Derivation of the electron drift velocity vector in gas under crossed ac electric and dc magnetic fields assuming constant-collision-frequency models

Abstract

The periodic variation of the average electron velocity vector under crossed ac electric and dc magnetic fields is formulated analytically on the basis of kinetic equations for single-electron motion assuming constant-collision-frequency models with and without ionization. The velocity vector draws elliptic loci with the alternation of the electric field, and this is verified by Monte Carlo simulations. The amplitude and the mean deflection angle of the velocity vector, which represent basic features of electron transport in magnetized plasmas, are explicitly described with the collision frequency, the ac angular frequency, and the intensities of the fields.

Elliptic vector loci of average electron velocity of electron swarm in constant-collision-frequency model gas under ac electric and dc magnetic fields crossed at arbitrary angles

“…Here, we utilize a feature that the average electron velocity of a subset varies in the same way as the single electron motion starting from v = 0 at t = t ′ . This approach has been adopted for electron swarms under E ⊥ B [50] and E(t) ⊥ B [48], and is applicable also to the present condition E(t) ̸ ⊥ B as elucidated below. First, for the assumption of isotropic scattering, the initial value ⟨v(t ′ )⟩ of the electrons belonging to a newborn subset is zero; any v of an electron is canceled by its counterpart having −v.…”

“…Compared with a specic case θ = π/2 presented in [48,49,51], it is seen in ( 14) (16) that W B x (t) and W B y (t) have the same dependence on the parameters except for an additional factor sin θ and that where v 1eV is the electron speed associated with 1 eV. The parallelograms are the intersections between the cube and the vector planes including the elliptic vector loci non-zero with a factor of cos θ for θ ̸ = π/2.…”

“…The direction of the major axis of the ellipse is considered to represent that of the average Hall deection [48,51]. The lengths L + and L − of the semi-major and semi-minor axes, respectively, represent the sensitivity of the W(t) response along and perpendicular to the direction of the Hall deection.…”

“…It is mentioned in Ref. [48] for E(t) ⊥ B that the solution in the presence of ionization and/or electron…”

“…Its major axis deviates from the direction of E(t) monotonously with |B|, which is considered to be an appearance of the Hall deection. After this report, W(t) under E(t) ⊥ B was derived analytically assuming that the electron collision frequency ν is constant and the electron scattering is isotropic [48,49]. The basic behavior of the elliptic vector locus observed in Ar was reproduced also in the constant-collision-frequency (CCF) model.…”