Measuring & Modeling The Temperature of WIRX Plasma

Measuring & Modeling The Temperature of WIRX Plasma

GIF that I made in MATLAB. This was not directly related to the research effort :)

Intro to the Experiment:

The Wheaton Impulsive Reconnection eXperiment (WIRX) is a direct current pulsed plasma arcade experiment that was designed by Dr. Darren Craig. The electrodes are housed within a vacuum chamber and the plasma is confined by a magnetic field produced by pulsing coils that are embedded within the electrode structure. The plasma is produced by ionizing hydrogen gas that is puffed into the vacuum chamber every time the experiment is fired. The summer after my Junior year I accepted a research position and worked on the experiment for ten weeks. I am also currently working on a senior honors thesis that continues my work from the summer of 2014. I am using MATLAB to model the effects that the adjustable experimental parameters have on the plasma temperature and density. I am comparing the model with data that I am taking on the experiment and am modifying the experiment through the addition of some parts that I machined to try to acheive higher plasma temperatures.


Schematic of WIRX Plasma Discharge. The Length, L, was particularly important to my model of plasma temperature. (image Credit: Cole Adams)

The Wheaton Impulsive Reconnection Experiment (WIRX) is a new plasma physics experiment which aims to study magnetic reconnection. Magnetic reconnection is a mechanism for converting energy stored in magnetic fields to thermal or kinetic energy. It occurs in plasmas (hot ionized gases) and is important in the solar conoar, the earth’s magnetosphere, and in magnetic confinement devices developed to harness the power of controlled thermonuclear fusion.
-WIRX Description

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My Project:

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The goal was to reliably measure the temperature of the plasma produced each time current was discharged between the electrodes. 

The long term desire is to be able to create plasmas that have an electron temperature of about 10 eV. The plasma electron temperature can be changed by varying the experimental parameters. When preparing the experiment the two parameters that the experimenter has control over is how much current is run through the plasma and the area of the electrodes. The current can be changed by charging up the capacitor bank for a greater length of time. The area of the electrodes is adjusted by covering part of them with macor covers that I machined t fit over the electrodes. My MATLAB model predicts how adjusting these two parameters will affect the plasma temperature and density. The model uses two equations and a minimization algorithm to produce the temperature and density values for the grid of possible experimental parameters. In order to quantify the effects of the experimental parameters the plasma is treated as if it is in steady state (this is not too bad of an assumption given the energy loss time). So the equations to model the steady state plasma are the resistivity equation and a power balance expression. The resistivity equation measures the energy dissipated into the plasma using ohm’s law on the circuit that drives the discharge. The power balance expression just says that the amount of energy flowing into the plasma is equal to the plasma flowing out of the plasma. Combined these two equations can produce predictions for temperature and density that can be verified experimentally. To confirm that these adjustments do indeed increase the plasma temperature I developed experimental techniques to measure the temperature.

Model of possible plasma temperatures achievable in the experimental parameter space. The values were produced using a minimization algorithm.

Model of possible plasma temperatures achievable in the experimental parameter space. The values were produced using a minimization algorithm.

Hydrogen Line Ratios:


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Langmuir Probe:

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Electrodes protruding from Boron Nitride Shield and a Langmuir Probe positioned to be in the middle of the plasma discharge.

Electrodes protruding from Boron Nitride Shield and a Langmuir Probe, that I designed and constructed,  positioned to be in the middle of the plasma discharge.

Langmuir probe isolation circuit to protect the computer from the plasma.

Langmuir probe isolation circuit to protect the computer from the plasma.

Unexpected Aspects of the Project:


The LabView program that drives the experiment did not work at the beginning of the summer because the computer systems updated to a new operating system. I got to spend a lot of time fixing this program and re-writing much of it in the process. This taught me a lot about LabView and the inner workings of the experiment!

The Spectrometer:

The spectrometer that we used had a broken control panel and had to be adjusted by hand. I used a microcontroller programmed with C and some photo-gates (to read the position of the grating) to allow the spectrometer to be controlled by a computer. I also wrote a python application to run the spectrometer so that it functions “Like New”.

A well timed phone picture through the vacuum chamber’s viewport!

Future Development:

This page will be updated as I continue work on my senior honors thesis. I also will be presenting the results at the spring APS conference.

Abstract for the APS presentation:

We develop a theoretical model and experimental techniques to provide a better picture of how the adjustable parameters such as the current, and electrode geometry affect the temperature and density of WIRX plasmas. Our model predicts the plasma temperature and density by balancing the Ohmic heating with convective losses. The Ohmic heating is measured directly as the product of the voltage drop between the electrodes and the plasma current. Temperature and density are measured independently using spectroscopic methods. Stark broadening of the H-Beta line is used to measure density. To measure the electron temperature of the plasma the line ratios of various hydrogen transitions were compared with the predictions of the Boltzmann thermal equilibrium model and the coronal equilibrium model. Preliminary experimental results are consistent with the plasma parameters predicted by our model. This work will be used to inform future modifications to the experiment with the intent of producing higher temperatures in WIRX plasma, making magnetic reconnection more probable. Work supported by US DOE.

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