Abstract
We investigate how collective modes and colored noise conspire to produce a beam halo with much larger amplitude than could be generated by either phenomenon separately. The collective modes are lowest-order radial eigenmodes calculated self-consistently for a configuration corresponding to a direct-current, cylindrically symmetric, warm-fluid Kapchinskij-Vladimirskij equilibrium. The colored noise arises from unavoidable machine errors and influences the internal space-charge force. Its presence quickly launches statistically rare particles to ever-growing amplitudes by continually kicking them back into phase with the collective-mode oscillations. The halo amplitude is essentially the same for purely radial orbits as for orbits that are initially purely azimuthal; orbital angular momentum has no statistically significant impact. Factors that do have an impact include the amplitudes of the collective modes and the strength and autocorrelation time of the colored noise. The underlying dynamics ensues because the noise breaks the Kolmogorov-Arnol'd-Moser tori that otherwise would confine the beam. These tori are fragile; even very weak noise will eventually break them, though the time scale for their disintegration depends on the noise strength. Both collective modes and noise are therefore centrally important to the dynamics of halo formation in real beams.
Highlights
We recently demonstrated [1] that the combination of colored noise and global oscillations in intense chargedparticle beams can create much larger halo amplitudes than would arise in the absence of noise
This was done using generic ‘‘particle-core’’ models as representations of time-dependent potentials associated with nonequilibrium beams [2,3]; the ‘‘core’’ established a time dependence in the form of a harmonic oscillation reminiscent of the presence of a global collective mode, and test particles orbited in response to that potential
The foregoing results illustrate that collective modes can have a critical impact on halo formation by destabilizing the phase space near the beam boundary
Summary
We recently demonstrated [1] that the combination of colored noise and global oscillations in intense chargedparticle beams can create much larger halo amplitudes than would arise in the absence of noise. We sequentially computed 10 000 orbits while assigning to each orbit its own unique, random manifestation of the colored noise, and we cataloged the maximum amplitudes of these orbits Though this approach proved sufficient to demonstrate the noise-enhanced production of beam halo, it suffers a number of shortcomings. It lacks self-consistency; with one exception, the oscillation frequencies of the core were chosen ad hoc, the exception relating to a space-charge-limited core. Many (typically 106 ) test particles, assigning each test particle its own random manifestation of colored noise, and tracking their orbits, we compute the evolution of the halo We do this for two extremes of initial particle velocities, the first corresponding once again to purely radial orbits, and the second corresponding to purely circular orbits.
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