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 on nuclear power for space.

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!

IAC 2022 is underway! Annie Price, a former PSS intern, and Mike Paluszek are attending. The Congress has hundreds of technical talks and poster presentations. In addition, there is a huge technology showcase area. Both companies and government organizations have booths. Here are some photos from the show floor.

I also met engineers from Boeing, DLR, Teledyne, Lockheed Martin, MDA, Sierra, Rolls-Royce, Saudi Arabia, South Korea, Slovakia, Sweden, and many other companies and countries. There were at least three robot arms on display, including one by Kinetik Space.

This one has selectable end-effectors.

I met an engineer who worked on the Apollo program. His area was radiation hardness. He said back then, no one knew much about the problem.

There were excellent talks on Tuesday on formation flying and rendezvous. Annie is presenting our talk on a fusion-powered Titan aircraft on Thursday, in SESSION 10-C3.5, Joint Session on Advanced and Nuclear Power and Propulsion Systems,” In W08 at 13:45.

I attended the 2022 HiSST meeting, the 2ND INTERNATIONAL CONFERENCE ON HIGH-SPEED VEHICLE SCIENCE AND TECHNOLOGY, in Bruges, Belgium. Bruges is a lovely city and I highly recommend a visit. It is walkable and has many excellent restaurants, museums, breweries, and chocolate shops.

Our session was on Rotating Detonation Engines. Ralf Deiterding (University of Scotland) and Sarah Mecklem (University of Queensland) were the chairs. There were three talks, mine on “Rotational Detonation Engine for Hypersonic Flight”, a talk by Prof. Deiterding of the University Of Southampton on, “Design and testing of a low mass flow RDE running on ethylene-oxygen,” and one by Yue Huang on, “Study on Fuel Injection and Geometry of Plane-radial Rotating Detonation Combustor.”

Prof. Deiterding’s talk showed his team’s impressive experimental work. He had movies of their experiments in operation.

Yue Huang discussed fuel injection into an RDE showing the pros and cons of three different approaches. His team’s work looked at mixing in the combustor instead of pre-mixing.

My talk gave an overview of RDE technology. I discussed research at Princeton University on the stabilization of the RDE flame front. Good results have been obtained with ozone injection and plasma injection. I gave the results of our analysis showing performance advantages over a conventional turboramjet. We use a turbocharger to pressure the RDE at low Mach number.

I discussed applications including hypersonic boost guide passenger airliners and two stage to orbit launch vehicles. An RDE might allow first-stage Mach numbers in excess of Mach 7.

On Thursday the Conference dinner was held. It was a three course dinner at a restaurant on the North Sea. The rain cleared for the event.

The venue was beautiful. A band played throughout the reception and dinner.

It was announced that the 2024 HiSST meeting will be held in Pusan, South Korea.

This paper talks about a collisional-radiative (CR) model that extracts the electron temperature, T_{e}, of hydrogen plasmas from Balmer-line-ratio measurements and is examined for the plasma electron density, n_{e}, and T_{e} ranges of 10^{10}–10^{15} 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.

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.

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).

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.

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.

My name is Pavit Hooda, and I was an intern at the Princeton Plasma Physics Laboratory during the summer of 2022. In my time there, I took on the start-up problem of the Direct Fusion Drive (DFD) and developed a compelling solution. A system to power on or re-start the DFD in space is essential for its use, especially in long-duration missions. Therefore, my work has helped us get closer to a space-faring future where the DFD is the means of propulsion for humanity’s missions to the Moon, Mars, and beyond.

The problem at hand was to create an auxiliary power unit that can generate a sufficient amount of power with the use of the Deuterium fuel and liquid Oxygen oxidizer that were on board. The Deuterium is one of the fuels of the fusion within the DFD, and the Oxygen can be recycled from the cabin of the crew. After the power is generated, the objective is to eventually split the deuterium-oxide product back into its constituents for use in their respective areas of the spacecraft. This electrolysis can be done after the fusion core is started and there is a sufficient amount of surplus energy from the DFDs.

The design of the heat engine first begins with the electric pumps that feed the fuel and the oxidizer into the combustion chamber. A turbopump-based feeding system was decided against due to the low mass flow rates that are required to power the DFD. Additionally, the accurate throttle control granted by the use of electric pumps, and the ability to use the batteries on board to spin the pumps, make electric pumps the more viable option. Before the deuterium fuel is fed into the coaxial swirl injector, it is ran across cooling channels surrounding the combustion chamber. This regenerative cooling is performed to heat the deuterium to increase its reactivity and lengthen the lifespan of the combustion chamber by minimizing the effect of the high temperature it is operating at. Additionally, the cooling system provides a healthy temperature gradient for the thermoelectric generation layer that is also wrapped around the combustion chamber. The oxidizer is directly injected into the combustion from its propellant tank.

After passing through the injector and combusting in a successful ignition, the deuterium-oxide steam exhaust is directed towards a turbine system. The turbine system and the combustion chamber are attached with a flange. The turbine system consists of two sets of blades that are separated by a disk that acts like a stator in a steam turbine. The exhaust is first directed towards a doughnut-shaped casing that allows for the heavy water steam to hit the blades in a direction that is parallel to the blade disk’s central normal axis. The two turbine disks are attached to a common axis that extends outside the turbine system’s casing. The rotation of this axle is then used to generate power with an electric generator. Finally, the steam then exits through a large exhaust manifold tube that directs it to a temporary storage container. This design of a heat engine would result in producing 3 MJ, the sufficient amount of power to start up a PFRC, in about 10 minutes. An illustration of the entire design of this system can be seen below.

In the pursuit to study the feasibility of this engine, various parts were selected. A 600 W electric generator that matches both the power and mass specifications of the heat engine was found and is shown below.

Additionally, the turbine casing in the heat engine matches the geometry and function of a turbocharger that is found as a component in some car engines. The part is displayed below.

A significant amount of extensive work still needs to be put into the creation of this heat engine. However, I truly believe that this work presents itself as a good first step in the right direction towards this engine’s small but significant role in humanity’s journey to the Moon, Mars, and beyond.

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!

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?

Foe 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!