Abstract
Particle data obtained by in situ spacecraft measurements can be used to solve the dispersion relation of plasma waves, providing us with valuable information on possible wave modes. A common approach to solving plasma dispersion relations is to model the measured particle velocity distribution function using a Maxwellian distribution, which significantly alleviates the corresponding numerical computation.
Here we investigate the possibilities of modeling ring distributions of two events measured by the Van Allen Probes and Cluster spacecraft using a subtracted Maxwellian distribution and lastly we numerically evaluate the dispersion relations, where we identify wave instabilities.