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Using the dielectric theory for a weakly coupled plasma, we investigate the stopping power of an ion in an anisotropic two-temperature electron plasma in the presence of a magnetic field. The analysis is based on the assumption that the energy variation of the ion is much less than its kinetic energy. A general expression for the stopping power is analyzed for weak and strong magnetic fields (i.e., for the electron cyclotron frequency less than and greater than the plasma frequency), and for low and high ion velocities. It is found that the usually velocity independent friction coefficient contains an anomalous term which diverges logarithmically as the projectile velocity approaches zero. The physical origin of this anomalous term is the coupling between the cyclotron motion of the electrons and the long-wavelength, low-frequency fluctuations produced by the projectile ion.

A retarding electrostatic field energy analyzer for low-energy beams has been designed, simulated, and tested with electron beams of several keV, in which space-charge effects play an important role. A cylindrical focusing electrode is used to overcome the beam expansion inside the device due to space-charge forces, beam emittance, etc. The cylindrical focusing voltage is independently adjustable to provide proper focusing strength. Single particle simulation and theoretical error analysis using beam envelopes show that this energy analyzer can get very high resolution for low-energy beams (up to 10 keV), which was found to be in good agreement with experimental results. The measured beam energy spectrum is both temporally and spatially resolved. In addition, a computer-controlled automatic system is developed and significantly improves the speed and efficiency of the data acquisition and processing. The measured beam energy spreads, are in remarkably good agreement with the intrinsic limits set by the effects of nonadiabatic acceleration in the electron gun and that of Coulomb collisions, as predicted by theory.

Beams in which space charge forces are stronger than the force from thermal pressure are nonneutral plasmas, since particles interact mostly via the long-range collective potential. An ever-increasing number of applications demand such high-brightness beams. The University of Maryland Electron Ring ͓P. G. O'Shea et al., Nucl. Instrum Methods Phys. Res. A 464, 646 ͑2001͔͒, currently under construction, is designed for studying the physics of space-charge-dominated beams. Indirect ways of measuring beam emittance near the UMER source produced conflicting results, which were resolved only when a direct measurement of phase space indicated a hollow velocity distribution. Comparison to self-consistent simulation using the particle-in-cell code WARP ͓D. P. Grote et al., 193 ͑1996͔͒ revealed sensitivity to the initial velocity distribution. Since the beam is born with nonuniformities and granularity, dissipation mechanisms and rates are of interest. Simulations found that phase mixing by means of chaotic particle orbits is possible in certain situations, and proceeds much faster than Landau damping. The implications for using beams to model other N-body systems are discussed.

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