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Recent observations from RHESSI have revealed that the number of non-thermal electrons in the coronal part of a flaring loop can exceed the number of electrons required to explain the hard X-ray-emitting footpoints of the same flaring loop. Such sources cannot, therefore, be interpreted on the basis of the standard collisional transport model, in which electrons stream along the loop while losing their energy through collisions with the ambient plasma; additional physical processes, to either trap or scatter the energetic electrons, are required. Motivated by this and other observations that suggest that high-energy electrons are confined to the coronal region of the source, we consider turbulent pitch-angle scattering of fast electrons off low-frequency magnetic fluctuations as a confinement mechanism, modeled as a spatial diffusion parallel to the mean magnetic field. In general, turbulent scattering leads to a reduction of the collisional stopping distance of non-thermal electrons along the loop, and hence to an enhancement of the coronal hard X-ray source relative to the footpoints. The variation of source size L with electron energy E becomes weaker than the quadratic behavior pertinent to collisional transport, with the slope of L(E) depending directly on the mean free path λ associated with the non-collisional scattering mechanism. Comparing the predictions of the model with observations, we find that λ ∼ (108-109) cm for ∼30 keV, less than the length of a typical flaring loop and smaller than, or comparable to, the size of the electron acceleration region. [ABSTRACT FROM AUTHOR]

Observations with RHESSI have enabled the detailed study of the structure of dense hard X-ray coronal sources in solar flares. The variation of source extent with electron energy has been discussed in the context of streaming of non-thermal particles in a one-dimensional cold target model and the results used to constrain both the physical extent of, and density within, the electron acceleration region. Here, we extend this investigation to a more physically realistic model of electron transport that takes into account the finite temperature of the ambient plasma, the initial pitch angle distribution of the accelerated electrons, and the effects of collisional pitch angle scattering. The finite temperature results in the thermal diffusion of electrons, which leads to the observationally inferred value of the acceleration region volume being an overestimate of its true value. The different directions of the electron trajectories, a consequence of both the non-zero injection pitch angle and scattering within the target, cause the projected propagation distance parallel to the guiding magnetic field to be reduced, so that a one-dimensional interpretation can overestimate the actual density by a factor of up to ∼6. The implications of these results for the determination of acceleration region properties (specific acceleration rate, filling factor, etc.) are discussed. [ABSTRACT FROM AUTHOR]

We establish a classification scheme for stochastic acceleration models involving low-frequency plasma turbulence in a strongly magnetized plasma. This classification takes into account both the properties of the accelerating electromagnetic field, and the nature of the transport of charged particles in the acceleration region. We group the acceleration processes as either resonant, non-resonant, or resonant-broadened, depending on whether the particle motion is free-streaming along the magnetic field, diffusive, or a combination of the two. Stochastic acceleration by moving magnetic mirrors and adiabatic compressions are addressed as illustrative examples. We obtain expressions for the momentum-dependent diffusion coefficient D(p), both for general forms of the accelerating force and for the situation when the electromagnetic force is wave-like, with a specified dispersion relation ω = ω(k). Finally, for models considered, we calculate the energy-dependent acceleration time, a quantity that can be directly compared with observations of the time profile of the radiation field produced by the accelerated particles, such as those occuring during solar flares. [ABSTRACT FROM AUTHOR]

We present electron images of an extended solar flare source, deduced from RHESSI hard X-ray imaging spectroscopy data. We apply the electron continuity equation to these maps in order to determine empirically the form of the energy loss rate for the bremsstrahlung-emitting electrons. We show that this form is consistent with an energy transport model involving Coulomb collisions in a target with a temperature of about 2 × 107 K, with a continuous injection of fresh deka-keV electrons at a rate of approximately 10–2 electrons s–1 per ambient electron. [ABSTRACT FROM AUTHOR]