Our latest paper on DFD applications, “A Fusion-Propelled Transportation System to Produce Terrestrial Power Using Helium-3 From Uranus”, is now available from AIAA. This paper was part of the Future Flight Propulsion track and AIAA SciTech 2023. For those with AIAA membership, there is a video recording of the presentation as well! Download the paper here.

Our goal with this paper is to create a framework within which we can study the potential cost of electricity produced on Earth using helium-3 mined from Uranus. The scarcity of terrestrial helium-3, along with the radioactivity of methods to breed it, lead to extraterrestrial sources being considered as a means to enable clean helium-3 fusion for grid-scale electricity on Earth.

This paper builds on the work of Bryan Palaszewski who has published numerous papers on mining the atmospheres of the outer planets. Palaszewski’s work assumed fission-based power and propulsion systems, with a much lower (worse) specific power than we anticipate from a PFRC-based Direct Fusion Drive. We consider both transport and mining vehicles that are instead fusion-powered, including a fusion ramjet. This ramjet may be able to be both the mining vehicle and the orbital transfer vehicle to bring the refined helium-3 to the interplanetary transport,

The results allow us to estimate levelized cost of electricity, LCOE, for the electricity produced on Earth as a function of assumed cost of the fusion transports and mining system, cost of the PFRC reactors, amount of helium-3 stored on each transport and numbers of trips per year, etc. You can learn more about LCOE from the NREL website. Uranus is likely the most economical outer planet for mining due to its lower gravity and radiation environment and high concentration of helium in its atmosphere, about 15%. We find that with our set of assumptions, the resulting cost of electricity could potentially be competitive with wind and solar.

Future work will include analysis of the fusion ramjet trajectories between mining and transfer altitudes, and research into sizing a mining payload using membranes and adsorption to separate the helium-3 from the helium, rather than depend on heavy cryogenic techniques.

Annie Price, who was an intern at Princeton Satellite Systems during the summer of 2021, presented our paper, “Nuclear Fusion Powered Titan Aircraft,” at session C4,10-3.5 which was the Joint Session on Advanced and Nuclear Power and Propulsion Systems.

There were many interesting papers. One was on generating electric power in the magnetic nozzle of a pulsed fusion engine. Another was on the reliability of nuclear thermal engines. The lead-off paper was on a centrifugal nuclear thermal engine with liquid fission fuel.

Annie’s paper covered the design of a Titan aircraft that can both do hypersonic entry and operate at subsonic speeds. Her design uses a 1 MWe nuclear fusion power plant based on PFRC and six electric propeller engines.

She discussed the aerodynamic design, why Titan is so interesting and how the available power would enable new scientific studies of Titan. Annie also described how a PFRC rocket engine or power plant operates. She included a slide on our latest results.

The paper was well received. She had a couple of good questions after her talk and engaged in interesting discussions after the session. Great job Annie!

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.

We received a comment on LinkedIn about how fast the “Mars run” could be achieved with a sustained 1 G acceleration. The reader suggested this could be done in 40 hours. What engine parameters would be required to make that happen?

Using a simple constant-acceleration, straight-line analysis, you can indeed compute that the trip should take only a couple of days. Assuming a Mars conjunction, the straight distance is about 0.5 AU. At this speed you can ignore the gravitational effects of the sun and so the distance is a simple integral of the acceleration: d = 1/2 at^{2}. The ship accelerates for half the time then decelerates, and the change in velocity is ΔV = at. Combining the two halves of the trip, at an acceleration of 9.8 m/s^{2}, the trip takes about 2.1 days.

% straight line: distance s = 0.5*at^2
acc = 9.8; % accel, m/s^2
aU = Constant('au'); % km
dF = 0.5*aU*1000; % distance, m
t = sqrt(4*dF/acc); % time for dF, s
dV = t*acc/1000; % km/s
fprintf('\nAccel: %g m/s^2\n',acc)
fprintf('Time: %g days\n',t/86400)
fprintf('Delta-V: %g km/s\n',dV)
Accel: 9.8 m/s^2
Time: 2.02232 days
Delta-V: 1712.34 km/s

Now, your ship mass includes your payload, your engine, your fuel tanks and your fuel. Assume we want to move a payload of 50,000 kg, somewhat larger than the NASA Deep Space Habitat. The engine mass is computed using a parameter called the specific power, in units of W/kg. The fuel tank mass is scaled from the fuel mass, typically adding another 10%. When we run the numbers, we find that the engine needs to have a specific power of about 1×10^{8} W/kg, and an exhaust velocity of about 5000 km/s results in the maximum payload fraction. We can compute the fuel mass and trajectory using our MassFuelElectricConstantUE and StraightLineConstantAccel toolbox functions:

The power needed is… over 2.8 terawatts! That’s about equal to the total power output of the entire Earth, which had an installed power capacity of 2.8 terawatts in 2020. And the engine would need to weigh less than 30 tons, about the size of a loaded tractor-trailer truck. For comparison, we estimate a Direct Fusion Drive would produce about 1 MW per ton, which is a specific power of 1×10^{3} W/kg. So, this is why you see us trying to design an engine that can do the Mars transfer in 90 days and not 3 days!

Now, there is another consideration here. Namely, constant acceleration at 1 G is not the optimal solution by any means. The optimal solution for a fast, light transfer is actually a linear acceleration profile. This knowledge goes way back: 1961! Here’s a reference:

Leitmann, George. "Minimum Transfer Time for a Power-Limited Rocket." Journal of Applied Mechanics 28, no. 2 (June 1, 1961): 171-78. https://doi.org/10.1115/1.3641648.

This would mean that the engine changes its exhaust velocity during trip, passing through infinity at the switch point. We compute this in our “straight-line, power-limited” or SLPL function series. While this can’t be done physically, even an approximation of this with a variable impulse thruster will one day be more efficient than constant acceleration or thrust. How much better? The power needed is nearly 1/2 the constant acceleration solution, 1.5 TW, and the specific power needed is reduced by half, to 5.6×10^{7} W/kg. However, those are still insane numbers!

mD = 80000; % dry mass: engine, tanks, payload
m0 = 1.5*mD; % wet mass: with fuel
tF = 3*86400;
vF = 0;
[Pj,A,tau] = SLPLFindPower( aU, tF, vF, mD, m0 );
mTank = 0.05*(m0-mD); % tanks, scale with fuel
mLeft = mD-mTank;
mEngine = mLeft - mPayload;
disp('Straight-line Power-limited (linear accel)')
fprintf('Engine power is %g GW\n',Pj*1e-9);
fprintf('Engine mass is %g kg\n',mEngine);
fprintf('Payload mass is %g kg\n',mPayload);
fprintf('sigma is %g W/kg\n',Pj/mEngine);
SLPLTrajectory( A, tau, Pj, m0, tF )
Straight-line Power-limited (linear accel)
Engine power is 1573.26 GW
Engine mass is 28000 kg
Payload fraction is 0.416667
sigma is 5.6188e+07 W/kg

The trajectory and engine output are plotted below. The linear acceleration results in a curved velocity plot, while in the constant acceleration case, we saw a linear velocity plot. You can see the spike in exhaust velocity at the switch point, which occurs exactly at the halfway point.

Distance, velocity, and linear accelerationFuel mass, exhaust velocity, and thrust

After all, who needs 1G gravity when the trip only takes 2 days?

For even more fun though, we computed a planar trajectory to Mars using the parameters we found – just to confirm the straight-line analysis is in fact a good approximation. This figure shows the paths the optimization takes:

Earth to Mars Trajectory, 2.1 days, 0.5 AU traversed

It is in fact approximately a straight line!

In reality though, these power system numbers are not even remotely plausible with any technology we are aware of today. That’s why we are designing engines to reduce the Mars trip time to 90 days from 8 or 9 months – still a big improvement!

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!

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)

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.

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)

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!

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.

People from all over the country called and emailed in their questions about fusion and fusion-propelled spaceflight, and we had a great discussion! David has been running this educational program for 20 years and there are almost 4000 archived episodes covering a wide range of space topics. Author David Brin, whom I met during my NASA NIAC fellowship, is going to be on next week!

So have listen and add to the conversation on The Space Show website!