Theory and high-performance computing

 
 

PIC simulation of a 10 kA FLASHForward like beam transversing a uniform plasma of 1.2 x 1018. A short (770 as) bunch is injected by means of wakefield-induced ionisation (WII) in a high-accelerating phase of the plasma wake. The bunch features high peak current (5 kA) and low normalised emittance (270 nm).

Theoretical analyses and computational modelling of plasma based accelerators are of fundamental importance, propelling the innovations within the field. Theoretical analyses are crucial for the understanding of the basic processes in the accelerators. Simulations serve as a bridge between theory and experiment, allowing for the benchmarking of theoretical models and for a realistic emulation of the experiment in order to facilitate the technical design as well as to allow for an interpretation of experimental results.

The most widespread numerical method for the efficient computational modelling of plasma-based accelerators is the particle-in-cell (PIC) technique. Several codes based on this technique are employed by our group on high-performance computers in order to simulate processes in plasmabased accelerators. We also (co-)develop PIC codes so as to enhance their versatility, efficiency and user-friendliness. Moreover, we work on interfaces between several simulation codes to have the capability to perform start-to-end simulations. The generated simulation data is analysed and visualised by use of post-processing software packages which are being developed in our group.

These tools are used to investigate a variety of physical topics. We perform conceptual studies for the generation of high-quality beams in plasma wakefield accelerators (PWFAs) and their qualitypreserving acceleration and transport. The start-to-end simulation framework is used to model PWFAs, in particular the FLASHForward experiment, with an unprecedented realism. This is crucial to tailor the drive and accelerated beams and the plasma target in the experiment e.g. to reduce transverse beam-plasma instabilities or to optimise the energy transfer (transformer ratio) from the drive beam to the accelerated beam. All theoretical and numerical studies serve the ultimate goal to generate stable, highly energetic election beams with a sufficient quality to drive a free-electron laser.

 

Computational methods


The particle-in-cell technique

​Many phenomena occurring in PWFAs need to be addressed by a kinetic description in terms of the Maxwell-Vlasov system. However, in general, the Maxwell-Vlasov equations cannot be solved analytically for problems in plasma-based accelerators. Hence, numerical methods must be employed for the computation of the Maxwell-Vlasov system. A widespread numerical method in this context is the particle-in-cell (PIC) technique, which allows for the efficient full scale modelling of PWFAs on modern supercomputers. In the PIC method, the phase-space distribution of a particle species, e.g. the plasma electrons, is discretised by means of numerical particles which evolve according to the Lorentz force. The current density of these numerical particles is deposited onto a grid on which the Maxwell’s equations are solved numerically. This discretisation allows for a full numerical modelling of the relevant phenomena in plasma-based acceleration. The computational load is thereby distributed over a number of processors and a proficient softwareimplementation of this parallelised scheme in the PIC codes OSIRIS and HiPACE enables the efficient use of modern supercomputers. Currently, we use the codes OSIRIS and HiPACE on high-performance computing clusters like “Maxwell” at DESY or “JUQUEEN” at JSC.

Particle-in-cell code development

The three-dimensional (3D) PIC code HiPACE (Highly efficient Plasma Accelerator Emulation), developed in our group is relativistic, fully electromagnetic and fully MPI-parallelised. It uses the quasi-static approximation to efficiently model particle-beam driven plasma-wakefield accelerators. HiPACE exploits the disparity of time scales in the interaction of highly relativistic particle beams with plasma to decouple beam and plasma evolution. This enables time steps which are many times greater than those used in finite-difference time-domain PIC codes and therefore renders possible a reduction of the required number of core hours by orders of magnitude. We continue to implement new features to the code, improve its algorithmic and computational efficiency and enhance its user friendliness. HiPACE now computes all field components, allowing for the fully consistent simulation of non-cylindrically-symmetric phenomena, such as the hose instability.

OSIRIS is a state of the art, fully explicit electrodynamic and relativistic PIC framework, which is massively parallelised and developed at the University of California Los Angeles (UCLA) and Instituto Superior Técnico Lisboa (IST). We contribute to the develop OSIRIS by implementing new features, e.g. the possibility to import and initialise realistic 6D beam distributions provided by particle tracking codes

Start-to-end simulation framework

Conceptual studies with PIC simulations are fundamental for a better understanding of a variety of phenomena in PWFAs and have facilitated innovations for the generation of high-quality beams and the quality-preserving acceleration and transport into- or out of the plasma target. However, these conceptual studies assume perfectly symmetric beam distributions. We therefore develop a simulation framework which enables the modelling of PWFAs with realistic 6D beam distributions obtained from particle tracking codes. We develop the required interfaces between a number of different accelerator codes and perform start-to-end simulations on the FLASHForward facility

Post-processing and data visualisation

Three-dimensional PIC simulations generate a large amount of data with information about the electromagnetic fields and the macroparticles. In order to extract the relevant physical information from this data, post-processing routines for data visualisation and analysis are required. The group continuously works at improving several data analysis frameworks to provide a better understanding of the underlying physics. We also develop advanced 3D visualisation tools, enabling an illustration of the three-dimensional structure of the fields and plasma and beam density distributions.

Different electron injection methods: (a) Density- Downramp Injection (b) Laser-Induced Ionisation Injection (c) Beam-Induced Ionisation Injection (d) Wakefield-Induced Ionisation Injection