Three-dimensional kinetic stability theorem for high-intensity charged particle beams
- Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 (United States)
Global conservation constraints obtained from the nonlinear Vlasov{endash}Maxwell equations are used to derive a three-dimensional kinetic stability theorem for an intense non-neutral ion beam (or charge bunch) propagating in the {ital z} direction with average axial velocity v{sub b}=const and characteristic kinetic energy ({gamma}{sub b}{minus}1)mc{sup 2} in the laboratory frame. Here, {gamma}{sub b}=(1{minus}v{sub b}{sup 2}/c{sup 2}){sup {minus}1/2} is the relativistic mass factor, and a perfectly conducting cylindrical wall is located at radius r=r{sub w}, where r=(x{sup 2}+y{sup 2}){sup 1/2} is the radial distance from the beam axis. The particle motion in the beam frame ({open_quotes}primed{close_quotes} coordinates) is assumed to be nonrelativistic, and the beam is assumed to have sufficiently high directed axial velocity that v{sub b}{gt}{vert_bar}{bold v}{sup {prime}}{vert_bar}. Space-charge effects and transverse electromagnetic effects are incorporated into the analysis in a fully self-consistent manner. The nonlinear Vlasov{endash}Maxwell equations are Lorentz-transformed to the beam frame, and the applied focusing potential is assumed to have the (time-stationary) form {psi}{sub sf}{sup {prime}}({bold x}{sup {prime}})=({gamma}{sub b}m/2)[{omega}{sub {beta}{perpendicular}}{sup 2}(x{sup {prime}2}+y{sup {prime}2})+{omega}{sub {beta}z}{sup 2}z{sup {prime}2}], where {omega}{sub {beta}{perpendicular}} and {omega}{sub {beta}z} are constant focusing frequencies. It is shown that a sufficient condition for linear and nonlinear stability for perturbations with arbitrary polarization about a beam equilibrium distribution f{sub eq}({bold x}{sup {prime}},{bold p}{sup {prime}}) is that f{sub eq} be a monotonically decreasing function of the single-particle energy, i.e., {partial_derivative}f{sub eq}(H{sup {prime}})/{partial_derivative}H{sup {prime}}{le}0. Here, H{sup {prime}}={bold p}{sup {prime}2}/2m+{psi}{sub sf}{sup {prime}}({bold x}{sup {prime}})+{phi}{sub eq}({bold x}{sup {prime}}), where {phi}{sub eq}({bold x}{sup {prime}}) is the space-charge potential. {copyright} {ital 1998 American Institute of Physics.} thinsp
- OSTI ID:
- 641534
- Journal Information:
- Physics of Plasmas, Vol. 5, Issue 9; Other Information: PBD: Sep 1998
- Country of Publication:
- United States
- Language:
- English
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