Our IAC paper on a fusion-powered Titan mission is now available in preprint on Acta Astronautica online, with the final version to come soon! Our mission concept utilizes two PFRC reactors: one configured as a Direct Fusion Drive rocket for the journey to Titan, and a second configured as a power source for the electric aircraft that will survey Titan. The paper includes a detailed design of the aircraft and analysis of optimal entry into the atmosphere and landing on the moon’s surface.

# Author Archives: Stephanie Thomas

# Crowdfunding for fusion development closing at the end of April

Our crowdfunding opportunity at is scheduled to close at the end of the month. We’ve raised over $100K so far to support fusion development and specifically, the PFRC-2 experiment at Princeton Plasma Physics Laboratory as we close in on our ion heating milestone. This is the last two weeks to invest in our raise on SpacedVentures!

# Producing Terrestrial Power with Helium-3 from Uranus using PFRC/DFD

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.

# NIF: Net (Scientific) Gain Achieved in Inertial Fusion! What is the impact on PFRC?

The internet was abuzz last week with the news that the National Ignition Facility had achieved that elusive goal: a fusion experiment that achieved net (scientific) energy gain. This facility, which uses 192 lasers to compress a peppercorn-sized pellet of deuterium and tritium, released 3 MJ of energy from 2 MJ of input heat.

We have to use the caveat that this is “scientific” gain because it does not account for the total amount of energy needed to make the laser pulse. As a matter of fact, the lasers require 400 MJ to make those 2 MJ that reach the plasma. If we account for this energy, we can call it the “wall plug” gain or “engineering” gain since it includes all the components needed. This gain for laser-induced fusion is still less than 1%, because the lasers are very inefficient.

Nonetheless, this is great news for all fusion researchers. Since we often get asked: Has anyone achieved net (scientific) gain yet? Now we can say: Yes! It is physically possible to release net energy from a fusing plasma, to get more energy output than direct energy input. This advance has been achieved through various new technology: machine learning to select the best fuel pellets, wringing more energy from the lasers, more exact control over the laser focusing. Modern technology, especially computing for predicting plasma behavior, explains why progress in fusion energy development is now accelerating.

Tokamaks have also come close to net gain, and in fact the JT-60 tokamak achieved conditions that ** could** have produced net gain,

**it had used tritium [1].**

*if*The reason JT-60 did not use tritium in those shots is very relevant to our fusion approach, the PFRC. Tritium is radioactive, rare, expensive to handle, and releases damaging neutrons during fusion. Tritium is also part of the easiest fusion reaction to achieve in terms of plasma temperature, the deuterium-tritium reaction. It makes sense for fusion experiments to use such a reaction, but this reaction presents many difficulties to a future working power reactor.

The PFRC is being designed to burn deuterium with helium-3, rather than with tritium, precisely to make the engineering of a reactor easier. The deuterium-helium-3 reaction releases no neutrons directly. Some deuterium will fuse with other deuterium to produce neutrons and tritium, but the PFRC is small enough easily expel tritium ash. This results in orders of magnitude less neutrons per square meter reaching the walls. Once we have scientific gain, like the NIF has now demonstrated for laser fusion, we have an easier path to engineering gain — that is, net electricity.

So while the laser fusion milestone doesn’t directly impact our work on the PFRC, it is important to the field. We will continue to follow the progress of all our peers as we work to achieve higher plasma temperatures in our own experiments!

[1] T. Fujita, et al. “High performance experiments in JT-60U reversed shear discharges,” Nuclear Fusion **39** 1627 (1999). DOI: 10.1088/0029-5515/39/11Y/302

# Practical MATLAB Deep Learning, Second Edition

Our latest textbook on MATLAB programming is now available from Apress. Practical MATLAB Deep Learning, A Projects-Based Approach, is in its second edition. It is available in both electronic and hard copy from SpringerLink.

New coauthor Eric Ham, a deep learning research specialist, joins Michael Paluszek and Stephanie Thomas. Mr. Ham led the development of a new chapter on generative modeling of music.

The software is available from GitHub:

https://github.com/Apress/practical-matlab-deep-learning-2e

## About the Book

Harness the power of MATLAB for deep-learning challenges. *Practical MATLAB Deep Learning, Second Edition*, remains a one-of a-kind book that provides an introduction to deep learning and using MATLAB’s deep-learning toolboxes. In this book, you’ll see how these toolboxes provide the complete set of functions needed to implement all aspects of deep learning. This edition includes new and expanded projects, and covers generative deep learning and reinforcement learning.

Over the course of the book, you’ll learn to model complex systems and apply deep learning to problems in those areas. Applications include:

**NEW**: An aircraft that lands on Titan, the moon of Saturn, using reinforcement learning**NEW**: Music creation using generative deep learning**NEW**: Earth sensor processing for spacecraft- Aircraft navigation
- MATLAB Bluetooth data acquisition applied to dance physics
- Stock market prediction
- Natural language processing
- Plasma control

You will:

- Explore deep learning using MATLAB and compare it to algorithms
- Write a deep learning function in MATLAB and train it with examples
- Use MATLAB toolboxes related to deep learning
- Implement tokamak disruption prediction

The book primarily features the Deep Learning Toolbox and the Reinforcement Learning toolboxes. Some examples in the book feature other MathWorks toolboxes, include the Instrument Control toolbox, Optimization toolbox, Statistics and Machine Learning, and Image Processing toolbox.

## Our other books

This new second edition joins our other books available from Apress:

- MATLAB Machine Learning Recipes: A Problem-Solution Approach (2019)
- MATLAB Recipes: A Problem-Solution Approach (2020)

# Doing the Mars run with fusion propulsion at 1 G

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:

```
d = StraightLineDataStructure;
d.dF = 0.5*aU; % 0.5 AU
d.tF = 2*86400; % 2.1 days
d.uE = 5000; % km/s
d.eta = 1; % jet power sigma
d.sigma = 1e8; % W/kg
d.mP = 50000; % kg
dOut = MassFuelElectricConstantUE( d )
StraightLineConstantAccel(dOut)
fprintf('Acceleration: %g m/s^2\n',dOut.a*1e3)
fprintf('Exhaust velocity: %g km/s\n',d.uE)
fprintf('Initial power: %g GW\n',dOut.p(1)*1e-9)
fprintf('Engine mass: %g kg\n',dOut.mE)
fprintf('Payload fraction: %g\n',dOut.mP/dOut.m0)
Acceleration: 10.02 m/s^2
Exhaust velocity: 5000 km/s
Specific Power: 1e+08 W/kg
Initial power: 2832.61 GW
Engine mass: 28326.1 kg
Payload fraction: 0.442172
```

This produces the following plots:

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.

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:

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!

# Our Crowdfunding Campaign for Fusion Propulsion is Testing the Waters!

Our prelaunch campaign is now live on the Spaced Ventures crowdfunding portal! We will be raising money for our new DOE INFUSE awards, to support PFRC-2 experimental operations with new diagnostics, and to design a superconducting PFRC-3!

Potential investors can go to the site, create an account and indicate interest in our raise. This is called “testing the waters!” Those who sign up now will be the first to know when our raise goes live.

Thank you to the Out of This World Design graphics team and the Spaced Ventures team for their support in putting together the pitch! The beautiful new spacecraft render is now on our homepage. The team also made really cool line drawings that show how DFD works!

#fusionenergy #rocketscience

# 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.

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.

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!

# 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:

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 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