Research Summary

Group Member: Ian Ellis

I am studying the wakes of charged particles passing through plasmas in 3D. The analytic theory describing the wake was derived back in 1987, but only during the past few years have computers become powerful enough to compute the solution at multiple points in space in 3D and perform particle simulations to compare the results with. I wrote a program to calculate and plot the wake using the analytic solution and am performing particle simulations for comparison purposes using UCLA's particle-in-cell code BEPS and Lawrence Livermore National Lab's particle-particle particle-mesh code ddcMD.

I’ve put the results below in scaled plasma units.  λDe is the Debye length, which we use to measure distance, and ωpe is the plasma frequency, whose inverse we use to measure time.  We measure speed in terms of the electron thermal speed, vth = λDepe.

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Image 1. The conceptual layout of the process used in the particle-in-cell (PIC) algorithm. PIC uses a mesh to calculate the fields to achieve greater computational efficiency than calculating pair-wise interactions between particles directly. Image 2. The conceptual layout of the process used in the particle-particle particle-mesh (PPPM) algorithm. PPPM calculates long-range forces like PIC, but then takes into account pair-wise interactions within a certain cutoff sphere, allowing the method to accurately model collisions.
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Image 3. A plot of the electrostatic potential, showing the wake produced by an electron in a BEPS simulation. The simulation was 3D, so I've plotted a slice containing the path of the electron. The test electron starts at x=128 λDe and z=64 λDe and travels with a constant velocity of 5 vth in the +z direction. It is at x=128 λDe and z=214 λDe at the current time. Image 4. A plot of the electrostatic potential from the simulation shown in Image 3 at a later time.
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Image 5. The electrostatic potential along the trajectory of a particle traveling at 3 vth according to various models. The black line is the the analytic solution and the blue is the result from a BEPS simulation. The red line is a modification of the analytic solution that takes into account some known effects unique to particle-in-cell codes. Image 6. A plot of the electrostatic potential, showing the wake produced by an electron in a ddcMD simulation. The simulation was 3D, so I've plotted a slice containing the path of the electron. The test electron starts at x=64 λDe and z=32 λDe and travels at a constant speed of 5 vth in the +z direction. It is at x=64 λDe and z=52 λDe at the current time. The “bubbles” that appear in the plot indicate electrons that have undergone large-angle c ollisions, and appear due to a differencing technique we use during data analysis.


 

 

 

LLNL-WEB-471724

This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 and by the University of California, Los Angeles under Grant DE-FG52-09NA29552.