Phys. Rev. ST Accel. Beams 6, 044401 (2003) [10 pages]

Kinetic analysis of intense sheet beam stability properties for uniform phase-space density

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Edward A. Startsev and Ronald C. Davidson
Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543

Received 3 December 2002; published 17 April 2003

This paper makes use of the Vlasov-Maxwell equations to investigate collective excitations in an intense sheet beam, infinite in the y and z directions, propagating in the z direction with directed kinetic energy (γb-1)mbc2. The beam is confined in the x direction by the smooth-focusing force Ffoc=-γbmbωβ⊥2xex, and perfectly conducting walls are located at xxw. A self-consistent water bag equilibrium fb0 satisfying the steady-state (∂/∂t=0) Vlasov-Maxwell equations is shown to be exactly solvable for the beam density nb0(x) and electrostatic potential φ0(x). A closed Schrödinger-like eigenvalue equation is derived, assuming small-amplitude perturbations (δfb,δφ) about the self-consistent water bag equilibrium, and the eigenfrequency spectrum is shown to be purely real. The WKB approximation is employed to determine the eigenfrequency spectrum as a function of the normalized beam intensity sb=ω-^ pb2b2ωβ⊥2, where ω-^ pb2=4πn-^ beb2bmb and n-^ b=nb(x=0) is the on-axis number density of beam particles.


©2003 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevSTAB.6.044401
DOI: 10.1103/PhysRevSTAB.6.044401
PACS: 29.27.–a, 41.75.–i

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