Fermilab, Batavia
A purely imaginary Space Charge Impedance (SCI) is a part of the entire impedance which takes into account local electromagnetic field carried by a beam only. Such impedance is unable to cause the beam instability by itself (negative mass instability is the unique exclusion derived from a lack of longitudinal focusing in coasting beams). Real part of the impedance is just the one directly responsible for the instability, and it is generated by any retarding (wake) field. However, SCI affects on all the instability characteristics including threshold, frequency, ramp rate and shape of intra-bunch oscillations (head-tale modes). This influence can be crucially important in proton synchrotrons where SCI, typically, constitutes a significant or even dominant part of the impedance. In such conditions, the wake field can be treated as a small perturbation which controls parameters of collective beam modes at given head-tale bunch mode. This talk is designated to analyze the mentioned effects in frames of these assumptions. The emphasis is on the problem of transverse oscillations of a bunched beam.
GSI, Darmstadt
Significant progress has been made recently in the understanding of the effects of direct space charge on the transverse head-tail bunch dynamics. Different analytic approaches for head-tail modes in bunches for different space-charge parameter regimes have been suggested. Besides head-tail eigenmode characteristics, Landau damping in a bunch exclusively due to space charge has been predicted. In this contribution we compare results of particle tracking simulations with theoretical predictions for the eigenfrequencies and eigenfunctions of head-tail modes in a Gaussian bunch. We demonstrate the space-charge induced Landau damping in a bunch and quantify damping rates for different modes and space-charge tune shifts. Under conditions below the mode coupling threshold we study the head-tail instability with space charge. Our results show that the space-charge induced damping can suppress the instability for moderately strong space charge. For strong space charge the instability growth rates asymptotically reach constant vales, in agreement with theoretical predictions.
IHEP Beijing, Beijing
The China Spallation Neutron Source (CSNS) accelerator operates at 25 Hz repetition rate with an initial design beam power of 100 kW and is upgradeable to 500 kW. The accelerator of CSNS consists of a low energy linac and a Rapid Cycling Synchrotron (RCS). In this kind of high power accelerators, especially in the low energy end, the beam is space charge dominated, and the space charge effects are the main source of beam loss. The space charge effects limit the maximum beam density, as well as beam power. Many simulation works were done for the study of space charge effects for CSNS accelerators, by using code ORBIT , SIMPSONS and PARMILA. Various conditions are considered in simulations, including the effects of different lattice structure, different tune, the combine effect of sextupole field and space charge, the combine effects of higher order field, error and space charge effects, different painting beam distribution for RCS, etc. The beam loss and emittance growth are compared for different conditions. A brief introduction to beam dynamics design is also given.
KEK, Ibaraki
Nonlinear space charge interaction in high intensity proton rings causes beam loss, which limits the performance. Simulations based on the particle in cell (PIC) method has been performed for JPARC-Rapid Cycle Synchrotron (RCS) and Main Ring (MR). Beam loss estimation during acceleration and resonances analysis are discussed with various simulations using dynamic and frozen models.