Automatic Beam Path Analysis of Laser Wakefield Particle Acceleration Data

Motivation:

Laser wakefield particle accelerators (LWFAs) can accelerate particles to high energy levels over very short distances. LWFAs utilize an electron plasma wave to accelerate charged particles (e.g., electrons) to high energy levels and can create and sustain electric and magnetic fields several thousand times stronger than possible using conventional technologies. Researchers at the LOASIS program have demonstrated high-quality electron beams at 0.1 to 1 GeV using mm long plasmas [2, 3].

Analysis, understanding, and control of the complex physical processes of plasma-based particle acceleration is a challenging task and requires one to understand how particles become trapped in the plasma wave and how particle beams are formed and accelerated. These processes are best understood by tracing the particles that form a beam over time and investigating their temporal evolution. In real-world experiments it is, however, impossible to record the complete evolution of an experiment and much less to trace single particles within a plasma.Numerical simulations of laser wakefield particle accelerators, hence, play a key role in the understanding of the fundamental physics of plasma-based acceleration, understanding of the processes observed in experiments, as well as improvement of experiments.

As the size and complexity of simulation output grows, one main challenge is the need for computational techniques that aid in scientific knowledge discovery. One main feature researchers are interested in are beams of high-energy particles formed during the coarse of LWFA simulations. To enable efficient and accurate analysis of these particle beams, dedicated mechanisms for selection and detection of particle beams are needed.

Overview:

The automatic beam path analysis consists of a set of data-understanding algorithms that work in concert in a pipeline fashion to automatically locate and analyze high energy particle bunches undergoing acceleration in very large simulation datasets [1]. These techniques work cooperatively by first identifying features of interest in individual time steps, then integrating features across time steps, and based on the information derived perform analysis of temporally dynamic features. This combination of techniques supports accurate detection of particle beams enabling a deeper level of scientific understanding of physical phenomena than has been possible before. By combining efficient data analysis algorithms and state-of-the-art data management based on H5Part and FastBit we enable high-performance analysis of extremely large particle datasets in 3D. The automatic analysis of particle beams based on temporal particle paths enables accurate classification of particle beams and supports analysis of the temporal beam evolution.

Algorithm Design:

To achieve high performance, the proposed algorithm employs an efficient analysis pipeline aimed at quickly reducing the amount of data that needs to be considered during the analysis (see Figure 1). In the initial analysis steps the algorithm first analysis the different time steps independently to gather additional information about the particle bunches and to reduce the workload for later analysis steps. Efficient grid-based methods enable fast identification and segmentation of particle bunches at individual time steps independent of the size of the underlying data. After completion of the initial timestep analysis, the algorithm merges the results from the individual time steps and computes for each detected bunch a reference path describing its temporal evolution. We extended FastBit with dedicated new functions for computation of 3D histograms and evaluation of histogram-based data queries to further improve the performance of the bunch segmentation.






Figure 1: After initalization and identification of the relevant time steps, the different timestep are first analyzed independently to detect the most prominent particle bunch at each timestep using a combination of efficient grid-based analysis methods (a). The results are merged to define a single consolidated description of each bunch based on the information from the different time steps (b-c). In the example dataset the algorithm detected two separate bunches shown in figure b and c. Based on this information the algorithm identifies for each bunch a set of reference particles that belong with high propabilty to the bunch (red particles).


To enable accurate classification of particle bunches, the algorithm then completes the analysis by computing a set of distance fields describing the distance of a particle’s path to a bunch (see Figure 2). Based on these path distance fields a user can effectively define which particles from a bunch of interest. In addition, the analysis provides the user with further information about the different temporal phases of a bunch, e.g., when was a bunch formed or accelerated.





Figure 2: In the final path analysis step the algorithm first computes a single reference path for each bunch bases on the temporal paths of the reference particles (colored paths in the bottom left images). Based the reference path the analysis derives the different temporal phases of a bunch, e.g., when was a bunch formed (blue) or accelerated (green) (see left figures). Finally, the algorithm computes for each candidate particle the distance of its path in physical space (ds) and momentum space (dm) to the reference path. Based on these bunch distance fields the user can effectively and intuetively define the bunches. Figure a, b provide an overview of the path analysis for the two bunches detected in the example dataset. Left: Paths of all candidate particles (gray) and the reference particles colored according to the temporal phases of the bunch. Right: Overview of the path distance fields dm and ds for the two detected bunches.


Performance:

We studied the performance of the automatic beam path analysis on a varity of datasets with varing spatial and temporal resolution. Datasets A-D are 2D datasets with a total size of ~1,320 - 13,990 MB, ~405,000 - 2,400,000 particle per timestep, and 36-226 time steps. We also tested the analysis on a massive 3D dataset (E) with a total size of ~623,964MB and ~229,850,00 particle per timestep at 26 time steps.  The test system was equipped with eight 2GHz dual core AMD OpteronTMProcessor 870 with 8GB of memory per core running Ubuntu Linux. For the presented serial analysis shown in Figure 3, we used only one core and the memory limit was set to 8GB while the peak memory usage of the analysis did not exceed 2.5GB in any case.

For the example 2D datasets our implementation was able to complete the analysis in less than 45 seconds in all cases. Even in the case of the large 3D dataset —which was produced by a hundred-thousand-processor-hour class simulation— the analysis took only ~185 seconds.





Figure 3: a) Absolute timings for the serial analysis of five different datasets using the automatic beam path analysis method. The length of each horizontal bar represents the total time used for the complete analysis of the corresponding dataset. b) Relative timings for the different steps of the analysis pipeline as percentage of the total analysis time. In both figures color is used to indicate the timings of different parts of the algorithm. In all cases the histogram computation and the particle tracing are the most expensive analysis steps. This is expected since these are the two main steps during which the raw data needs to be accessed. We can see that the algorithm shows good performance in all cases and scales well with increasing dataset size


Results:

We applied our algorithm to  all above mentioned datasets which showed that the analysis is able to deal with datasets of varying spatial and temporal resolution and effectively detect the main particle bunches of interest. Figure 4 shows an example rendering of the 3D dataset E showing two particle bunches automatically identified by the analysis.





Figure 4: Example illustrating the application of the automatic beam path analysis to a large 3D particle dataset (E). The particles of the two detected particle bunches are shown in color with color indicating momentum in x direction (px). A volume rendering of the plasma density (gray) illustrates the plasma wave.

References

[1] O. Rübel, C.G.R. Geddes, E. Cormier-Michel, K. Wu, Prabhat, G.H. Weber, D. M. Ushizima, P. Messmer, H. Hagen, B. Hamann, and E.W. Bethel, "Automatic Beam Path Analysis of Laser Wakefield Particle Acceleration Data", IOP Computational Science & Discovery, 2009 (to appear)

[2] C.G.R. Geddes, C. Toth, J. van Tilborg, E. Esarey, C. Schroeder, D. Bruhwiler, C. Nieter, J. Cary, and W. Leemans, “High-Quality Electron Beams from a Laser Wakefield Accelerator Using Plasma-Channel Guiding,” Nature, vol. 438, pp. 538–541, 2004, LBNL-55732.

[3] W. P. Leemans, B. Nagler, A. J. Gonsalves, C. Toth, K. Nakamura, C. G. R. Geddes, E. Esarey, C. B. Schroeder, and S. M. Hooker, “GeV electron beams from a centimeter-scale accelerator,” Nature Physics, vol. 2, pp. 696 – 699, 2006