Abstract
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).
Highlights
The energy distribution of ions released by secondary plasmas reflects plasma potential with features down to the scale of a few volts, which makes necessary an accurate analysis of the measuring equipments, as a Retarding Field Energy Analyzer (RFEA)[1,2,3] considered here
In order to put the detector response to plasma ion temperature T i into clear evidence, we need simplified models of the ion distribution impinging on the retarding field energy analyzer (RFEA), with a minimal number of features and other parameters, here the plasma potential V p and electron temperature T e; three such models are discussed in the following
It may be argued that slow ions can be deflected to a large angle by grids and that emittance growth due to grids[4] affects RFEA operation; here we study these effects showing that they are not larger than the effects of the input ion temperature in typical conditions, and both can be tolerated in typical design, corroborating the previous design criteria for grid (b small) and introducing the typical lateral diffusion lengths Sn, fairly well contained inside our RFEA design
Summary
The energy distribution of ions (or electrons) released by secondary plasmas (which are produced by collisions of intense ion beams with residual gases or vacuum chamber walls) reflects plasma potential with features down to the scale of a few volts, which makes necessary an accurate analysis of the measuring equipments, as a Retarding Field Energy Analyzer (RFEA)[1,2,3] considered here. RFEA concepts can be used to analyze low energy primary ion beams (as in the case of beam produced by Hall effect thrusters5) or electron beams[6] or plasmas of ion sources, with the necessary modification in voltages and Faraday cup power handling capability.[7,8,9] Typical overall sizes are often dictated by the space available, with outer diameter Do ranging from 15 mm to 0.1 m. Another overall parameter is Di/Do (ranging from 0.1 to 0.2), with Di the input hole diameter. Additional detail of multipole effects in grids is given in Appendix B
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