At MIT, we are given the month of January off from classes to pursue our own interests, whether they be career-oriented or hobby-based. During these five weeks, I have worked at PSS as a power electronics intern. My time at PSS has given me the opportunity to explore so many of the industry based applications of electronics and electrical engineering amongst some of the most innovative minds in the aerospace and energy industries.
Within the GAMOW (Galvanizing Advances in Market-Aligned Fusion for an Overabundance of Watts) project, my work centered around helping redesign, assemble, and test a power load switch, the resulting prototype of which is shown above. Within this project, I received a wide array of experience ranging from 3D-modeling PCB boards with Eagle software, to physical board assembly, to designing testing procedures for the completed board. Initially, I worked on redesigning the load switch PCB to reduce loop currents and noise. My next steps were to source and order all needed components for in-house assembly. During the assembly process, I worked with both a soldering iron and hot air rework station to assemble surface mounted devices (SMDs) and through-hole components.
I also dipped into some software based components of the project, programming in C and Python to create hardware based signals to our desired testing specifications. Specifically, I was aiming to make Pulse Width Modulation (PWM) signals of a specific duration for the Raspberry Pi to output. This led to various tests on the outputs of the code, through the use of an oscilloscope (two PWM pulses on the oscilloscope are shown below). Ultimately, I had the chance to start testing the board in connection with a power supply and the Raspberry Pi’s program.
Moreover, I had the opportunity to dip into so many different branches of electrical engineering and project design. In attending meetings about all of the individual components of the massive GAMOW project, I saw how the team plans and executes each individual collaborative part of the project. This experience in the project process and cutting edge electrical project design as a whole have given me many insights into the professional world of electrical engineering.
Our paper gives an overview of the Princeton Field-Reversed Configuration (PFRC) fusion reactor concept and includes the status of development, the proposed path toward a reactor, and the commercialization potential of a PFRC reactor.
The Journal of Fusion Energy features papers examining the development of thermonuclear fusion as a useful power source. It serves as a journal of record for publication of research results in the field. This journal provides a forum for discussion of broader policy and planning issues that play a crucial role in energy fusion programs.
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.
The frequency we describe is that of the rotating magnetic field (RMF) which is generated by four radio-frequency antenna loops surrounding the machine. The RMF is responsible for creating a higher density field-reversed configuration plasma out of an initial lower density seed plasma and for heating the ions and electrons in the plasma.
The video below shows bright plasma pulses of increased density driven by RMF, now in various gases (argon, helium, and hydrogen):
Achieving bright plasma pulses is an important first step in operating at the new RMF frequency. This frequency will be within the range at which we expect ion heating to occur once we finish installation of the belt coils to increase magnetic field. We first observed bright plasma pulses at the new frequency of 1.8 MHz in argon gas due to its lower ionization potential in comparison to that of molecular hydrogen. In the experiment runs following the run with argon, we tuned parameters such as magnetic field, pressure, and seed plasma power until we began to see bright flashes in helium and hydrogen (where there is still a small percentage of argon). We are continuing work on optimizing the bright flashes for these gases.
In other good news, our two INFUSE awards with PPPL, which were announced this summer, have finally received all necessary approvals from DOE and are kicking off. Sangeeta and I (Chris) are at the lab helping to run the PFRC-2 experiment every week and will soon be running software simulations for the INFUSE projects. We will be studying plasma stabilization techniques and new antenna configurations, all to maximize plasma heating efficiency!
Stay tuned as we continue to update on our progress with the PFRC-2!
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, if it had used tritium .
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!
 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
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 , 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 , 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.
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.
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  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 . 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.
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 (Ho).
Calibration of the Ho density was accomplished by comparison with Krypton (Kr) TALIF. Measurements on plasmas formed of either molecular hydrogen (H2) or Kr fill gases allowed examination of nominally long and short ionization mean-free-path regimes. With multi-kW plasma heating and H2 fill gas, a spatially uniform Ho density of order 1017 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.
Ho 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.