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.
The internet was abuzz last week with the news that the National Ignition Facility had achieved that elusive goal: a fusion experiment that achieved net (scientific) energy gain. This facility, which uses 192 lasers to compress a peppercorn-sized pellet of deuterium and tritium, released 3 MJ of energy from 2 MJ of input heat.
We have to use the caveat that this is “scientific” gain because it does not account for the total amount of energy needed to make the laser pulse. As a matter of fact, the lasers require 400 MJ to make those 2 MJ that reach the plasma. If we account for this energy, we can call it the “wall plug” gain or “engineering” gain since it includes all the components needed. This gain for laser-induced fusion is still less than 1%, because the lasers are very inefficient.
Nonetheless, this is great news for all fusion researchers. Since we often get asked: Has anyone achieved net (scientific) gain yet? Now we can say: Yes! It is physically possible to release net energy from a fusing plasma, to get more energy output than direct energy input. This advance has been achieved through various new technology: machine learning to select the best fuel pellets, wringing more energy from the lasers, more exact control over the laser focusing. Modern technology, especially computing for predicting plasma behavior, explains why progress in fusion energy development is now accelerating.
Tokamaks have also come close to net gain, and in fact the JT-60 tokamak achieved conditions that could have produced net gain, if it had used tritium [1].
The reason JT-60 did not use tritium in those shots is very relevant to our fusion approach, the PFRC. Tritium is radioactive, rare, expensive to handle, and releases damaging neutrons during fusion. Tritium is also part of the easiest fusion reaction to achieve in terms of plasma temperature, the deuterium-tritium reaction. It makes sense for fusion experiments to use such a reaction, but this reaction presents many difficulties to a future working power reactor.
The PFRC is being designed to burn deuterium with helium-3, rather than with tritium, precisely to make the engineering of a reactor easier. The deuterium-helium-3 reaction releases no neutrons directly. Some deuterium will fuse with other deuterium to produce neutrons and tritium, but the PFRC is small enough easily expel tritium ash. This results in orders of magnitude less neutrons per square meter reaching the walls. Once we have scientific gain, like the NIF has now demonstrated for laser fusion, we have an easier path to engineering gain — that is, net electricity.
So while the laser fusion milestone doesn’t directly impact our work on the PFRC, it is important to the field. We will continue to follow the progress of all our peers as we work to achieve higher plasma temperatures in our own experiments!
[1] T. Fujita, et al. “High performance experiments in JT-60U reversed shear discharges,” Nuclear Fusion 39 1627 (1999). DOI: 10.1088/0029-5515/39/11Y/302
We have commenced operations at 1.8 MHz in PFRC-2, after installing new capacitors over the summer to allow us to lower the frequency from the previous value of 4.3 MHz. A lower frequency should allow the RF system to directly heat the plasma ions, not just the lighter electrons.
With each new operating frequency, we need to explore how the plasma responds: to fill pressure, RMF power, magnetic field, mirror ratio, and more. We have now achieved “big bright flashes” with Argon plasmas in PFRC-2! The seed plasma, on the left, is a dimly glowing column. The RMF heated plasma, on the right, produces a bright flash.
RMF pulse at 1.8 MHz with Argon
This bright light is atomic or molecular line emission, depending on the fill gas. This occurs in the PFRC when the plasma gets dense and energetic due to the RMF current drive. With Argon, we have achieved bright discharges at about 50 kW, or 1/4 of the total RF power available. Argon gas produces a higher density plasma in the PFRC because it has a lower ionization energy.
We are now working to find the parameters which will produce these bright, energetic discharges in our target operating gas of hydrogen. The hydrogen gas must dissociate as well as get ionized. We can experiment with other gases too, like helium and neon, to learn more about the system.
We recently learned of this great article written on FRCs and the PFRC in particular: “Small-scale fusion tackles energy, space applications”. It was posted on the website for the Proceedings of the National Academy of Sciences (PNAS) in 2020.
The article is well written and provides information on the PFRC innovation, fusion fuel choice, and development plan. It does a great job explaining the heating methods of the main FRC approaches in industry today: the RF-heated PFRC, the beam-heated TAE approach, and the merged-and-compressed Helion Energy approach. Dr. Sam Cohen, Stephen Dean, Michl Binderbauer (TAE), and Michael Paluszek are quoted.
Cohen, for his part, has been pursuing his Princeton Field Reversed Configuration (PFRC) design since 2002, with a strong emphasis on simplicity and compactness… The idea, says Cohen, is to drive oscillating currents through these coils in a way that sets up a rotating magnetic field inside the tube: a loop of flux that whirls through the plasma like a flipped coin and drags the plasma particles around and around the waist of the cylinder. In the process, he says, “the fields create, stabilize, and heat the FRC”—all in a single deft maneuver.
Small-scale fusion tackles energy, space applications, M. Mitchell Waldrop, January 28, 2020, 117 (4) 1824-1828
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!
