On the existence of transiently negative diffusion coefficients for electrons in gases inE×Bfields

Abstract

A recent study (Raspopović Z et al 2000 J. Phys. D: Appl. Phys. 33 1298) reported the existence of negative diagonal diffusion tensor elements for electrons in a neutral gas under the influence of crossed radiofrequency electric and magnetic fields. In this paper we demonstrate, using a time-dependent multi-term solution of the Boltzmann equation and time-resolved Monte Carlo simulation, that this phenomenon is a transient relaxation effect obtainable under dc crossed field conditions.

A multi term Boltzmann equation analysis of non-conservative electron transport in time-dependent electric and magnetic fields

“…We observe that it has all the features of anomalous diffusion [3] but perhaps the most striking phenomena is the presence of negative transiently diffusivity in the limit of the highest B 0 /n 0 of 2000 Hx (1Hx = 10 −27 Tm 3 ). These results independently confirm the previous calculations and the reader is referred to [14] for details. Generally speaking, the temporal profiles presented in Fig.…”

Visualization of Electron Transport Coefficients in RF Electric and Magnetic Fields Crossed at Arbitrary Angles

“…There is no easy way out-studies of nonlocal and kinetic effects in electron transport in varying configurations of RF electric and magnetic fields require a full kinetic approach Solution of the Boltzmann equation for charged particle swarms under the influence of time-dependent electric and magnetic fields has been recently detailed by Dujko et al [2], and we emphasize here only the following critical points: 1) The angular dependence of the phase space distribution function in velocity space is represented in terms of a spherical harmonic expansion; 2) the speed dependence of the phase space distribution function is resolved through an expansion about a Maxwellian at an arbitrary time-dependent temperature in terms of Sonine polynomials; and 3) under hydrodynamic conditions, a sufficient representation of the space dependence and implicit time dependence is an expansion of the distribution function in terms of powers of the density gradient operator. In this paper, we consider the Reid ramp model [3] for electrons in RF electric and magnetic fields. The applied reduced angular frequency Ω/n 0 is set to 2 × 10 −14 rad · m −3 · s −1 while the electric and magnetic field amplitudes are 12 Td (1 Td = 10 −21 V · m 2 ) and 1000 Hx (1 Hx = 10 −27 T · m 3 ), respectively.…”

“…We employ a coordinate system where E defines the z-axis while B lies in the y-z plane, making an angle ψ with respect to E. Calculations have been performed only for angles between 0 and π/2 rad. Extension to other angles can be made through the use of symmetry properties outlined in our previous publications [2], [3]. Fig.…”

“…For n 0 D zz , the opposite situation holds: The diffusion becomes transiently negative in the limit of an orthogonal field configuration and large ψ. Having in mind these phenomena and the fact that the code has been tested against all known benchmarks [2], [3], the present data may be used for further testing of new codes and plasma models.…”

“…This reduces the average collision frequency and, hence, the ability of the swarm to respond to changes in the field. Consequently, the additional structure in the RF profiles then follows [3]. In contrast to W y and W z , the asymmetry in the W x profiles is clearly evident and further increased for an increasing ψ.…”