**Figure 9.**

*Cross section of the CusPIG arc chamber, permanent magnet version. The magnetic field has a null running the length of the arc chamber, in line with the hot cathode.*

section shown. There is a field null located within the arc chamber, just behind the exit slit. Two rods of molybdenum run the length of the arc chamber and are biased positive at a voltage between about 60 and 150 V. These are the only surfaces at anode potential, and are located where fast electrons from the hot cathode cannot reach them without crossing magnetic field lines with an integrated strength of about 0.3 T. mm. The crucial feature is that the magnetic cusps do not leak electrons, because they are blocked by walls at cathode potential. This is a form of quadrupole Penning trap, where cathode potential is placed at the magnetic cusps, and anode potential only exists in the region away from the cusps. We coined the name CusPIG to describe this geometry [19].

There are other alternative implementations: the quadrupole magnetic field could be re-oriented by rotating 45 degrees, the magnetic poles being located near the corners. But the basic principle is a quadrupole magnetic field enhanced by Penning Trap potentials.

It was found that the efficiency of confinement varied very little with the strength of the field, so this permanent magnet arrangement became standard. The simplest construction provides two extended north poles each excited by an array of ¼" Neodymium-iron-boron magnets, one at each side, extending the length of the arc chamber, i.e. for the breadth of the beam. The arc chamber was graphite, and allowed to run hot, but was surrounded by a water-cooled aluminum case. A magnetic yoke surrounds three and a half sides of the arc chamber, provides a discrete south pole at the base, and provides two rudimentary weak south poles on either side of the beam exit slot. This creates a quadrupole field with a significant sextupole component; the fields are strongest in the back of the arc chamber and weaker near the exit, while the null line is located just behind the exit slot. Anode potential is confined to the two metal rods located where the magnetic field is strongest. This is the preferred construction.

Within a plasma magnetized by such a quadrupole field, fast electrons have a cycloidal path around magnetic field lines with a constantly changing curvature. Unless scattered by an ionizing event, the fast electrons have very low mobility normal to the field lines. But there will be a weak electric field normal to the field lines, giving rise to some electron cross-field drift at velocity **v** = **ExB** along the length of the arc chamber, in opposite directions in adjacent quadrants. Modeling also appears to reveal chaotic drifting along the arc chamber. Electrons are magnetically blocked from reaching the anodes, and are electrostatically blocked from reaching the walls. On reaching the end of the arc chamber there is a high chance of the electron hopping into another quadrant and returning in the opposite direction. By means of modeling the ballistic trajectories in the modeled magnetic field, and approximated electric field, using OPERA/TOSCA, we show that the whole arc chamber fills rapidly and uniformly with fast electrons except very close to the walls.

In **Figure 10**, the left view shows a transverse cross section of the electron trajectories as produced by the source of **Figure 9**. The Penning trap arrangement prevents any electron loss where the magnetic confinement would fail. The color represents the electron velocity; blue is low velocity, red is high—so the deceleration and reflection of electrons at the cusps can be seen. The quadrupole magnetic confinement shields the anode rods, while providing a zero field zone near the center of the chamber. Weak electric fields in and near the plasma sheath create **ExB** drift of the electrons, weakly emulating a magnetron racetrack, to help circulate the electrons around the discharge zone and enhance uniformity. The electron motion is very complex, consisting of cycloidal motion, but since the energy changes rapidly in the plasma sheath, this motion is somewhat chaotic. It extends rapidly down the length of the arc chamber, as shown.

Gas is introduced through orifices shown in **Figure 9**, blocked by the anode rods from direct line-of-sight to the exit slot. This makes for very efficient ionization of the introduced gas. If the mass flow is precisely known, and the ion current is precisely known, one can calculate the ionization efficiency, in terms of the fraction of the gas that is introduced which exits as beam ions. This is a function of many factors, the arc voltage and current, which determine both the fast electron density and the cross section. Operating the ion source for a constant ion current, as the gas flow is reduced, a higher arc current is required. Using 6A of arc current and an anode voltage of 120 V, with argon gas, the ionization efficiency had a highest value of 30% at 8.9 sccm.

The cathode is at one end of the arc chamber. The density of ionizing electrons is observed to fall with distance from the cathode, since electrons which ionize an atom or molecule lose energy, are less effective, and rapidly diffuse out of the core zone. We found that this attenuation was a strong function of the anode voltage—the higher the voltage, the further the mean distance that the electrons traveled before being lost from the useful population. We have measured the attenuation of the ionizing electrons as a function of distance from the cathode by measuring the uniformity of the ion beam. The result is informative and useful. First, an arc voltage minimum of about 38 V is required to get a discharge, and the current density falls very rapidly with distance. At 70 V, the electrons travel 3 m before the ionization falls to 1/e of the initial value. (Incidentally, because their paths are not straight, this is equivalent to about
