PFRC inventor Dr. Sam Cohen and his student Taosif Ahsan have published a new journal paper, “An analytical approach to evaluating magnetic-field closure and topological changes in FRC devices,” in Physics of Plasmas (Phys. Plasmas 29, 072507 (2022)). The paper is an Editor’s Pick and has important implications for confining plasma in Field-Reversed Configurations (FRCs).
We describe mathematical methods based on optimizing a modified non-linear flux function (MFF) to evaluate whether odd-parity perturbations affect the local closure of magnetic field lines in field-reversed configurations. Using the MFF methodology, quantitative formulas are derived that provide the shift of the field minimum and the threshold for field-line opening, a discontinuous change in field topology.
Paper Abstract
This paper follows up on a 2000 paper by Cohen and Milroy, which made qualitative assertions about changes in magnetic field topology, e.g., movement of the center of separatrix, separator line, and other geometric parameters. Ahsan and Cohen developed the modified flux function (MFF) mathematical tool to quantitatively understand the effects of perturbations on a Solov’ev FRC field structure. The analytical results from this function have reproduced the previous numerical observation that small odd-parity perturbation preserves FRC field structure. In particular, the contours around the equilibrium stay closed.
Closure of magnetic field lines limits plasma losses that would occur due to charged particles leaving the FRC by traveling along open field lines. The paper points out that in a reactor-scale FRC where ions have a large gyroradius relative to the field structure, but electrons have a small radius and follow the field lines, particle and energy losses on the open field lines outside the FRC will be significant. Hence, ensuring closure of field lines is a crucial step toward improved plasma confinement in FRCs.
3D contours of a perturbed FRC using the modified flux function (MFF)
Electron density profiles on PFRC with USPR: Ultrashort Pulse Reflectometry (USPR) is a plasma diagnostic technique that would be used on the Princeton Field-Reversed Configuration (PFRC) to measure electron density profiles. Such profile measurements provide insight into the structure of PFRC plasma and can improve our estimates of confinement time. Our University partner is University of California, Davis, PI Dr. Neville Luhmann.
Evaluating RF antenna designs for PFRC plasma heating and sustainment: We intend to analyze RF antenna performance parameters critical to the validity of robust PFRC-type fusion reactor designs. Team member University of Rochester will support TriForce simulations and contractor Plasma Theory and Computation, Inc. will support RMF code simulations. Our national lab partner is Princeton Plasma Physics Laboratory, PI Dr. Sam Cohen.
Stabilizing PFRC plasmas against macroscopic low frequency instabilities: This award will use the TriForce code to simulate several plasma stabilization techniques for the PFRC-2 experiment. Our lab partner is PPPL and the team again includes the University of Rochester.
These awards will help us advance PFRC technology. Contact us for more information!
The following movie is by Woodruff Scientific, Inc. It was developed under an ARPA-E Grant. The movie shows a five PFRC modular power plant. The technician is shown for scale. Modular power plants are ideal for power systems because they allow for incremental capital investment. Modules would be added as needed. You can read more about PFRC here.
Experimental work on PFRC-2 was funded by an ARPA-E OPEN 2018 grant. ARPA-E is funding many cutting edge fusion projects including new mirror machines, stellarators and many others.
It was exciting to meet and network with fusion industry and power electronics researchers, and influential leaders from both the private and public sectors at the Summit.
We displayed a prototype Class E amplifier, silicon carbide (SiC) JFET wafers, a PCB board of a load switch, and brochures of NREL.
Princeton Fusion Systems in collaboration with Princeton University, Qorvo, and NREL is developing integrated, power-dense, reliable, and scalable switching power amplifier boards for plasma heating and control applications. We presented the Class E prototype, some samples of the wide bandgap semiconductor silicon carbide (SiC) JFET wafers, and a PCB board for a load switch at our booth at the ARPA-E Summit. A previous post on our website has links to our marketing and technical documents.
The photos below show Stephanie Thomas and Sangeeta Vinoth at the Registration desk of the ARPA-E-2022-Summit.
The picture of the Class E prototype that the PFS presented at the booth has been added to the ARPA-E Innovation Summit website.
Class E prototype build by Princeton University
More pictures of the ARPA-E Summit can be found here.
The Summit helped us to understand the Fusion industry’s needs for power electronics. We design, test, and qualify circuit boards as building blocks for various applications: short pulses, control pulses, and RF amplifiers.
A key takeaway was that there was interest in SiC and GaN wide bandgap semiconductor requirements for high power and high frequency. Researchers asked about radiation-hardened electronics, and some were also interested in high voltage electronics.
There were talks at the Summit about climate change, rethinking solutions for resilience, reliability, and security of electric grid infrastructure, and decarbonization.
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 info@psatellite.com 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.
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!
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.
Our team presented a number of posters at the 63rd Annual Meeting of the APS Division of Plasma Physics, representing work supported by our ARPA-E OPEN contract and other supporting programs.
Electrostatic Energy Analyzer and Gas Stripping Cell to Measure Ion Temperature in the PFRC-2, Matthew Notis: https://meetings.aps.org/Meeting/DPP21/Session/JP11.192
Hi! I’m Paige, and I’m an undergraduate at Princeton interested in physics and science communications. This January, I got to work as an intern here at Princeton Satellite Systems. These past few weeks, I’ve been writing about the fusion-related projects PSS is working on, such as their Princeton Field-Reversed Configuration (PFRC) fusion reactor concept and plans for a space propulsion engine.
My first task was to write a four-page report on the PFRC, including its design, market demand, and development timeline. I knew very little about fusion coming into this internship, so first I had to learn all I could about the process that powers the sun and has the potential to supply the earth with clean, practically limitless energy.
Various types of fusion reactors are under development by companies and coalitions all over the world; they differ in the reactors they use and their methods of confining and heating plasma. ITER, for instance, is an example of a tokamak under construction in France; it uses superconducting magnets to confine plasma so that the reaction of tritium and deuterium can occur.
The PFRC, currently in the second stage of experiments at the Princeton Plasma Physics Laboratory, uses radio frequency waves to create a rotating magnetic field that spins and heats the plasma inside, which is contained by closed magnetic field lines in a field-reversed configuration resulting from the opposition of a background solenoidal magnetic field to the field created by the rotating plasma current. The fusion reaction within the PFRC is that of helium-3 and deuterium, which offers multiple advantages over reactions involving tritium. Compared with other fusion reactors, the PFRC is incredibly compact. It will be about the size of a minivan, 1/1000th the size of ITER; this compactness makes it ideal for portable or remote applications.
After learning about the design and market applications of the PFRC, I created a four page brochure about PFRC, writing for a general audience. I included the basics of the reactor design and its advantages over other reactors, as well as market estimates and the research and development timeline. I went on to write four page brochures about PSS’s Direct Fusion Drive engine, which will use PFRC technology for space propulsion purposes, and GAMOW, the program under which PSS is collaborating on developing various power electronics for fusion reactors.
These past few weeks have been quite informative to me, and I realized how much I loved writing about science and technology! I learned all about fusion, and I especially loved learning the details of the PFRC reactor design. To summarize the design, research, and development of the PFRC and other technologies within four page flyers, I had to learn how to write about technology and research comprehensively and engagingly for a general audience, which improved my science communication skills.
The Space subcommittee of the Fusion Industry Association, of which we are a member, has prepared a new white paper recommending government funding for a fusion propulsion development program, styled similarly to ARPA-E and DARPA.
The goal is to provide funding not just for “paper studies,” but enough funding to build real hardware and start to test fusion propulsion concepts. We want the US to remain competitive in the upcoming Deep Space Race – building a human presence on the Moon, and then Mars, and beyond.
The PFRC is directly applicable, configured as Direct Fusion Drive – a variable thrust, variable specific impulse rocket in the 1 to 10 MW range. With sufficient funding, we could build a PFRC-3 to test a fully superconducting configuration’s ability to achieve fusion-relevant plasma temperatures, and a separate propulsion testbed to develop the thrust augmentation system. This is the actual mechanism to transfer the energy from the fusion products to a rocket propellant – a fusion reactor is not a rocket until you have accelerated a propellant! For more on the Direct Fusion Drive, see our related videos:
