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 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.

[1] Freidberg, Mangiarotti, and Minervini, “Designing a tokamak fusion reactor–How does plasma physics fit in?”, Physics of Plasmas 22, 070901 (2015); https://doi.org/10.1063/1.4923266
[2] http://www-fusion-magnetique.cea.fr/gb/iter/iter02.htm
[3] https://news.mit.edu/2021/MIT-CFS-major-advance-toward-fusion-energy-0908

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:

https://www.princetonfusionsystems.com/2022/05/20/arpa-e-2022-summit/

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

OPEN 2018 Booth Featuring PFRC

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!

Hohmann Transfer Simulation with the Spacecraft Control Toolbox

Hohmann transfers are a well-known maneuver used to change the semi-major axis of an orbit. The Spacecraft Control Toolbox allows you to compute the required velocity changes, and integrate them into a full simulation.

In this demonstration, we create a 6U CubeSat that has 3 orthogonal reaction wheels and a single hydrazine thruster. The thruster is aligned with the body x-axis and must be aligned with the velocity vector to do the maneuver. An ideal Hohmann maneuver is done with impulsive burns at two points in the orbit. In reality, with a thruster, we have to do a finite burn.

The Hohmann transfer is computed with the following Spacecraft Control Toolbox code:

rI = [-7000;0;0];
vI = [0;-sqrt(mu/Mag(rI));0];
OrbMnvrHohmann(Mag(rI),rF);
[dV,tOF] = OrbMnvrHohmann(Mag(rI),rF);

The first time OrbMnvrHohmann is called, it generates the plot below of the planned Hohmann transfer. The function computes the delta-V and also the time of flight, which will be used to determine the start time of the second thruster burn.

We create a short script with numerical integration to implement the maneuver using a thruster. The burn durations are computed based on the thrust and the mass of the spacecraft. In this case, they are about three minutes long. The maneuver is quite small, so the mass change is not important. The attitude control system uses the PID3Axis function which is a general-purpose attitude control algorithm. The simulation is a for loop, shown below. The ECI vector for the burn is passed to the attitude control system, which updates every step of the simulation.

% Simulation loop
for k = 1:n

  % Update the controller
  dC.eci_vector = uBurn(:,kMnvr);
  [tRWA, dC]    = PID3Axis( x(7:10), dC );

  % Start the first burn
  inMnvr = false;
  if( t(k) > tStart(1) && t(k) < tEnd(1) )
    inMnvr = true;
  end

  % Switch orientation
  if( t(k) > tEnd(1) )
    kMnvr = 2;
  end

  % Start the second burn
  if( t(k) > tStart(2) && t(k) < tEnd(2) )
    inMnvr = true;
  end
  
  if( inMnvr )
    dRHS.force = thrustE*QTForm(x(7:10),dC.body_vector)*nToKN; % kN
  else
    dRHS.force = [0;0;0];
  end
  el = RV2El(x(1:3),x(4:6));
  xP(:,k) = [x;tRWA;Mag(dRHS.force)/nToKN;el(1);el(5)];

  % Right hand side
  dRHS.torqueRWA = -tRWA;
  x = RK4(@RHSRWAOrbit,x,dT,0,dRHS);
end

The maneuver logic just waits a quarter orbit then performs the first burn, by applying the thrust along the body vector. It then waits for the time of flight and then starts the next burn. The start and stop times are pre-computed. RK4 is Fourth Order Runge-Kutta, a popular numerical algorithm included with the toolbox.

At the final orbit radius an attitude maneuver is needed to reorient for the final burn.

The spacecraft body rates, in the body frame, during the maneuver are shown below.

The reaction wheel rates are shown below. The simulation does not model any particular wheel. Friction is not included in the simulation, although the right-hand-side function can include friction.

The wheel torques and rocket thrust are shown below. The thruster is a 0.2 lbf hydrazine thruster that is based on the Aerojet-Rocketdyne MR-103. The PID controller does not demand much torque.

The semi-major axis and eccentricity are shown below. The middle portion is during the transfer orbit.

The eccentricity is zero at the start and finish. Note the slope in both eccentricity and semi-major axis due to the finite acceleration. At the end of the simulation, we print the achieved orbital elements:

Final SMA        7099.72 km
  SMA error         0.28 km
Final e          1.3e-05

The result is very close to the ideal solution!

This post shows how you can easily integrate attitude and orbit control. Email us for more information! We’d be happy to share the script. We can also offer a 30 day demo to let you explore the software.

Nuclear Space Propulsion Zoom Talk for the Foundation for the Future

Michael Paluszek of Princeton Satellite Systems, will talk about nuclear propulsion for space at the Foundation for the Future Zoom meeting on Thursday, May 19 at noon EDT.

A nuclear fusion powered spacecraft near Mars.

The talk will discuss space propulsion and how fusion and fission power will revolutionize space exploration.

The Foundation for the Fusion has many other excellent speakers on both Wednesday and Friday of this week. Please join in!

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.

eBook Textbook now available on Barnes & Noble

Our aerospace theory textbook, Spacecraft Attitude and Orbit Control, has been included with purchases of the Spacecraft Control Toolbox for years and available for purchase as a standalone PDF. We have now compiled our book as an eBook and it is available from Barnes and Noble for Nook:

https://www.barnesandnoble.com/w/spacecraft-attitude-and-orbit-control-textbook-4th-edition-michael-paluszek

The companion tutorial software for the book (Chapter 2) is available for download from our website.

IAEA Nuclear Systems for Space Exploration Webinar: Recordings now Available

The recordings of this webinar from February 15-16, 2022, are now available on YouTube. Each segment is two hours long. Ms. Thomas’ presentation is in Part 2 at about 30:30.

Organized by the International Atomic Energy Agency (IAEA), this webinar focuses on nuclear systems for space exploration. It gives an overview and historical perspective on the status of development in this area and showcases the ways in which nuclear systems can be used for space exploration, as well as discuss possible future innovations in the field.

IAEAvideo, YouTube

Part 1 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)
  • Q&A
Part 1, February 15, 2022

Part 2 Agenda:

  • 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) – at time 30:30
  • NASA Investments in Space Nuclear Fission Technology | Mr Anthony Calomino (NASA)
  • Q&A
Part 2, February 16, 2022

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: https://iaea.webex.com/iaea/onstage/g.php?PRID=a626af96640b6b59dbee10fcc4910e15

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:

https://www.iaea.org/newscenter/news/nuclear-technology-set-to-propel-and-power-future-space-missions-iaea-panel-says

A Third Planet Discovered Orbiting Proxima Centauri

Introduction

A third planet, as large as 26% of the mass of Earth, has been discovered orbiting our nearest stellar neighbor, Proxima Centauri .Astronomer João Faria and his collaborators detected Proxima Centauri d using the Echelle Spectrograph for Rocky Exoplanets and Stable Spectroscopic Observations.

It would be exciting to send a spacecraft to enter the Alpha-Centauri system and orbit this planet. At Princeton Satellite System we’ve looked at interstellar flight using the Direct Fusion Drive nuclear fusion propulsion system.

Interstellar Fusion Propulsion

At the 2021 Breakthrough Energy Conference we presented findings for both flyby and orbital missions. Flyby missions are easier, but orbit entry would allow detailed study of the planet. A flyby gets your spacecraft close, but it is moving really fast!

The following charts give an outline of our talk. The first shows the optimal exhaust velocity based on sigma, the ratio of power to mass. Our designs have a sigma from 0.75 to 2 kW/kg. With 2 kW/kg, the optimal exhaust velocity is 4000 km/s. The mission would take about 800 years. Our current designs can’t get exhaust velocities higher than 200 km/s. We’d need another method to produce thrust.

Mission Analysis

The next plot shows a point mission that reaches Alpha Centauri in 500 years. This requires a sigma of about 20. The spacecraft accelerates and decelerates continuously. The mission could be improved by staging, much like on a rocket that launches from the Earth into orbit.

Selected Mission

The next figure shows how the starship would enter the Alpha Centauri system.

Alpha Centauri System Insertion

The final plot shows the orbital maneuvers that lower the orbit and rendezvous with the planet.

Lowering the orbit to rendezvous with the planet.

Even 500 years is a long time! This is over ten times the lifetime of Voyager, but much less than some engineering marvels built on the Earth.

We hope to someday be able to build fusion powered spacecraft that will head into interstellar space!

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.