Last week, I attended the American Physical Society Division of Plasma Physics (APS DPP) 2022 Meeting. As the name entails, it was a meeting full of plasma physics with applications ranging from astrophysics to nuclear fusion energy. There were many great talks and posters on plasma physics research by companies, national labs, and universities, and one could sense an overall feeling of excitement around fusion shared by many attendees.

I had a pleasant time in Spokane, WA. Pictures from outside of the conference center (with many conference attendees standing nearby), including the nice view from the conference center, are shown below.

I presented a talk on the Princeton Field-Reversed Configuration (PFRC) fusion reactor concept, and how we can leverage public-private partnerships for its development. The talk discussed technical details of the PFRC, including the past modeling and experiments, current investigation, and future research & development plans. The talk also described the markets and commercialization opportunities for this reactor concept, including disaster relief and asteroid deflection. Here I am at the podium speaking.

I also presented a poster on our recent investigations of x-ray diagnostics on the PFRC-2 experiment for electron temperature and density measurements, which was mounted on a poster board in the conference center. Many people came by to ask about my poster as well as about general PFRC questions, which kept me talking for the majority of the 3-hour poster block session! It was great to discuss ideas and results with many scientists and students at the conference.

Dr. Sangeeta Vinoth also had a poster at this conference on collisional-radiative model developments to extract electron temperature measurements from spectroscopy, which she presented virtually. APS DPP 2022 was an exciting conference to attend, and I’m looking forward to seeing updates from presenters at this conference. That also includes us, as we have more research and investigation to do — stay tuned!

This summer, I worked on creating a plasma circuit model as part of PSS’s work under the ARPA-E GAMOW grant. As part of this project, I wrote MATLAB functions to reproduce the results of two papers on impedance of radio frequency (RF)-driven circuits for plasma heating. Both functions take in some plasma and geometric parameters and return impedance values as well as plots of impedance as a function of other parameters.

The first function is based on reference [1], which uses the transformer model to describe the coupling between the plasma and the rest of the circuit. This means that the plasma can be represented as a resistor-inductor circuit that is inductively coupled with the main circuit. In addition to calculating the equivalent circuit impedance for values in passed-in density and frequency ranges, I reproduced the figures showing resistance/inductance and reflection coefficient as a function of the electron density of the plasma. Plotting over many orders of magnitude of density, you can see drastic changes in the plasma resistance and inductance.

Since ion cyclotron resonance heating (ICRH) is a leading technique for plasma heating in fusion reactors, we also wanted a function that dealt specifically with ICRH in its plasma model. I then read through some literature on ICRH in order to find a suitable reference to model in MATLAB. I found this in reference [2], which became the basis for my second function. This model uses transmission line theory to calculate the antenna impedance with the effects of the plasma incorporated. This paper also compared a previously-formulated 2D model with its own 3D model, and the implications of this extension to three dimensions can be seen in the way impedance changes as a function of the wavenumber.

The impedance values produced from both of these models can be used to help account for the effect of plasma on antennas used in RF heating, especially ICRH. While assumptions are made in these models to allow for analytical calculations to be made (notably assuming uniform current density and neglecting volume propagation effects) and adjustments are needed to resolve minor discrepancies between the MATLAB models and the figures in the reference papers, they should be a reasonable first approximation of the physics that is occurring and the impedance generated by the plasma.

This summer has given me a lot more knowledge about plasma physics, in particular about resonance heating. I have also gained a lot of experience in conducting literature reviews, reproducing published results, and working in MATLAB.

[1] Nishida, K., et al., “Equivalent circuit of radio frequency-plasma with the transformer model.” Rev. Sci. Instrum. 85, 02B117 (2014); https://doi.org/10.1063/1.4832060.
[2] Bhatnagar, V.P., et al., “A 3-D analysis of the coupling characteristics of ion cyclotron resonance heating antennae.” Nucl. Fusion 22, 280 (1982); https://doi.org/10.1088/0029-5515/22/2/011.

This research builds on the investigation of measuring electron density and temperature by collecting plasma-emitted x rays using a diagnostic called the Silicon Drift Detector (SDD). The x rays emitted via Bremsstrahlung (German word for “breaking radiation”), can be mapped to a distribution that gives electron temperature and density. We observed changes to the x-ray spectra when changing the size of the aperture during experiments with the Rotating Magnetic Field (RMF), which was found to be connected to a phenomenon called “pulse pileup”. Essentially, pulse pileup means that too many x rays coming in at once can combine in energy and so skew the distribution that is measured — this would be misleading for temperature measurements, since they are connected to the slope of the distribution! To solve this issue, we decided to investigate the use of a Mylar filter, see below, because of its favorable filtering properties relevant to our experiment:

We performed calibration with an x-ray target tube and tested the filter with various plasma conditions for the PFRC-2. When running in a high-ultraviolet-flux mode of the PFRC-2 (with RMF) we found that the Mylar filter substantially reduced the low energy signal, which supports our hypothesis that the pulse pileup was causing x rays to be measured at higher energies. See the figure below for a striking comparison between no-Mylar and Mylar cases. The Mylar filter helps us eliminate pulse pileup effects and uncover the true x-ray distribution reaching the SDD for accurately measuring electron number density and temperature in the PFRC.

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.

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

Last week, PSS Mike Paluszek visited ITER, the international fusion research experiment under construction in France. In light of Mike’s recent visit to ITER, we wanted to showcase an application of our tokamak Fusion Reactor Design function to the design of ITER. This function is part of the Fusion Energy Toolbox for MATLAB, a toolbox that includes a variety of physics and engineering tools for designing fusion reactors and studying plasma physics. We will also compute design parameters for ITER’s successor, the DEMOnstration power plant (DEMO), a fusion reactor currently in the design phase which is planned to achieve net electricity output.

We first apply the Fusion Reactor Design function to ITER. Note that ITER is expected to produce 500 Megawatts (500 MW) of fusion power, but this will not be converted into electric power, the power that goes into the electrical grid. DEMO, on the other hand, is planned to produce 500 MW of electric power from 2000 MW of fusion power. The Fusion Reactor Design function asks for the net electric power output of the reactor, P_E, as an input, so we generate a value for P_E for ITER by using the same ratio of electric-to-fusion power as in DEMO, giving us a P_E of 125 MW for ITER. The inputs used for the ITER design are shown below (see references [1,2]), where we use a data structure “d_ITER”:

d_ITER.a = 2; % plasma minor radius (m)
d_ITER.B_max = 13; % maximum magnetic field at the coils (T)
d_ITER.P_E = 125; % electric power output of the reactor (MW)
d_ITER.P_W = 0.57; % neutron wall loading (MW/m^2)
d_ITER.H = 1; % H-mode enhancement factor
d_ITER.consts.eta_T = 0.25; % thermal conversion efficiency
d_ITER.consts.T_bar = 8; % average ion temperature (keV)
d_ITER.consts.k = 1.7; % plasma elongation
d_ITER.consts.f_RP = 0.25; % recirculating power fraction

The first five inputs were described in our original post on the Fusion Reactor Design function. The function can be called to perform a parameter sweep over any of these inputs. We also specify values for some constants: the thermal conversion efficiency ‘eta_T’, the average ion temperature ‘T_bar’, the plasma elongation ‘k’, which is a measure of how elliptical the plasma cross-section is, and the recirculating power fraction ‘f_RP’. We can perform a parameter sweep over the minor radius (from a = 1.8 meters to a = 2.2 meters, with 100 points in between) and display a table of results simply with two lines of code:

d_ITER = FusionReactorDesign(d_ITER,'a',1.8,2.2,100); % run function
d_ITER.parameters % show table of resulting parameters

Looking at the results table from d_ITER.parameters, we see overall agreement with parameters for ITER [1,2]. The plasma major radius (essentially the tokamak radius) R_0 output is about 5 m, which is in the ballpark of the 6.2 m radius of ITER design, and the magnetic field at R_0 (on plasma axis) output is 4.8 Tesla, close to the ITER design value of 5.3 Tesla. The plasma current output is 17.5 MegaAmps, which is also close to ITER’s design of 15 MegaAmps.

The Fusion Reactor Design function also outputs plots that show whether or not the reactor satisfies key operational constraints for tokamaks, see the figure below. The first three curves check various constraints to ensure the plasma is stable, which we see are met as they are located in the unshaded region (though the green curve is marginally close to the constraint boundary). The blue curve’s position deep into the shaded region indicates that the reactor is far from producing enough electric current to sustain itself. The designers of ITER anticipated this, which is why ITER will additionally use a pulsed inductive current and test a combination of other techniques to drive the plasma current.

We now consider DEMO, which is in the design phase with the goal of net electrical power output. Similarly to running the ITER case, we set up a data structure (now called ‘d_DEMO’) with known DEMO input parameters [3] and perform a parameter sweep over the minor radius ranging from a = 2.7 meters to a = 3.1 meters:

d_DEMO.a = 2.9; % plasma minor radius (m)
d_DEMO.B_max = 13; % maximum magnetic field at the coils (T)
d_DEMO.P_E = 500; % electric power output of the reactor (MW)
d_DEMO.P_W = 1.04; % neutron wall loading (MW/m^2)
d_DEMO.H = 0.98; % H-mode enhancement factor
d_DEMO.consts.eta_T = 0.25; % thermal conversion efficiency
d_DEMO.consts.T_bar = 12.5; % average ion temperature (keV)
d_DEMO.consts.k = 1.65; % plasma elongation
d_DEMO.consts.f_RP = 0.25; % recirculating power fraction
d_DEMO = FusionReactorDesign(d_DEMO,'a',2.7,3.1,100); % run function
d_DEMO.parameters % show table of resulting parameters

The outputs for the DEMO case also show overall agreement with DEMO parameters [3]. The plasma major radius R_0 output is 7.8 m, which is not far from the 9 m design radius for DEMO. The resulting on-axis magnetic field output is 6.2 T, close to the 5.9 T of the DEMO design. The plasma current output is now 21 MegaAmps, which is less than 20% away from the design value of 18 MegaAmps. It is important to note that in each of these parameters, we see an increase going from ITER to DEMO, which is consistent both in our model’s output and the actual design parameters in the papers [1-3].

The operational constraints plot for DEMO is shown in the figure below. DEMO is a larger reactor than ITER, and given the favorable scaling of tokamak operation with size, we expect improved results for operational constraints in DEMO. The three curves which check plasma stability are all satisfied. Unlike in the case of ITER which had the green curve close to the shaded region, the green curve in the case of DEMO stays safely in the unshaded region. The blue curve is still in the unshaded region, but much closer to the boundary of the unshaded region than ITER (now ~1.8, much closer to 1 than in the case of ITER which was ~4). This shows an improvement for DEMO compared to ITER as it is closer to producing enough self-sustaining plasma current, though it will still need some help from other current-generating techniques which will be tested on ITER.

This function is part of release 2022.1 of the Fusion Energy Toolbox. Contact us at info@psatellite.com or call us at +01 609 275-9606 for more information.

In this paper, a femtosecond two-photon-absorption laser-induced-fluorescence (fs-TALIF) diagnostic was designed, installed, and operated on the Princeton-Field-Reversed Configuration-2 device to provide non-invasive measurements of the time and spatially resolved neutral-atom densities in its plasmas. We demonstrated that fs-TALIF can provide spatially, to ±2 mm, and temporally resolved, to 10 µs, measurement of the density of certain previously inaccessible atoms, e.g., atomic hydrogen (H^{o}).

Calibration of the H^{o} density was accomplished by comparison with Krypton (Kr) TALIF. Measurements on plasmas formed of either molecular hydrogen (H_{2}) or Kr fill gases allowed examination of nominally long and short ionization mean-free-path regimes. With multi-kW plasma heating and H_{2} fill gas, a spatially uniform H^{o} density of order 10^{17} m^{−3} was measured with better than ±2 mm and 10 µs resolution. Under similar plasma conditions but with Kr fill gas, a 3-fold decrease in the in-plasma Kr density was observed.

H^{o} density is essential to several plasma diagnostics including time-of-flight and ion energy analyzers, and high-resolution spectroscopy, as by CPT (coherent population trapping) and DFSS (Doppler-free saturation spectroscopy). It was also used in Collisional Radiative Modelling for predicting the Electron temperature diagnostic in PFRC-2.

On September 22 Marilyn, Eric, and I visited ITER, the International Tokamak Experimental Reactor in Saint-Paul-lez-Durance, France, about 45 minutes from Aix-en-Provence. We took the TGV from Paris to Aix-en-Provence.

Our tour started with a talk by Akko Maas who gave a great presentation on fusion. He talked about building ITER. The complexity of the project and the large international team both present challenges. He also discussed the advantages of fusion in comparison to wind and solar. He noted that while a fusion reactor would have some waste, both wind and solar, when decommissioned, have waste. He talked about the next phase after ITER called DEMO. ITER is designed to produce 500 MW of fusion power from an input of 50 MW heating power. Akko had a slide listing some of the commercial fusion efforts.

Katya Rauhansalo was our tour guide. She had a couple of assistants. They were all really helpful and very knowledgeable. We discussed many fine points of Tokamak design and fusion in general. Marilyn, Eric, and I were combined with a larger group, due to Covid absences. We chatted with members of the other group about PFRC.

A Tokamak is shown below. The green coils are the center stack coils used to induce a current in the plasma. The gray coils are the poloidal coils. The purple coils are the toroidal coils. In ITER, all coils are superconducting. The green donut in the middle of the D coils is the plasma.

The following image shows the Tokamak building.

The first stop was the manufacturing facility for the poloidal coils. The following video shows a crane in operation in the assembly hall.

The top and bottom coils are small enough that they can be shipped complete. The others need to be manufactured. The following figure shows the cryostat for testing the poloidal coils.

This poster gives the details of the testing.

We then moved through the entrance to the Tokamak. We were able to enter the Tokamak building itself. Here is Eric in front of an installed toroidal superconducting coil.

First plasma was scheduled for 2025 but may be delayed. This was partly due to Covid and partly due to the inevitable technical glitches in such a complex project.

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!

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.