Analytical theory and nonlinear $\delta f$ perturbative simulations of temperature anisotropy instability in intense charged particle beams (Englisch)

In plasmas with strongly anisotropic distribution functions $(T_{\parallel b}/T_{\perp b}\ll 1)$ a Harris-like collective instability may develop if there is sufficient coupling between the transverse and longitudinal degrees of freedom. Such anisotropies develop naturally in accelerators and may lead to a deterioration of beam quality. This paper extends previous numerical studies [E. A. Startsev, R. C. Davidson, and H. Qin, Phys. Plasmas 9, 3138 (2002)] of the stability properties of intense non-neutral charged particle beams with large temperature anisotropy $(T_{\perp b}\gg T_{\parallel b})$ to allow for nonaxisymmetric perturbations with $\partial /\partial \theta \ne 0$. The most unstable modes are identified, and their eigenfrequencies, radial mode structure, and nonlinear dynamics are determined. The simulation results clearly show that moderately intense beams with $s_b={\hat{\omega }}_{pb}^2/2{\gamma }_b^2{\omega }_{\beta \perp }^2\gtrsim 0.5$ are linearly unstable to short-wavelength perturbations with $k_z^2{r}_b^2\gtrsim 1$, provided the ratio of longitudinal and transverse temperatures is smaller than some threshold value. Here, ${\hat{\omega }}_{pb}^2=4\pi {\hat{n}}_b{e}_b^2/{\gamma }_b{m}_b$ is the relativistic plasma frequency squared, and ${\omega }_{\beta \perp }$ is the betatron frequency associated with the applied smooth-focusing field. A theoretical model is developed based on the Vlasov-Maxwell equations which describes the essential features of the linear stages of instability. Both the simulations and the analytical theory predict that the dipole mode (azimuthal mode number $m=1$) is the most unstable mode. In the nonlinear stage, tails develop in the longitudinal momentum distribution function, and the kinetic instability saturates due to resonant wave-particle interactions.