Electron shock-drift acceleration at weak and sub-critical coronal shocks: a testparticle study of Type II radio burst sources

Coronal Type II radio bursts are produced by shocks whose Alfvénic Mach numbers, Ma ≈ 1.1–3, lie far below the thresholds that kinetic theory sets for whistler-mediated electron injection. We ask whether shock-drift acceleration of thermal electrons can nevertheless supply the electron beams that drive Type II emission at such weak, and often marginally subcritical, shocks. To answer this, we use a test-particle model in the de Hoffmann–Teller frame, with the shock compression, plasma 𝛽, and Mach number taken from a standard coronal model (Newkirk density, Dulk–McLean field, 1.5 MK). An analytic solution and a Monte Carlo calculation agree to within a few per cent, and full-orbit integrations confirm the guidingcentre treatment for shock ramps wider than a few electron gyroradii. Beam-capable electrons, reflected with speeds above three electron thermal speeds, are produced only in a narrow obliquity range, 𝜃≈ 83–87°; there, up to ~1% of the incident electron flux is reflected at ~0.05–0.1 c for an 800 km/s shock at 2𝑅⨀. Because the cross-shock potential grows with shock speed, the beam fraction peaks at Ma ≈ 1.8–2.5 and falls on both sides, reproducing the window of efficient Langmuir-wave excitation found by Mann et al. (2022). Perpendicular electron heating in the shock foot raises the beam fraction by factors of 2–16. When the model is applied to an expanding shock front, a purely radial field produces no beams, but a local field direction that scatters by ~30° turns 5–10% of the front into a beam source, even when the front is sub-critical. A suprathermal kappa tail in the upstream electrons leaves the obliquity window in place once the reflected electrons are compared with the ambient tail; it does, however, soften the upper edge of the Mach window and enlarge the beam-source area of the front by up to a factor of ≈ 6. Electron acceleration at coronal Type II shocks is therefore controlled by the local field geometry and the upstream electron population rather than by the global Mach number.