Analysis of grid size and ion temperature effects in retarding field energy analyzers (RFEA)

The self-potential of a high current ion beam may be fairly balanced by a secondary plasma with plasma potential Vp; the retarding field energy analyzer (RFEA) measuring the secondary ion outflow is a promising diagnostic of these plasmas. A detailed analysis of a planar RFEA is here discussed, with a focus on the response (in stationary condition) of the detector to the secondary plasma characteristics, and on the determination of design rules for the parameters of a compact RFEA. First, energy distributions of the secondary ion plasma outflow are discussed, as a function of ion temperature Ti and electron temperature Te. Second, the modulation of grid potential (depending on grid pitch b and wire radius a) is calculated both for 2D and 3D models, reaching a good agreement with accompanying electrostatic simulations. Beam emittance (or temperature) growth and beam diffusion are then discussed, also when input ion energy matches the discrimination voltage Vd; corrections to the usual paraxial dynamics result are then introduced. As regards the response of the whole detector (also called transmission function) and the beam dynamics evolution, systematic 3D multiparticle simulations were performed in order to study the behavior of the detector as a function of Vd and of the secondary plasma parameters Vp, Ti and Te and to determine the design parameter effects on instrumental precision (found to be about 0.1 b |Ez| with Ez the axial field near grids)