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• W2160048274 abstract "High intensity charged particle beam propagation in a periodic focusing lattice has been studied numerically using a model in which the beam equilibrium and dynamic behavior are described self-consistently by the nonlinear Vlasov-Maxwell equations. For a long coasting which is inhomogeneous in the transverse direction, the solutions to the Vlasov-Maxwell equations for periodic focusing configurations can only be determined numerically. To carry out this investigation, the Beam Equilibrium Stability and Transport (BEST) code which uses a 3D low-noise perturbative particle simulation method, has been extended. The scheme begins with a smooth-focusing lattice which is the smooth-focusing approximation for the periodic lattice, and adiabatically replaces the smooth-focusing lattice by the periodic lattice. With this approach, periodic solenoidal configurations have been investigated using a slow turn-on time to minimize beam mismatch, and periodic quadrupole configurations are now being studied. Objective and Method I The objective is to find practical solutions for Intense Charged Particle Beam (ICPB) in Periodic Focusing Configurations so that we can determine the detailed equilibrium, stability, and transport properties; I BEST code is used to numerically solve the Vlasov-Maxwell equations; I With the δf simulation method, the BEST code succeeds in reducing the noise by a factor of f δf ; I To apply the δf simulation method, the numerical scheme begins with a smooth-focusing lattice model for the periodic lattice, and adiabatically replaces the smooth-focusing lattice by the periodic lattice. Current Status of the Problem I Analytical approch: I The nonlinearity of the Vlasov-Maxwell equations makes it impossible to find a general analytical solution; I The only analytical solution is the Kapchinskij-Vladimirskij distribution, which is of limited practical interest; I Using Hamiltonian Averaging Techniques, it is possible to obtain approximate analytical solutions. I Numerically, the δf simulation method is promising. To apply this method, a quasi-equilibrium solution is needed. Vlasov-Maxwell Equations The Vlasov-Maxwell equations in a two-dimensional slice model are:  ∂ ∂s + x ′ ∂ ∂x + y ′ ∂ ∂y − „ κx (s) x + ∂ψ ∂x « ∂ ∂x ′ − „ κy (s) y + ∂ψ ∂y « ∂ ∂y ′ ff Fb = 0, and „ ∂ ∂x2 + ∂ ∂y2 « ψ = −b Nb Z dx dy ′ Fb, in which κx (s) and κy (s) are lattice functions, and the transverse focusing force on a beam particle is given by Ffoc = − [κx (s) x ex + κy (s) y ey ]. Here, Kb = 2Nbe b/γ 3 bmbβ 2 bc 2 is the self-field perveance, and ψ = ebφ/γ bmbβ 2 bc 2 is the normalized self-field potential. Periodic Focusing Solenoidal Field (a) (b) z B sol z S I I 2 1 1 / + − S B sol S 2 / I 1 + I 1 + I 1 +" @default.
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• W2160048274 date "2006-11-01" @default.
• W2160048274 modified "2023-09-27" @default.
• W2160048274 title "Perturbative Particle Simulation Studies of Periodically Focused Intense Charged Particle Beams." @default.
• W2160048274 hasPublicationYear "2006" @default.
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