Simons Hour Talks

Date / Time Speaker Topic Title
Dec 9, 2021
8:00-8:10 EST
8:10-9:00 EST
A. Bhattacharjee
Zhisong 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