New Fusion Reactor Design Function

The Fusion Energy Toolbox for MATLAB is a toolbox for designing fusion reactors and for studying plasma physics. It includes a wide variety of physics and engineering tools. The latest addition to this toolbox is a new function for designing tokamaks, based on the paper in reference [1]. Tokamaks have been the leading magnetic confinement devices investigated in the pursuit of fusion net energy gain. Well-known tokamaks that either have ongoing experiments or are under development include JET, ITER, DIII-D, KSTAR, EAST, and Commonwealth Fusion Systems’ SPARC. The new capability of our toolboxes to conduct trade studies on tokamaks allows our customers to take part in this exciting field of fusion reactor design and development.

The Fusion Reactor Design function checks that the reactor satisfies key operational constraints for tokamaks. These operational constraints result from the plasma physics of the fusion reactor, where there are requirements for the plasma to remain stable (e.g., not crash into the walls) and to maintain enough electric current to help sustain itself. The tunable parameters include: the plasma minor radius ‘a’ (see figure below), the H-mode enhancement factor ‘H’, the maximum magnetic field at the coils ‘B_max’, the electric power output of the reactor ‘P_E’, and the neutron wall loading ‘P_W’, which are all essential variables to tokamak design and operation. H-mode is the high confinement mode used in many machines.

Illustration of the toroidal plasma of a tokamak. R is the major radius while a is the minor radius of the plasma. The red line represents a magnetic field line which helically winds along the torus. Image from [2].

This function captures all figure and table results in the original paper. We implemented a numerical solver which allows the user to choose a variable over which to perform a parameter sweep. A ‘mode’ option has been incorporated which allows one to select a desired parameter sweep variable (‘a’, ‘H’, ‘B_max’, ‘P_E’, or ‘P_W’) when calling the function. Some example outputs of the function are described below.

As an example, we will consider the case of tuning the maximum magnetic field at the coils ‘B_max’. The figure below plots the normalized operation constraint parameters for a tokamak as functions of B_max from 10 Tesla to 25 Tesla. The unshaded region, where the vertical axis is below the value of 1, is the region where operational constraints are met. We see that for magnetic fields below about 17.5 Tesla there is at least one operation constraint that is not met, while for higher magnetic fields all operation constraints are satisfied, thus meeting the conditions for successful operation. This high magnetic field approach is the design approach of Commonwealth Fusion Systems for the reactor they are developing [3].

Operational constraint curves as a function of B_max. Successful operation occurs if all of the curves are in the unshaded region. Note, f_B/f_NC, a ratio of the achievable to required bootstrap current, is set equal to 1. In this case P_E = 1000 MW, P_W = 4 MW/m2, and H = 1. For more details on the plotted parameters and how they function as operational plasma constraints, see reference [1].

Note, however, that there is a material cost associated with achieving higher magnetic fields, as described in reference [1]. This is illustrated in the figure below, which plots the cost parameter (the ratio of engineering components volume V_I to electric power output P_E) against B_max. There is a considerable increase in cost at high magnetic fields due to the need to add material volume that can structurally handle the higher current loads required.

Cost parameter (units of volume in cubic meters per megawatt of power, m3/MW) as a function of B_max.

In this post we illustrated the case of a tunable maximum magnetic field at the coils, though as mentioned earlier, there are other parameters you can tune. This function is part of release 2022.1 of the Fusion Energy Toolbox. Contact us at or call us at +01 609 276-9606 for more information.

Thank you to interns Emma Suh and Paige Cromley for their contributions to the development of this function.

[1] Freidberg, Mangiarotti, and Minervini, “Designing a tokamak fusion reactor–How does plasma physics fit in?”, Physics of Plasmas 22, 070901 (2015);

ARPA-E 2022 Summit

We will be at the 2022 ARPA-E Summit in Denver, CO next week, May 23-25! PFS will have booths for both of our projects, WIDE BAND GAP SEMICONDUCTOR AMPLIFIERS FOR PLASMA HEATING AND CONTROL and Next-Generation PFRC. This post has links to the documents that we will have at our booth both physically and on the summit mobile app!

Wide Band Gap Amplifiers (GAMOW)

Next-Generation PFRC (OPEN 2018)

PFRC video including animation of how it works
7-minute tech demo video of PFRC-2 experiment from 2021 Virtual Summit

The ARPA-E 2022 Nuclear Fusion Annual Meeting in San Francisco

I attended the ARPA-E 2022 Fusion Annual Meeting at the Westin St. Francis hotel in San Francisco. This is a meeting for all companies that have ARPA-E grants and are working on nuclear fusion technology. Below is the poster for our Princeton Field Reversed Configuration ARPA-E OPEN 2018 grant. The poster gives an overview of the technology and the latest results from the work.

Below is our ARPA-E GAMOW poster on power electronics. It includes work by Princeton Fusion Systems, Princeton University, Qorvo and the National Renewable Energy Laboratory (NREL). The first panel explains the benefits of wide bandgap semiconductors. The second panel shows the latest results on Class-E amplifiers for plasma heating. The next panel shows Qorvo’s latest 2 V SiC cascodes. The final panel shows the cooling systems being designed by NREL.

The meeting had two days of interesting talks by distinguished speakers. Dr. Robert Mumgaard of Commonwealth Fusion Systems talked about their work on advanced high-temperature superconducting magnets and the theory behind high field Tokamaks. Dennis Stone of NASA discussed NASA COTS programs. Dr. Wayne Sullivan of General Atomic talked about their research programs. General Atomics has been operating a Tokamak possibly longer than anyone else. We heard talks on the Centrifugal Mirror at the University of Maryland and WHAM, the high field mirror, at the University of Wisconsin. Andrew Holland of the Fusion Industry Association gave an overview of funding resources for fusion research. He said FIA had verified 31 companies that were developing fusion power technology. This is a huge change from just a few years ago when only large government entities were conducting fusion research.

We talked to several organizations in need of high voltage and high current power electronics. We plan to pivot our GAMOW work to meet the needs of these potentially near-term customers.

The meeting had breakout sessions in which we discussed funding for fusion research and how to help gain social acceptance for nuclear fusion power. Both are challenging.