HiFiStell Seminars

Date / Time (ET)SpeakerTitle of Talk (PDF Link)
W. SenguptaPeriodic Korteweg-de Vries soliton potentials generate magnetic field strength with excellent quasisymmetry
Abstract: Quasisymmetry (QS) is a hidden symmetry of the magnetic field strength, |B|, that con- fines charged particles effectively in a three-dimensional toroidal plasma equilibrium. Here, we show that QS has a deep connection to the underlying symmetry that makes solitons possible. Our approach uncovers a hidden lower dimensionality of |B| on a magnetic flux sur- face, which could make stellarator optimization schemes significantly more efficient. Recent numerical breakthroughs (M. Landreman and E. Paul, Phys. Rev. Lett. 128, 035001 (2022)) have yielded configurations with excellent volumetric QS and surprisingly low magnetic shear. Our approach elucidates why the magnetic shear is low in these configurations. Furthermore, we deduce an upper bound on the maximum toroidal volume that can be quasisymmetric and verify it for the Landreman-Paul precise quasiaxisymmetric (QA) stellarator configuration. In the neighborhood of the outermost surface, we show that the |B| approaches the form of the 1-soliton reflectionless potential (I. Gjaja and A. Bhattacharjee, Phys. Rev. Lett. 68, 2413 (1992)). We present three independent approaches to demonstrate that quasisymmetric |B| is described by well-known integrable systems such as the Korteweg-de Vries (KdV) equation. The first approach is weakly nonlinear multiscale perturbation theory, which highlights the crucial role that magnetic shear plays in QS. We show that the overdetermined problem of finding quasisymmetric vacuum fields admits solutions for which the rotational transform is not free but highly constrained. We obtain the KdV equation (and, more specifically, Gard- ner’s equation for certain choices of parameters). Our second approach is non-perturbative and based on ensuring single-valuedness of |B|, which directly leads to its Painlevé property shared by the KdV equation. Our third approach uses machine learning, trained on a large dataset of numerically optimized quasisymmetric stellarators. We robustly recover the KdV (and Gardner’s) equation from the data.
H. ZhuZonal Flows in Stellarators
F. FuFast Global Stellarator Coil Optimization with Quadratic Objectives
Abstract: Most present stellarator designs are produced by costly two-stage optimization: the first for an optimized equilibrium, and the second for a coil design reproducing its magnetic configuration. Few proxies for coil complexity and force exists at the equilibrium stage. Rapid initial state finding for both stages is a field of active research. Most present fast coil optimization codes use the least square current potential method by Merkel (NESCOIL) [1], with recent improvement in regularization by Landreman (REGCOIL)[2] and Boozer[3]. While elegant, the method is limited to modeling the norms of linear functions in coil current. We present QUADCOIL, a fast, global coil optimization method that targets combinations of linear and quadratic functions of the current. It can directly constrain and/or minimize a wide range of physics unavailable in NESCOIL and REGCOIL, including stored magnetic energy, Lorentz force [4], curvature, and field-current alignment. QUADCOIL requires no initial guess, finds the global optima in the design space, and runs in core-seconds. It supports most regularization techniques developed for NESCOIL and REGCOIL. We demonstrate agreement between QUADCOIL and local optimization using a prototype using cvxpy[5] and MOSEK as optimizer. For a given equilibrium and winding surface, QUADCOIL can rapidly estimate the best achievable value for engineering metrics. It can also provide improved initial guesses for high-fidelity coil optimization.
(Video recording of talk)
R. RamasamyNonlinear MHD Studies of Soft Beta Limits in W7-AS
Abstract: Nonlinear MHD simulation studies are presented towards understanding the underlying mechanism behind experimentally observed soft beta limits in W7-AS. First, linear benchmarks of a (2, 1) tearing mode in W7-AS geometry, and interchange modes in a finite beta, net-zero current carrying stellarator with low magnetic shear are used to demonstrate the capabilities of a recently derived reduced nonlinear MHD model. A validation study is then conducted on experimental reconstructions of finite beta W7-AS discharges. In agreement with past experimental and computational analysis, it is shown that (i) the MHD activity is resistive, (ii) a soft beta limit is observed, when the plasma resistivity approaches the estimated experimental value, and (iii) low n MHD activity is observed at intermediate beta values. The soft beta limit is a result of the mild saturated MHD activity, such that the plasma volume remains separated into distinct sub-volumes in which field lines are ergodically confined. The limitations in the current modeling are described, alongside an outlook for characterising soft beta limits in more detail in future work.
(Video recording of talk)
W. Sengupta & N. NikulsinAsymptotic Grad-Shafranov Equations For Large Aspect Ratio High-Beta Quasisymmetric Stellarators
Abstract: We study approximate quasisymmetric MHD equilibria with finite plasma beta by expanding the magnetic field of a quasisymmetric stellarator around a vacuum field, assuming the ratio of the gradients parallel and perpendicular to the vacuum field to be small. We first expand around an axisymmetric vacuum field, which results in Freidberg's high-beta stellarator (HBS) model with quasisymmetry. We derive an elliptic Grad-Shafranov equation for three-dimensional equilibria, resolving the overdetermination problem while retaining considerable freedom in flux surface-shaping. We demonstrate that quasi-axisymmetric stellarator solutions can be obtained from a tokamak by simply applying a toroidally varying vertical shift to each poloidal plane. We also discuss linear ballooning stability for the near-axisymmetric case. We then consider the more general case and show that in contrast to the quasi-axisymmetric HBS model, the overdetermination problem can still be resolved but with constraints on flux-surface shaping. Nevertheless, we can still find classes of special solutions far from axisymmetry that satisfy the overdetermined system of equations. The most prominent class is equilibria with rotating elliptical cross-sections, but we will also present other classes of solutions.
(Video recording of talk)
11:00am-12:00 EST
A. CoelhoGlobal Fluid Simulations of Plasma Turbulence in Stellarators 
(pptx version with embedded video)
Abstract:  We present the first 3D, global, two-fluid, flux-driven simulations of plasma turbulence in stellarators with different configurations: one with an island divertor; another one corresponding to the TJ-K stellarator; and a set of equilibria with increasing torsion and ellipticity. The simulations were carried out with the GBS code [1], which solves the two-fluid drift-reduced Braginskii equations.
The vacuum magnetic field of the island divertor configuration corresponds to a 5-field period stellarator and was constructed using the Dommaschk potentials [2]. It was found that the radial particle and heat transport is mainly driven by a field-aligned mode with low poloidal wavenumber, whose origin is investigated theoretically [3]. Transport is observed to be larger on the high-field side of the device and this is explained by means of a non-local linear theory. In contrast to tokamak simulations and experiments, but in agreement with edge measurements in W7-X [4], radial propagation of coherent filamentary structures (blobs) is not observed, revealing important differences between stellarator and tokamak edge transport mechanisms.
We further present the first validation of a simulation of plasma turbulence in a stellarator configuration against experimental measurements in the TJ-K stellarator [5]. The comparison shows that GBS retrieves the main turbulence properties observed in the device, namely the fact that transport is dominated by fluctuations with low poloidal mode number.
Finally we present simulations in a set of equilibria with increasing ellipticitiy and increasing torsion generated by VMEC. The limit of zero ellipticity and zero torsion corresponds to a tokamak with circular flux surfaces, allowing to study edge turbulence in the transition between a tokamak and a stellarator.  The role of ellipticity and torsion as well as of magnetic shear is discussed.
(Video recording of talk)
11:00am-12:00 EST
S. BullerImpurity Transport In Stellarators With Implications For Stellarator Optimization
Abstract: The stellarator concept relies on careful optimization to confine trapped particle orbits. The two main approaches for confining particles in stellarators is to either optimize for quasi-symmetry or quasi-isodynamicity. The different approaches result in very different collisional impurity transport, and may require different strategies for avoiding accumulation of heavy impurities in reactor scenarios.
Quasi-isodynamic configurations, as a result of having very low parallel current, have very low collisional impurity transport. Therefore, such configurations likely have to rely on turbulence to flush out the impurities. We may thus expect quasi-isodynamic configurations optimized for low turbulent transport to be especially susceptible to accumulation of heavy impurities like tungsten. In this talk, we'll review the theory of impurity transport in stellarators, and with an eye towards potential strategies for avoiding impurity accumulation based on what we know and what we don't know.
(Video recording of talk)