The Effect of Wave Escape on Fast-wave Turbulence in Solar Flares

One candidate for particle acceleration in solar flares is stochastic acceleration by plasma waves. This idea is often linked with resonant interactions that require high-frequency waves. Wave turbulence can provide high-frequency waves from low-frequency waves that are generated when outflows from a magnetic reconnection site high in the corona encounter magnetic loops lower in the corona. Many previous works have considered the coupled processes of stochastic acceleration and wave turbulence together. To the best of our knowledge, these works have all neglected the loss of wave energy as waves propagate out of the solar-flare acceleration region. In this work, we investigate the effects of wave propagation on wave turbulence. We determine the conditions needed for flares to generate high-frequency waves via wave-wave interactions involving compressive fast magnetosonic waves. We find that wave loss sets the minimum threshold on the amplitude of low-frequency waves that must be reached in order for a significant fraction of the wave energy to cascade to high frequencies before the waves escape. We evaluate this threshold as a function of the correlation length of the low-frequency waves.