Theoretical studies of envelope oscillations and instabilities of mismatched intense charged-particle beams in periodic focusing channels

TL;DR

This paper provides a theoretical analysis of envelope oscillations and instabilities in mismatched intense charged-particle beams within periodic focusing channels, using analytical, numerical, and simulation methods.

Contribution

It introduces a comprehensive theoretical framework combining smooth-approximation, numerical evaluation, and computer simulations to study beam envelope behaviors and instabilities.

Findings

Envelope oscillation frequencies are derived analytically.

Phase shifts and growth rates of instabilities are calculated.

Simulation results compare K-V and Gaussian distributions.

Abstract

The behavior of mismatched intense charged-particle beams in periodic transport channels of the solenoid and quadrupole type is studied theoretically. The envelope-oscillation frequencies of the mismatched beam are obtained by the smooth-approximation method and by numerical evaluation of the linearly perturbed K-V envelope equations. Phase shifts of the envelope oscillations and growth rates in the case of instability are calculated for a solenoid and a magnetic quadrupole (FODO) channel using the parameters of the Maryland and GSI beam transport experiments. For comparison and the purpose of illustration, the K-V equations are integrated numerically, and envelope curves as well as single-particle trajectories for for mismatched beams are shown in graphical form. In addition, computer simulation studies with the PARMILA code were performed, and results are presented both for K-V and a Gaussian distribution in transverse phase space.