Analysis of railgun magnetic probe signals to determine the plasma armature current distribution

Methods were developed for determining the position, velocity, and functional form of a plasma armature from B-dot probe signals. The B-dot probe signal is shown to be a convolution of the armature current density with the B-dot probe impulse response. The methods described here were developed utilizing the knowledge that the probe signal is a convolution. The method for determining the armature position and velocity utilizes the physical processes governing the plasma armature to model the leading edge of the armature as a unit-step function. The model is convolved with the B-dot probe impulse response to give the probe unit-step response which is a function of the velocity and time of passage of the leading edge of the armature. The unit-step response is compared with the B-dot probe signal using a local-area cross-correlation calculation. Two-parameter iteration determines the time of passage and velocity estimates as the values for which the correlation coefficient is maximized. The functional form of the plasma armature is estimated by deconvolving the B-dot probe signal to recover the armature current density. Jansson's relaxation based nonlinear iterative method has been developed for use with B-dot probe signals, and it is presented as a method for estimating the armature current density. This approach has advantages over other methods in that only the physical limits of the data need to be known. Verification of these methods was performed using simulated B-dot probe signals. The simulations indicate that estimates within 10 sampling intervals for the time of passage and 5 percent for the velocity are achievable. Figures are presented of position versus time and velocity versus time for simulated and experimental data. Current density estimates gave improved results over previously used methods. Plots of deconvolved armature current distributions are shown for simulated and experimental data. Also, Jansson's method estimate is compared to the Wiener filter estimate. Application of these methods to experimental B-dot probe signals has been performed with encouraging results.