A Paul trap configuration to simulate intense non-neutral beam propagation over large distances through a periodic focusing quadrupole magnetic field
- Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)
This paper considers an intense non-neutral 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 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 simulated in a compact Paul trap configuration in which a long non-neutral 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 degree sign 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}. (c) 2000 American Institute of Physics.
- OSTI ID:
- 20215460
- Journal Information:
- Physics of Plasmas, Vol. 7, Issue 3; Other Information: PBD: Mar 2000; ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
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