Winter Power Electronics Internship

At MIT, we are given the month of January off from classes to pursue our own interests, whether they be career-oriented or hobby-based. During these five weeks, I have worked at PSS as a power electronics intern. My time at PSS has given me the opportunity to explore so many of the industry based applications of electronics and electrical engineering amongst some of the most innovative minds in the aerospace and energy industries. 

Within the GAMOW (Galvanizing Advances in Market-Aligned Fusion for an Overabundance of Watts) project, my work centered around helping redesign, assemble, and test a power load switch, the resulting prototype of which is shown above. Within this project, I received a wide array of experience ranging from 3D-modeling PCB boards with Eagle software, to physical board assembly, to designing testing procedures for the completed board. Initially, I worked on redesigning the load switch PCB to reduce loop currents and noise. My next steps were to source and order all needed components for in-house assembly. During the assembly process, I worked with both a soldering iron and hot air rework station to assemble surface mounted devices (SMDs) and through-hole components. 

Raspberry Pi setup for PWM

I also dipped into some software based components of the project, programming in C and Python to create hardware based signals to our desired testing specifications. Specifically, I was aiming to make Pulse Width Modulation (PWM) signals of a specific duration for the Raspberry Pi to output. This led to various tests on the outputs of the code, through the use of an oscilloscope (two PWM pulses on the oscilloscope are shown below). Ultimately, I had the chance to start testing the board in connection with a power supply and the Raspberry Pi’s program.

Moreover, I had the opportunity to dip into so many different branches of electrical engineering and project design. In attending meetings about all of the individual components of the massive GAMOW project, I saw how the team plans and executes each individual collaborative part of the project. This experience in the project process and cutting edge electrical project design as a whole have given me many insights into the professional world of electrical engineering.

Winter Mechanical Engineering Internship

During my time at Princeton Satellite Systems, I worked on a momentum unloading project for NASA’s Gateway, a component of the Artemis program. I designed a deployable parasol that is controlled by Canadarm using Solidworks.

Solidworks is a platform I am familiar with, but I was still able to learn new functions. My favorite part of working with Solidworks is the puzzle-like nature of assemblies. When trying to make dynamic parts you have to think about how to best add relations without over-constricting or under-constricting the part. Once I finalized my initial design I was able to attend a Zoom meeting and present it to another company.

When not working on my Gateway project, I fiddled with the 3D printer to print models of the PFRC fusion reactor.

Although I have used 3D printers several times before, this time was more of a learning process. I was an acting 3D printer technician and wrote a guide with troubleshooting tips for future employees. Due to problematic unspooling and tangled filament the printer became jammed a few times, and I was unable to do the typical loading/unloading to set the filament free. This gave me the opportunity to take apart the 3D printer and see the internal mechanisms, which in turn allowed me to unjam the printer and solve the problem. I was thrilled to see inside the 3D printer and how the parts blend together!

Through my internship I learned about the complexity of the design process and how many things you need to consider when creating a product. Conceptualizing is one step, but bringing that concept into the real world requires much more research and planning. Overall, this internship was a great opportunity that allowed me to learn how to solve several engineering problems.

PFRC Article in the Journal of Fusion Energy

Our latest paper, The Princeton Field-Reversed Configuration for Compact Nuclear Fusion Power Plants, is available in the Journal of Fusion Energy, Volume 42, Issue 1, June 2023. This paper is the first released in “The emergence of Private Fusion Enterprises” collection. A view-only version is available for free here.

Our paper gives an overview of the Princeton Field-Reversed Configuration (PFRC) fusion reactor concept and includes the status of development, the proposed path toward a reactor, and the commercialization potential of a PFRC reactor.

The Journal of Fusion Energy features papers examining the development of thermonuclear fusion as a useful power source. It serves as a journal of record for publication of research results in the field. This journal provides a forum for discussion of broader policy and planning issues that play a crucial role in energy fusion programs.

APS Division of Plasma Physics 2022 Meeting in Spokane, Washington

Last week, I attended the American Physical Society Division of Plasma Physics (APS DPP) 2022 Meeting. As the name entails, it was a meeting full of plasma physics with applications ranging from astrophysics to nuclear fusion energy. There were many great talks and posters on plasma physics research by companies, national labs, and universities, and one could sense an overall feeling of excitement around fusion shared by many attendees.

I had a pleasant time in Spokane, WA. Pictures from outside of the conference center (with many conference attendees standing nearby), including the nice view from the conference center, are shown below.

I presented a talk on the Princeton Field-Reversed Configuration (PFRC) fusion reactor concept, and how we can leverage public-private partnerships for its development. The talk discussed technical details of the PFRC, including the past modeling and experiments, current investigation, and future research & development plans. The talk also described the markets and commercialization opportunities for this reactor concept, including disaster relief and asteroid deflection. Here I am at the podium speaking.

I also presented a poster on our recent investigations of x-ray diagnostics on the PFRC-2 experiment for electron temperature and density measurements, which was mounted on a poster board in the conference center. Many people came by to ask about my poster as well as about general PFRC questions, which kept me talking for the majority of the 3-hour poster block session! It was great to discuss ideas and results with many scientists and students at the conference.

Dr. Sangeeta Vinoth also had a poster at this conference on collisional-radiative model developments to extract electron temperature measurements from spectroscopy, which she presented virtually. APS DPP 2022 was an exciting conference to attend, and I’m looking forward to seeing updates from presenters at this conference. That also includes us, as we have more research and investigation to do — stay tuned!

Plasma Circuit Models for RF Heating

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.

Plasma resistance (solid lines) and inductance (dashed lines) as a function of electron density for five different frequencies, based on the transformer model in [1].

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.

Antenna reactance (left) and resistance (right) as a function of the parallel wavenumber, based on the transmission line model in [2].

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);

[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);

Practical MATLAB Deep Learning, Second Edition

Our latest textbook on MATLAB programming is now available from Apress. Practical MATLAB Deep Learning, A Projects-Based Approach, is in its second edition. It is available in both electronic and hard copy from SpringerLink.

New coauthor Eric Ham, a deep learning research specialist, joins Michael Paluszek and Stephanie Thomas. Mr. Ham led the development of a new chapter on generative modeling of music.

The software is available from GitHub:

About the Book

Harness the power of MATLAB for deep-learning challenges. Practical MATLAB Deep Learning, Second Edition, remains a one-of a-kind book that provides an introduction to deep learning and using MATLAB’s deep-learning toolboxes. In this book, you’ll see how these toolboxes provide the complete set of functions needed to implement all aspects of deep learning. This edition includes new and expanded projects, and covers generative deep learning and reinforcement learning.

Over the course of the book, you’ll learn to model complex systems and apply deep learning to problems in those areas. Applications include:

  • NEW: An aircraft that lands on Titan, the moon of Saturn, using reinforcement learning
  • NEW: Music creation using generative deep learning
  • NEW: Earth sensor processing for spacecraft
  • Aircraft navigation
  • MATLAB Bluetooth data acquisition applied to dance physics
  • Stock market prediction
  • Natural language processing
  • Plasma control

 You will:

  • Explore deep learning using MATLAB and compare it to algorithms
  • Write a deep learning function in MATLAB and train it with examples
  • Use MATLAB toolboxes related to deep learning
  • Implement tokamak disruption prediction

The book primarily features the Deep Learning Toolbox and the Reinforcement Learning toolboxes. Some examples in the book feature other MathWorks toolboxes, include the Instrument Control toolbox, Optimization toolbox, Statistics and Machine Learning, and Image Processing toolbox.

Our other books

This new second edition joins our other books available from Apress:

Applying our Toolboxes to ITER and DEMO fusion reactors

Last week, PSS Mike Paluszek visited ITER, the international fusion research experiment under construction in France. In light of Mike’s recent visit to ITER, we wanted to showcase an application of our tokamak Fusion Reactor Design function to the design of ITER. This function is part of the Fusion Energy Toolbox for MATLAB, a toolbox that includes a variety of physics and engineering tools for designing fusion reactors and studying plasma physics. We will also compute design parameters for ITER’s successor, the DEMOnstration power plant (DEMO), a fusion reactor currently in the design phase which is planned to achieve net electricity output.

We first apply the Fusion Reactor Design function to ITER. Note that ITER is expected to produce 500 Megawatts (500 MW) of fusion power, but this will not be converted into electric power, the power that goes into the electrical grid. DEMO, on the other hand, is planned to produce 500 MW of electric power from 2000 MW of fusion power. The Fusion Reactor Design function asks for the net electric power output of the reactor, P_E, as an input, so we generate a value for P_E for ITER by using the same ratio of electric-to-fusion power as in DEMO, giving us a P_E of 125 MW for ITER. The inputs used for the ITER design are shown below (see references [1,2]), where we use a data structure “d_ITER”:

d_ITER.a     = 2; % plasma minor radius (m)
d_ITER.B_max = 13; % maximum magnetic field at the coils (T)
d_ITER.P_E   = 125; % electric power output of the reactor (MW)
d_ITER.P_W   = 0.57; % neutron wall loading (MW/m^2)
d_ITER.H     = 1; % H-mode enhancement factor
d_ITER.consts.eta_T = 0.25; % thermal conversion efficiency
d_ITER.consts.T_bar = 8; % average ion temperature (keV)
d_ITER.consts.k     = 1.7; % plasma elongation
d_ITER.consts.f_RP  = 0.25; % recirculating power fraction

The first five inputs were described in our original post on the Fusion Reactor Design function. The function can be called to perform a parameter sweep over any of these inputs. We also specify values for some constants: the thermal conversion efficiency ‘eta_T’, the average ion temperature ‘T_bar’, the plasma elongation ‘k’, which is a measure of how elliptical the plasma cross-section is, and the recirculating power fraction ‘f_RP’. We can perform a parameter sweep over the minor radius (from a = 1.8 meters to a = 2.2 meters, with 100 points in between) and display a table of results simply with two lines of code:

d_ITER = FusionReactorDesign(d_ITER,'a',1.8,2.2,100); % run function
d_ITER.parameters % show table of resulting parameters

Looking at the results table from d_ITER.parameters, we see overall agreement with parameters for ITER [1,2]. The plasma major radius (essentially the tokamak radius) R_0 output is about 5 m, which is in the ballpark of the 6.2 m radius of ITER design, and the magnetic field at R_0 (on plasma axis) output is 4.8 Tesla, close to the ITER design value of 5.3 Tesla. The plasma current output is 17.5 MegaAmps, which is also close to ITER’s design of 15 MegaAmps.

The Fusion Reactor Design function also outputs plots that show whether or not the reactor satisfies key operational constraints for tokamaks, see the figure below. The first three curves check various constraints to ensure the plasma is stable, which we see are met as they are located in the unshaded region (though the green curve is marginally close to the constraint boundary). The blue curve’s position deep into the shaded region indicates that the reactor is far from producing enough electric current to sustain itself. The designers of ITER anticipated this, which is why ITER will additionally use a pulsed inductive current and test a combination of other techniques to drive the plasma current.

We now consider DEMO, which is in the design phase with the goal of net electrical power output. Similarly to running the ITER case, we set up a data structure (now called ‘d_DEMO’) with known DEMO input parameters [3] and perform a parameter sweep over the minor radius ranging from a = 2.7 meters to a = 3.1 meters:

d_DEMO.a     = 2.9; % plasma minor radius (m)
d_DEMO.B_max = 13; % maximum magnetic field at the coils (T)
d_DEMO.P_E   = 500; % electric power output of the reactor (MW)
d_DEMO.P_W   = 1.04; % neutron wall loading (MW/m^2)
d_DEMO.H     = 0.98; % H-mode enhancement factor
d_DEMO.consts.eta_T = 0.25; % thermal conversion efficiency
d_DEMO.consts.T_bar = 12.5; % average ion temperature (keV)
d_DEMO.consts.k     = 1.65; % plasma elongation
d_DEMO.consts.f_RP  = 0.25; % recirculating power fraction
d_DEMO = FusionReactorDesign(d_DEMO,'a',2.7,3.1,100); % run function
d_DEMO.parameters % show table of resulting parameters

The outputs for the DEMO case also show overall agreement with DEMO parameters [3]. The plasma major radius R_0 output is 7.8 m, which is not far from the 9 m design radius for DEMO. The resulting on-axis magnetic field output is 6.2 T, close to the 5.9 T of the DEMO design. The plasma current output is now 21 MegaAmps, which is less than 20% away from the design value of 18 MegaAmps. It is important to note that in each of these parameters, we see an increase going from ITER to DEMO, which is consistent both in our model’s output and the actual design parameters in the papers [1-3].

The operational constraints plot for DEMO is shown in the figure below. DEMO is a larger reactor than ITER, and given the favorable scaling of tokamak operation with size, we expect improved results for operational constraints in DEMO. The three curves which check plasma stability are all satisfied. Unlike in the case of ITER which had the green curve close to the shaded region, the green curve in the case of DEMO stays safely in the unshaded region. The blue curve is still in the unshaded region, but much closer to the boundary of the unshaded region than ITER (now ~1.8, much closer to 1 than in the case of ITER which was ~4). This shows an improvement for DEMO compared to ITER as it is closer to producing enough self-sustaining plasma current, though it will still need some help from other current-generating techniques which will be tested on ITER.

This function is part of release 2022.1 of the Fusion Energy Toolbox. Contact us at or call us at +01 609 275-9606 for more information.

[1] Aymar, Barabaschi, and Y Shimomura (for the ITER Team), “The ITER Design”, Plasma Physics and Controlled Fusion 44, 519–565 (2002);
[2] Sips et al., “Advanced scenarios for ITER operation”, Plasma Physics and Controlled Fusion 47 A19 (2005);
[3] Kembleton et al., ” EU-DEMO design space exploration and design drivers”, Fusion Engineering and Design 178, 113080 (2022);

Research paper on “A diagnostic to measure neutral-atom density in fusion-research plasmas” has been published in the Review of Scientific Instruments

A research paper on neutral-atom density diagnostics on the PFRC-2, written with our colleagues and collaborators, has been published and is titled “A diagnostic to measure neutral-atom density in fusion-research plasmas” DOI: It is part of the “Proceedings of the 24th Topical Conference on High-Temperature Plasma Diagnostics.”

In this paper, a femtosecond two-photon-absorption laser-induced-fluorescence (fs-TALIF) diagnostic was designed, installed, and operated on the Princeton-Field-Reversed Configuration-2 device to provide non-invasive measurements of the time and spatially resolved neutral-atom densities in its plasmas. We demonstrated that fs-TALIF can provide spatially, to ±2 mm, and temporally resolved, to 10 µs, measurement of the density of certain previously inaccessible atoms, e.g., atomic hydrogen (Ho).

Calibration of the Ho density was accomplished by comparison with Krypton (Kr) TALIF. Measurements on plasmas formed of either molecular hydrogen (H2) or Kr fill gases allowed examination of nominally long and short ionization mean-free-path regimes. With multi-kW plasma heating and H2 fill gas, a spatially uniform Ho density of order 1017 m−3 was measured with better than ±2 mm and 10 µs resolution. Under similar plasma conditions but with Kr fill gas, a 3-fold decrease in the in-plasma Kr density was observed.

Ho density is essential to several plasma diagnostics including time-of-flight and ion energy analyzers, and high-resolution spectroscopy, as by CPT (coherent population trapping) and DFSS (Doppler-free saturation spectroscopy). It was also used in Collisional Radiative Modelling for predicting the Electron temperature diagnostic in PFRC-2.

TALIF H-α signal (arb units) at r = 40 mm vs time for (identical) RMFo-heated discharges (Pf ∼ 60 kW). The maximum Ho density is 2 × 1017 m−3. The non-zero Ho density before and after RMFo is due to the seed plasma. RMFo power applied between 3.7 and 9.5 ms.

Our Visit to ITER in the South of France

On September 22 Marilyn, Eric, and I visited ITER, the International Tokamak Experimental Reactor in Saint-Paul-lez-Durance, France, about 45 minutes from Aix-en-Provence. We took the TGV from Paris to Aix-en-Provence.

Our tour started with a talk by Akko Maas who gave a great presentation on fusion. He talked about building ITER. The complexity of the project and the large international team both present challenges. He also discussed the advantages of fusion in comparison to wind and solar. He noted that while a fusion reactor would have some waste, both wind and solar, when decommissioned, have waste. He talked about the next phase after ITER called DEMO. ITER is designed to produce 500 MW of fusion power from an input of 50 MW heating power. Akko had a slide listing some of the commercial fusion efforts.

Katya Rauhansalo was our tour guide. She had a couple of assistants. They were all really helpful and very knowledgeable. We discussed many fine points of Tokamak design and fusion in general. Marilyn, Eric, and I were combined with a larger group, due to Covid absences. We chatted with members of the other group about PFRC.

A Tokamak is shown below. The green coils are the center stack coils used to induce a current in the plasma. The gray coils are the poloidal coils. The purple coils are the toroidal coils. In ITER, all coils are superconducting. The green donut in the middle of the D coils is the plasma.

The following image shows the Tokamak building.

The first stop was the manufacturing facility for the poloidal coils. The following video shows a crane in operation in the assembly hall.

The top and bottom coils are small enough that they can be shipped complete. The others need to be manufactured. The following figure shows the cryostat for testing the poloidal coils.

This poster gives the details of the testing.

We then moved through the entrance to the Tokamak. We were able to enter the Tokamak building itself. Here is Eric in front of an installed toroidal superconducting coil.

The coil is shaped like a D which works better than a circular coil.

First plasma was scheduled for 2025 but may be delayed. This was partly due to Covid and partly due to the inevitable technical glitches in such a complex project.

Collisional Radiative Model paper Published in Review of Scientific Instruments 

Our new collisional radiative model paper is titled “Evaluation of a collisional radiative model for electron temperature determination in hydrogen plasma” DOI: It is part of the “Proceedings of the 24th Topical Conference on High-Temperature Plasma Diagnostics.”

This paper talks about a collisional-radiative (CR) model that extracts the electron temperature, Te, of hydrogen plasmas from Balmer-line-ratio measurements and is examined for the plasma electron density, ne, and Te ranges of 1010–1015 cm−3 and 5–500 eV, respectively. The first tests of the CR model on the Princeton Field Reversed Configuration-2 (PFRC-2) have been made, including comparisons with other diagnostics. These comparisons are informative as different diagnostics sample different parts of the electron energy distribution function.

Extracted Te(t) for the data for two values of Pc. The shaded region represents the statistical error bar.