# Simons Hour Talks

Date / Time (ET) Speaker Title of Talk (Link)
Mar 23 - 24, 2023 Various Hidden Symmetries Annual Meeting @ Simons Foundation (NYC)
Rogerio Manuel Cabete de Jesus Jorge, IST Lisbon, Portugal
Nathan Duignan, University of Sydney
Daniel Ginsberg, Princeton University
Egemen Kolemen, Princeton University
Gabriel Plunk, Max Planck Institute for Plasma Physics
Josefine Proll, Technical University of Eindhoven
Mar 20 - 22, 2023 Various Hidden Symmetries Team Meeting @ Princeton University (Carnegie Center)
Agenda: TBA
Mar 16(17), 2023
7:00-7:05pm (EST)
7:05-8:00pm (EST)
D. Bindel
D. Anderson
History of the HSX, Optimization and Design

(Video recording of talk)
Mar 2(3), 2023
10:00-10:05am (EST)
10:05-11:00am (EST)
D. Bindel
S. Hudson

Introduction to Quadratic Flux Minimizing Surfaces and Ghost Surfaces

An introduction/tutorial on ghost surfaces (GS) and (weighted) quadratic-flux-minimizing (QFM) surfaces, perhaps better described as action-gradient-squared surfaces, and why QFM surfaces (without the "weight") are like snowflake fractals on a hot summer's day, and under what conditions ghost-surfaces and QFM surfaces coincide, and how these surfaces are isotherms of the anisotropic diffusion equation in the limit that \kappa_\perp approaches zero, and why don't we use perturbation theory to solve for the anisotropic diffusion equation by expanding about \kappa_\perp = 0.
(Video recording of talk)
Feb 16(17), 2023
7:00-7:05pm (EST)
7:05-8:00pm (EST)
D. Bindel
M. Nemec
Aerodynamic Shape Optimization
(Video recording of talk)
Feb 2(3), 2023
10:00-10:05am (EST)
10:05-11:00am (EST)
D. Bindel
I. Farcas / B. Peherstorfer
Leveraging Machine Learning for Large-Scale Multi-Fidelity Uncertainty Quantification
Recent advances in computational science and high-performance computing enable the simulation of large-scale real-world problems such as turbulent transport in magnetic confinement devices with ever-increasing realism and accuracy. However, these simulations remain computationally expensive even on large supercomputers, which prevents straightforward approaches to important many-query applications such as uncertainty quantification. In contrast, data-driven machine-learning methods such as those based on deep neural networks provide computationally cheaper low-fidelity models, but typically require large training sets of high-fidelity model evaluations to be predictive, which hampers a straightforward application in large-scale, computationally expensive problems. In this presentation, we demonstrate that data-driven low-fidelity models learned from few data samples can nevertheless be effectively used for large-scale uncertainty quantification: The key is to combine these low-fidelity models with the high-fidelity model in a multi-fidelity fashion. The first part of this presentation focuses on a multi-fidelity Monte Carlo sampling approach in which a hierarchy of data-driven low-fidelity models is constructed using both the full set of uncertain inputs and subsets comprising only selected, important parameters. We illustrate the proposed method in a plasma micro-turbulence simulation scenario concerning turbulence suppression via energetic particles with $14$ stochastic parameters, demonstrating that it is about two orders of magnitude more efficient than standard Monte Carlo methods measured in single-core performance. This translates into a runtime reduction from around eight days to one hour on 240 cores on parallel machines.
The second part of this presentation introduces a context-aware multi-fidelity Monte Carlo method that optimally balances the costs of training low-fidelity models with the costs of Monte Carlo sampling. Our theory shows that low-fidelity models can be overtrained, which is in stark contrast to traditional surrogate modeling and model reduction techniques that construct low-fidelity models with the primary goal of approximating well the high-fidelity model outputs. Numerical experiments in a plasma micro-turbulence simulation scenario with 12 uncertain inputs show speedups of up to two orders of magnitude compared to standard methods, which corresponds to a runtime reduction from 72 days to about four hours on 32 cores on parallel machines.
(Video recording of talk)
Jan 19(20), 2023
7:00-7:05pm (EST)
7:05-7:30pm (EST)
7:35-8:00pm (EST)

D. Bindel
F. Law /
M. Nakata

Talk 1 - Meta Variance Reduction Schemes for Estimation of Alpha Particle Confinement
Numerical estimation of energetic particle confinement using Monte Carlo methods remains a computationally demanding task in stellarator optimization loops, due to the large number of simulated trajectories required at each iteration. We introduce meta estimators to accelerate the estimation of confinement statistics, by simultaneously leveraging multiple constituent variance reduction techniques including multifidelity Monte Carlo, importance sampling, and information reuse. Each constituent technique takes advantage of a different facet of the estimation problem, leading to quasi-multiplicative speedup when combined. We test our meta estimators, using data-driven surrogates and biasing densities, on a coil optimization seeking to reproduce a quasi-axisymmetric configuration (Landreman and Paul, 2022). We observe that each meta estimator outperforms its constituent variance reduction techniques, with the highest performing meta estimator yielding two orders of magnitude speedup compared to standard Monte Carlo estimation at an equivalent computational cost.  (Video recording of Law talk)

Talk 2 - Geometry Induced Activation of Zonal Flows in Stellarator Plasmas
One of the prominent physical processes in confined plasmas is spontaneous formation of mesoscopic coherent structures, e.g., zonal flows, geodesic acoustic oscillations, and radially elongated streamers, which are nonlinearly excited in microscopic turbulence. Then, how can we “activate” or “enhance" such nonlinear structures? The diversity of 3D magnetic geometries in stellarators motivates us to explore the capabilities of enhancing the zonal-flow formation. This talk presents a recent activity on the geometry-induced activation of the zonal flows in a context of stellarator optimizations with a nonlinear proxy model.  (Video recording of NAKATA talk)
Jan 5(6), 2023
10:00-10:05am (EST)
10:05-11:00am (EST)
D. Bindel
D. Ginsberg
On the Distribution of Heat in Integrable and Non-Integrable Magnetic Fields

We study the equilibrium temperature distribution in a model for strongly magnetized plasmas in dimension two and higher. Provided the magnetic field is sufficiently structured (integrable in the sense that it is fibered by co-dimension one invariant tori, on most of which the field lines ergodically wander) and the effective thermal diffusivity transverse to the tori is small, it is proved that the temperature distribution is well approximated by a function that only varies across the invariant surfaces. The same result holds for "nearly integrable" magnetic fields up to a "critical" size. In this case, a volume of non-integrability is defined in terms of the temperature defect distribution and related to the non-integrable structure of the magnetic field, confirming a physical conjecture of Paul-Hudson-Helander. Our proof crucially uses a certain quantitative ergodicity condition for the magnetic field lines on full measure set of invariant tori, which is automatic in two dimensions for magnetic fields without null points and, in higher dimensions, is guaranteed by a Diophantine condition on the rotational transform of the magnetic field.
(Video recording of Ginsberg talk)
Dec 22(23), 2022
7:00-7:05pm (EST)
7:05-8:00pm (EST)
D. Bindel
H. Yamaguchi

Development of Coil Shaping Based Optimization Code at NIFS
(Video recording of talk)
Dec 8(9), 2022
10:00-10:05am (EST)
10:05-11:00am (EST)

D. Bindel
Y. Suzuki

Strong Nonlinearity of MHD Stability in Stellarators
In stellarators, one of characteristics on MHD is strong nonlinearity. Because, sophisticated mode couplings of the 3D equilibrium and instability must be considered, and those are saturated nonlinearly. For example, in the LHD experiment, although the Mercier criterion predicts the linearly unstable plasma, the non-disruptive discharge could be realized. The dissipation and damping mechanisms are still mysteries. In this talk, some of results from 3D nonlinear simulations will be discussed to understand the strong nonlinearity of MHD in stellarators.
(Video recording of Suzuki talk)
Nov 10(11), 2022
10:00-10:05am (EST)
10:05-11:00am (EST)
M. Landreman
D. Spong
History of the HSX and QPS Stellarator Designs

QPS (Quasi Poloidal Stellarator) design history from 1990-2008.
(Video recording of Spong talk)
Oct 27(28), 2022
7:00-7:05pm (EDT)
7:05-8:00pm (EDT)

D. Bindel
J. Meiss

Introduction to Turnstiles & Transports

Turnstiles were introduced by MacKay, Meiss and Percival in 1984 as a mechanism to quantify the flux through broken invariant surfaces, such as the homoclinic tangle formed by an unstable periodic orbit or a cantorus that is the remnant of an invariant torus. A turnstile is constructed from the stable and unstable manifolds of a pair of orbits, and allows one to visualize the transport as the flux through a partial barrier, and show that it can be localized to a single “gap” in the orbit pair. MacKay’s renormalization theory gives a scaling law for the growth of the flux as a function of perturbation strength as a torus is broken. A related power law appears to hold for the exit-time distribution from a chaotic region containing regular islands, though a complete theoretical justification is still lacking.
(Video recording of Meiss talk)
Oct 13(14), 2022
10:00-10:10am (EDT)
10:10-11:00am (EDT)
D. Bindel
R. MacKay /
N. Shibabrat / E. Paul
Update on Isodrasticity
(MacKay Slides) (Shibabrat Slides) (Paul Slides)
Group Presentation on Isodrasticity
(Video recording of MacKay/Shibabrat/Paul talk)
Sep 29(30), 2022
7:00-7:10pm (EDT)
7:10-8:00pm (EDT)
D. Bindel / A. Bhattacharjee

D. Bindel
Optimization Under Stability Constraints

In this talk, we survey some prior work on the treatment of optimization problems with stability constraints in fields other than plasma physics, and we describe the types of technical issues that frequently occur when incorporating eigenvalue-based functions in the objectives or constraints of an optimization problem.  We then give a very preliminary discussion of how we are thinking of incorporating stability constraints in stellarator optimization problems.
(Video recording of Bindel talk)
Sep 15, 2022
10:00-10:10am (EDT)
10:10-11:00am (EDT)

D. Bindel
F. Pasqualotto

On The Construction Of 3D MHD Equilibria In General Bounded Domains

This talk will discuss a recent paper (https://arxiv.org/abs/2208.11109) concerning the construction of magnetohydrostatic (MHS) equilibria in a general 3D domain via a long-time limit of a suitably regularized MHD system. It is a rigorous justification of “magnetic relaxation” in the context of a regularized MHD system.
(Video recording of Pasqualotto talk)
Sep 1, 2022
8:00-8:10 (EDT)
8:10-9:00 (EDT)

D. Bindel
G. Roberg-Clark

Coarse-Grained Gyrokinetics For The Critical Ion Temperature Gradient In Stellarators
This talk will present a modified gyrokinetic theory to predict the critical gradient that determines the linear onset of the ion temperature gradient (ITG) mode in stellarator plasmas. A coarse-graining technique is applied to the drift curvature, entering the standard gyrokinetic equations, around local minima. Thanks to its simplicity, this novel formalism yields an estimate for the critical gradient with a computational cost low enough for application to stellarator optimization. When comparing against a gyrokinetic solver, our results show good agreement for an assortment of stellarator designs. Insight gained here into the physics of the onset of the ITG-driven instability enables us to devise a compact configuration, similar to the Wendelstein 7-X device, but with almost twice the ITG linear critical gradient, an improved nonlinear critical gradient, and reduced ITG mode transport above the nonlinear critical gradient. Preliminary optimization results applying the coarse-graining technique to quasisymmetric stellarator design using SIMSOPT will also be discussed.
(Video recording of Roberg-Clark talk)
Aug 18, 2022
8:00-8:10 (EDT)
8:10-9:00 (EDT)

A. Bhattacharjee
A. Boozer

Omnigeneous Toroidal Plasma Equilibria (Slides)
Omnigeneous Toroidal Plasma Equilibria (Paper)

A simple condition is derived for omnigeneous toroidal plasma equilibria, which means that in a collisionless plasma the turning points of a trapped particle remain on the same magnetic surface. Omnigeneity is important for it assures that collisionless particle trajectories are consistent with achieving ignition in toroidal fusion systems. When the magnetic field strength depends on only one angular coordinate in Boozer coordinates, the magnetic field is quasi-symmetric, and drift trajectories are confined by a conserved canonical momentum. It is shown that a magnetic field is omnigeneous when it obeys the single-angle constraint at extrema of the field strength. Elsewhere it can be far from quasi-symmetric, but must obey a symmetry in a function R about field strength minima. When the field strength depends only on the poloidal angle near extrema, it is called quasi-poloidally symmetric. For this case, it is shown that bootstrap current need not be zero and the sign of the electric potential is more obscure than generally assumed.
https://arxiv.org/pdf/2208.02391
(Video recording of Boozer talk)
Aug 4, 2022
8:00-8:10 (EDT)
8:10-9:00 (EDT)

A. Bhattacharjee
T. Kruger

Minimizing Island Width Sensitivity to Maximize Stellarator Coil Tolerances
Stellarators have advantageous physical properties but require complicated engineering.  Stellarator equilibrium magnetic fields are non-integrable in general, while the integrability of stellarator magnetic fields is targeted in optimization and typically determines coil tolerances.  This talk discusses the use of FOCUS to optimize coils using gradient based algorithms in order to minimize magnetic field errors.
(Video recording of Kruger talk)
July 21, 2022
8:00-8:10 (EDT)
8:10-9:00 (EDT)
A. Bhattacharjee
A. Zocco
Kinetic Infernal Modes and Magnetic Reconnection in Magnetically Confined Fusion Plasmas  (Abstract)
Magnetically confined fusion plasmas must meet some basic magnetohydrodynamic (MHD) stability requirements in order to be of any use in a reactor. In particular, they must not experience long wavelength instabilities. These can involve the whole plasma column, and have to be either operationally avoided or altogether inhibited by design. The free energy needed for such instabilities to grow is provided by current density and plasma pressure gradients. In this talk I will review the basic concepts of the theory of infernal modes, paying attention to their relation to the reconnecting internal kink mode (especially in W7-X) and discuss their extension to fusion relevant regimes in which both electron and ion kinetics are important.
(Video recording of Zocco talk)
June 9, 2022
8:00-8:15 (EDT)
8:15-9:00 (EDT)
P. Helander/
A. Bhattacharjee
E. Paul
Greifswald Retreat, June 27-July 8 (15 minutes)
Energetic Particle Loss Mechanisms In Reactor-Scale Equilibria Close To Quasisymmetry
The transport of fusion-born alpha particles in 3D equilibria is largely determined by collisionless physics. Several transport mechanisms have been implicated in stellarator configurations, including stochastic diffusion due to transitions, ripple trapping, and superbanana orbits. On longer time scales, many lost trajectories undergo transitions between trapping classes, either with periodic or irregular behavior. Possible optimization strategies for each of the relevant transport mechanisms and perform a comparison between classified guiding center losses and metrics for superbanana transport will be discussed.
(Video recording of Helander/Bhattacharjee/Paul talk)
May 12, 2022
8:00-8:10 (EDT)
8:10-9:00 (EDT)
A. Bhattacharjee
W. Sengupta
Preferred Magnetic Axes For Optimal Quasi-Axisymmetry

This talk will discuss the preferred choice of the magnetic axes for optimal quasisymmetry, which is evident from the numerical optimization of asymptotic expansions near the magnetic axis.  The talk will show that the magnetic axis is well described for small rotational transforms by the same equations that govern Euler-Kirchhoff elastic rod centerlines, and present analytical and numerical evidence applicable for a broad range of quasi-axisymmetric stellarators.
(Video recording of Sengupta talk)
Apr 28, 2022
8:00-8:10 (EDT)
8:10-9:00 (EDT)
A. Bhattacharjee
F. Volpe &
C. Smiet

Renaissance Fusion - Technology and Plans

Renaissance Fusion strives to make stellarators smaller via High-Temperature Superconducting (HTS) coils. It makes them less radioactive and more resilient to alpha particle losses by flowing mesoscale liquid metal walls and simpler to build - by using simpler coil winding surfaces and HTS manufacturing. Initial results will be presented in the areas of coil force minimization, simplification of the coil winding surface, neutronic optimization of the liquid wall materials, design point of a compact, profitable stellarator reactor and retrofitting of a fission power-plant. Paradigm-shifting ways of manufacturing HTS stellarator coils and extracting Tritium will be presented.
(Video recording of Volpe & Smiet talk)
Apr 14, 2022
8:00-8:10 (EDT)
8:10-9:00 (EDT)
A. Bhattacharjee
R. Mackenbach
Available Energy and its Relation to Turbulent Transport
Any collisionless plasma possesses some "available energy" (AE), which is that part of the thermal energy that may be converted into instabilities and turbulence. This talk investigates the AE carried by electrons, which are trapped in a magnetic mirror, and the ability to quickly and cheaply assess the turbulence levels, driven by these trapped electrons.
(Video recording of Mackenbach talk)
Mar 17, 2022
8:00-8:10 (EDT)
8:10-9:00 (EDT)
A. Bhattacharjee
R. Dewar
Quasi-Relaxed Magnetohydrodynamics (QRxMHD) incorporating Ideal Ohm's Law Constraint (IOL) (part 2)
The gap between a recently developed dynamical version of relaxed magnetohydrodynamics (RxMHD) and ideal MHD (IMHD) is bridged by approximating the zero-resistivity "Ideal" Ohm's Law (IOL) constraint using an augmented Lagrangian method borrowed from optimization theory. The augmentation combines a pointwise vector Lagrange multiplier method and global penalty function method and can be used either for iterative enforcement of the IOL to arbitrary accuracy, or for constructing a continuous sequence of magnetofluid dynamics models running between RxMHD (no IOL) and weak IMHD (IOL almost everywhere). This is illustrated by deriving dispersion relations for linear waves on an MHD equilibrium.
(Video recording of Dewar talk part 2)
Mar 3, 2022
8:00-8:10 (EST)
8:10-9:00 (EST)
A. Bhattacharjee
R. Dewar
Quasi-Relaxed Magnetohydrodynamics (QRxMHD) incorporating Ideal Ohm's Law Constraint (IOL) (part 1)
The gap between a recently developed dynamical version of relaxed magnetohydrodynamics (RxMHD) and ideal MHD (IMHD) is bridged by approximating the zero-resistivity "Ideal" Ohm's Law (IOL) constraint using an augmented Lagrangian method borrowed from optimization theory. The augmentation combines a pointwise vector Lagrange multiplier method and global penalty function method and can be used either for iterative enforcement of the IOL to arbitrary accuracy, or for constructing a continuous sequence of magnetofluid dynamics models running between RxMHD (no IOL) and weak IMHD (IOL almost everywhere). This is illustrated by deriving dispersion relations for linear waves on an MHD equilibrium.
(Video recording of Dewar talk part 1)
Feb 17, 2022
8:00-8:10 (EST)
8:10-9:00 (EST)
A. Bhattacharjee
A. Punjabi
Magnetic Turnstiles in Nonresonant Stellarator Divertor
Nonresonant stellarator divertors have a pair of magnetic flux tubes.  One has field lines that go from just outside the outermost confining surface to the surrounding chamber wall, and the other has lines that come inward from the wall.  This outward-inward action led to the name magnetic turnstile.  Plasma is diverted along both tubes of the pair.  The pair of flux tubes cross the annulus between the outermost confining surface and the walls through holes in magnetic cantori, which are the fractal remnants of magnetic surfaces.  The exiting and entering flux tubes can be adjacent as in the literature on turnstiles.  But, tubes were also found that have the unexpected feature of the entering and the exiting the region near the outermost confining surface at separated locations. Not only can there be two types of turnstiles but pseudo-turnstiles can also exist. A pseudo-turnstile is formed when an outer surface has a sufficiently large, although limited, radial excursion to strike the wall. The existence of non-adjacent and adjacent turnstiles and pseudo-turnstiles resolves issues that arose in earlier simulations of nonresonant stellarator divertors.
(Video recording of Punjabi talk)
Feb 03, 2022
8:00-8:10 (EST)
8:10-9:00 (EST)
A. Bhattacharjee
N. Nikulsin
Models and Methods for Nonlinear Magnetohydrodynamic Simulations of Stellarators
The JOREK code has recently been extended to allow nonlinear fully 3D stellarator simulations. This is made possible by generalizing the JOREK reduced MHD model to support stellarator geometries, and by allowing the grid to be non-axisymmetric, so that it can be aligned to the flux surfaces in a stellarator. The stellarator reduced model differs mainly in that the magnetic field can be represented as any curl-free field plus a perturbation in the stellarator model, whereas in the tokamak model it is a toroidal field plus a perturbation. It is shown that this model conserves energy, but introduces an error into momentum conservation. An alternate model, which does not guarantee energy conservation, but has a smaller momentum conservation error is also derived. The energy and momentum conservation properties of the main and alternate models are then studied numerically in the tokamak limit. The main model was then tested on a set of l=2 stellarator equilibria based on Wendelstein 7-A. The simulations demonstrate that stable full MHD equilibria are preserved in the reduced model: the flux surfaces do not move throughout the simulation, and closely match the full MHD flux surfaces. Further, both tearing and ballooning modes were simulated, and their growth rates benchmarked against the linear full MHD code CASTOR3D, showing good agreement.
(Video recording of Nikulsin talk)
Jan 20, 2022
8:00-8:10 (EST)
8:10-9:00 (EST)
A. Bhattacharjee
E. Rodriguez
Understanding the Space of Quasisymmetric Configurations: Phases and Phase Transitions
Optimisation plays a central role in the pursuit of viable stellarator designs. Customarily, such designs result from a search in a large parameter space, guided by desirable physics requirements. This approach has proven useful but the complexity of the space makes the approach, to a large extent, a 'black box'.
The talk presents our attempt to shed light on the space of quasisymmetric configurations. We identify designs with a reduced set of functions and parameters that describe the configurations approximately by expansions about their magnet axes. This allows us to structure the space in an effective and powerful way. The presentation will focus on the first step in this approach, which identifies configurations at the most basic level through fundamental geometric properties of their magnetic axes. We show that this reduced level of description is sufficient to naturally divide the space of configurations into quasisymmetric phases and phase transitions. The basic structure of the space can be leveraged to contextualise typical quasisymmetric designs and describe several important properties. We will also present some results on extensions of the basic reduced model.
(Video recording of Rodriguez talk)
Dec 9, 2021
8:00-8:10 (EST)
8:10-9:00 (EST)
A. Bhattacharjee
Z. Qu
On The Non-Existence Of Stepped-Pressure Equilibria Far From Symmetry
The Stepped Pressure Equilibrium Code (SPEC) has been successful in the construction of equilibria in 3D configurations that contain a mixture of flux surfaces, islands and chaotic magnetic field lines. In this model, the plasma is sliced into sub-volumes separated by ideal interfaces, and in each volume the magnetic field is a Beltrami field. In the cases where the system is far from possessing a continuous symmetry, such as in stellarators, the existence of solutions to a stepped-pressure equilibrium with given constraints, such as a multi-region relaxed MHD minimum energy state, is not guaranteed but is often taken for granted. Using SPEC, we have studied two different scenarios in which a solution fails to exist in a slab with analytic boundary perturbations. We found that with a large boundary perturbation, a certain interface becomes fractal, corresponding to the break-up of a Kolmogorov–Arnold–Moser (KAM) surface. Moreover, an interface can only support a maximum pressure jump while a solution of the magnetic field consistent with the force balance condition can be found. An interface closer to break-up can support a smaller pressure jump. We discovered that the pressure jump can push the interface closer to being non-smooth through force balance, thus significantly decreasing the maximum pressure it can support. Our work shows that a convergence study must be performed on a SPEC equilibrium with interfaces close to break-up. These results may also provide insights into the choice of interfaces and have applications in finding out the maximum pressure a machine can support.
(Video recording of Qu talk)
Nov 24, 2021
8:00-8:10 (EST)
8:10-9:00 (EST)
A. Bhattacharjee
R. Nies
Adjoint Methods for Quasisymmetry of Vacuum Fields on a Surface
Stellarator optimisation can be significantly sped up by using adjoint methods instead of finite-differences to obtain derivative information. In this work, we apply adjoint methods to stellarator vacuum fields, considering objective functions targeting quasisymmetry and rotational transform on the boundary. To define quasisymmetry on the surface, a novel way of constructing approximate flux coordinate on an isolated flux surface is proposed. The obtained adjoint equations are of a simple form such that they can be solved with existing numerical tools, and yield highly accurate derivatives. Using adjoint methods, we obtain configurations with highly accurate quasisymmetry on the boundary, and we are able to systematically investigate the interplay between quasisymmetry and other optimisation targets, such as the aspect ratio and rotational transform.
(Video recording of Nies talk)
Oct 28, 2021
8:00-8:10 (EDT)
8:10-9:00 (EDT)
A. Bhattacharjee
D. Spong
Suppression of Energetic Particle-Driven Instabilities in Stellarators

Good energetic particle (EP) confinement is essential for stellarators to achieve efficient heating and protection of plasma facing components. EP confinement is influenced by several mechanisms: classical orbit confinement, slowing-down timescales, and EP-driven instabilities. Stellarator optimization has recently made significant progress towards improved quasi-symmetry (which improves classical EP confinement). However, experimental evidence has shown that EP instabilities can enhance EP transport to levels of the same order as classical orbit losses. While EP instability driven transport can to some extent be influenced by profile control, three-dimensional shaping is also expected to affect these instabilities. Shaping can be used to control either the MHD wave structures that EP populations resonate with, or the particle-wave resonance dynamics. The physics of EP instabilities will be reviewed and some of the new possibilities for EP instability optimization targets described.
(Video recording of Spong talk)
Oct 14, 2021
8:00-8:10 (EDT)
8:10-9:00 (EDT)
A. Bhattacharjee
P. Helander
Upper Bounds on Gyrokinetic Instabilities

Energy confinement in Stellarators is mostly limited by turbulence, in particular when the plasma temperature is low or  the neoclassical transport has been reduced by optimization of the magnetic field. The turbulence and the underlying micro-instabilities are thought to be well described by the gyrokinetic set of equations, which have been the subject of thousands of papers and millions of lines of computer code. Yet, little is known about the general properties of the solutions to these equations. Here, a family of rigorous upper bounds on the growth rate of local gyrokinetic instabilities is derived. These bounds hold for both electrostatic and electromagnetic instabilities, regardless of the number of particle species, their collision frequency, and the geometry of the magnetic field. A large number of results that have earlier been derived in special cases and observed in numerical simulations are thus brought into a unifying framework. These bounds apply not only to linear instabilities but also imply an upper limit to the nonlinear growth of the free energy.
(Video recording of Helander talk)
Sep 30, 2021
8:00-8:10 (EDT)
8:10-9:00 (EDT)
A. Bhattacharjee
Y-M. Huang
Structure of Pressure-Driven Current Singularities

The objective of this study is to work out a prototype problem with p' <> 0 on the resonant surface as a concrete example. For that purpose, we use The Hahm-Kulsrud-Taylor (HKT) problem, which 1 - is amenable to analytic solutions; 2 - has been studied with various codes including a Grad-Shafranov solver, a fully Lagrangian code, and SPEC for the case with p = 0.
(Video recording of  Huang talk)
Sep 16, 2021
8:00-8:30 (EDT)
A. Giuliani Optimization For Quasi-Symmetry on Surfaces in Single-Stage Coil Design
In this talk, we'll give an update on our single-stage approach to optimizing for quasi-symmetry on surfaces. Previously, we've presented our new technique for computing surfaces in Boozer coordinates, currently available in SIMSOPT.  In this talk, we'll give addition details and describe how these surfaces can be used in a gradient-based approach to optimize for quasi-symmetry.
(Video recording of Giuliani talk)
Sep 16, 2021
8:30-9:00 (EDT)
F. Law Multifidelity Monte Carlo Estimation of Energetic Particle Confinement in Stellarators
In the design of Stellarators, energetic particle confinement is a critical point of concern which remains challenging to analyze from a numerical point of view. Due to the absence of fully reliable proxy functions in quantifying the energetic particle confinement properties of magnetic configurations, studies are typically based on a standard Monte Carlo analysis.
(Video recording of Law talk)
Sep 2, 2021
8:00-9:00 (EDT)
N. Sato

Quasisymmetric Magnetic Fields in Asymmetric Toroidal Domains
(Video recording of Sato talk)
Aug  5, 2021
8:00-9:00 (EDT)
M. Landreman Magnetic Fields With Excellent Quasisymmetry Throughout a Volume
(Video recording of Landremantalk)
July 22, 2021
8:00-9:00 (EDT)
S. Henneberg Representing The Plasma Boundary in Stellarator Optimization
(Video recording of Henneberg talk)
July 8, 2021
8:00-9:00 (EDT)
R. White Particle Resonances in Toroidal Plasmas
(Video recording of White talk)
Jun 24, 2021
8:00-9:00 (EDT)
D. Peralta-Salas MHD Equilibria with Non-Constant Pressure in Nondegenerate Toroidal Domains
(Video recording of Peralta-Salas talk)
May 27, 2021
8:00-9:00 (EDT)
A. Carlton-Jones
E. Stenson
Computing The Shape Gradient of Stellarator Coil Complexity With Respect to the Plasma Boundary
(Video recording of Carlton-Jonestalk)
Computational Studies of Mu-Breaking in a Magnetic Dipole and Other Simple Coil Configurations
(Video recording of Stenson talk)
Apr 29, 2021
8:00-9:00 (EDT)
M. Landreman Update on SIMSOPT
(Video recording of Landreman talk)
Apr 15, 2021
8:00-9:00 (EDT)
Y-M. Huang Numerical Approach to ∂-function Current Sheets Arising From Resonant Magnetic Perturbations
(Video recording of Huang talk)
Apr 1, 2021
2:00-3:00 (EDT)
A. Geraldini Adjoint Calculation of Magnetic Island Width Sensitivity
(Video recording of Geraldini talk)
Mar 18, 2021
2:00-3:00 (EDT)
R. MacKay /
J. Burby
Isodrastic Magnetic Fields
(Video recording of MacKay talk)
Mar 4, 2021
2:00-3:00 (EST)
J. Lion Generalization of the Systems Code PROCESS to Stellarators
Feb 18, 2021
2:00-3:00 (EST)
F. Wechsung Single-Stage Gradient-Based Stellarator Coil Design
Feb 4, 2021
2:00-3:00 (EST)
S. Henneberg Algorithms for Combined Plasma and Coil optimization
Jan 7, 2021
2:00-3:00 (EST)
N. Duignan A Presymplectic View of Magnetic Fields
Dec 11, 2020
9:10-10:00 (EST)
W. Sengupta Obtaining exact quasisymmetry on a single flux surface: a near-surface expansion approach
Nov 20, 2020
9:10-10:00 (EST)
A. Guiliani Single-stage gradient-based stellarator coil design:
Optimization for near-axis quasi-symmetry
Oct 30, 2020
9:20-10:00 (EDT)
E. Rodriguez Avoiding the problem of overdetermination in quasisymmetric near-axis
Oct 2, 2020
9:20-10:00Am (EDT)
J. -F. Lobsien Stochastic Stellarator Coil Optimization
July 24, 2020
9:30-10:00Am (EDT)
N. McGreivy Finite-Build Stellarator Coil Design & Automatic Differentiation
June 26, 2020
9:20-10:00Am (EDT)
T. Pedersen Introduction to (Stellarator) Divertors
June 12, 2020
9:20-10:00Am (EDT)
J. Burby Grad-Shafranov Equation For Non-Axisymmetric MHD Equilibria (slides)
https://arxiv.org/pdf/2005.13664.pdf (paper)
May 29, 2020
9:00-9:20Am (EDT)
A. Bhattacharjee Summer School 2020 Schedule
May 29, 2020
9:20-10:00Am (EDT)
R. Granetz Applying High Temperature Superconductor Technology to Stellarators
May 15, 2020
9:00-10:00Am (EDT)
B. Khesin Madelung Transform and Binormal Flows
in the Euler Hydrodynamics
May 1, 2020
9:05-9:30Am (EDT)
E. Rodriguez Constructing Quasisymmetry
May 1, 2020
9:35-10:00Am (EDT)
N. Kallinikos Approximate Quasisymmetry
Apr. 17, 2020
9:00-10:00Am (EDT)
S. Glas Optimization Under Uncertainty
Apr. 6, 2020
3:00‑4:00Pm (EDT)
D. Ginsberg Quasisymmetric Equilibria
Mar. 23, 2020
3:00‑4:00Pm (EDT)
P. Helander Stellarators with Permanent Magnets
Mar. 9, 2020
3:00‑4:00Pm (EDT)
A. Bader Stellarator Optimization in Practice
And Where We Can Improve
Mar. 2, 2020
3:00‑4:00Pm (EST)
D. Malhotra Integral Equation Methods for Calculating
Stepped-Pressure Equilibrium in Stellarators
Feb. 24, 2020
3:00‑4:00Pm (EST)
Stellarator Optimization
Feb. 10, 2020
3:00‑4:00Pm (EST)
E. Paul Efficient Stellarator Shape Optimization
and Sensitivity Analysis
Jan. 27, 2020
3:00‑4:00Pm (EST)
R. Dewar and
Z. Qu
MRxMHD With Flow
Jan. 10, 2020
9:00‑10:00Am (EST)
M. Landreman SIMSOPT phase 1: MANGO
Dec. 13, 2019
9:00‑10:00Am (EST)
F. Hindenlang GVEC: A newly developed 3D ideal MHD
Galerkin Variational Equilibrium Code
Nov. 29, 2019
9:00‑10:00Am (EST)
J. Loizu Direct Prediction of Nonlinearly Saturated
Tearing Modes with SPEC
Nov. 15, 2019
9:00‑10:00Am (EST)
B. Faber Stellarator Optimization at the
Nov. 8, 2019
8:30‑9:30Am (EST)
Special Discussion on SIMSOPT
Nov. 1, 2019
9:00‑10:00Am (EDT)
R. Jorge Near-Axis Expansion Framework at Arbitrary
Order in the Distance to the Magnetic Axis
Sep. 20, 2019
9:00‑10:00Am (EDT)
Dhariya Malhotra Higher-Order Integration for Singular
Integrals in Magnetostatics
Sep. 6, 2019
9:00‑10:00Am (EDT)
Allen Boozer Curl-free Magnetic Fields for Stellarator Optimization
Aug. 5, 2019
3:00‑4:00Pm (EDT)
David Bindel Surrogate Optimization
May 13, 2019
3:00‑4:00Pm (EDT)