A plasma expansion model is developed. It is used to compute flash-over propagation upon spacecraft solar panels. In order to take into consideration the plasma extinction, a cathode spot model is developed and coupled to a plasma expansion model. A minimum on the sheath potential has been found, and it explains the end of plasma emission by the cathode and, therefore, the end of the plasma expansion. Numerical results are compared with experimental measurements and are in good agreement with them. The model can be later used to prevent arcing on spacecrafts solar panels.