Electric Fields with Application to the Planar Magnetron.

摘要

Complete characterization of planar magnetron behavior is achieved for intermediate relativistic energies where radiation loss is of no serious consequence. The cut off condition in the neighborhood of the rest energy of the particle shows a linear dependency on the product of electrode separation and magnetic field LH rather than the classical (LH)sq. The modified period assumes a particularly simple form (2pi/omegaL/(L -GAMMA)3/2) gamma being the ratio of electric and magnetic fields which reflects a voltage dependency of the period not encountered in the classical case. A parametric solution for the periodic orbits is derived on the basis of a transformation related to the delineation of the velocity space and, as such, represents a new variety of transcendental curve which degenerates into the cycloid for the limiting case of gamma approaches 0. The spatial time dependent mass, momenta, and energy relations take on especially straightforward forms in terms of the trajectory parametric solution.