Theory for Geosynchronous Spacecraft Charging Index

Geosynchronous spacecraft are likely to be charged to several or even tens of thousands of kilovolts due to the high-energy plasma during substorms (tens of keV), leading to detrimental electronic system anomalies. Recently, a debate on what is the best index for geosynchronous spacecraft charging is opened. Ferguson, D. C. et al. presented that the total thermal electron flux above a certain minimum energy that is well above the second crossover point in secondary electron emission is the best index for spacecraft charging and verified the charging index by comparing Nascap-2k results with charging and flux measurements on some geosynchronous satellites. In this paper, such a charging index is verified theoretically. Meanwhile, the best minimum energy and the electron flux above it are obtained for both single and double Maxwellian plasmas based on charging threshold theory. The theoretical estimations agree well with Ferguson's results. Such a charging index is important, which will probably make prediction of geosynchronous spacecraft charging simple and convenient in the future. Plain Language Summary Geosynchronous spacecraft are likely to be charged to thousands of kilovolts by the high-energy plasma during substorms, leading to detrimental electronic system anomalies. What is the best index for geosynchronous spacecraft charging? This article provides an answer to this question theoretically. It presents that the total thermal electron flux above a certain minimum energy is the best index for spacecraft charging. This theory is applicable to both single and double Maxwellian plasmas, by which geosynchronous plasma is generally characterized. The theoretical estimations agree well with Ferguson's results. Such a charging index is important, which will probably make prediction of geosynchronous spacecraft charging simple and convenient in the future.