A maximum-likelihood algorithm for reduction of Langmuir probe data

The reduction of Langmuir triple and quadruple probe data, i.e., the determination of the electron temperature T(e) from the measured voltages and currents, requires the solution of an implicit transcendental equation in T(e), at every point in time. Random errors and noise in the measurements occasionally precludes solution of the equation, resulting in an indeterminate temperature at those times. We present a method for overcoming this problem that uses the method of maximum likelihood. The experimental uncertainties, assumed to be normally distributed, are used in solving the implicit equation in T(e). At every point in time, a likelihood function is calculated, and the temperature which maximizes this function is taken to be the solution T(e). The uncertainty in the resulting measurement is taken to be the width of the likelihood function. Examples of this technique are shown.