Line Shapes in a Magnetic Field: Trajectory Modifications I: Electrons

Abstract

In recent work, the effect of a magnetic field on the line shapes via the modification of electron perturber trajectories was considered. In the present paper we revisit this idea using a variation of the Collision-time Statistics method, in order to account for a l l relevant perturbers. We also obtain line profiles for the hydrogen L α line for conditions of astrophysical interest. Although the Collision-time statistics method works for both electrons and ions, we apply a simplification here that results in an excessive number of ions having to be simulated. As a result, the present, simplified version, is typically only appropriate for electrons.

Line Shapes in a Magnetic Field: Trajectory Modifications II: Full Collision-Time Statistics

“…As in [1] we assume that: a. the distribution functions, e.g. the Maxwellian velocity distribution is not affected by the B-field.…”

“…To include all and only the relevant perturbers, we use a modification of the collision-time statistics method of Hegerfeld and Kesting [3] with Seidel's improvement [4]-see Ref. [5] for details, as discussed in [1].…”

“…As in [1] we consider as "relevant " perturbers those that come closer to the emitter than a distance R max , defined so that the interaction is negligible for distances larger than R max during the time interval of interest (0,τ). For a Debye interaction, we usually take R max ≈ 3λ D , where λ D denotes the shielding(Debye) length.…”

“…In such cases the motion of the perturbers in the plane perpendicular to the magnetic field may be quite far from completing a full cycle. As a result in the simplified treatment of [1] a large number of ineffective perturbers would be included in that case. It is believed [2] that "as long as the gyro-radii of the electrons are much larger than the Debye sphere" the particle trajectories, or, equivalently, the dielectric function would be unaffected by the magnetic field, since the perpendicular motion involves presumably much smaller length scales than the parallel motion, although this belief remains to be quantified.…”

“…This means that in this limit |ψ − θ| ≈ π, e.g. we get a ∆ψ ≈ 0 (but note that in that limit we had divergencies in the relevant functions when computing the collision volume in [1]). Figure 4.…”