Theoretical analysis of charging data from rocket with charged beam emission

To gain physical understanding, an approximate analysis is made of charging data from the flight of a three conductor rocket at night in the lower F region of the ionosphere. Values of coefficients of potential, capacity, and induction are calculated, and a method of measuring them is given. Sheath radii are calculated. The extended probe is near the sheath's edge for 1 micro A, and inside the sheath for all other (larger) beam currents. The potential of the rear section is calculated; it is near zero, and is negative. The other potentials follow from measurements of potential differences. Probe theory is used to calculate the plasma-return current to the forward section and is found to account for the high negative values of potential measured for unsaturated beam currents. The 374 micro A and, especially, -10 mA beam-current cases are found to be highly saturated. Approximate formulae are developed to calculate the potential due to sheath charge. These, the coefficients, and the potentials give the conductor and sheath charges and the part of the conductor potentials due to the sheath. The charge on the forward section is nearly doubled due to the presence of the rear section. The potential at the position of the probe with the probe removed is calculated and found to differ greatly from the probe potential. The charging time constant due to rocket current and capacitances is an order of magnitude larger than the plasma period. The time to reach steady state is determined by the charging time constant due to capacitance for ion beam currents, and by the ion transit time for the electron beam current.