Intense nonneutral beam propagation through a periodic focusing quadrupole field I--A compact Paul trap configuration to simulate beam propagation over large distances

Journal Article · Fri Dec 10 04:00:00 EST 1999 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.1302132· OSTI ID:21210367

Davidson, Ronald C; Hong, Qin; Shvets, Gennady ^[1]

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1. Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)

This paper considers an intense nonneutral charged particle beam propagating in the z-direction through a periodic focusing quadrupole magnetic field with transverse focusing force, -{kappa}{sub q}(s)[xe{sub x}-ye{sub y}], on the beam particles. Here, s={beta}{sub b}ct is the axial coordinate, ({gamma}{sub b}-1)m{sub b}c{sup 2} is the directed axial kinetic energy of the beam particles, q{sub b} and m{sub b} are the charge and rest mass, respectively, of a beam particle, and the oscillatory lattice coefficient satisfies {kappa}{sub q}(s+S)={kappa}{sub q}(s), where S is the axial periodicity length of the focusing field. The particle motion in the beam frame is assumed to be nonrelativistic, and the Vlasov-Maxwell equations are employed to describe the collisionless nonlinear evolution of the distribution function f{sub b}(x,y,x{sup '},y{sup '},s) and the (normalized) self-field potential {psi}(x,y,s)=q{sub b}{phi}(x,y,s)/{gamma}{sub b}{sup 3}m{sub b}{beta}{sub b}{sup 2}c{sup 2} in the transverse laboratory-frame phase space (x,y,x{sup '},y{sup '}), assuming a thin beam with characteristic radius r{sub b}<<S. It is shown that collective processes and the nonlinear transverse beam dynamics can be fully simulated in a compact Paul trap configuration in which a long nonneutral plasma column (L>>r{sub p}) is confined axially by applied dc voltages V=const. on end cylinders at z={+-}L, and transverse confinement in the x-y plane is provided by segmented cylindrical electrodes (at radius r{sub w}) with applied oscillatory voltages {+-}V{sub 0}(t) over 90 deg. segments. Here, V{sub 0}(t+T)=V{sub 0}(t), where T=const. is the oscillation period, and the oscillatory quadrupole focusing force on a particle with charge q and mass m near the cylinder axis is -m{kappa}{sub q}(t)[xe{sub x}-ye{sub y}], where {kappa}{sub q}(t){identical_to}8qV{sub 0}(t)/{pi}mr{sub w}{sup 2}. This configuration offers the possibility of simulating intense beam propagation over large distances in a compact configuration which is stationary in the laboratory frame.

• OSTI ID: 21210367
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 498; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
BEAM DYNAMICS
BEAM-PLASMA SYSTEMS
BOLTZMANN-VLASOV EQUATION
CHARGED PARTICLES
COMPUTERIZED SIMULATION
CYLINDRICAL CONFIGURATION
DISTRIBUTION FUNCTIONS
ELECTRIC POTENTIAL
KINETIC ENERGY
MAGNETIC FIELDS
NONLINEAR PROBLEMS
PERIODICITY
PHASE SPACE
PLASMA
PLASMA CONFINEMENT
PLASMA SIMULATION
QUADRUPOLES
TRAPS