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Plasma Physics Log
Vlasov’s equation
Complicated 6-dimensional function
Relies on the “phase space” of the plasma
Using linear theory, you can rely predict the certain traits of the plasma
Magnetic reconnection
Magnetic field lines have tension
When field lines break and reconnect, they release energy which is absorbed into the plasma
Instability
Magnetic reconnection is driven by the decreased density of plasmas on the outer ends
Changes in pressure and energy throughout the plasma cause instabilities which are in turn modeled by the Vlasov Equation
Definition of a Plasma
Statistical collection of mobile charged particles
Few Assumptions:
Average kinetic energy >> Average Potential energy (between two particles)
Affected by E & M Force
q(E+v x B)
Temperature are in units of energy
Research Goals:
Tackle 2 problems, resistive tearing mode and collisionless tearing mode.
Resistive tearing mode is simpler, we will be able to do the math and simulating ourselves, and collisionless will be done using Jimmy’s help
UPDATE: The methods we were going to try to use to simulate tearing mode were not sophisticated enough, and se we refocused research into studying the behavior of the Weibel instability
Debye length
Electron fields associated with the plasmas which have a length before they are screened out
The Debye cube is based on this length but in 3 dimensions
Plasma Parameter
This is the average number of particles in a debye cube
This is calculated by using the average distance between particles in a plasma and average potential and kinetic energies
Plasma Frequency
Fluttering of electron plates over one another (Simple harmonic motion)
Gyrofrequency
Oscillation of a single charged particle in a plasma
Harmonic
Gamma is the gyrofrequency
Gyroradius
Radius of the circle made by the particle in a plasma
This is then the gyro radius
Numerical Methods
Finite difference is the discrete analog of the derivative (the difference quotient)
Finite volume is similar to a representation of a surface integral, it breaks the measured problem up into cells
Finite element divides a problem up into smaller more approachable components
Weibel Instability
Present in plasmas with an anisotropy, meaning different temperatures are going in different directions
It can be understood by the superposition of multiple counterstreaming beams
This will bend magnetic fields around to enhance one magnetic field
Computing
Using CERN Stampede cluster
Started with a pbs file which processed the job, requesting a certain number of hours, holding the location of the lua scripts, and writing lua files that the location of the final script.
Doing all this from MobaXterm, which faced many issues combined with my computer’s graphics card
The parameters that we changed were polyOrder, k0, X resolution, and velocity resolution
We put the lua and pbs files in a scratch directory, and then within that directory, made subdirectories for each modified parameter.
Commands needed to be changed because we originally didn't have access to the files in Jimmy's folder that needed to be run, we needed to change the heading on one of the graphs, and we needed to request more processors than I initially had.
None of the runs created the text file I wanted, and one of them actually said that I cancelled the run myself.
At this point in the project, I faced a lot of issues with the code because at the time, my laptop was facing a lot of difficulties and it would shut down once certain applications and scripts were ran. For this reason, my group members, Shaina and Matt, sent the graph jobs for me, and I myself focused on doing background research on the actual physics for our final presentation, and then concluding statements.
Expected results:
PolyOrder Results:
Varying NX resolution:
Varying K0
Varying Velocity Resolution
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