Calculation of the characteristics of the radiation from a generator with a virtual cathode

Analysis of the formation of structures and chaotic dynamics in a nonrelativistic electron beam with a virtual cathode in the presence of a decelerating field

“…The application of this method in the analysis of the complicated behavior of the VC in a beam of charged particles enables one to select space-time structures in the electron flux that have characteristic spatial distributions and time scales in the electron beam (electron bunches) whose interaction can explain features of a beam with a VC [9,12,13]. The method of orthogonal decomposition involves solution of the following integral equation: (7) where K(x, x*) is the equation kernel represented as…”

“…The significance of this problem has been indicated in a substantial number of related works (see, for example, [1][2][3][4][5][6][7][8][9][10]). This study is important for the fundamental investigation processes governing formation of the chaotic dynamics and structures in the beam-plasma systems [5,6,8,9,[11][12][13], for the applied analysis related to the development and optimization of the VC-based high-power microwave oscillators (vircators) [4,5,8,14], for acceleration of charged particles with an oscillating VC [15,16], and for creation of the sources of broadband noiselike radiation with different power levels [10,17].…”

Experimental and theoretical investigation into the effect of the electron velocity distribution on chaotic oscillations in an electron beam under virtual cathode formation conditions

“…The space charge density was found by linear weighting of the particles (leaves) on a spatial mesh with a reduced noise (the particle-in-cell method) [36]. In this method, the space charge density at a jth node of the spatial mesh, i.e., at a point with coordinate x j = j∆x, is expressed as (5) where x i is the coordinate of an ith particle, N is the total number of large particles, n 0 is the parameter of the computing scheme that equals the number of particles per cell in the undisturbed state, and ( 6) is a piecewise linear shape function that specifies weighting of a large particle on a spatial mesh with step ∆x.…”

“…Hot interest in a new class of powerful electron devices that emerged on the border between 1970s and 1980s and embraces devices using a virtual-cathode (VC) electron beam as an active medium [1][2][3][4] still persists [5][6][7][8][9]. Even in pioneering experiments and calculations, the complicated time-varying radiation pattern of VC oscillators was noted [10][11][12][13][14].…”