Analytical and numerical studies of heavy ion beam transport in the fusion chamber

Abstract

The propagation of a high-current finite-length ion charge bunch through a background plasma is of interest for many applications, including heavy ion fusion, plasma lenses, cosmic ray propagation, and so forth. Charge neutralization has been studied both analytically and numerically during ion beam entry, propagation, and exit from the plasma. A suite of codes has been developed for calculating the degree of charge and current neutralization of the ion beam pulse by the background plasma. The code suite consists of two different codes: a fully electromagnetic, relativistic particle-in-cell code, and a relativistic Darwin model for long beams. As a result of a number of simplifications, the second code is hundreds of times faster than the first one and can be used for most cases of practical interest, while the first code provides important benchmarking for the second. An analytical theory has been developed using the assumption of long charge bunches and conservation of generalized vorticity. The model predicts nearly complete charge neutralization during quasi-steady-state propagation provided the beam pulse duration t b is much longer than the inverse electron plasma frequency v p Ϫ1 , where v p ϭ~4pn p e 2 0m e ! 102 and n p is the background plasma density. In the opposite limit, the beam head excites large-amplitude plasma waves. Similarly, the beam current is well neutralized provided v p t b . . 1 and the beam radius is much larger than plasma skin depth d p ϭ c0v p . Equivalently, the condition for current neutralization can be expressed in terms of the beam current as

Analytical and Numerical Studies of the Complex Interaction of a Fast Ion Beam Pulse with a Background Plasma

“…In contrast to steady-state propagation, where the plasma waves establish a stationary stripe-like pattern [4,6,8], after the beam exits the plasma the plasma waves form a nonstationary periodic pattern resembling butterfly-wing motion. In summary, steady-state ion beam propagation through a background plasma has been described in detail in previous publications [4][5][6][7][8]. The analytical results agree well with the results of PIC numerical simulations for ion beam charge and current neutralization for the case of steady-state ion beam propagation in a background plasma.…”

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

“…The neutralization of the ion beam pulse current by the plasma has been calculated using a fluid description for the electrons, extending our previous studies of beam neutralization without an applied magnetic field [21]. Analytical investigations show that the solenoidal magnetic field starts to influence the radial electron motion if electron cyclotron frequency is larger than electron plasma frequency times the speed of the beam ions divided by the speed of light.…”

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]…”