Ronald Davidson, W. Wei-li Lee, Hong Qin, and Edward Startsev, Princeton Plasma Physics Laboratory

Nonlinear df simulation of electron-proton two-stream instability for the Proton Storage Ring at LANL. When a background electron component is introduced, the l = 1 dipole mode can be destabilized for a certain range of axial wavenumber and a certain range of electron temperature. Simulation results showed that the instability growth rate increases with increasing beam current and decreases with increasing momentum spread. In the simulation, electrons, protons, and self-fields were self-consistently followed for 4 x 1011 particle time-steps.

Research Objectives
This project will enable us to perform realistic particle simulations for collective processes and instabilities, such as stable beam oscillations and electron-ion two-stream instabilities, in high-intensity particle beams. Utilizing the large-scale computing power provided by the IBM SP computers, we will be able to carry out 3D multi-species nonlinear particle simulations based on the self-consistent Vlasov-Maxwell equations. The newly developed beam equilibrium stability and transport (BEST) code will be used and will be further developed to include more numerical capabilities and physics contents.

Computational Approach
We use a 3D multi-species nonlinear perturbative particle simulation method to simulate the collective processes and instabilities in high-intensity particle beams. The perturbative particle simulation method used in the BEST code solves the fully nonlinear Vlasov-Maxwell equations and offers a significantly reduced noise level for the problems being studied. The BEST code advances the particle motions using a leapfrog method, and solves Maxwell's equations in cylindrical geometry. For those fast particle motions which require much larger sampling frequency than the frequency of the mode being studied, the code uses an adiabatic field pusher to advance the particles many time steps without solving for the perturbed fields.

Accomplishments
In FY 2001 we carried out large-scale particle simulations for the two-stream instability and pressure anisotropy instability. The IBM SP provided the necessary computing power to simulate these instabilities for realistic accelerator parameters. For example, we were able to push 4 x 10¹¹ particle steps to simulate the electron-proton two-stream instability for the Proton Storage Ring at Los Alamos National Laboratory. Our simulation results agreed with the experimental results in terms of eigenmode structures, eigenfrequencies, and growth rates. Our simulations also suggested possible approaches to avoid the instability so that higher proton beam intensity can be achieved.

Significance
High-intensity particle beams have a wide range of applications, ranging from basic scientific research in high energy and nuclear physics, to applications such as heavy ion fusion and spallation neutron source. Of particular importance at the high beam currents of practical interest are the collective processes and instabilities. Because the governing equations, the nonlinear Vlasov-Maxwell equations, are intrinsically difficult to solve analytically, our understanding obtained from large-scale computer simulations directly impacts on the quality of the high-intensity particle beams and thus the success of the scientific efforts mentioned above.

Publications
H. Qin, R. C. Davidson, W. W. Lee, and R. Kolesnikov, "3D multispecies nonlinear perturbative particle simulations of collective processes in intense particle beams for heavy ion fusion," Nuc. Instr. Meth. Phys. A 464, 477 (2001).

H. Qin, R. C. Davidson, and W. W. Lee, "Three-dimensional multispecies nonlinear perturbative particle simulations of collective processes in intense particle beams," Phys. Rev. Special Topics on Accel. and Beams 3, 084401, 109901 (2000).

H. Qin, R. C. Davidson, and W. W. Lee, "3D nonlinear perturbative particle simulations of two-stream collective processes in intense particle beams," Phys. Lett. A 272, 389 (2000).

http://w3.pppl.gov/~nnp/best.htm