This work is devoted to the modeling of a Penning discharge with a hot cathode, which is used to create a background plasma with a radial electric field in a plasma mass separator. We used a 2D3V electrostatic particle-in-cell plus Monte Carlo Collision (PIC/MCC) simulation model with a gyrokinetic approximation for magnetized electrons and a geometrical scaling scheme. The proposed model predicts the development of a rotating spoke structure, leading to fluctuations in the electric potential. The fluctuation amplitude and the averaged radial profile of the potential are in qualitative agreement with experiment. On the example of a model flow of silver and lead ions, we have shown that potential fluctuations can impair separation, leading to a partial overlap of ion deposition spots on a substrate. Each of the separated fractions contain about 11% impurities.