Uncertainty and Data Analysis of ExB Probe including Field Non-Uniformity and Transmittancy

An ExB probe is a pass-band velocity filter for an ion beam, and it can provide a measurement of the ion velocity distribution function (IVDF). However, the finite pass-band filter window size leads to differences in the true IVDF and measured ExB probe spectrum. The ExB probe spectra from three different ExB probe designs are compared to a synthetically defined test IVDF to study how the ExB probe geometry affects the differences. The E- and B-fields in the ExB probe is typically not uniform and not identical in shape, and this also leads to the difference in the IVDF and the ExB probe spectrum. An analytical formula that corrects the field non-uniformity effect is proposed in this work and is tested through the simulation of the single ion particle trajectory. The analytical correction formula captures the ion deflections under the non-uniform fields with an error of -1.0 mm (approximately 30% percentage difference) or less for the displacement and -750 m/s (approximately 33% percentage difference) or less for the velocity change. It is found that using the B-field strength at the center of the filter section overestimates the overall B-field strength and causes underestimation of the ion velocity by approximately 10%. In the second numerical experiment test, the two distinct, closely adjacent peaks, which are observable in one ExB probe design, become one large peak when the collimator and the drift tube lengths are halved from 130 mm to 65 mm. The ExB probe broadens the peak width up to 287%, in which case inferring the ion velocity spread from the ExB probe may not be a valid approach. The relative ion species fraction calculated from the ExB probe spectra showed a good agreement within an error of 0.1% or less. Finally, an approach to account for the space-charge ion beam expansion, which is often neglected in the ExB probe analysis is discussed.