Spectral features in solar hard X-ray and radio events and particle acceleration

Hard X-ray and radio intensities of two major solar outbursts are found to anticorrelate in time with their spectral indices, which, furthermore, are in satisfactory correlation with each other. The radio emission must be synchrotron radiation from the same electron population that causes the X-ray bremsstrahlung. A delay of temporal features, increasing with energy, is clearly observed in one of the X-ray events. The observations are interpreted with a simple model, which assumes ion-acoustic instability in a current sheet, transformation of turbulence energy into Langmuir waves, and their escape into the ambient plasma where they accelerate particles. A power-law index of the electron energy distribution is derived for acceleration being balanced by escape of particles. Anticorrelation of intensity and spectral index then follows naturally from variations of the spectral wave energy density or the dimension of the acceleration region. The finite collision time in the acceleration region and its increase with energy introduce a perturbation which can explain the observed drift of temporal features.