Longitudinal Space-charge Effects in a Retarding Field Energy Analyzer

Experimental and theoretical work has been carried out to study the longitudinal space-charge effects in a retarding field energy analyzer. A one-dimensional model for both a mono-energetic beam and a thermal beam has been developed for this purpose. The study shows that, if the current density inside the device were higher than a critical value, the longitudinal space-charge effects would distort the measured energy spectrum. The measured mean energy will be shifted toward the low-energy side and the resulting spectrum will have a tail at the highenergy side. The measured FWHM and rms energy spread may also be affected. INTRODUCTION In order to characterize the energy spread in UMER [1], a retarding field energy analyzer has been developed and tested. The design and testing results of the device have been reported elsewhere [2, 3]. During the experiment, it was found that, when the current density in the analyzer is higher than a certain value, the measured energy spectrum is shifted towards the low-energy side compared to the one measured with low injected current. Fig. 1 depicts such a case, where Curve I is for a low-current case and Curve II is for a high-current case. At the same time, the energy spectrum measured with high current density has a tail at high-energy side. This is believed to be due to the longitudinal space-charge force in the device. The mean energy shift due to the space-charge effect was observed before in studies of the energy spread in a beam from an ion source, for example see Refs. [4, 5]. Ref. [6] gave an approximate analytical solution to explain the spacecharge effect in the ion source, the result of which is similar to the Langmuir-Child equation. In this paper, we will, via analytical analysis and simulations, present new results for the longitudinal space-charge effect in this kind of devices.