Fluctuations Do Matter: Large Noise-Enhanced Halos in Charged-Particle Beams

Abstract

The formation of beam halos has customarily been described in terms of a particle-core model in which the space-charge field of the oscillating core drives particles to large amplitudes. This model involves parametric resonance and predicts a hard upper bound to the orbital amplitude of the halo particles. We show that the presence of colored noise due to space-charge fluctuations and/or machine imperfections can eject particles to much larger amplitudes than would be inferred from parametric resonance alone.

Experimental investigation of random noise-induced beam degradation in high-intensity accelerators using a linear Paul trap

“…This is a practical compromise to overcome the difficulty of measuring small changes in charge signals ( $ 1 fC) in the PTSX device (particularly for the tail distribution or halo particles in the off-axis regions). Nonetheless, in modern high-intensity accelerators, loss of only a few particles per meter can cause radioactivation that would preclude routine hands-on maintenance [4]. Therefore, it is highly relevant to verify the validity of numerical tools and to test the physics models for beam loss in experiments with parameters even somewhat beyond the actual tolerance limits.…”

“…These simulation results can also be interpreted as indicating enhanced halo formation. One possible underlying mechanism for enhanced halo formation has been proposed by Bohn and Sideris [4,7]. By extending the particle-core model [33,38], they showed that the combination of colored noise and core envelope oscillations (breathing modes in their case) can eject particles to a much larger degree than would be achieved in the absence of noise.…”

“…Thus, any ripples in the driven currents or ground vibration can comprise a colored noise in the quadrupole focusing gradient with a finite autocorrelation time (e.g., several focusing periods) [32]. In recent papers [4,7], Bohn and Sideris pointed out that the presence of colored noise can boost a small number of particles to much larger amplitudes than inferred from a parametric resonance alone [33], by continually kicking halo particles back into the right phase with the core envelope oscillation. Hence, in this section, we describe a preliminary experimental study that investigates the possible synergistic effect between colored noise and the collective modes indicated by Bohn and Sideris.…”

“…One critical but unavoidable problem in highintensity accelerators is the presence of undesired random noise due to machine imperfections, and its influence on the long-time-scale beam dynamics [4,5]. The machine imperfections may include quadrupole magnet and rf cavity alignment errors, quadrupole focusing gradient errors, rf field amplitude and phase errors, to mention a few examples [6].…”

“…The machine imperfections may include quadrupole magnet and rf cavity alignment errors, quadrupole focusing gradient errors, rf field amplitude and phase errors, to mention a few examples [6]. Usually, random noise in the machine components acts as a continuous supply of free energy to the beam, which results in irregular mismatch oscillations of the beam envelope [5], enhanced halo formation [4,7], and emittance growth [8], particularly over long propagation distances. Consequently, the associated beam degradation defines the practical and/or economic tolerances in the machine design and operation [3,9].…”