Asher Davidson

Exploiting multi-scale parallelism for large scale numerical modelling of laser wakefield accelerators

A new generation of laser wakefield accelerators (LWFA), supported by the extreme accelerating fields generated in the interaction of PW-Class lasers and underdense targets, promises the production of high quality electron beams in short distances for multiple applications. Achieving this goal will rely heavily on numerical modelling to further understand the underlying physics and identify optimal regimes, but large scale modelling of these scenarios is computationally heavy and requires the efficient use of state-of-the-art petascale supercomputing systems. We discuss the main difficulties involved in running these simulations and the new developments implemented in the OSIRIS framework to address these issues, ranging from multi-dimensional dynamic load balancing and hybrid distributed/shared memory parallelism to the vectorization of the PIC algorithm. We present the results of the OASCR Joule Metric program on the issue of large scale modelling of LWFA, demonstrating speedups of over 1 order of magnitude on the same hardware. Finally, scalability to over ∼106 cores and sustained performance over ∼2 P Flops is demonstrated, opening the way for large scale modelling of LWFA scenarios.

Mitigation of numerical Cerenkov radiation and instability using a hybrid finite difference-FFT Maxwell solver and a local charge conserving current deposit

Abstract A 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.

Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction

Abstract 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 ˆ 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 along 1 ˆ 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 plasma, 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.

Some observations on trapping in nonlinear multi-dimensional wakes

Using the code OSIRIS we examine the wakes and particle trapping for non-evolving drivers. We examine how the trapping threshold depends on wake amplitude and wake phase velocity as well on the pseudo-potential. We concentrate on particle beam drivers and vary the driver strength (normalized current), driver shape, spot size and velocity. We compare the phase velocity of the wake to that of the driver beam. We find that as one nears the onset of trapping the phase velocity of the wake can evolve even if the driver does not evolve.

Enabling Lorentz boosted frame particle-in-cell simulations of laser wakefield acceleration in quasi-3D geometry

When modeling laser wakefield acceleration (LWFA) using the particle-in-cell (PIC) algorithm in a Lorentz boosted frame, the plasma is drifting relativistically at β b c towards the laser, which can lead to a computational speedup of ~ γ b 2 = ( 1 - β b 2 ) - 1 . Meanwhile, when LWFA is modeled in the quasi-3D geometry in which the electromagnetic fields and current are decomposed into a limited number of azimuthal harmonics, speedups are achieved by modeling three dimensional (3D) problems with the computational loads on the order of two dimensional r - z simulations. Here, we describe a method to combine the speedups from the Lorentz boosted frame and quasi-3D algorithms. The key to the combination is the use of a hybrid Yee-FFT solver in the quasi-3D geometry that significantly mitigates the Numerical Cerenkov Instability (NCI) which inevitably arises in a Lorentz boosted frame due to the unphysical coupling of Langmuir modes and EM modes of the relativistically drifting plasma in these simulations. In addition, based on the space-time distribution of the LWFA data in the lab and boosted frame, we propose to use a moving window to follow the drifting plasma, instead of following the laser driver as is done in the LWFA lab frame simulations, in order to further reduce the computational loads. We describe the details of how the NCI is mitigated for the quasi-3D geometry, the setups for simulations which combine the Lorentz boosted frame, quasi-3D geometry, and the use of a moving window, and compare the results from these simulations against their corresponding lab frame cases. Good agreement is obtained among these sample simulations, particularly when there is no self-trapping, which demonstrates it is possible to combine the Lorentz boosted frame and the quasi-3D algorithms when modeling LWFA. We also discuss the preliminary speedups achieved in these sample simulations.

An examination of the scaling laws for LWFA in the self-guided nonlinear blowout regime

A detailed study of the scaling laws for LWFA in the self-guided, nonlinear blowout regime is presented. The study is enabled through the recent implementation of the quasi-3D algorithm into OSIRIS, which permits particle-in-cell simulations of LWFA at lower densities and higher laser energy. We find that the scaling laws continue to work well when we fix the normalized laser amplitude, pulse-length, and spot size, while reducing the plasma density. We examine parameters for which the self-injected electron energies are between 1 and 10 GeV. Over a wide parameter space, the evolution of the electron energy and laser spot size are similar when plotted in normalized units.

3D simulations of pre-ionized and two-stage ionization injected laser wakefield accelerators

In plasma based accelerators (LWFA and PWFA), the methods of injecting high quality electron bunches into the accelerating wakefield is of utmost importance for various applications. To fully understand the numerical effect of simulating the trapping process, numerous numerical convergence tests were performed to ensure the correctness of preionized simulations which confirm the physical picture first proposed in [1]. We Further investigate the use of a two-stage ionization injected LWFA to achieve high quality monoenergetic beams through the use of 3D PIC simulations. The first stage constitutes the Injection Regime, which is 99.5% He and 0.5% N, while the second stage constitutes the Acceleration Regime, which is entirely composed of He. Two of the simulations model the parameters of the LWFA experiments for the LLNL Callisto laser, at laser powers of 90 and 100TW. energies as high as 680MeV were observed in the 90TW simulation, and those as high as 1.44GeV were observed in the 100TW simulation. The aff...