MEASUREMENT OF PLASMA CURRENT DISTRIBUTION USING MAGNETIC PROBES

Magnetic probes are commonly used for measuring current distributions in plasmas. Unfortunately they must be placed inside the plasma, pertu rbing the current distribution under measurement. Other authors have s tudied the influence of a magnetic probe on a current sheet for both t hin and thick current distributions. For the case of thick current she ets (as happens in plasma focus discharges), the measured voltage can be written as a first kind convolution of a Volterra equation. In orde r to get the real current distribution, an inversion of this equation is needed. First kind Volterra equations (Abel integrals included) are in some sense not a well-posed problem and, for numerical inversion, the input data must be smoothed. Further, the magnetic probe problem r epresents a particular case among first kind Volterra equations becaus e the kernel is singular and the illness of the problem becomes more s evere. On the other hand, we are interested in inverting experimental data with errors, so it is mandatory to evaluate the error in the inve rted profile. For Volterra integral equations, error propagation has n ot been widely discussed in the literature. In this work a direct meth od, the matrix method plus an explicit filter, is used to obtain the s olution. One of the main advantages of the method is the easy calculat ion of the error in the inverted signal from the errors of the paramet ers and the input data. In order to minimize error magnification, some limitations to the geometrical configuration of the probe are found. Also, it is shown that this method is a good compromise between accura cy and computational speed (it can be used on line working with thousa nds of data points).