Stationary to nonstationary transition in crossed-field devices

Abstract

The previous results based on numerical simulations showed that a cold electron beam injected in a crossed field gap does not reach a time independent stationary state in the space charge limited regime [P. J. Christenson and Y. Y. Lau, Phys. Plasmas 1, 3725 (1994)]. In this work, the effect of finite injection temperature in the transition from stationary to nonstationary states is investigated. A fully kinetic model for the electron flow is derived and used to determine the possible stationary states of the system. It is found that although there is always a stationary solution for any set of parameters, depending on the injection temperature the electron flow becomes very sensitive to fluctuations and the stationary state is never reached. By investigating the nonlinear dynamics of a characteristic electron, a theory based on a single free parameter is constructed to predict when the transition between stationary and nonstationary states occurs. In agreement with the previous numerical results, the theory indicates that for vanishing temperatures the system never reaches the time independent stationary state in the space charge limited regime. Nevertheless, as the injection temperature is raised it is found a broad range of system parameters for which the stationary state is indeed attained. By properly adjusting the free parameter in the theory, one can be able to describe, to a very good accuracy, when the transition occurs.

Space-charge and thermal effects in relativistic crossed-field devices

“…In fact, the Vlasov equation only sets a maximum density that can be found in the phase-spacen 0 in this case -but does prevent the occurrence of lower densities in a coarse grained sense. 23,24 In any case, it is worth mentioning that the onset of lower density distributions was not observed in previous nonrelativistic studies 16,17 and is, therefore, a consequence of the relativistic and self-current effects. Since the tenuous distribution is bounded by the 6P y ðy; P 0lim Þ curves in phase space, we notice that these particles are not in contact with neither the cathode nor the anode; they are actually trapped in the gap region and do not contribute to the anode current.…”

“…It has been shown that thermal velocity spread may affect the magnetic insulation and lead to the onset of stationary states in the space charge limited regime, among other effects. [14][15][16][17][18] However, as a simplifying assumption, all the theoretical investigations done so far that include thermal effects neglect the self-magnetic fields.…”

Single electron dynamics in a Hall thruster electromagnetic field profile

“…In practice, given the dimensions of a device, namely, the cathode-anode axial distance L and the accelerating channel radius R, one can use Eqs. (11) and (12) to determine the parameters that guarantee that the electrons will not hit the cathode and the accelerating channel wall by imposing jz min j < L and r max < R. From Eq. 12, we note that g b > g e must be satisfied to exist a real maximum radius.…”

“…This can be readily verified using Eqs. (11) and (12) and the normalizations introduced that lead to eV a =mc 2 ¼ g e r 2 0 =2ðg b À g e Þ and jz min j=r…”

“…Simplistically, in a Hall thruster, electrons are accelerated and confined by crossed electric and magnetic fields 11,12 in an acceleration channel. There, they collide with atoms of a propellant gas, generating ions.…”