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Phys. Rev. ST Accel. Beams 6, 024402 (2003) [8 pages]

Truncated thermal equilibrium distribution for intense beam propagation

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Ronald C. Davidson and Hong Qin
Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543

Steven M. Lund
Lawrence Livermore National Laboratory, University of California, Livermore, California 94550

Received 6 December 2002; published 24 February 2003

An intense charged particle beam with directed kinetic energy (γb-1)mbc2 propagates in the z direction through an applied focusing field with transverse focusing force modeled by Ffoc=-γbmbωβ2x in the smooth-focusing approximation. This paper examines properties of the axisymmetric, truncated thermal equilibrium distribution Fb(r,p)=Aexp⁡(-H/T̂b)⊕(H-Eb), where A, T̂b, and Eb are positive constants, and H is the Hamiltonian for transverse particle motion. The equilibrium profiles for beam number density, nb(r)=∫d2pFb(r,p), and transverse temperature, Tb(r)=[nb(r)]-1d2p(p2/2γbmb)Fb(r,p), are calculated self-consistently including space-charge effects. Several properties of the equilibrium profiles are noteworthy. For example, the beam has a sharp outer edge radius rb with nb(rrb)=0, where rb depends on the value of Eb/T̂b. In addition, unlike the choice of a semi-Gaussian distribution, FbSG=Aexp⁡(-p2/2γbmbT̂b)⊕(r-rb), the truncated thermal equilibrium distribution Fb(r,p) depends on (r,p) only through the single-particle constant of the motion H and is therefore a true steady-state solution (∂/∂t=0) of the nonlinear Vlasov-Maxwell equations.

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© 2003 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevSTAB.6.024402
DOI:
10.1103/PhysRevSTAB.6.024402
PACS:
29.27.Bd, 41.85.Ct, 41.85.Ew