Abstract
In plasmas with strongly anisotropic distribution functions $({T}_{\ensuremath{\parallel}b}/{T}_{\ensuremath{\perp}b}\ensuremath{\ll}1)$ 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 $({T}_{\ensuremath{\perp}b}\ensuremath{\gg}{T}_{\ensuremath{\parallel}b})$ to allow for nonaxisymmetric perturbations with $\ensuremath{\partial}/\ensuremath{\partial}\ensuremath{\theta}\ensuremath{\ne}0$. 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 ${s}_{b}={\stackrel{^}{\ensuremath{\omega}}}_{pb}^{2}/2{\ensuremath{\gamma}}_{b}^{2}{\ensuremath{\omega}}_{\ensuremath{\beta}\ensuremath{\perp}}^{2}\ensuremath{\gtrsim}0.5$ are linearly unstable to short-wavelength perturbations with ${k}_{z}^{2}{r}_{b}^{2}\ensuremath{\gtrsim}1$, provided the ratio of longitudinal and transverse temperatures is smaller than some threshold value. Here, ${\stackrel{^}{\ensuremath{\omega}}}_{pb}^{2}=4\ensuremath{\pi}{\stackrel{^}{n}}_{b}{e}_{b}^{2}/{\ensuremath{\gamma}}_{b}{m}_{b}$ is the relativistic plasma frequency squared, and ${\ensuremath{\omega}}_{\ensuremath{\beta}\ensuremath{\perp}}$ 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.
Highlights
Periodic focusing accelerators, transport systems, and storage rings [1,2,3,4,5] have a wide range of applications ranging from basic scientific research in high energy and nuclear physics, to applications such as heavy ion fusion, spallation neutron sources, tritium production, and nuclear waste transmutation, to mention a few examples
Of particular importance at the high beam currents and charge densities of practical interest are the effects of the intense self-fields produced by the beam space charge and current on determining the detailed equilibrium, stability, and transport properties
While considerable progress has been made in understanding the self-consistent evolution of the beam distribution function, fb x; p; t, and self-generated electric and magnetic fields, Es x; t and Bs x; t, in kinetic analyses based on the nonlinear Vlasov-Maxwell equations [1,6 –10], in numerical simulation studies of intense beam propagation
Summary
Transport systems, and storage rings [1,2,3,4,5] have a wide range of applications ranging from basic scientific research in high energy and nuclear physics, to applications such as heavy ion fusion, spallation neutron sources, tritium production, and nuclear waste transmutation, to mention a few examples. It is important to extend theoretical studies of the kinetic stability properties of anisotropic beams to distribution functions other than the KapchinskijVladimirskij (KV) distribution [6] This is because the KV distribution has an (unphysical) inverted population in transverse phase-space variables, which provides the free energy to drive collective instabilities at sufficiently high beam intensity that are intrinsic to this inverted population [7,8]. P2x p2y 1=2 is the transverse particle momentum, r x2 y2 1=2 is the radial distance from the beam axis, !f const is the transverse frequency associated with the applied focusing field in the smoothfocusing approximation, and 0 r is the equilibrium space-charge potential determined self-consistently from Poisson’s equation,.
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