Bright plasma pulses achieved for various gases at a new frequency in the PFRC-2

We have been operating the Princeton Field-Reversed Configuration-2 (PFRC-2) at the new, lower frequency of 1.8 MHz since mid-November. We have blogged about some developments towards operating at this new frequency including installation of the new capacitors as well as power supplies and holders for the belt coils.

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 the next few months we plan to increase the magnetic field and measure the plasma with the ion energy analyzer built by the Princeton Plasma Physics Laboratory (PPPL) for this experiment with support from ARPA-E. This will show us how much plasma heating is happening!

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!

APS Division of Plasma Physics 2022 Meeting in Spokane, Washington

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!

New Paper Published: Implementation of Mylar filter in x-ray diagnostics of PFRC-2

We have recently published a research paper titled: “Use of a Mylar filter to eliminate vacuum ultraviolet pulse pileup in low-energy x-ray measurements”[1]. This paper is published as part of the “Proceedings of the 24th Topical Conference on High-Temperature Plasma Diagnostics”, along with the papers mentioned in earlier PSS blog posts on the collisional-radiative model and the neutral atom density diagnostic.

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:

Picture of Mylar filter, diameter ~ 1 centimeter, thickness ~ 1 micron (1/10000 cm). Image from [1].

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.

Comparison of x-ray spectra for high-UV-flux condition: without Mylar (blue) and with Mylar (red). A substantial reduction of the pulse pileup helps us uncover the true x-ray spectrum for measurement. Image from [1].
[1] Galea, Swanson, Cohen, and Thomas, Review of Scientific Instruments 93, 093531 (2022);
 https://doi.org/10.1063/5.0101712

Applying our Toolboxes to ITER and DEMO fusion reactors

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.

[1] Aymar, Barabaschi, and Y Shimomura (for the ITER Team), “The ITER Design”, Plasma Physics and Controlled Fusion 44, 519–565 (2002); https://doi.org/10.1088/0741-3335/44/5/304
[2] Sips et al., “Advanced scenarios for ITER operation”, Plasma Physics and Controlled Fusion 47 A19 (2005); https://doi.org/10.1088/0741-3335/47/5A/003
[3] Kembleton et al., ” EU-DEMO design space exploration and design drivers”, Fusion Engineering and Design 178, 113080 (2022); https://doi.org/10.1016/j.fusengdes.2022.113080

Installation of the new capacitors in the Princeton Field-Reversed Configuration-2

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.

New Fusion Reactor Design Function

The Fusion Energy Toolbox for MATLAB is a toolbox for designing fusion reactors and for studying plasma physics. It includes a wide variety of physics and engineering tools. The latest addition to this toolbox is a new function for designing tokamaks, based on the paper in reference [1]. Tokamaks have been the leading magnetic confinement devices investigated in the pursuit of fusion net energy gain. Well-known tokamaks that either have ongoing experiments or are under development include JET, ITER, DIII-D, KSTAR, EAST, and Commonwealth Fusion Systems’ SPARC. The new capability of our toolboxes to conduct trade studies on tokamaks allows our customers to take part in this exciting field of fusion reactor design and development.

The Fusion Reactor Design function checks that the reactor satisfies key operational constraints for tokamaks. These operational constraints result from the plasma physics of the fusion reactor, where there are requirements for the plasma to remain stable (e.g., not crash into the walls) and to maintain enough electric current to help sustain itself. The tunable parameters include: the plasma minor radius ‘a’ (see figure below), the H-mode enhancement factor ‘H’, the maximum magnetic field at the coils ‘B_max’, the electric power output of the reactor ‘P_E’, and the neutron wall loading ‘P_W’, which are all essential variables to tokamak design and operation. H-mode is the high confinement mode used in many machines.

Illustration of the toroidal plasma of a tokamak. R is the major radius while a is the minor radius of the plasma. The red line represents a magnetic field line which helically winds along the torus. Image from [2].

This function captures all figure and table results in the original paper. We implemented a numerical solver which allows the user to choose a variable over which to perform a parameter sweep. A ‘mode’ option has been incorporated which allows one to select a desired parameter sweep variable (‘a’, ‘H’, ‘B_max’, ‘P_E’, or ‘P_W’) when calling the function. Some example outputs of the function are described below.

As an example, we will consider the case of tuning the maximum magnetic field at the coils ‘B_max’. The figure below plots the normalized operation constraint parameters for a tokamak as functions of B_max from 10 Tesla to 25 Tesla. The unshaded region, where the vertical axis is below the value of 1, is the region where operational constraints are met. We see that for magnetic fields below about 17.5 Tesla there is at least one operation constraint that is not met, while for higher magnetic fields all operation constraints are satisfied, thus meeting the conditions for successful operation. This high magnetic field approach is the design approach of Commonwealth Fusion Systems for the reactor they are developing [3].

Operational constraint curves as a function of B_max. Successful operation occurs if all of the curves are in the unshaded region. Note, f_B/f_NC, a ratio of the achievable to required bootstrap current, is set equal to 1. In this case P_E = 1000 MW, P_W = 4 MW/m2, and H = 1. For more details on the plotted parameters and how they function as operational plasma constraints, see reference [1].

Note, however, that there is a material cost associated with achieving higher magnetic fields, as described in reference [1]. This is illustrated in the figure below, which plots the cost parameter (the ratio of engineering components volume V_I to electric power output P_E) against B_max. There is a considerable increase in cost at high magnetic fields due to the need to add material volume that can structurally handle the higher current loads required.

Cost parameter (units of volume in cubic meters per megawatt of power, m3/MW) as a function of B_max.

In this post we illustrated the case of a tunable maximum magnetic field at the coils, though as mentioned earlier, there are other parameters you can tune. 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.

Thank you to interns Emma Suh and Paige Cromley for their contributions to the development of this function.

[1] Freidberg, Mangiarotti, and Minervini, “Designing a tokamak fusion reactor–How does plasma physics fit in?”, Physics of Plasmas 22, 070901 (2015); https://doi.org/10.1063/1.4923266
[2] http://www-fusion-magnetique.cea.fr/gb/iter/iter02.htm
[3] https://news.mit.edu/2021/MIT-CFS-major-advance-toward-fusion-energy-0908

Space Rapid Transit – Landing Gear Design

Hello everyone, I am an MIT extern here at Princeton Satellite Systems through MIT’s Externship Program. Over the past three weeks, I have been able to play a part in and help out with a number of assignments. The most recent assignment is what I will be detailing in this post.

One of the projects PSS is working on is Space Rapid Transit, a two-stage-to-orbit launch vehicle with horizontal takeoff (think space vehicle that can “launch” like an airplane).  I was given the task of designing the nose landing gear, and in particular figuring out what type of linear electric actuator should be used to handle the load of retracting the landing gear.  Here is a preliminary design drawing I sketched to conceptualize the task.

prelimdesign

In order to find a solution, I first needed to make a few design assumptions.  The first assumption was that the landing gear would retract toward the nose (which is a reasonable assumption because it allows more space behind the landing gear).  Next, I chose to model the retraction under the assumption that the vehicle is undergoing a 2-g turn.  I then selected the strut and tire sizes and found the maximum speed and altitude at which operation of the landing gear is allowed, using the specifications of the Airbus A320 because of its similar takeoff mass.  I now had enough information to approximate the force on the linear actuator.  For this I made a simplified sketch, drawing the side and top view of the landing gear as it undergoes retraction.

Using the side view in the diagram above, I simplified the landing gear retraction into a torque balance problem, where all torques were evaluated about the fixed pivot.  I found the time it takes to retract the landing gear to be around 10 seconds and estimated a full sweep angle of the landing gear (from fully extended to fully retracted) to be 90 degrees.  Assuming constant angular acceleration, I was able to calculate this angular acceleration using the time and angle noted above.  I then calculated the distance of the center of mass of the wheel and strut configuration from the pivot as well as the moment of inertia.  After this I computed the drag force and gravitational force (from the 2-g turn) on the strut and wheels and computed how much torque each force would apply about the pivot.  Since the angular acceleration was so small that the resultant torque was negligible, the problem became a balance of the torque applied by the actuator with the torques resulting from air flow and the 2-g turn.

With this new found torque required from the actuator, I searched for linear electric actuators that could supply the force and stroke length.  The stroke length was approximated as the distance of the applied actuator force from the pivot.  As a result, I selected a Size 5 Moog Standard Linear Electric Actuator because it fit the design requirements.

side view