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 after only the first harmonic. 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.
Abstract-The Relativistically Induced Transparency Acceleration (RITA) scheme of proton and ion acceleration using laser-plasma interactions is introduced, modeled and compared to the existing schemes. Protons are accelerated with femtosecond relativistic pulses to produce quasi-monoenergetic bunches with controllable peak energy. The RITA scheme works by a relativistic laser inducing transparency[1] to densities higher than the cold-electron critical density, while the background heavy-ions are stationary. The rising laser pulse creates a traveling acceleration structure, at the relativistic critical density by ponderomotively[2] driving a local electron density inflation, creating a snowplow and a copropagating electrostatic potential. The snowplow advances with a velocity determined by the rate of the rise of laser's intensity envelope and the heavy-ion plasma density gradient scale length. The rising laser is incrementally rendered transparent to higher densities such that the relativisticelectron plasma frequency is resonant with the laser frequency. In the snowplow frame, trace density protons reflect off the electrostatic potential and get snowplowed while the heavier background-ions are relatively unperturbed. Quasimono-energetic bunches of velocity equal to twice the snowplow velocity can be obtained and tuned by controlling the snowplow velocity using laser-plasma parameters. Laser-plasma accelerators can generate proton and ion beams with unprecedented characteristics of high bunch charge, low emittance and ultra-short bunch lengths using a very compact system. However, existing mechanisms for acceleration [4][5][6] with femto-second lasers have been unable to simultaneously achieve the desired energy gain and spectral control needed for the applications of interest. Here we demonstrate with analysis and PIC simulations [3] that using heavy-ion targets, we can control the laser propagation by means of relativistically induced transparency [1]. By varying the laser rise-time or plasma density gradient it is possible to tune the energy of the mono-energetic beams. The results provide a pathway for achieving the beam properties needed for a wide-array of applications ranging from hadron therapy [7] to high-charge injectors [8], particle physics [9] and high energy density physics [10].Experimentally, target normal sheath acceleration (TNSA) scaling laws have been studied extensively [11][12], and lowenergy quasi-mono-energetic beams demonstrated [13]. The
In this paper we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1 direction). We show that this eliminates the main NCI modes with moderate |k 1 |, while keeps additional main NCI modes well outside the range of physical interest with higher |k 1 |. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along1 which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss' Law is satisfied. We present simulation examples of one relativistically drifting plasmas, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.
a b s t r a c tA hybrid Maxwell solver for fully relativistic and electromagnetic (EM) particle-in-cell (PIC) codes is described. In this solver, the EM fields are solved in k space by performing an FFT in one direction, while using finite difference operators in the other direction(s). This solver eliminates the numerical Cerenkov radiation for particles moving in the preferred direction. Moreover, the numerical Cerenkov instability (NCI) induced by the relativistically drifting plasma and beam can be eliminated using this hybrid solver by applying strategies that are similar to those recently developed for pure FFT solvers. A current correction is applied for the charge conserving current deposit to ensure that Gauss's Law is satisfied. A theoretical analysis of the dispersion properties in vacuum and in a drifting plasma for the hybrid solver is presented, and compared with PIC simulations with good agreement obtained. This hybrid solver is applied to both 2D and 3D Cartesian and quasi-3D (in which the fields and current are decomposed into azimuthal harmonics) geometries. Illustrative results for laser wakefield accelerator simulation in a Lorentz boosted frame using the hybrid solver in the 2D Cartesian geometry are presented, and compared against results from 2D UPIC-EMMA simulation which uses a pure spectral Maxwell solver, and from OSIRIS 2D lab frame simulation using the standard Yee solver. Very good agreement is obtained which demonstrates the feasibility of using the hybrid solver for high fidelity simulation of relativistically drifting plasma with no evidence of the numerical Cerenkov instability.
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