Simulations of beam envelope dynamics in circular accelerators

Abstract

The envelope instability of high intensity beams in circular accelerators is studied via multiparticle simulations. The space charge kicks are derived from a Gaussian potential model for an efficient tracking. The evolution of the envelope phase space coordinates are derived from the bunch distribution. We found that the envelope stop band played an important role in emittance growth. Correction schemes of the envelope stop bands are studied. Because the space charge force pushes the envelope tunes downward, harmonics less than twice the betatron tunes are also important on emittance growth. Our code is efficient and fast, it can be used to study the effect of space charge force on high power accelerators.

Envelope dynamics and stability with non-linear space-charge forces

“…We attribute this to the intrinsic space-charge coupling. This observation is consistent with [3], where the tune spread also increases for that mode. Furthermore, we find third-order difference resonance and a fifth-order sum resonance, which are space-charge driven.…”

“…The lattice we use throughout this work consists of a ring with 324 m circumference, comprised of 18 identical FODO-cells. We have reconstructed this lattice from information in [3]. The qualitative configuration of one cell is depicted in Fig.…”

“…This indicates that non-linear space-charge forces cause instability around the integer tune, even in the absence of lattice errors. In [3], crossing the integer tune leads to an increase in tune spread, because the rms envelope is calculated from single particle coordinates. These particles can rearrange themselves in the case of light instabilities.…”

“…PIC codes are usually computationally expensive, depending on grid sizes and the amount of interactions taken into account. In [3], the authors use tracking of single particles with space-charge kicks derived from the potential of an upright Gaussian distribution, which itself is derived from the rms quantities of the single particles. Through this calculation sequence, the number of applied space-charge kicks is limited if simulations are to be completed in a limited time-frame.…”

Characterization and minimization of the half-integer stop band with space charge in a hadron synchrotron

“…half-integer resonance occurs on the coherently shifted tune, and [8] elaborates on the envelope dynamics under space charge conditions and the stop band correction.…”