Solution of the equations for a regular beam emitted by a curvilinear surface in the nonstationary case

Abstract

An analytical solution is given of the equations for a regular beam (§1) emitted by an arbitrary surface in the nonstationary case and the ρ- and T-limited states for nonzero initial velocity (§ §2-4). It is assumed that the emitter is the coordinate surface x1=0 in the orthogonal system x1 (i=1, 2, 3), and the current density J, the electric field ɛ, and the magnetic field H are given functions J(t, x2,x3), ɛ(t, x2, x3), and H (x1, x2, x3). The solution is given in the form of series in terms of (X1)И with coefficients that are functions of t, x2, and x3. These coefficients are determined from recurrence relations (χ =1/3, 1/2, 1, depending on the emission conditions). Plane, cylindrical, and spherical diodes are considered in § 5 in the case in which the high-frequency component of the current density J is not small in comparison with its constant components.