Observations and Simulations of Particle-density Oscillations in an Apertured, Space-charge Dominated Electron Beam∗

Experiments and particle-in-cell (PIC) simulations in connection with the University of Maryland Electron Ring [1] demonstrate the appearance and evolution of transverse space-charge waves in a space-charge dominated electron beam. The waves are observed regardless of the focusing system, although the strength of the focusing affects their onset and evolution. An aperture induces the perturbation in the particle distribution in an initially freely-expanding beam. Simulations show that the effect of the aperture can be modeled approximately by a beam with an initially semi-Gaussian particle distribution with a temperature profile. Furthermore, simple tracking of test particles initially near the aperture’s edge reproduce well the onset of the perturbation. For the parameters investigated, simulations further indicate that the perturbation damps out over a few plasma periods without causing any emittance growth. Detailed understanding of the effects of space charge in the transport of intense beams is important in all areas of research and applications where beam quality is crucial. A rarely discussed aspect concerns the evolution of beams from the source to equilibrium, if any, including the role of source errors or aberrations, apertures and other factors that affect the initial particle distribution in phase space. The initial density profile of a beam has long been recognized as an important factor in determining its evolution (i.e., emittance growth, instabilities, etc.) [2]. A less appreciated influence on the dynamics is the initial temperature profile of the beam. For the Kapchinskij-Vladimirskij (KV) distribution [3], Gluckstern [4, 5] has derived transverse kinetic oscillation modes that involve an exchange between the temperature and density profiles. However, since the K-V distribution is highly idealized, the Gluckstern modes, which can become unstable, have been thought not to exist for a physical beam. Using a warm-fluid model, Lund and Davidson [6] have rederived the Gluckstern modes and extended them to an arbitrary equilibrium distribution. Further, recent computer simulations by Lund et al. [7], relating to experiments at Lawrence Berkeley National Laboratory, exhibit density oscillations similar to Gluckstern modes, in a beam whose initial temperature or density pro∗Work supported by the U.S. Department of Energy. † Email: [email protected] files are perturbed. Despite the important insights provided by these studies, no clear connection has been established in either experiments or simulations between the physical cause(s) of the initial beam perturbation, the resulting phase-space distribution, and the long term evolution of this distribution. This paper [8] presents concrete experimental evidence, augmented by self-consistent particle-in-cell (PIC) computer simulations, for the occurrence of wave-like transverse density oscillations in an electron beam. The beam is perturbed by an aperture near the source, giving rise to an initial distribution that is far from equilibrium around the beam’s edge. Two transport experiments over a distance of about one meter and with similar overall focusing strengths (as given by the zero-current phase advance in the corresponding matched beams) demonstrate the onset and evolution of the beam perturbation. Figure 1 shows the schematics of a transport experiment with three short solenoids of the type employed extensively at Maryland. The second experiment uses a solenoid and five printed-circuit (PC) air-core quadrupoles similar to the lenses introduced recently for the University of Maryland Electron Ring [1]. SOLENOID WINDOW DIFF. PUMP STEERING 10 CM HELMHOLTZ CCD CAMERA PEARSON PHOSPHOR APERTURE