Particle-in-cell simulations for virtual cathode oscillator including foil ablation effects

Abstract

We have performed two- and three-dimensional, relativistic, electromagnetic, particle-in-cell simulations of an axially extracted virtual cathode oscillator (vircator). The simulations include, for the first time, self-consistent dynamics of the anode foil under the influence of the intense electron beam. This yields the variation of microwave output power as a function of time, including the role of anode ablation and anode–cathode gap closure. These simulations have been done using locally developed particle-in-cell (PIC) codes. The codes have been validated using two vircator designs available from the literature. The simulations reported in the present paper take account of foil ablation due to the intense electron flux, the resulting plasma expansion and shorting of the anode–cathode gap. The variation in anode transparency due to plasma formation is automatically taken into account. We find that damage is generally higher near the axis. Also, at all radial positions, there is little damage in the early stages, followed by a period of rapid erosion, followed in turn by low damage rates. A physical explanation has been given for these trends. As a result of gap closure due to plasma formation from the foil, the output microwave power initially increases, reaches a near-flat-top and then decreases steadily, reaching a minimum around 230 ns. This is consistent with a typical plasma expansion velocity of ∼2 cm/μs reported in the literature. We also find a significant variation in the dominant output frequency, from 6.3 to 7.6 GHz. This variation is small as long as the plasma density is small, up to ∼40 ns. As the AK gap starts filling with plasma, there is a steady increase in this frequency.

Conservative fourth-order finite-volume Vlasov–Poisson solver for axisymmetric plasmas in cylindrical (r,v,v) phase space coordinates

“…The objective here is to model this collisionless configuration along the radial direction, with ion dynamics modeled in (r, v r , v θ ) phase space coordinates, and electron distribution assumed to be fixed for all time. In an equilibrium setting this system can be described by the two-fluid model, such that ion pressure is balanced by the electric field ∂ P i ∂r = q i n i E r (41) and electron pressure is balanced by the electric and magnetic field,…”

“…Techniques have been developed for PIC methods to handle particles traversing cells with non-uniform volumes, including: specialized weighting and interpolation [27][28][29][30], procedures involving recurring mapping from Cartesian to cylindrical or to curvilinear geometry [31][32][33], advancing particles in three dimensions for axisymmetric configurations to circumvent problems at the axis [34], and combinations of these techniques [35]. Applications of various PIC methods to axisymmetric and cylindrically symmetric configurations include high-power microwaves [36][37][38][39][40], Hall thrusters [41][42][43], wakefield accelerators [44,35], particle beams [45][46][47], pulsed-power configurations [48][49][50][51], Z-pinches [52][53][54][55][56], and field-reversed configurations [57,58]. Research literature on continuum kinetic methods for discretizing cylindrical phase space coordinates is extremely sparse and typically does not include convergence studies, making it difficult to assess generalizability.…”

Higher harmonics generation in relativistic electron beam with virtual cathode

“…3,6,[11][12][13][14] The fundamental generation frequency, x VCO , of known vircator modifications in the absence of an external resonant structure is determined by the plasma frequency, x 0 p , of an undisturbed electron beam (undisturbed plasma frequency) as x VCO ¼ k 0 x 0 p , where the coefficient of proportionality, k 0 , is in the range ½0:5; 2 and depends on the configuration of a virtual cathode oscillator (VCO) and operating regime. 3,6,[15][16][17] In practical cases x VCO lies usually in the range 1,20 GHz. At the same time, the creation of effective high-power generators in poorly developed sub-THz/THz ranges is an actual problem of the modern plasma physics and high-power microwave electronics.…”

“…2,3,14 A possible direction for the improvement of vircator characteristics is the development and design of the new modifications of VCOs that use newly discovered effects occurring in the relativistic and ultrarelativistic electron beams with overcritical currents. 10,16,23,24 A promising way to increase the radiation frequency of a vircator system up to sub-THz range is the use of the higher harmonics of the fundamental frequency of VCOs in the strongly nonlinear regime of a VCO operation. Currently, a generation at higher harmonics is widely applied in gyrotrons.…”

Microwave radiation power of relativistic electron beam with virtual cathode in the external magnetic field

“…One of the most important directions of research in the high power vacuum and plasma electronics is the study of the virtual cathode (VC) oscillators (vircators) which attract great attention of scientific community. [1][2][3][4][5][6][7][8] The vircator is a microwave generator whose operation is based on the oscillations of the VC in the electron beam with the overcritical current. 1,4,9 Microwave oscillators with VC are perspective devices of high-power microwave electronics for the generation of the impulses of the wide-band microwave radiation due to their high output microwave radiation power, a simple construction (particularly, vircators can operate without the external focusing magnetic field), a possibility of a simple frequency tuning and regime switching.…”