Resonant interactions between particles and plasma waves play an important role in both the solar wind and solar flares. The dynamics of plasma turbulence in these settings controls the strength of the interactions, by determining the amplitudes of the small-scale electromagnetic fluctuations that have the largest effect on the particles. Because turbulence and wave-particle interactions are so closely inter-related, it is essential to study them together. Although resonant interactions in turbulent plasmas have been studied extensively, most previous studies have employed highly simplified assumptions about the wave power spectra and/or particle velocity distributions, for example, taking the wave power spectra to be isotropic, or taking all the wavevectors to be parallel to the background magnetic field. In this work, we investigate resonant interactions between particles and weakly turbulent waves in the more realistic, anisotropic, two-dimensional wavenumber and particle-velocity space. The quasilinear theory is adopted for the resonant interactions and weak turbulence theory is used to model the wave turbulence. For simplicity, we assume a homogenous plasma. In the first part of this work, we present new numerical results on resonant cyclotron interactions between protons and oblique Alfven/Ion-cyclotron waves in collisionless plasmas. We find that if some mechanism generates oblique high-frequency A/IC waves, then these waves initially make the proton velocity distribution function so anisotropic that the plasma becomes unstable to parallel waves. Parallel waves are then amplified to the point that they dominate the wave energy at the large wave numbers at which the waves resonate with protons. We show that these processes allow oblique A/IC waves to be more effective at heating protons than parallel A/IC waves. In the second part of this work, we present new numerical results on the stochastic electron acceleration in solar flares by weakly turbulent fast magnetosonic waves ("fast waves"). For this work, we assume that large-scale flows triggered by magnetic reconnection excite large-wavelength fast waves, and that fast-wave energy then cascades from large wavelengths to small wavelengths. Electron acceleration by large-wavelength fast waves is weak, and so the model relies upon the small-wavelength waves produced by the turbulent cascade. We first investigate the effects of wave escape using the wave kinetic equation for fast waves in weak turbulence theory, supplemented with a homogeneous wave-loss term. We find that the amplitude of large-wavelength fast waves must exceed a minimum threshold in order for a significant fraction of the wave energy to cascade to small wavelengths before the waves leave the acceleration region. We then investigate the effects of plasma parameters on the acceleration and find that the electron distribution function fe develops a power-law-like non-thermal tail within a restricted range of energies E ∈ ( Ent, Emax). We obtain approximate analytic expressions for Ent and E max that describe how these minimum and maximum energies depend upon plasma parameters such as the electron temperature and number density. We compare our results to previous studies that assume that wave power spectrum Fk and fe are isotropic and use our analysis to explain the observed hard x-ray spectrum seen in the June 27, 1980 flare. In our numerical simulations, the electron energy spectra are softer (steeper) than in models with isotropic Fk and fe and closer to the values inferred from observations of solar flares.
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