(Color) Oscillation frequency (upper plot) and Landau damping constant (bottom plot) as a function of the energy spread (K γ) and emittance parameter for D = 1 and K β ≫ 1.
(Color online) Ballistic evolution of a helical charge density perturbation associated with an m = 1 transverse mode.
(Color) Schematics of the plasma-betatron beatwave mechanism. The blue line represents the time evolution of the electric field, the red dashed line shows the envelope of the beatwave, evolving according to the effective oscillation frequency δΩ.
(Color) Fundamental mode oscillation frequency as a function of D for the laminar beam limit (blue curve) and for the high betatron frequency limit (red curve) as found with the matrix method for a cold beam. For comparison, the variational solutions are plotted as dashed lines.
(Color) Mode profile for the fundamental m = 0 mode, for K β ≫ 1 and D = 10 (blue curve), D = 1 (red curve), D = 0.1 (black curve). For comparison, the beam density profile is plotted as a black dotted line.
(Color) Effective plasma oscillation frequency δΩ as a function of D for the E 1,1,0 (red solid line) and E 2,0,0 (red dashed line) modes for K β ≫ 1. The blue lines show the oscillation frequency Ω for the corresponding eigenmodes in the laminar beam limit (K β ≪ 1), i.e., the E 1,0 (blue solid line) and E 2,0 (blue dashed line) modes.
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