This summer, I worked on creating a plasma circuit model as part of PSS’s work under the ARPA-E GAMOW grant. As part of this project, I wrote MATLAB functions to reproduce the results of two papers on impedance of radio frequency (RF)-driven circuits for plasma heating. Both functions take in some plasma and geometric parameters and return impedance values as well as plots of impedance as a function of other parameters.

The first function is based on reference [1], which uses the transformer model to describe the coupling between the plasma and the rest of the circuit. This means that the plasma can be represented as a resistor-inductor circuit that is inductively coupled with the main circuit. In addition to calculating the equivalent circuit impedance for values in passed-in density and frequency ranges, I reproduced the figures showing resistance/inductance and reflection coefficient as a function of the electron density of the plasma. Plotting over many orders of magnitude of density, you can see drastic changes in the plasma resistance and inductance.

Since ion cyclotron resonance heating (ICRH) is a leading technique for plasma heating in fusion reactors, we also wanted a function that dealt specifically with ICRH in its plasma model. I then read through some literature on ICRH in order to find a suitable reference to model in MATLAB. I found this in reference [2], which became the basis for my second function. This model uses transmission line theory to calculate the antenna impedance with the effects of the plasma incorporated. This paper also compared a previously-formulated 2D model with its own 3D model, and the implications of this extension to three dimensions can be seen in the way impedance changes as a function of the wavenumber.

The impedance values produced from both of these models can be used to help account for the effect of plasma on antennas used in RF heating, especially ICRH. While assumptions are made in these models to allow for analytical calculations to be made (notably assuming uniform current density and neglecting volume propagation effects) and adjustments are needed to resolve minor discrepancies between the MATLAB models and the figures in the reference papers, they should be a reasonable first approximation of the physics that is occurring and the impedance generated by the plasma.

This summer has given me a lot more knowledge about plasma physics, in particular about resonance heating. I have also gained a lot of experience in conducting literature reviews, reproducing published results, and working in MATLAB.

[1] Nishida, K., et al., “Equivalent circuit of radio frequency-plasma with the transformer model.” Rev. Sci. Instrum. 85, 02B117 (2014); https://doi.org/10.1063/1.4832060.

[2] Bhatnagar, V.P., et al., “A 3-D analysis of the coupling characteristics of ion cyclotron resonance heating antennae.” Nucl. Fusion 22, 280 (1982); https://doi.org/10.1088/0029-5515/22/2/011.

This summer I worked on the design of a millisecond pulse generator as part of the ARPA-E GAMOW grant. The goal of this project was to supply pulses of very high current to a fusion reactor’s plasma control antenna using solid-state power electronics. Some key design considerations were the ability to parallelize the pulse generator to scale to many power levels, to operate at high voltages, and to minimize the current rise time through the load antenna. I spent most of my time working in LTspice XVII to simulate the circuit and its response to rapid pulses of current. I wanted to make sure the circuit performed as desired, while also remaining safe for both the devices in the circuit and the operators controlling the circuit.

We based the design of the circuit on a load switch developed previously at Princeton Satellite Systems by Cindy Li and Eric Ham. Our biggest progress was in the selection of switching devices and the improvement of the gate drive circuitry. Because our goal is to switch current as quickly as possible, we did not want to rely on outdated klystrons as our switches. We decided to use many parallel MOSFETs to switch the current. The device we chose was a 650 V silicon carbide cascode JFET from UnitedSiC. This FET has low on-state resistance, meaning that it does not heat up as much when pulling large amounts of current. By using many devices in parallel, we can pull more total current while keeping each individual FET below its current capacity. Then by using multiple boards in parallel, we can reach different power levels for different fusion reactors. 

Implementing safe gate driver circuitry was another important step. The power MOSFETs used to switch the current cannot be turned on directly from a computer control signal, due to both power and safety concerns. A logic-level signal is not powerful enough to activate the FET, and directly connecting the computer to the high-voltage circuitry is unsafe. To solve both problems, I designed a galvanically-isolated gate drive circuit based on an Infineon gate driving IC. The intermediate circuit takes the computer control signal and steps it up to an intermediate voltage level high enough to activate the MOSFET, while keeping the both sections electrically isolated from each other. Each MOSFET has its own gate drive circuit, enabling independent control.

Working on the millisecond pulse generator was a great experience as an intern. I gained lots of practice working with team members across organizations and disciplines. I became much more proficient in LTspice, and I learned how to rigorously approach challenging engineering problems.