Space charge induced beam instability in periodic focusing channel^a)

The transverse evolution of the envelope of an intense, unbunched ion beam in a linear periodic transport channel can be modeled for the approximation of linear self-fields by the Kapchinskij-Vladimirskij envelope equation. The envelope mismatched modes, or the second order even mode [I. Hofmann, Phys. Rew. E 57, 4713 (1998)], are the lowest order of resonance leading to collective instability that the designer should avoid, which suggests that an accelerator system should be established in the parameter region where the zero beam current phase advance σ₀ less than 90°. In this paper, we systemically studied the resonance mechanisms which result in confluent resonance in quadrupole Focusing-Defocusing (FD) channel and parametric resonance in solenoid channel. We propose that the mismatch modes cannot be exactly separated in FD channel; if one mode is excited, there is always some contribution of the other. To verify the influence of the confluent resonance and parametric resonance, the 2D Poissons solver in the self-consistent particle-in-cell simulation code TOPOPIC is adopted to study the beam evolution in both channels. Our simulations results show that the emittance show significant growth both in the confluent resonance stop band and parametric resonance stop band. The influences of the higher order of resonance are also discussed.