Kevin Paul

Characteristics of an envelope model for laser-plasma accelerator simulation

Simulation of laser-plasma accelerator (LPA) experiments is computationally intensive due to the disparate length scales involved. Current experiments extend hundreds of laser wavelengths transversely and many thousands in the propagation direction, making explicit PIC simulations enormously expensive and requiring massively parallel execution in 3D. Simulating the next generation of LPA experiments is expected to increase the computational requirements yet further, by a factor of 1000. We can substantially improve the performance of LPA simulations by modeling the envelope evolution of the laser field rather than the field itself. This allows for much coarser grids, since we need only resolve the plasma wavelength and not the laser wavelength, and therefore larger timesteps can be used. Thus an envelope model can result in savings of several orders of magnitude in computational resources. By propagating the laser envelope in a Galilean frame moving at the speed of light, dispersive errors can be avoided and simulations over long distances become possible. The primary limitation to this envelope model is when the laser pulse develops large frequency shifts, and thus the slowly-varying envelope assumption is no longer valid. Here we describe the model and its implementation, and show rigorous benchmarks for the algorithm, establishing second-order convergence and correct laser group velocity. We also demonstrate simulations of LPA phenomena such as self-focusing and meter-scale acceleration stages using the model.

New Developments in the Simulation of Advanced Accelerator Concepts

Improved computational methods are essential to the diverse and rapidly developing field of advanced accelerator concepts. We present an overview of some computational algorithms for laser‐plasma concepts and high‐brightness photocathode electron sources. In particular, we discuss algorithms for reduced laser‐plasma models that can be orders of magnitude faster than their higher‐fidelity counterparts, as well as important on‐going efforts to include relevant additional physics that has been previously neglected. As an example of the former, we present 2D laser wakefield accelerator simulations in an optimal Lorentz frame, demonstrating >10 GeV energy gain of externally injected electrons over a 2 m interaction length, showing good agreement with predictions from scaled simulations and theory, with a speedup factor of ∼2,000 as compared to standard particle‐in‐cell.

Scaled simulations of a 10 GeV accelerator

Laser plasma accelerators are able to produce high quality electron beams from 1 MeV to 1 GeV. The next generation of plasma accelerator experiments will likely use a multi-stage approach where a high quality electron bunch is first produced and then injected into an accelerating structure. In this paper we present scaled particle-in-cell simulations of a 10 GeV stage in the quasi-linear regime. We show that physical parameters can be scaled to be able to perform these simulations at reasonable computational cost. Beam loading properties and electron bunch energy gain are calculated. A range of parameter regimes are studied to optimize the quality of the electron bunch at the output of the stage.

Laser wakefield simulation using a speed‐of‐light frame envelope model

Simulation of laser wakefield accelerator (LWFA) experiments is computationally intensive due to the disparate length scales involved. Current experiments extend hundreds of laser wavelengths transversely and many thousands in the propagation direction, making explicit PIC simulations enormously expensive and requiring massively parallel execution in 3D. We can substantially improve the performance of laser wakefield simulations by modeling the envelope modulation of the laser field rather than the field itself. This allows for much coarser grids, since we need only resolve the plasma wavelength and not the laser wavelength, and therefore larger timesteps. Thus an envelope model can result in savings of several orders of magnitude in computational resources. By propagating the laser envelope in a frame moving at the speed of light, dispersive errors can be avoided and simulations over long distances become possible. Here we describe the model and its implementation, and show simulations and benchmarking of laser wakefield phenomena such as channel propagation, self-focusing, wakefield generation, and downramp injection using the model.

PPPS-2013: Fast and accurate simulations of 10 GEV-scale laser plasma accelerators

Because of their ultra-high accelerating gradient, laser plasma based accelerators (LPA) are contemplated for the next generation of high energy colliders and light sources. The upcoming BELLA project will explore acceleration of electron bunches to 10 GeV in a meter long plasma, where a wakefield is driven by a PW-class laser. Particle-in-cell (PIC) simulations are used to design the upcoming experiments. Simulations are challenging because of the disparity of length scale between the laser wavelength (~1 micron) that needs to be resolved and the simulation length (~ 1 m). We report on recent developments of the Laser Envelope Model, a reduced model for laser-plasma interactions that has previously demonstrated orders of magnitude speedup. In particular, we present the implementation of the model in cylindrical coordinates, allowing for quite rapid prototyping of laser acceleration stages. We discuss the performance benefits as well as the limitations and trade-offs of this model. In parallel, high frequency noise in PIC simulations makes it difficult to accurately represent beam energy spread and emittance. We show that calculating the beam self-fields using a static Poisson solve in the beam frame dramatically reduces particle noise, allowing for more accurate simulation of the beam evolution.

Benefits of higher-order particles in simulating microwave plasma interactions using a Particle-in-Cell code

Researchers often would like to apply Particle-in-Cell (PIC) methods to model cold, high pressure plasmas in order to discern any kinetic, nonlinear or space charge effects. However, the PIC method typically does not perform well at low temperatures and high densities due to limitations on time and space scales for numerical and practical reasons. One of these limitations is the requirement to resolve the Debye length. Failure to resolve the Debye length in a PIC simulation typically results in artificial heating of the plasma known as grid heating. For applications such as plasma processing, the rate of plasma production is a sensitive function of the electron temperature, so grid heating can make simulation results entirely unreliable. The use of higher-order particle algorithms that smooth out the particle current and charge can help to eliminate this unphysical heating and allow cold, dense plasmas to be simulated using PIC. We present results of using higher-order particles for modeling a plasma sustained by microwaves and we compare to results using standard first-order particles. Specifically, we compare the electron temperature, sheath size, and rate of plasma formation for simulations with an argon gas of 0.05 Torr pressure with an applied microwave power at 2.45 GHz.

Recent Developments in Simulations of an Inverse Cyclotron for Intense Muon Beams

A number of recent developments have led to simulations of an inverse cyclotron for cooling intense muon beams for neutrino factories and muon colliders. Such a device could potentially act as a novel beam cooling mechanism for muons, and it would be significantly smaller and cheaper than other cooling channel designs. Realistic designs are still being explored, but the first simulations of particle tracking in the inverse cyclotron, with accumulation in the cyclotron core, have been done with electrostatic simulations in the particle‐in‐cell code VORPAL. We present an overview of the muon inverse cyclotron concept and recent simulation results.

Simulation-driven optimization of heavy-ION production in ECR sources

Next-generation heavy-ion beam accelerators require a wide variety of high charge state ion beams (from protons to uranium) with up to an order of magnitude higher intensity than that demonstrated with conventional electron cyclotron resonance (ECR) ion sources. Optimization of the ion beam production for each element is therefore required. Efficient loading of the material into the ECR plasma is one of the key elements for optimizing the ion beam production. High-fidelity simulations provide a means to understanding the deposition of uncaptured metal atoms along the walls. This information would help to optimize the loading process into the ECR plasma. We are currently extending the plasma simulation framework VORPAL with models to investigate effective loading of heavy metals into ECR ion source via alternate mechanisms, including vapor loading, ion sputtering and laser ablation. First results of the ion production for different loading scenarios are presented.