Simulation of longitudinal Landau damping in bunches with space charge

TL;DR

This paper investigates the longitudinal Landau damping in particle bunches affected by space charge, analyzing frequency spectra and validating numerical methods to improve long-term simulation accuracy in ion synchrotrons.

Contribution

It introduces a detailed analysis of Landau damping near the loss threshold and compares grid-based and grid-less space charge solvers, emphasizing the importance of the cut-off parameter.

Findings

Branching point frequency is independent of cut-off parameter h_c.

Dipole mode damping is unaffected by h_c for realistic beam pipes.

Validation shows consistency between grid-based and grid-less solvers.

Abstract

For a single hadron bunch affected by longitudinal space charge in a stationary rf bucket we analyze the frequency spectrum close to the expected loss of Landau damping for the lowest order dipole mode. For different bunch intensity parameters we obtain the bunch oscillation spectrum from a conventional longitudinal particle tracking code with a grid-based space charge solver. We validate selected results against a grid-less space charge solver. We highlight the importance of the choice of the cut-off parameter $h_c$ in the space charge impedance for the long-term accuracy of grid-based schemes. For typical bunch parameters in an ion synchrotron at injection energies we find that the branching point, where the dipole mode frequency emerges from the incoherent synchrotron frequency spectrum, as well as the damping of the dipole mode do not depend on $h_c$, chosen well below the actual value for realistic beam pipes.