Thermal equilibrium theory of periodically focused charged-particle beams

A thermal equilibrium theory of periodically focused charged-particle beams is presented in the framework of both warm-fluid and kinetic descriptions. In particular, the thermal beam equilibria are discussed for paraxial beams in periodic solenoidal and quadrupole magnetic focusing fields, and the theory is compared with the experimental measurements. A warm-fluid equilibrium theory for a thermal beam in a periodic solenoidal focusing field is presented. The warm-fluid beam equilibrium equations are solved in the paraxial approximation, and the beam density and flow velocity are obtained. The self-consistent root-mean-square (rms) beam envelope equation and the self-consistent Poisson equation, governing the beam density and potential distributions, are derived. The beam equilibrium is adiabatic, i.e., there is no heat flow in the system, which results in rms beam emittance being conserved. The beam temperature is constant across the cross-section of the beam. For high-intensity beams, the beam density profile is flat in the center of the beam and falls off rapidly within a few Debye lengths at the edge of the beam. Such density profile provides a more realistic representation of a laboratory beam than the uniform density profile in the Kapchinskij-Vladimirskij beam equilibrium which had been used in experimental data analyses. A kinetic equilibrium theory for the thermal beam in the periodic solenoidal focusing field, which is equivalent to the warm-fluid equilibrium theory, is also presented. The Hamiltonian for single-particle motion is analyzed to find the approximate and exact invariants of motion, i.e., a scaled transverse Hamiltonian (nonlinear space charge included) and the angular momentum, from which a Maxwell-Boltzmann-like beam equilibrium distribution is constructed.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Nuclear Science and Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2008

Author dc:creator

• Samokhvalova, Ksenia R

Advisor dc:contributor.advisor

• Chiping Chen.

• Nuclear Science and Engineering.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/44788

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/44788