Spacecraft Charging Probabilities as a Function of Altitude

Nearly all of the available information on spacecraft charging due to hot (keV) plasma pertains to geosynchronous altitude. An altitude-dependent model is therefore necessary for estimating charging parameters for spacecraft at other altitudes (e.g., GPS). This paper describes a probability model which is an extension of altitude-dependent calculations previously published (Reference 1). The probability of hot plasma with a given energy density being formed in the geomagnetic tail was calculated from the probabilities of various solar wind parameters (the "tube-of-toothpaste" model). The lowest altitude which the plasma could reach was calculated by equating its energy density to that of a dipole-approximated geomagnetic field. The probabilities thus calculated decrease from ~10 percent (at geomagnetic altitude) to <0.1 percent (for GPS altitudes) to <10-4 percent (at 3.5 RE altitude, measured from the center of the earth).