Wall-impedance-driven collective instability in intense charged particle beams

[摘要]

The linearized Vlasov-Maxwell equations are used to investigate detailed properties of the wall-impedance-driven instability for a long charge bunch ($\mathrm{\text{bunch}}\mathrm{\text{length}}{\ell }_b\gg \mathrm{\text{bunch}}\mathrm{\text{radius}}{r}_b$) propagating through a cylindrical pipe with radius $r_w$ and wall impedance $\tilde{Z}(\omega )$. The stability analysis is carried out for perturbations about a cylindrical Kapchinskij-Vladimirskij beam equilibrium with a flattop density profile in the smooth-focusing approximation. The perturbations are assumed to be of the form $\delta \psi (\mathbf{x},t)=\delta {\psi }^{\ell }(r)\exp (i\ell \theta +i{k}_{z}z-i\omega t)$, where $(r,\theta )$ are the radial and azimuthal coordinates in the transverse direction, and $z$ is the coordinate in the longitudinal direction. Here, $\ell =1,2,\dots$ is the azimuthal mode number of the perturbation in the transverse direction, $k_z$ is the wave number in the longitudinal direction, and $\omega$ is the oscillation frequency. As an example, detailed stability properties are determined for dipole-mode perturbations $(\ell =1)$ assuming negligibly small axial momentum spread of the beam particles. The stability analysis is valid for a general value of the normalized beam intensity $s_b={\widehat{\omega }}_{pb}^2/2{\gamma }_b^2{\omega }_{\beta \perp }^2$ in the interval $0<s_b<1$, where ${\widehat{\omega }}_{pb}=(4\pi {\widehat{n}}_b{e}_b^2/{\gamma }_b{m}_b{)}^{1/2}$ is the relativistic plasma frequency and ${\omega }_{\beta \perp }$ is the applied focusing frequency.

[发布日期] 2003-10-07