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

An analytical solution is given of the equations for a regular beam (§1) emitted by an arbitrary surface in the nonstationary case and the - 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 , and the magnetic field H are given functions J(t, x²,x³), (t, x², x³), and H (x¹, x², x³). The solution is given in the form of series in terms of (X¹) with coefficients that are functions of t, x², and x³. These coefficients are determined from recurrence relations ( =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.