Simons Hour Talks

Date / Time Speaker Title of Talk (Link)
May 26, 2022
8:00-8:10 EDT
8:10-9:00 EDT
A. Bhattacharjee
TBA
Hidden Symmetries Study Updates
TBA
May 12, 2022
8:00-8:10 EDT
8:10-9:00 EDT
A. Bhattacharjee
W. Sengupta
Hidden Symmetries Study Updates
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 Talk)
Apr 28, 2022
8:00-8:10 EDT
8:10-9:00 EDT
A. Bhattacharjee
F. Volpe & 
C. Smiet 
 
Hidden Symmetries Study Updates
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 Talk)
Apr 14, 2022
8:00-8:10 EDT
8:10-9:00 EDT
A. Bhattacharjee
R. Mackenbach
Hidden Symmetries Study Updates
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 Talk)
Mar 17, 2022
8:00-8:10 EST
8:10-9:00 EST
A. Bhattacharjee
R. Dewar
Hidden Symmetries Study Updates
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 Talk)
Mar 3, 2022
8:00-8:10 EST
8:10-9:00 EST
A. Bhattacharjee
R. Dewar
Hidden Symmetries Study Updates
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 Talk)
Feb 17, 2022
8:00-8:10 EST
8:10-9:00 EST
A. Bhattacharjee
A. Punjabi
Hidden Symmetries Study Updates
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 Talk)
Feb 03, 2022
8:00-8:10 EST
8:10-9:00 EST
A. Bhattacharjee
N. Nikulsin
Hidden Symmetries Study Updates
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 Talk)
Jan 20, 2022
8:00-8:10 EST
8:10-9:00 EST
A. Bhattacharjee
E. Rodriguez
Hidden Symmetries Study Updates
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 Talk)
Dec 9, 2021
8:00-8:10 EST
8:10-9:00 EST
A. Bhattacharjee
Z. Qu
Hidden Symmetries Study Updates
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 Talk)
Nov 24, 2021
8:00-8:10 EST
8:10-9:00 EST
A. Bhattacharjee
R. Nies
Hidden Symmetries Study Updates
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 Talk)
Oct 28, 2021
8:00-8:10 EDT
8:10-9:00 EDT
A. Bhattacharjee
D. Spong
Hidden Symmetries Study Updates
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 Talk)
Oct 14, 2021
8:00-8:10 EDT
8:10-9:00 EDT
A. Bhattacharjee
P. Helander
Hidden Symmetries Study Updates
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 Talk)
Sep 30, 2021
8:00-8:10 EDT
8:10-9:00 EDT
A. Bhattacharjee
Y-M. Huang
Hidden Symmetries Study Updates
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 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 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 Talk)
Sep 2, 2021
8:00-9:00 EDT
N. Sato
佐藤直木
Quasisymmetric Magnetic Fields in Asymmetric Toroidal Domains
(Video Recording of Talk)
Aug  5, 2021
8:00-9:00 EDT
M. Landreman Magnetic Fields With Excellent Quasisymmetry Throughout a Volume
(Video Recording of Talk)
 July 22, 2021
8:00-9:00 EDT
S. Henneberg Representing The Plasma Boundary in Stellarator Optimization
(Video Recording of Talk)
July 8, 2021
8:00-9:00 EDT
R. White Particle Resonances in Toroidal Plasmas
(Video Recording of 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 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 ET
A. Bader Stellarator Optimization in Practice
And Where We Can Improve
Mar. 2, 2020
 3:00‑4:00PM ET
D. Malhotra Integral Equation Methods for Calculating
Stepped-Pressure Equilibrium in Stellarators
Feb. 24, 2020
 3:00‑4:00PM ET
A. Giuliani Adjoint-Based Vacuum-Field
Stellarator Optimization
Feb. 10, 2020
 3:00‑4:00PM ET
E. Paul Efficient Stellarator Shape Optimization
and Sensitivity Analysis
Jan. 27, 2020
 3:00‑4:00PM ET
R. Dewar and
Z. Qu
MRxMHD With Flow
Jan. 10, 2020
 9:00‑10:00AM ET
M. Landreman SIMSOPT phase 1: MANGO
Dec. 13, 2019
 9:00‑10:00AM ET
F. Hindenlang GVEC: A newly developed 3D ideal MHD
Galerkin Variational Equilibrium Code
Nov. 29, 2019
 9:00‑10:00AM ET
 J. Loizu Direct Prediction of Nonlinearly Saturated
Tearing Modes with SPEC
Nov. 15, 2019
 9:00‑10:00AM ET
B. Faber Stellarator Optimization at the
University of Wisconsin-Madison
Nov. 8, 2019
 8:30‑9:30AM ET
  Special Discussion on SIMSOPT
Nov. 1, 2019
 9:00‑10:00AM ET
R. Jorge Near-Axis Expansion Framework at Arbitrary
Order in the Distance to the Magnetic Axis
Sep. 20, 2019
 9:00‑10:00AM ET
Dhariya Malhotra Higher-Order Integration for Singular
Integrals in Magnetostatics
Sep. 6, 2019
 9:00‑10:00AM ET
Allen Boozer Curl-free Magnetic Fields for Stellarator Optimization
Aug. 5, 2019
 3:00‑4:00PM ET
David Bindel Surrogate Optimization
May 13, 2019
 3:00‑4:00PM ET
Georg Stadler Optimization
Apr. 29, 2019
 3:00‑4:00PM ET
Amitava Bhattacharjee Summer School Schedule
Mar. 18, 2019
 3:00‑4:00PM ET
Amitava Bhattacharjee Team meeting in PCTS, 
Annual Meeting at Simons Foundation