Analytical theory and nonlinearδfperturbative simulations of temperature anisotropy instability in intense charged particle beams

Abstract

In plasmas with strongly anisotropic distribution functions T kb =T ?b 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 ?b T kb to allow for nonaxisymmetric perturbations with @=@ Þ 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 ! ! 2 pb =2 2 b ! 2 ? * 0:5 are linearly unstable to short-wavelength perturbations with k 2 z r 2 b * 1, provided the ratio of longitudinal and transverse temperatures is smaller than some threshold value. Here,! ! 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.

US Heavy Ion Beam Research for High Energy Density Physics Applications and Fusion

“…In the acceleration and transport regions, the investigations have included: determination of the conditions for quiescent beam propagation over long distances; the electrostatic Harris-type instability [25,26] and the electromagnetic Weibel-type instability [27] in strongly anisotropic one-component nonneutral ion beams; and the electron-ion dipole-mode two-stream (electron cloud) instability driven by an (unwanted) component of background electrons using the 3D nonlinear delta-f code BEST [5 , 6]. In the plasma neutralization and target chamber regions, collective processes associated with the interaction of the intense ion beam with a chargeneutralizing background plasma have been assessed, including: the electrostatic two-stream instability, the electromagnetic multispecies Weibel instability, and the resistive hose instability [24,28].…”

Thermodynamic bounds on nonlinear electrostatic perturbations in intense charged particle beams

“…One example of the instabilities that occur in these systems is the electrostatic Harris instability [9][10][11][12]15,16 , which is driven by the strong temperature anisotropy (T /T ⊥ 1, where the subscripts and ⊥ denote parallel and perpendicular to the beam propagation) that develops naturally in the frame of an accelerated charged particle beam. Much numerical work has been carried out to characterize this type of instability [9][10][11][12][17][18][19] , and it is therefore of particular importance to develop an analytical framework for comparison with these results.…”

“…Thus, much effort has been devoted to understanding the underlying physics of the nonlinear processes occurring in these beams. An important, tractable approach to solving the detailed dynamics of such systems is often to rely on advanced numerical tools such as particle-in-cell (PIC) simulations [6][7][8] , eigenmode codes 9,10 , and Monte-Carlo codes [11][12][13][14] which can simulate the linear and nonlinear phases of instabilities that may cause a degradation of beam quality.…”

“…Much numerical work has been carried out to characterize this type of instability [9][10][11][12][17][18][19] , and it is therefore of particular importance to develop an analytical framework for comparison with these results. Previous theoretical work has concentrated on investigations of the detailed dynamics of beams with Kapchinskij-Vladimirskij (KV) distributions 20,21 , and two-temperature bi-Maxwellian distributions 11,12 . The formalism presented in here is an important generalization of the Fowler bound 22,23 that fully incorporates effects of the strong self-fields, finite geometry, and nonlinear behavior of intense non-neutral particle beams.…”

Weibel and Two-Stream Instabilities for Intense Charged Particle Beam Propagation through Neutralizing Background Plasma

“…Nonetheless, often with the aid of numerical simulations, there has been considerable recent analytical progress in applying the Vlasov-Maxwell equations to investigate the detailed equilibrium and stability properties of intense charged particle beams. These investigations include a wide variety of collective interaction processes ranging from the electrostatic Harris instability [29][30][31][32][33][34][35] and electromagnetic Weibel instability [36][37][38][39][40][41] driven by large temperature anisotropy with T ⊥b T b in a one-component nonneutral ion beam, to wall-impedance-driven collective instabilities [42][43][44][45], to the dipole-mode two-stream instability for an intense ion beam propagating through a partially neutralizing electron background [45][46][47][48][49][50][51][52][53][54][55][56], to the resistive hose instability [57][58][59][60][61][62][63] and the sausage and hollowing instabilities [64][65][66] for an intense ion beam propagating through a background plasma [67][68][69]…”