Dept. of Physics, The Open University, Milton Keynes, MK7 6AA, UK

Understanding coronal and chromospheric hard X-rays requires modeling the acceleration and subsequent transport of energetic particles in the solar atmosphere. Most commonly, such modeling requires numerical solution of the Fokker-Planck equation for the particle distribution function. In contrast, existing analytic methods can only yield mean quantities (e.g. mean column depth reached by particles of given initial energy). Although numerical solution allows a description of many physical scenarios, it requires and produces data that is far more detailed than current observations (potentially even HESSI) can sustain. A less detailed, and more intuitive approach, that goes beyond traditional mean analytic estimates, would therefore be useful in assessing the main issues, whilst removing obscuring detail. A method that can do this is presented here that involves solving for moments of the distribution function, given only its initial moments, and can, for example, yield expressions for the mean and variance of particle position as functions of particle energy. These quantities can then be used to obtain expressions describing the apparent size and location of hard X-ray sources as a function of both time and photon energy. Applications of such methods to potential HESSI data are illustrated, highlighting how they can allow a more immediate and intuitive understanding of solar hard X-ray images.