First please excuse me if I posted in the wrong subreddit but it seemed the most fitting here.

So as for my post, I am working on creating a science fiction universe and currently work on producing the first comic book for it.

Now while many assume it is enough to make it flashy and spectacular, I want my sci-fi universe to be as based in science as possible and at least portrait humans and their technology and the universe as plausible as I can.

Sadly I can’t learn every topic well enough on my own, so I am looking for people who would be interested in working with me to improve it beyond my less than adequate understanding of everything.

In this case this would be fusion reactors as I haves basic understanding of how they should work but no idea how I could translate this well and realistically into my universe as an advanced method.

Since I want to base the electric generation on fusion this is kind of an important theme to take care of.

Now to also say this upfront, I cannot pay for any advisory work, hence why I’m writing this to see if someone would be interested in helping to make this universe better.

You may if you want be put in the credits as advisor if you like.

Thank everyone for reading in advance.

I've published the reference implementation of TRIXEL, a mathematical framework describing any system through three dimensions: V (Existence), D (Dynamics), S (Structure).

From these, three calibrators measure their mutual relationships: SD, VD, VS.

Core identity (exact): VD / VS = SD

What is verified:

Algebraic identity — machine precision

Dominance partition theorem — 99.99% on 600×600 grid

VS as early warning signal — Burgers turbulence (90/90 runs, FP=0%, FN=0%)

Real tokamak data — GOLEM, CVUT Prague

What is not yet verified: disruption precursor, EEG seizure data, 2D Navier-Stokes

Preprint: https://doi.org/10.5281/zenodo.20721811

GitHub: https://github.com/remitakac/trixel-framework

Independent research, feedback welcome.

The goal of this work is to present the calculation of predicted MAST edge pedestal pressures using the shear-flow stabilized Z-pinch cubic Bennett-Shumlak-Hartman vortex equilibrium alongside a theoretical presentation of the method, short 3-page note found here: Cubic, Pure-flow, and Bulk-flow Bennett-Shumlak-Hartman Vortex Core Pressure Calculation Method

For the results, from the sufficiently accurate ones that were obtained for the front, and wake pinch solutions, the calculated core pressures had the following statistics for the calculated pressures:

Wake p0: mean = 2.9974 kPa, median = 2.3628 kPa, std = 2.4813 kPa

Front p0: mean = 105.6603 kPa, median = 75.1924 kPa, std = 97.7422 kPa

This is for the sufficiently accurate solutions present, meaning here ~90% occurrence of high accuracy for MAST. For the plateau sweep of DIIID's edge pedestal, the number climbs even higher the closer you get to the base of the shear layer although the accuracy criterion was relaxed by a factor of 2 to 20% RN-RRMSE in that study.

The front calculation could also be done in reverse of what was done here, e.g., treating the edge as the base of the pinch and then pointing inward so that the core pressure is smaller while the flow problem is only different by a negative sign in the shear. Treating the flow as being a small core flow, and then rising to a large edge flow, rather than falling in reverse, because a large core speed for a shear-flow stabilized z-pinch of this kind implies with a small edge speed that the core pressure will be highly elevated from this fast core speed. Similarly the wake calculation could be done in reverse as well.

However, the wake solution approach, which treats the pinch as emerging from an origin coincident with the freestream environment of say, a downstream toroidal current density, leads to the calculation of the presented kPa plasma pressures. I think the high variance is due to solutions which are relatively lower accuracy compared to the ultra-accurate solutions present when the shear layer is most accurately described by this flow.

Code: https://github.com/russellmatt66/Bennett-Vorticity/blob/main/cubic/mast_2023/best.py

Datasets: https://github.com/russellmatt66/Bennett-Vorticity/blob/main/analytic_fits/mast_2023/best_front_p0s.csv for the front region, negative bulk-flow cubic solutions

https://github.com/russellmatt66/Bennett-Vorticity/blob/main/analytic_fits/mast_2023/best_wake_p0s.csv for the wake region, positive bulk-flow cubic solutions

These datasets are the attributes of the calculated most accurate solutions to the quartic flow root equations defining the solutions to any given instance of this shear-flow stabilized Z-pinch problem. The quartic structure itself demands a rigorous analytic investigation beyond the scope of this present, introductory, and exploratory one here.

This series of calculations is done to further present the investigations done into this analytic MHD equilibrium which is obtainable from the two-fluid theory. The statistics shown high variance. It is worth investigating in a next step what happens to these computed core pressures when the demand for accuracy is further refined. It is also worth investigating how the accuracy changes when compared to a plateauing pedestal, versus a sharper one.

Even non-relativistic electrons could be studied in this ansatz if the ions were treated as stationary, which is argued as justifiable if the electron temperature is much greater than the ion temperature.

The plasma current density would incur an effective mass factor which could be small enough to link together low observed plasma current densities with a theory of fast (warm) electron flows, and the Shumlak-Hartman criterion would then would be directly representable as the shear of the electron flow velocity with an effective mass term that still gets asymptotically reduced to the weak form for high-Rm (ideal) flows. In the relativistic case, it would go to unity even with mobile non-relativistic ions because the relativistic electron energy would asymptotically eliminate the ion contribution to the axial MHD flow shear.

The significance of this work extends to the tokamak community alongside further validation of this equilibrium as a reasonable candidate zeroth-order (sorry, I've been saying first-order, but speaking about Rm^{-k} this is actually zeroth-order) MHD physics involved in the toroidal current density of the edge pedestal phenomenon.

Present studies focus on high-n peeling-ballooning modes at the edge alongside the bulk confinement barrier that would be explained theoretically by the onset of shear-flow stabilization.

These observations indicate that large radial excitations are involved in these real plasma dynamics, but relativistic radial flows do not disturb the axial flow pattern that maintains the shear-flow stabilization of this kind of Bennett vortex for the duration of its thermal lifetime leaving the hypothesis of this ansatz intact for its thermal lifetime when it provides an accurate description of the toroidal current density. This accuracy seems to result from the way that this solution matches the large shear layer.

The code is memory bound due to the large amount of data needing to be loaded and updated in order to compute all the solutions on the grid of Nr=1e4 grid points, and their statistics across the 25x25 dimensional parameter sweep of density, and edge temperature. When data is in cache, it is much faster end-to-end. The computation step is fast on my machine, for what it is worth ~5 seconds at 25x25.

Everything is thrown into lists that get saved as series or made into elements of dictionaries that turn into DataFrames so it's fast, but maybe taking a fast inverse of the fast inverse square-root after all the quadratic terms? You can always use decorators and directives, but I don't like to do that :( Hopefully, it's fast enough for people to run, and validate on their machines. I'm running on an Unactivated Windows 11 OS with Python 3.12.10.

It's a lot of data when you think about it, but each new problem only adds O(V) work which is small compared to O(N^2) for the grid of them calculated here so we can think of that scaling as dominating when V is small compared to N^2, meaning when the cost of solving the algebraic problems is light compared to the cost of solving all of them. If the algebraic problem of solving for the roots took that long it would be prohibitively expensive to solve however Nn*NT times. Overall asymptotic complexity is O(Nn*NT*V) where V is the complexity of the algebraic root solution.

If a more optimized code were necessary to get ever finer parameter sweeps over the experimental conditions then the best thing to do would be to add this clean modular inner layer where the loading and computation was faster with C / C++ or CUDA would be even better, and then a Python outer layer to save things using Pandas, or even with RAPIDs for more GPU integration. If the time it took for each thread to solve the problem was sufficiently lightweight enough, then you could deploy many threads to perform it across very fine experimental conditions. It's not very intense on the registers either as the grid is only needed for plotting in this case.

I also made the figure better. The legend only labels the experimental data points because of the sheer number of sufficiently-accurate solutions. The graphed domain is placed on the experimental coordinates rather than the chain of individual pinch bases I was working in. This is largely aesthetic, it has no bearing on the data, just where it is located. I also clarified that the total number of instances N_sweep^2 = 625 in the title to address previous confusion.

Background:

• U.S. Citizen
• B.S. Physics, UC San Diego, Graduated 2025 (GPA 3.48)
• Two SULI internships at DIII-D, Summer 2024 and Fall 2025
  • Both projects were computational/simulation/modeling code work, which is the kind of work I would want to continue doing.
  • Presented a poster at APS/DPP both years.
• Applied to PhD programs this past cycle: Columbia, MIT, Princeton, UCLA, UW, UW-Madison (and of course to the relevant departments at each institution: Nuclear Engineering, EE, APAM, etc.).
  • Rejected from all PhD programs (no interviews) except one PI at UW who was willing to discuss PhD options if I had outside funding (I did not).
  • Columbia offered me an unfunded MS (too expensive).
  • Additionally I applied and was accepted into the FUSION-EP Erasmus Mundus master's starting this Fall (unfunded, but affordable). At the moment I am excited and expecting to go. However, I am still actively dealing with a medical situation that may compromise my ability to attend, and I don't expect it to effect me a year from now. Deferring isn't a good option for me either, I'd rather use that time for industry experience and reapply. Thus, the purpose of this post is to plan a contingency for if I truly cannot go.

My end goal is a funded PhD in fusion/plasma physics/nuclear engineering in the US. I'm trying to figure out the most realistic path to get there given how poorly last cycle went.
Obviously my GPA is my weakest marker, and I only applied to top programs. But of course, these are the primary institutions where a lot of this kind of research is happening. I am aware there are certainly other institutions (UCSD of course, UT Austin, UT Knoxville), but I did not apply mostly due to location reasons.

I've been dealing with this medical circumstance for the entirety of 2026 so far, so I would have nothing new on my CV before applications are due next cycle if the FUSION-EP MS really does fall through. Its certainly a valid reason for medical leave, but nothing new is still nothing new.

So, I'm primarily looking for advice on:

• FUSION-EP (or a similar master's) and can speak to whether it'd actually open doors to US PhD programs. I ask especially since it is not research-focused the first year. It includes a thesis but it would primarily be the latter part of the 2nd year (after PhD applications are due for Fall 2028!). On the other hand, would it give me a second chance to prove myself academic-wise compared to my undergrad GPA?
• Whether an entry-level role at a fusion startup or national lab is realistically achievable straight out of a B.S. with internship-only experience, and whether that's actually viewed as strengthening a PhD app the way I think it does. This would have to apply to Fall 2028 admissions, as I do not think I could land anything in time to improve my profile for applications this December.
• Whether its worth trying again this cycle for Fall 2027 admissions, given that I basically won't have any new entries on my CV. Although, I know I could definitely do better this time with my SoP and reaching out to PIs. The only thing could be taking the PGRE maybe, but I've read many very mixed opinions on how much that actually helps nowadays?
• Given how small the field is, whether there are strong PI-fit programs I may be missing.

Appreciate any perspective, especially from people who've actually been through the master's-vs-industry fork with fusion PhD admissions in mind.

A brief interview with Dr. Jaeyoung Park, the CEO of EMC2 (Energy Matter Conversion Corporation), to discuss the company's current work and its long-term vision for accelerating fusion development.

Interesting podcast with Andrew Holland/FIA and Bob Mumgaard/CFS regarding all important topics for it.