Abstract
For many plasma physics problems, three-dimensional and kinetic effects are very important. However, such simulations are very computationally intensive. Fortunately, there is a class of problems for which there is nearly azimuthal symmetry and the dominant three-dimensional physics is captured by the inclusion of only a few azimuthal harmonics. Recently, it was proposed [1] to model one such problem, laser wakefield acceleration, by expanding the fields and currents in azimuthal harmonics and truncating the expansion. The complex amplitudes of the fundamental and first harmonic for the fields were solved on an r–z grid and a procedure for calculating the complex current amplitudes for each particle based on its motion in Cartesian geometry was presented using a Marder's correction to maintain the validity of Gauss's law. In this paper, we describe an implementation of this algorithm into OSIRIS using a rigorous charge conserving current deposition method to maintain the validity of Gauss's law. We show that this algorithm is a hybrid method which uses a particles-in-cell description in r–z and a gridless description in ϕ. We include the ability to keep an arbitrary number of harmonics and higher order particle shapes. Examples for laser wakefield acceleration, plasma wakefield acceleration, and beam loading are also presented and directions for future work are discussed.
Highlights
Particle-in-cell simulations are widely used and well established for simulating plasmas in fields ranging from magnetic fusion, inertial confinement fusion, plasma based acceleration, Preprint submitted to J
Due to the symmetry of the azimuthal modal geometry, we can merely ‘fold’ these current values into the physical cells located above the access, at each time step (J m,i,j=0,1,1 is added to J 0,1,2, J 0,1,0 is added to J 0,1,3, and so on)
We present simulation results for a laser wakefield accelerator (LWFA), a plasma wakefield accelerator (PWFA), and an LWFA case with beam loading case respectively
Summary
Several methods have been developed for more efficiently modeling plasma-based acceleration in three dimensions (or in lower dimensions) These include the moving window method [2], quasi-static methods [3, 4, 5], the ponderomotive guiding center (PGC) method for modeling laser propagation [3, 6], and the use of simulating the physics in Lorentz boosted frames [7, 8, 9, 10]. We reused as much of the existing 2D r-z structure as possible We view this algorithm as a hybrid between a traditional PIC method where quantities are defined on an r-z grid and a gridless method[20] in φ where quantities are expanded in global basis functions (e.g., Fourier modes) defined at all locations and the expansion is truncated.
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