Potentials and charges on conducting rocket sections

The potential differences measured between pairs of three rocket conductors hen various ion or electron beams are emitted were analyzed. Approximate values of coefficients of potential, capacity, and induction are calculated. A simple method of measuring them is presented. Approximate formulae are developed for sheath radius and are used to calculate this radius for each of six beam currents. The extended probe is inside the sheath for all of the beam currents except 1 Micro A. The potential of the rear section is close to zero, so is assumed equal to zero, which leads to the absolute potentials of the rocket sections. Approximate formulae are developed to calculate the sheath potential from the charge in the sheath. A fast converging reiteration gives the charge on each conductor, the sheath charge, and the part of the conductor potentials that are due to the sheath. Explanations are given for: (1) the charge on the rear section having the opposite sign of, and a smaller magnitude than that on the forward section; (2) the magnitude of the probe voltmeter reading being less than that of the rear section voltmeter for moderate beam currents, and the same for beam currents way beyond saturation; (3) the ratio of these two voltmeter readings approaching 1 with increasing magnitude of beam current; (4) the potential of the probe being negative for ion emission; (5) the magnitude of the probe potential reaching a maxmum, then approaching zero with increasing magnitude of beam current.