Plasma turbulence is thought to be associated with various physical processes involved in solar flares, including magnetic reconnection, particle acceleration and transport. Using Ramaty High Energy Solar Spectroscopic Imager ({it RHESSI}) observatio
ns and the X-ray visibility analysis, we determine the spatial and spectral distributions of energetic electrons for a flare (GOES M3.7 class, April 14, 2002 23$:$55 UT), which was previously found to be consistent with a reconnection scenario. It is demonstrated that because of the high density plasma in the loop, electrons have to be continuously accelerated about the loop apex of length $sim 2times 10^9$cm and width $sim 7times 10^8$cm. Energy dependent transport of tens of keV electrons is observed to occur both along and across the guiding magnetic field of the loop. We show that the cross-field transport is consistent with the presence of magnetic turbulence in the loop, where electrons are accelerated, and estimate the magnitude of the field line diffusion coefficient for different phases of the flare. The energy density of magnetic fluctuations is calculated for given magnetic field correlation lengths and is larger than the energy density of the non-thermal electrons. The level of magnetic fluctuations peaks when the largest number of electrons is accelerated and is below detectability or absent at the decay phase. These hard X-ray observations provide the first observational evidence that magnetic turbulence governs the evolution of energetic electrons in a dense flaring loop and is suggestive of their turbulent acceleration.
{This work aims to investigate the spectral structure of the parallel electric field generated by strong anisotropic and balanced Alfvenic turbulence in relation with the problem of electron acceleration from the thermal population in solar flare pla
sma conditions.} {We consider anisotropic Alfvenic fluctuations in the presence of a strong background magnetic field. Exploiting this anisotropy, a set of reduced equations governing non-linear, two-fluid plasma dynamics is derived. The low-$beta$ limit of this model is used to follow the turbulent cascade of the energy resulting from the non-linear interaction between kinetic Alfven waves, from the large magnetohydrodynamics (MHD) scales with $k_{perp}rho_{s}ll 1$ down to the small kinetic scales with $k_{perp}rho_{s} gg 1$, $rho_{s}$ being the ion sound gyroradius.} {Scaling relations are obtained for the magnitude of the turbulent electromagnetic fluctuations, as a function of $k_{perp}$ and $k_{parallel}$, showing that the electric field develops a component parallel to the magnetic field at large MHD scales.} {The spectrum we derive for the parallel electric field fluctuations can be effectively used to model stochastic resonant acceleration and heating of electrons by Alfven waves in solar flare plasma conditions}
Anisotropic Alfv{e}nic fluctuations with $k_{parallel}/k_{perp}ll 1$ remain at frequencies much smaller than the ion cyclotron frequency in the presence of a strong background magnetic field. Based on the simplest truncation of the electromagnetic gy
rofluid equations in a homogeneous plasma, a model for the energy cascade produced by Alfv{e}nic turbulence is constructed, which smoothly connect the large magnetohydrodynamics (MHD) scales and the small kinetic scales. Scaling relations are obtained for the electromagnetic fluctuations, as a function of $k_{perp}$ and $k_{parallel}$. Moreover, a particular attention is paid to the spectral structure of the parallel electric field which is produced by Alfv{e}nic turbulence. The reason is the potential implication of this parallel electric field in turbulent acceleration and transport of particles. For electromagnetic turbulence, this issue was raised some time ago in [A. Hasegawa, K. Mima, J. Geophys. Res. {bf 83} 1117 (1978)].
