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);

Installation of the new capacitors in the Princeton Field-Reversed Configuration-2

Further upgrades of the Princeton Field Reversed Configuration-2 (PFRC-2) are underway with the goal of achieving the milestone of ion heating. The PFRC-2 is predicted to have substantial ion heating once the RF antenna frequency is lowered and the magnetic field is increased. To lower the RF frequency, we have installed additional capacitors in the tank circuit of PFRC-2. The picture below shows three capacitors, each with capacitance of 2 nanoFarads (2 nF), installed in a custom-built copper box.

The copper box is also shown in the bottom part of the image below, where it will be connected with a robust cable to the top box, which is called the tuning box. The tuning box is an aluminum box with one fixed capacitor and two tunable capacitors which can be adjusted to change the resonance frequency of the circuit.

Changes have also been made to the inside of the tuning box in order to prevent electrical arcing, which is a common issue when working with high-power and high-voltage circuits. To help prevent arcing, conical structures of brass have been fabricated and installed. The brass structure is shown alone in the first image below and is shown enveloping the cable connection in the second image below. The shape of these structures allows a better spread of the charge in the tuning box so as to lower the chances of electrical breakdown. Taking these preventative design decisions is key to ensuring reliable operation once the upgraded system is running.

PFRC Fusion Article in the Proceedings of the National Academy of Sciences

This is a really excellent article on nuclear fusion, “Small-scale fusion tackles energy, space applications,” by M. Mitchell Waldrop, written January 28, 2020, Vol 117, No. 4 for the Proceedings of the National Academy of Sciences of the United States of America (PNAS). The article quotes team Dr. Cohen and Mr. Paluszek and provides an excellent and technically accurate discussion of FRCs, heating methods, and fusion fuel physics.

PNAS has many interesting articles!

Upgrade underway of Princeton Field Reversed Configuration-2


The Princeton Field Reversed Configuration-2 (PFRC-2) upgrade in field and frequency is underway. We are currently installing new coils around the experiment to increase the magnetic fields and new capacitors to help lower the RF operating frequency – all to reach our target milestones of measuring ion heating! This is an essential next step in our development of Direct Fusion Drive.

The power supplies are stacked in their rack, ready to supply power to the belt coils. The supplies must be programmed to energize for each pulse as they are not cooled and the coils would otherwise overheat. The belt coil holder component on the right was 3D printed at PPPL.

The new 2 nF capacitors, shown above (left image), must be enclosed in a custom copper box that will be part of the tank circuit of PFRC-2. Each component must be carefully designed, including the lengths of the connecting cables, for us to get the right frequency without exceeding voltage limits of the materials.

The above image is of the cable that will connect the tank circuit and the PFRC-2. These cables are very robust, and stiff so that the layout must be carefully planned. We will continue to post updates as we work towards that 2 MHz frequency milestone!

PFRC-2 has been funded by ARPA-E OPEN 2018, NASA NIAC and DOE Fusion Energy Sciences grants.

DOE Awards Princeton Fusion Systems Three INFUSE 2022a Grants

The Department of Energy announced the First Round of the FY 2022 Public-Private Partnership Awards to Advance Fusion Energy. The awards list contains 18 awardees. Princeton Fusion Systems, a doing-business-as name for Princeton Satellite Systems, received three awards:

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!

TriForce model of the PFRC-1 experiment

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 +01 609 275-9606 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 Energy Innovation Summit 2022

We will be at the 2022 ARPA-E Summit in Denver, CO next week – May 23 to 25 – representing our two ARPA-E programs, WIDE BAND GAP SEMICONDUCTOR AMPLIFIERS FOR PLASMA HEATING AND CONTROL and Next-Generation PFRC. The post on our Princeton Fusion Systems website has links to our marketing and technical documents. More information of the Princeton Fusion Systems-GAMOW project can be found here.

We will have booths for each program at the Technology Showcase. Here is our OPEN 2018 booth.

OPEN 2018 Booth Featuring PFRC

In the picture below, we are registering at the registration desk at the ARPA-E Innovation Summit at Denver. More pictures of the event can be seen on the ARPA-E Summit website.

Registration Desk of ARPA-E Innovation Summit, Denver, Co

Our ARPA-E funding has allowed us to increase the magnetic field and RF power in the PFRC-2 experiment in pursuit of hotter plasma, a key precursor to demonstrating the conditions needed for Direct Fusion Drive!

ARPA-E 2022 Fusion Annual Meeting

I attended the ARPA-E 2022 Fusion Annual Meeting at the Westin St. Francis hotel in San Francisco. Here is the poster for our Princeton Field Reversed Configuration ARPA-E OPEN 2018 grant.

Here 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.

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 said FIA had verified 31 companies that were developing fusion power technology.

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.

IAEA Atoms for Space: Nuclear Systems for Space Exploration

This webinar hosted by the IAEA, the International Atomic Energy Agency, is coming up this week, Feb. 15-16, 2022.

The exploration of space requires power at many stages, not only for the initial launch of the space vehicle, but also for various house loads such as instrumentation and controls, communication systems, maintaining the operating environment for the space mission’s essential hardware, etc. Nuclear can provide long-term electrical power in space. Nuclear systems can be configured in several ways for use in space exploration.

Atoms for Space: Nuclear Systems for Space Exploration

PSS VP Stephanie Thomas will give a talk during this webinar, Fusion Propulsion and Power for Advanced Space Missions.

Register here:

A recording of the webinar will be available! The full agenda:

  • Progress towards space nuclear power objectives | Mr Vivek Lall (General Atomics Global Corporation)
  • Developing the VASIMR® Engine Historical Perspective, Present Status and Future Plans | Mr Franklin R. Chang Díaz (Ad Astra Rocket Company)
  • Application of Space Nuclear Power Sources in Moon and Deep Space Exploration Missions in China | Mr Hui Du (Beijing Institute of Spacecraft System Engineering)
  • Promises and Challenges of Nuclear Propulsion for Space Travel | Mr William J Emrich (NASA)
  • Fusion Propulsion and Power for Advanced Space Missions | Ms Stephanie Thomas (Princeton Satellite Systems)
  • NASA Investments in Space Nuclear Fission Technology | Mr Anthony Calomino (NASA)

Here is the article posted on the webinar:

Writing about Fusion

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.