Particle traces of a full collimator with detector B10 were run. The effect of the sheath was simulated by a fixed potential V1 at 0.5 inches outside the collimator. The choice of 0.5 inches is mostly arbitrary but it is about a factor of 4 larger than the collimator slit so that the potential contours that far away will be relatively flat.
The potential in the sheath region is assumed to fall off exponentially. If the Debye length is more than 0.5 inches, the region inside of V1 has a nearly linear potential fall off. It can be approximated well by the free space potentials calculated by the simulation. The magnitude of the potential difference between the detector and the V1 point is based on the value of the exponential at 0.5in.
For a Debye length of 1 inch and a detector-to-plasma potential of 0.5V, the fixed voltage at V1 is set to 0.197V. Particles in the plasma are accelerated by 0.303 eV before reaching the V1 point. The trace grid starts at the V1 point and particles are accelerated by the additional 0.197V before entering the detector.
The trace paths that made it from V1 through the analyzer have their energy and angle at V1 backtracked to the external plasma by assuming that they were accelerated only in the x direction to reach V1. (Since the detector is cylindrical there will be some z acceleration for non-zero z paths but hopefully this effect is small over a small span of z values at large radius.)
All runs were done with the analyzer set to select 0.6 eV. This corresponds to 0.1eV in the external plasma and a detector-to-plasma accelerating potential of 0.5V.
Runs were done for Debye lengths of 1, 2 and 6 inches with and without an entrance screen. The data files from screen runs are shown on the left and named C10s, the ones without screens are on the right and named C10a.
The major effect of the sheath is to increase the effective entrance angle acceptance. For a 1 inch Debye length the effect is quite large but it decreases rapidly for larger Debye lengths. The sheath has little effect on overall energy resolution.
The overall throughput and energy resolution are not significantly changed by the entrance screen.
The sheath has only a minor effect on focus.
