Heavy-Ion Acceleration and Self-Generated Waves in Coronal Shocks

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Heavy-Ion Acceleration and Self-Generated Waves in Coronal Shocks Markus Battarbee University of Turku, Finland Timo Laitinen University of Central Lancashire, Preston, UK Rami Vainio University of Helsinki, Finland

Outline Model Simulations Summary Coronal shock model Particle acceleration model Simulations Evolution of proton and iron intensities upstream Analysis of particle spectra Wave spectra Summary

Coronal shock model Open magnetic flux tube with prescribed magnetic field Coronal upstream density and proton temperature from a semi-empirical model (Cranmer & van Ballegooijen 2005) Solar wind speed calculated using mass conservation Kappa distribution, ion kinetic temperature assumed to scale proportional to mass Parallel shock propagating at constant speed Vs with compression ratio computed from R-H conditions Vs

Particle acceleration model Monte Carlo simulation of particle transport and acceleration upstream the shock Particle transport: guiding center approximation Scattering rates computed from AW intensity AW growth rates computed from particle flux AW transport: WKB + some frequency diffusion Self-consistent treatment of particle acc. and escape Parker: → escape!

Upstream particle spectra β decreases with time from ~4 to ~2.

Evolution of spectral index Iron has a significantly harder upstream-integrated spectrum than proton. For slow shocks, iron spectrum softens as a function of time.

Cut-off energy vs. Q/A Simulations consistent with Ec (per nuc) ~ (Q / A)1.5. Theory (e.g., Zank et al. 2007): Ec ~ (Q / A)2 in parallel shocks

Wave evolution → → Low-frequency cut-off is not sharp → ions with higher mass (and lower Q / A) are accelerated to slightly higher rigidities

Summary Ion acceleration in coronal shocks governed by the temporal evolution of the shock and the seed population Self-generated waves produce a turbulent trapping region in the upstream Boundary given by Heavy-ion spectrum integrated over upstream is harder than proton spectrum Cut-off energy scales more softly than (Q / A)2 for parallel shocks. Simulations give Ec ~ (Q / A)1.5