No abstract

The analytic solution of the average electron velocity vector W(t) of an electron swarm in gas under ac electric and dc magnetic elds (E(t) and B, respectively) in a constant-collision-frequency model is extended to cover not only the known case of a right crossing angle (E(t) ⊥ B) but also the cases of arbitrary crossing angles (E(t) ̸ ⊥ B). The x, y, and z components of W(t) are obtained as explicit formulae with the following parameters: the amplitude E of E(t), the angle θ between E(t) and B, the angular frequency ω E of E(t), the cyclotron angular frequency ω B (subject to the strength B of B), and the electron collision frequency ν. A basic feature that W(t) draws elliptic locus in velocity space is unchanged even under E(t) ̸ ⊥ B, but the plane including the locus may tilt when ω E , ω B , or ν varies. The derivation of W(t) based on the analytic solution of single electron motion is detailed and fundamental behavior of the W(t) loci is observed to understand the electron transport under E(t) × B elds.