Nonlinear dynamics and chaoticity in an intense nonneutral heavy ion beam propagating through a periodic focussing field
- Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)
Properties of an intense nonneutral heavy ion beam propagating through a periodic quadrupole focussing magnetic field are studied analytically and numerically including self-field effects. For a Kapchinskj-Vladimirski (K-V) beam equilibrium with uniform density profile, the two nonlinear coupled envelope equations are solved for the case of a matched beam in the smooth-beam approximation. Space-charge effects are taken into account self-consistently. The analytical solutions for the envelope and the (space-charge-depressed) phase advance are compared with the (exact) numerical results, and the technique can be applied to a wide range of system parameters and choices of lattice functions {kappa}q(s)={kappa}q(s+S). Furthermore, a fully nonlinear study of the envelope equations for the case of a mismatched beam is carried out numerically. In certain parameter regimes, the beam envelope is found to exhibit bifurcation which results in chaotic behavior of the beam envelope when the focussing field strength is increased beyond a particular threshold. The (unstable) chaotic region in the parameter space ({sigma}0, KS/{epsilon}) is determined numerically. Here, {sigma}0 is a measure of the focussing strength defined by {sigma}{sup 2}0/S{sup 2} {identical_to}<({integral}{sup s}s0 ds{kappa}q(s)){sup 2}>, K is the self-field perveance, s is the periodicity length of the focussing lattice, and {epsilon} is the unnormalized beam emittance. The relationship between chaoticity and well-known linear instabilities is examined. In addition, for the case of a nonuniform density beam, it is found that the particle trajectory exhibits intrinsic chaoticity. The consequence of chaotic particle orbits is further investigated.
- OSTI ID:
- 21153794
- Journal Information:
- AIP Conference Proceedings, Vol. 331, Issue 1; Conference: Non-neutral plasma physics II: Berkeley workshop on non-neutral plasmas in traps, Berkeley, CA (United States), 17-20 Jul 1994; Other Information: DOI: 10.1063/1.47880; (c) 1995 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
Similar Records
Phase advance for an intense charged particle beam propagating through a periodic quadrupole focusing field in the smooth-beam approximation
Nonlinear dynamics of intense ion beam envelopes