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.

Nuclear Thermal Propulsion to Mars

For orbital transfers to Mars, a Hohmann transfer is often proposed since it minimizes the fuel consumed. Here is what that looks like.

This was generated by the Spacecraft Control Toolbox function DVHoh.m. 255.2 days is a long time for a crew to be exposed to cosmic radiation. NASA has proposed using a nuclear thermal engine to speed things up. The best combustion engines, like the RL10B-2, use hydrogen and oxygen and have a specific impulse of 465 seconds. This is obtained by running them hydrogen-rich. Nuclear thermal, which is only heating hydrogen, can reach 900 seconds. The higher your specific impulse, the less fuel you use for a given velocity change.

A mission to Mars consists of an Earth escape segment, a heliocentric segment, and Mars entry. You can do them all with the same rocket or use separate stages or methods. For example, you could depart from low-Earth orbit (LEO), do the transfer, and enter low-Mars orbit (LMO) with one stage. As an alternative, the launch vehicle could take the Mars transfer vehicle into a heliocentric orbit. Instead of using the transfer stage to do a powered entry into Mars orbit, you could use aerobraking. Aerobraking could be used, in theory, for both Mars entry and to replace the burn into Mars heliocentric orbit (that is, to match the heliocentric velocity of Mars).

We wrote a MATLAB script in the Spacecraft Control Toolbox to explore some of these concepts. Here are the results:

Specific impulse nuclear thermal 900.00
Specific impulse H2/O2 465.00
Tank Fraction 0.10

Time Hohmann 255.23 days
Time Fast Transfer 150.23 days

Mass fraction Nuclear Thermal Hohmann 0.30
Mass fraction Nuclear Thermal Fast 0.12
Mass fraction H2/O2 Hohmann 0.05
Mass fraction H2/O2 Lambert Only 0.03

Total Delta-V Hohmann 9.03 km/s
Delta-V Hohmann 4.41 km/s

Total Delta-V Fast Transfer 14.35 km/s
Delta-V Fast Transfer Lambert 9.73 km/s
   Departure 4.43 km/s
   Arrival 5.30 km/s
Delta-V Earth Escape 3.19 km/s
Delta-V Mars Entry 1.43 km/s

The Tank Fraction is the fraction of the spacecraft’s dry mass that is proportional to the fuel mass. This is composed mostly of fuel tanks. The mass fraction is how much mass is left when the spacecraft reaches Mars, not including the fuel tanks. The total Delta-V assumes one stage is used to go from LEO to LMO. Lambert’s law is used for the fast transfer. We break up the Lambert maneuver into departure and arrival velocity changes. In principle, you could aerobrake 5.3 km/s + 1.43 km/s.

The fast transfer is shown below. Contrast it with the Hohmann transfer.

Lambert fast transfer.

This was generated using the Spacecraft Control Toolbox function, PlanetTransferLambert.m.

The HiSST and IAC Conferences

I’ll be attending two conferences in Europe this September. The first is HiSST, the 2nd International Conference on High-Speed Science and Technology, 11-15 September in Bruges, Belgium. Our paper is “Rotational Detonation Engine for Hypersonic Flight.” My co-authors are
Dr. Christopher Galea, Mr. Miles Simpkins, Dr. Yiguang Ju, and Dr. Mikhail Shneider. The last three authors are from Princeton University. The conference is organized by CEAS, the Council of European Aerospace Societies. We are in session 1a on September 12.

The next conference is the International Astronautical Congress (IAC) in Paris, France 18-22 September. We are presenting the paper, “Nuclear Fusion Powered Titan Aircraft,” with co-authors Annie Price, Zoe Koniaris, Dr. Christopher Galea, Stephanie Thomas, Dr. Samuel Cohen, and Rachel Stutz. Annie will give the presentation. Dr. Samuel Cohen is the inventor of the reactor discussed in the paper and works at the Princeton Plasma Physics Laboratory.

My first overseas conference was IAC in Paris in 1982. I was working at Draper Laboratory at the time.

IAC is also famous from the movie, “2001: A Space Odyssey.” While on Space Station V, Heywood Floyd is asked by Elena, “Well, I hope that you and your wife can come to the I.A.C. conference in June.” To which he replies, “We’re trying to get there. I hope we can.”

After the conference, I’m heading to Aix-en-Provence to visit ITER, where a new experimental Tokamak is under construction. A Tokamak is a toroidal fusion reactor.

Please get in touch with me if you will be at any of the conferences or at ITER!

Plasma oscillations seen in seed and RMF plasma using Phantom Camera

The plasma rotation of the PFRC is being analyzed by the Phantom Camera in the Princeton Plasma Physics laboratory.

Video recording of RMF plasma

The above media was taken when we were running with the Rotating Magnetic Field (RMF) Heating System. The video from 10 to 23 seconds shows the plasma rotations are more pronounced and then stabilized later on. The stabilization of plasma is due to the gas puff introduced.

While the PFRC is under upgrade to lower the RF frequency, we have been running the seed plasma, which is PFRC plasma operation without RMF. We also observe rotation in the PFRC seed plasma.

Video recording of seed plasma

This video is taken using Phantom Camera with 1000 frames per second.

Seed plasma seen using Phantom Camera at 20k frames per second.

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

Ford Mach-E

Princeton Satellite Systems has been marketing SunStation electric vehicle charging stations for some time. We are also EV enthusiasts. One employee owns a Tesla Model 3. I now own a Ford Mach-E. It replaces a Nissan Leaf that was purchased in 2012.

Before we purchased the Mach-E we looked at the Hyundai Ioniq 5, the Volkswagen ID 4 and the Kia EV 6. They are all nice cars. It was a close decision between the Mach-E and the Ioniq 5. The good thing is that there are many EVs from which to choose. Even within models, there are many options so that you can pick the car that meets your needs. EV-specific requirements are range, charging network, and charging speed. Otherwise shopping for an EV isn’t much different than shopping for any other car. EVs are available in almost every form factor, including pickup trucks like the Ford F-150 Lightning.

The Mach-E is a 2021 model rear-wheel drive Premium Model with an extended range battery.

This gives a range of 335 miles, 10% more than the EPA value.

Fully charged!

The Level 2 charger is in the background. This is more than sufficient to reach all of the places we visit without charging along the route. The FordPass app will find a route for your trip and tell you when and where to charge. For our planned trips, it is showing that no en-route charging is needed, as long as we start near full charge. Tesla has an extensive Supercharger network that makes intercity driving really easy. All other EVs rely on networks such as ChargePoint and EVGo. There are many apps, besides FordPass, that will plan your trip including required charging stops.

We have a Level 2 charger at home that we bought for the Leaf. We also own a Prius Prime Plugin. The Prime is a plugin hybrid with about 30 miles range using the battery. The charging pattern during the week, when the Mach-E is used for commuting and shopping, is much like a gas car. We typically only charge the Mach-E once a week using the Level 2 charger at home. It takes about 10 hours to fully charge the battery. The Prius charges in 4 hours using a Level 1 charger. That is done daily.

If you owned a Mach-E and didn’t have a charger at home, it would mean you would only have to charge at a DC fast charger once a week if your driving patterns were like mine. If only Level 2 chargers were available, you’d need to find a Level 2 charger where you could park for 10 hours. In my town that would be hard because there only 6 Level-2 chargers!

Most recently we drove from Princeton to the Berkshires, then to Boston and then back to Princeton. The trips were made without any charging on the way. We used Level 2 chargers at our destinations. The Williams Inn, in Williamstown, had ChargePoint chargers, as did the Cambridge Marriott in Kendall Square in Cambridge, MA.

A great resource for those interested in EVs can be found at

Electric Vehicles 101: Everything You Need to Know

Our cars are charged mostly by our solar power system. This is supplemented by PSE&G’s network which gets a large portion of its power from a nuclear fission plant. We are working on compact nuclear fusion power plants. Perhaps, in the not too distant future one of our PFRC reactors will be the source of power for EVs.

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 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.

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.