An inversion software for the analysis of solar X-ray spectra within the NASA RHESSI Mission

NASA has recently launched the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) mission with the purpose of analysing solar flares, by combining 2D imaging with the spectral information given by high-resolution detectors. From a physical viewpoint, the dominant X-ray emission mechanism during solar flares is collisional bremsstrahlung of electrons with the ions of the solar plasma. From a mathematical viewpoint, the relation between the emitted photon spectrum and the electron flux spectrum is described by a Volterra integral equation whose kernel is an appropriate bremsstrahlung cross section. If addressed naively, the solution of this equation may lead to unstable and unphysical reconstructions of the electron spectra. In this talk we will show inversions of real RHESSI spectra by applying regularization techniques for the solution of numerically unstable inverse problems. Both the case of an isotropic cross section and the effects of angle dependency will be investigated. Finally a software tool implementing the regularization method will be described.