SPECTRUM: A computer algorithm to derive the flux-energy spectrum of precipitating particles from EISCAT electron density profiles

A program (SPECTRUM) that inverts electron density profiles measured by an incoherent scatter radar to obtain information on the flux-energy spectrum of precipitating electrons was developed. Improvements compared with the UNTANGLE program developed for the same purpose are described. Whereas UNTANGLE assumes that ionization has reached equilibrium, SPECTRUM includes the time rate of change of ionization. This can be measured on a time scale of a few seconds with the EISCAT radar during auroral precipitation. The fixed energies of the incident electron beams assumed in UNTANGLE are replaced by energies calculated according to the altitudes at which measurements are made. Thus the energy resolution and energy interval included in the derived spectra are determined in a physically reasonable way by the altitude resolution and the altitude interval of the electron density measurements. The equations relating the incident fluxes at each energy to the electron density at each altitude are written in matrix form which allows them to be solved using standard numerical algorithms. Proton fluxes rather than electron fluxes can be fitted.