Optimization of the profiles of electrodynamic system of relativistic TWT by using atomic function

Abstract

Self-consistent two-dimensional non-linear theory of relativistic TWT-0 with slowing system in form of arbitrary irregular smooth waveguide with taking into account the average forces of the relativistic electrons interaction is used. Equations of excitation are obtained by the method of transformation coordinates.We use a general theory of interaction of a relativistic electron beam (REB) with a field of modes Eo, ... Eo, of an irregular waveguides [l ... 31. Assume in the general equations to zero transversal velocities v,, vg, in REB, we receive the one-dimensional self-consistent equations of relativistic TWT-0 with arbitrary-irregular slowing system (SS).We use the following designations:radius of a waveguide; Po = V , 1 C; r, = hi, ri -radius of a tube of an electron stream, Kin = Ph 1 U, 11, I , qn -input power of signal U . -voltage, 1 1 , 1 -current of a relativistic electron beam, n -number of ring grooves of slowing system. The solution of the problem of optimization on efficiency of relativistic TWT-0 with using the amomic function for approximation of desired optimal profile of slowing system have been received. This approximation is where up&) is atomic function, h=l/n, n -is number groowes of slowing system. Variant 1. "Short" TWT: n=27, Li=31.4, I0=200A; r0=2,4; Pop,=0,729; k,,=O,06; t;l(eficiency)=81,4%. Optimal variants TWT-0 The profile of waveguide g(T), the plot of q(T) and the hnction of bunching (here i -number of a large particle, N-number of particles) are presented on the N G(T) = 1 --c e figures 1,a: 1-q( r ) ,2-G(T) and 1,s: g(T).The mechanism of optimum interaction in obtained variant noticeably differs from known [ 1,4]. It may be treated as the mechanism of a repeated strong phase focussing of an electron bunch and high-rate extraction of energy from it [ l f , The frrst section of an extraction of energy is located on an interval T=0,4-0,7, here wave is slowed down (groove go deep) and the bunch enters into a retarding phase of wave. If the extraction of energy will proceed, the bunch will break down [ 1,4]. To not suppose it and again to focus a bunch, on interval T=O, 7-0,9 waves again is accelerated (the depth of grooves decreases) is shifted in centre of focusing forces of already rising force fields. Due to this bunching is again improved and on a output interval T=0,9-1 bunch effectively return energy to a wave, slowed down on this section (groove again go deep on this interval). This is new physically interesting mechanism of optimum process of a phase focussing and extraction of energy in relativistic TWT-0. Variant 2. "Long" TWT: n=67; L0=62,8; 10=150A; ro=2,4; PoP,=0,89l; k,,,=0,092; t;l=81,4%. The performances of this variant are similar too of preceding variant.