Modeling rf resonant cavity method for measuring electron cloud effect using plasma dielectrics

Abstract

Electron cloud effect (ECE) is one of the main obstacles to achieving better performance and beam stability in current and future accelerators. For instance, ECE has been observed at the LHC at all bunch spacings, and the 2015 upgrade to 25 ns spacings is expected to require additional time for scrubbing in order to gain acceptable beam parameters. rf diagnostics of ECE are a non-destructive technique for measuring plasma density and the efficacy of mitigation in high-performance accelerators. Traveling wave rf diagnostic experiments have detected electron clouds by measuring side-bands from the modulation of phase shifts induced by electron cloud plasmas. However, it is difficult to measure the absolute plasma density using traveling wave techniques, and the effects of reflections and attenuation is not known, which increases the measurement error.An alternative method is the resonant cavity rf diagnostic. In these experiments, rf power is inserted into the beam pipe at a frequency just below the cutoff frequency, and the signal is measured in the same location as the transmitter. Since the rf is below the cutoff frequency, the wave does not propagate, but rather exponentially decays, effectively creating a resonant cavity at the location of the rf source. The resonant frequency of this virtual cavity changes due to the presence of an electron cloud that is modulated as the cloud builds up and dissipates. This frequency modulation is observed as side bands at intervals of the revolution frequency.We have previously developed numerical models of traveling wave rf diagnostics of ECE using an integrated PIC/plasma dielectric model. We apply that model here to the resonant cavity method, and simulate side bands due to frequency modulation when the rf is injected below the cutoff frequency for different magnetic fields. The rf modulation can be completely described using the dielectric properties of the electron cloud plasma. However, it is necessary to perform PIC simulations in order to accurately model electron cloud buildup and dissipation due to beam crossings. Simulations are run for many revolution periods to resolve side band structures, and so must be numerically stable over long simulation times.