Numerical Calculations of Charging Threshold at GEO Altitudes With Two Temperature Non-Extensive Electrons

Surface charging at geosynchronous altitude is one of the major concerns for satellites and spacecrafts. Spacecraft anomalies are often associated with extreme surface charging events, especially during substorms in which the GEO plasma is better modeled as two temperatures non-Maxwellian plasma. In such case, we employ two temperature q-non-extensive distribution function to determine the onset of spacecraft surface charging which becomes complex since many parameters control the surface charging. We developed a current balance equation which better explains the charging threshold in comparison to a Maxwellian distribution function. The effect of non-extensive parameters, temperature and density ratio on the current balance equation has been explained. The modified current balance equation predicts the critical and anti-critical temperatures for various space-grade materials both analytically and numerically. A significant change is observed in the quantities characterizing the charging current, average yield and density ratio in the presence of non-extensive two temperature electrons. The mechanism underlying different charging behaviors at or near the threshold is also indicated at various plasma parametric domains. Furthermore, the general conditions of potential jump are also obtained theoretically which predicts the sudden or smooth potential transition.