Papers
- Topological Holography for Mixed-State Phases and Phase Transitions
We extend the symmetry topological field theory (SymTFT) framework to open quantum systems. Using canonical purification, we embed mixed states into a doubled (2+1)-dimensional topological order and employ the slab construction to study (1+1)-dimensional mixed-state phases through condensable algebras in the doubled SymTFT. Hermiticity and positivity of the density matrix impose additional constraints on allowable anyon condensations, enabling a systematic classification of mixed-state phases - including strong-to-weak symmetry breaking (SWSSB) and average symmetry-protected topological (ASPT) phases. We present examples of mixed-state phase transitions involving SWSSB and show how gauging within the open SymTFT framework reveals connections among different mixed-state phases.
Physics, Strongly Correlated ElectronsJul 8, 2025 - Hilbert Space Fragmentation from Generalized Symmetries
Thea Budde, Marina Kristć Marinković, Joao C. Pinto Barros
Hilbert space fragmentation refers to exponential growth in the number of dynamically disconnected Krylov sectors with system size. It is taken as evidence of ergodicity breaking, since conventional symmetries generate at most a polynomial number of sectors. However, we demonstrate that generalized symmetries can fragment the Hilbert space. Models with higher-form, subsystem, and gauge symmetries can have exponentially many symmetry sectors. We further prove that non-invertible symmetries can induce additional fragmentation within individual symmetry sectors. Fragmentation in several known models arises from generalized symmetries, and the presence of exponentially many Krylov sectors therefore does not by itself imply ergodicity breaking. Finally, we show that disorder free localization arises naturally from Krylov-restricted thermalization when sectors lack translation invariance, requiring neither ergodicity breaking nor gauge symmetry.
Physics, High Energy Physics - LatticeApr 14, 2026 - Gauging non-invertible symmetries on the lattice
Sahand Seifnashri, Shu-Heng Shao, Xinping Yang
We provide a general prescription for gauging finite non-invertible symmetries in 1+1d lattice Hamiltonian systems. Our primary example is the Rep(D$_8$) fusion category generated by the Kennedy-Tasaki transformation, which is the simplest anomaly-free non-invertible symmetry on a spin chain of qubits. We explicitly compute its lattice F-symbols and illustrate our prescription for a particular (non-maximal) gauging of this symmetry. In our gauging procedure, we introduce two qubits around each link, playing the role of "gauge fields" for the non-invertible symmetry, and impose novel Gauss's laws. Similar to the Kramers-Wannier transformation for gauging an ordinary $\mathbb{Z}_2$, our gauging can be summarized by a gauging map, which is part of a larger, continuous non-invertible cosine symmetry.
Physics, Strongly Correlated ElectronsMar 4, 2025 - A Quantum Algorithm for Nonlinear Electromagnetic Fluid Dynamics via Koopman-von Neumann Linearization
Hayato Higuchi, Yuki Ito, Kazuki Sakamoto, Keisuke Fujii, Akimasa Yoshikawa
To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational resources that scale polynomially with the number of spatial grids, which poses a significant challenge for large-scale modeling. To address this issue, this study presents a quantum algorithm for simulating the nonlinear electromagnetic fluid dynamics that govern space plasmas. We map it, by applying Koopman-von Neumann linearization, to the Schrödinger equation and evolve the system using Hamiltonian simulation via quantum singular value transformation. Our algorithm scales $O \left(s N_x \, \mathrm{polylog} \left( N_x \right) T \right)$ in time complexity with $s$, $N_x$, and $T$ being the spatial dimension, the number of spatial grid points per dimension, and the evolution time, respectively. Comparing the scaling $O \left( s N_x^s \left(T^{5/4}+T N_x\right) \right)$ for the classical method with the finite volume scheme, this algorithm achieves polynomial speedup in $N_x$. The space complexity of this algorithm is exponentially reduced from $O\left( s N_x^s \right)$ to $O\left( s \, \mathrm{polylog} \left( N_x \right) \right)$. Numerical experiments validate that accurate solutions are attainable with smaller $m$ than theoretically anticipated and with practical values of $m$ and $R$, underscoring the feasibility of the approach. As a practical demonstration, the method accurately reproduces the Kelvin-Helmholtz instability, underscoring its capability to tackle more intricate nonlinear dynamics. These results suggest that quantum computing can offer a viable pathway to overcome the computational barriers of multiscale plasma modeling.
Physics, Quantum PhysicsSep 26, 2025 - exactory: An Open Verification Market Where Writing and Verifying Research Share One Evaluation Loop
Systems that write research papers end to end now exist, and the study presenting the flagship system appears in Nature. The capacity to verify what such systems produce has not kept pace. Audits of the 2025 literature count hallucinated citations at roughly 147,000 in one year as a stated lower bound, find that most pass preprint moderation and that most of those traced into journals persist through review, and show that reviewer scores are essentially uncorrelated with bibliographic integrity. We describe exactory, an operating platform built on one premise: the evaluation loop that disciplines writing and the institution that certifies the result should be the same object. On the writing side, a client pipeline enforces, through blocking gates, that a quantitative claim enters a draft only from an evidence ledger, that a reference enters a bibliography only as a registry-rendered record, and that a draft survives blind rubric review before deposit. On the market side, anyone with an API key can file a structured, attributed verdict on a DOI-pinned version of a deposited paper. The server authors no judgment of its own; it re-runs mechanical checks as versioned procedures whose evidence is published, settles them onto the record, and displays percentile predictions only against frozen, fully disclosed cohorts. A cold-cache corruption experiment on this paper's own 47-entry bibliography measures, against the live registries, what the citation gate blocks in nine failure-mode classes, including the boundary cases a maximal-corruption design would miss. An end-to-end case study on public records traces one loop execution: verifying a hep-th preprint (and filing a checkable finding that a printed equation bound is inconsistent with its own paper), deriving a structured open problem from it, and writing, depositing, submitting, and verifying a follow-up paper within two days. This paper was itself produced by the pipeline it describes, and its pre-deposit blind reviews are reported inside it, prediction, scores, and miss included. We state what the design does not solve, and we invite researchers and agent operators to verify, challenge, and extend the record. This preprint was prepared with AI assistance. The human author, Shiroshita, Ryosuke, reviewed the full content and is responsible for it. This preprint was prepared with AI assistance. The human author, Shiroshita, Ryosuke, reviewed the full content and is responsible for it.
Aug 31, 2026 - Fixing Divergence in Carleman Linearization via Analytical Continuation
Mingshuo Zhu, Hayato Higuchi, Hokuto Iwakiri, Kouki Nakamura, Naohisa Sueishi, Shih-Yen Tseng, Shoichiro Tsutsui
Nonlinear differential equations play a crucial role in modeling a wide range of phenomena, yet their solutions remain notoriously difficult to obtain. With the rapid development of quantum computing, quantum algorithms for efficiently solving such equations are actively being explored. One promising approach is based on Carleman linearization, which transforms nonlinear differential equations into linear systems. However, this method suffers from exponential divergence beyond a certain time scale. By reformulating the solutions in terms of eigenvalues and eigenvectors, we identify that this divergence originates from the Laurent expansion outside its neighborhood of convergence. To address this issue, we insert a regularized function to the divergent solution hinted by analytical continuation. We validate this divergence-correction method on both the logistic equation and some other partial differential equations like KPP-Fisher equations and Phase-Field models under periodic conditions. We implement our method for the logistic equation using the Linear Combination of Unitaries (LCU) quantum algorithm, providing a detailed complexity and error analysis.
Physics, Quantum PhysicsJul 7, 2026 - Detailed assessment of calculating drag force with quantum computers: Explicit time-evolution precludes exponential advantage for nonlinear differential equations
John Penuel, Amara Katabarwa, Peter D. Johnson, Parker Kuklinski, Benjamin Rempfer, Collin Farquhar, Yudong Cao, Michael C. Garrett
This study examines the potential for fault-tolerant quantum computers to provide utility in fluid dynamics simulations, with a focus on drag force calculations for ship hull design. We assess whether quantum algorithms can surpass classical computational limits by generating detailed quantum resource estimates (QREs) in terms of logical qubits and $T$-gate counts. Our analysis is based on a quantum algorithm leveraging Carleman linearization of the lattice Boltzmann method (LBM), which has been suggested to offer exponential speedup. We develop efficient block encodings for LBM matrices and a method for amplitude-encoding drag force. We apply the method to the simple case of fluid flow past a sphere across a range of Reynolds numbers ($\mathrm{Re}$). We estimate the required (logical qubits)$\times$($T$-gates), finding them to be prohibitively large, ranging from $10^{21}$ to $10^{39}$. While classical simulations scale as $O(\mathrm{Re}^3)$, our QREs exhibit a modest polynomial scaling of $O(\mathrm{Re}^{2.68})$, indicating no exponential quantum advantage. We attribute this limitation to an intrinsic power-law relationship between spatial grid resolution and time-stepping requirements that is a fundamental characteristic of explicit methods for evolving nonlinear differential equations. Thus, quantum computers are unlikely to provide utility in applications that require time-evolving fluids and other systems of nonlinear differential equations.
Physics, Quantum PhysicsJun 10, 2024 - The color code, the surface code, and the transversal CNOT: NP-hardness of minimum-weight decoding
Shouzhen Gu, Lily Wang, Aleksander Kubica
The decoding problem is a ubiquitous algorithmic task in fault-tolerant quantum computing, and solving it efficiently is essential for scalable quantum computing. Here, we prove that minimum-weight decoding is NP-hard in three quintessential settings: (i) the color code with Pauli $Z$ errors, (ii) the surface code with Pauli $X$, $Y$ and $Z$ errors, and (iii) the surface code with a transversal CNOT gate, Pauli $Z$ and measurement bit-flip errors. Our results show that computational intractability already arises in basic and practically relevant decoding problems central to both quantum memories and logical circuit implementations, highlighting a sharp computational complexity separation between minimum-weight decoding and its approximate realizations.
Physics, Quantum PhysicsMar 23, 2026 - Non-linear Sigma Model for the Surface Code with Coherent Errors
Stephen W. Yan, Yimu Bao, Sagar Vijay
The surface code is a promising platform for a quantum memory, but its threshold under coherent errors remains incompletely understood. We study maximum-likelihood decoding of the square-lattice surface code in the presence of single-qubit unitary rotations that create electric anyon excitations. We microscopically derive a non-linear sigma model with target space $\mathrm{SO}(2n)/\mathrm{U}(n)$ as the effective long-distance theory of this decoding problem, with distinct replica limits: $n\to1$ for optimal decoding, which assumes knowledge of the coherent rotation angle, and $n\to0$ for suboptimal decoding with imperfect angle information. This exposes a sharp distinction between the two decoders. The suboptimal decoder supports a "thermal-metal" phase, a non-decodable regime that is qualitatively distinct from the conventional non-decodable phase of the surface code under incoherent Pauli errors. By contrast, the metal phase cannot arise in optimal decoding, since the metallic fixed-point becomes unstable in the $n\to 1$ replica limit. We argue that optimal decoding may be possible up to the maximally-coherent rotation angle. Within the sigma model description, we show that the decoding fidelity is related to twist defects of the order-parameter field, yielding quantitative predictions for its system-size dependence near the metallic fixed point for both decoders. We examine our analytic predictions for the decoding fidelity as well as other physical observables with extensive numerical simulations. We discuss how the symmetries and the target space for the sigma model rely on the lattice of the surface code, and how a stable thermal metal phase can arise in optimal decoding when the syndromes reside on a non-bipartite lattice.
Physics, Statistical MechanicsMar 26, 2026 - Machine Learning Decoding of Circuit-Level Noise for Bivariate Bicycle Codes
John Blue, Harshil Avlani, Zhiyang He, Liu Ziyin, Isaac L. Chuang
Fault-tolerant quantum computers will depend crucially on the performance of the classical decoding algorithm which takes in the results of measurements and outputs corrections to the errors inferred to have occurred. Machine learning models have shown great promise as decoders for the surface code; however, this promise has not yet been substantiated for the more challenging task of decoding quantum low-density parity-check (QLDPC) codes. In this paper, we present a recurrent, transformer-based neural network designed to decode circuit-level noise on Bivariate Bicycle (BB) codes. For the $[[72,12,6]]$ BB code, at a physical error rate of $p=0.1\%$, our model achieves logical error rates almost $5$ times lower than belief propagation with ordered statistics decoding (BP-OSD), and roughly $5$ times larger than a most-likely error decoder. Moreover, while BP-OSD has a wide distribution of runtimes with significant outliers, our model has a consistent runtime and is an order-of-magnitude faster than the worst-case times from a benchmark BP-OSD implementation. On the $[[144,12,12]]$ BB code, our model obtains worse logical error rates but maintains the speed advantage. These results provide initial evidence that machine learning decoders can out-perform conventional decoders on small QLDPC codes, but suggest more complex architectures and/or training procedures are necessary to scale to larger code sizes.
Physics, Quantum PhysicsApr 17, 2025 - Classical shadows over symmetric spaces
Rebecca Chang, Maureen Krumtünger, Martin Larocca, Maxwell West
Efficiently learning expectation values of unknown quantum states via classical shadows has become an important primitive in both theoretical and experimental aspects of quantum computation. Typically, classical shadow protocols involve randomised measurements induced by sampling uniformly randomly from a compact group, a situation which is now quite well understood. In this work we go beyond this standard assumption, studying the classical shadow protocols occasioned by sampling uniformly randomly from the so-called compact symmetric spaces. We uncover a unifying theory of such protocols, extending the extent to which the general theory of classical shadows is understood at a mathematical level. Interestingly, for the estimation of observables sampled from certain distributions we further find that some of these protocols allow for slight improvements in sample-complexity over existing shadow schemes.
Physics, Quantum PhysicsMay 6, 2026 - Universal Sample Complexity Bounds in Quantum Learning Theory via Fisher Information Matrix
Hyukgun Kwon, Seok Hyung Lie, Liang Jiang
We show that the sample complexity required in quantum learning theory within a general parametric framework is fundamentally governed by the inverse Fisher information matrix. More specifically, we derive upper and lower bounds on the number of samples required to estimate the parameters of a quantum system within a prescribed small additive error, with high success probability under maximum-likelihood estimation. Notably, both the upper and lower bounds are determined by the supremum of the maximum diagonal entry of the inverse Fisher information matrix. We then apply the general bounds to Pauli channel learning and Pauli expectation value learning, which serve as representative tasks in quantum channel and state learning, respectively, in the asymptotic small-error regime. Furthermore, we identify the structural origin of exponential sample complexity in Pauli channel learning without entanglement and in Pauli expectation value learning without quantum memory by comparing the quantum Fisher information matrix and the classical Fisher information matrix. We then extend the analysis to an error criterion based on the Euclidean distance between the true parameter values and their estimators, deriving the corresponding upper and lower bounds on the sample complexity, which are likewise characterized by the inverse Fisher information matrix. As an application, we consider Pauli channel learning with entangled probes. We highlight two fundamental contributions to quantum learning theory. First, we establish a systematic framework that determines the task-independent sample complexity under maximum-likelihood estimation. Second, we show that, in the small-error regime, the learning sample complexity is governed by the inverse Fisher information matrix, which is the central quantity in quantum metrology that determines the ultimate achievable mean squared error.
Physics, Quantum PhysicsFeb 25, 2026 - Ansatz-free Hamiltonian learning with Heisenberg-limited scaling
Hong-Ye Hu, Muzhou Ma, Weiyuan Gong, Qi Ye, Yu Tong, Steven T. Flammia, Susanne F. Yelin
Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that interactions are local, but this assumption may not hold for arbitrary Hamiltonians. Previous methods all require high-order inverse polynomial dependency with precision, unable to surpass the standard quantum limit and reach the gold standard Heisenberg-limited scaling. Whether Heisenberg-limited Hamiltonian learning is possible without prior assumptions about the interaction structures, a challenge we term \emph{ansatz-free Hamiltonian learning}, remains an open question. In this work, we present a quantum algorithm to learn arbitrary sparse Hamiltonians without any structure constraints using only black-box queries of the system's real-time evolution and minimal digital controls to attain Heisenberg-limited scaling in estimation error. Our method is also resilient to state-preparation-and-measurement errors, enhancing its practical feasibility. We numerically demonstrate our ansatz-free protocol for learning physical Hamiltonians and validating analog quantum simulations, benchmarking our performance against the state-of-the-art Heisenberg-limited learning approach. Moreover, we establish a fundamental trade-off between total evolution time and quantum control on learning arbitrary interactions, revealing the intrinsic interplay between controllability and total evolution time complexity for any learning algorithm. These results pave the way for further exploration into Heisenberg-limited Hamiltonian learning in complex quantum systems under minimal assumptions, potentially enabling new benchmarking and verification protocols.
Physics, Quantum PhysicsFeb 17, 2025 - Benign Overfitting with Quantum Kernels
Joachim Tomasi, Sandrine Anthoine, Hachem Kadri
Kernel methods compare inputs through feature maps. Quantum kernels follow the same principle: input data are encoded into quantum states, which define quantum feature representations in Hilbert spaces. Kernel values are then obtained by estimating inner products between these states using suitable quantum circuit measurements. As a result, quantum kernels may be intractable to compute classically while remaining efficiently computable on quantum hardware, potentially leading to a quantum advantage. However, designing effective quantum kernels remains a major challenge. Many quantum kernels, such as the fidelity kernel, suffer from exponential concentration. This results in near-identity kernel matrices that fail to capture meaningful data correlations and lead to overfitting and poor generalization. In this paper, we propose a novel strategy for constructing quantum kernels that achieve good generalization performance, drawing inspiration from benign overfitting in classical machine learning. We introduce the concept of Local-Global quantum kernels, which combine two components: a local quantum kernel based on measurements of small subsystems, and a global quantum kernel derived from full-system measurements. To support the effectiveness of the proposed construction, we show theoretically and empirically that Local-Global quantum kernels exhibit benign overfitting.
Physics, Quantum PhysicsMar 21, 2025 - A unifying account of warm start guarantees for patches of quantum landscapes
Hela Mhiri, Ricard Puig, Sacha Lerch, Manuel S. Rudolph, Thiparat Chotibut, Supanut Thanasilp, Zoë Holmes
Barren plateaus are fundamentally a statement about quantum loss landscapes on average but there can, and generally will, exist patches of barren plateau landscapes with substantial gradients. Previous work has studied certain classes of parameterized quantum circuits and found example regions where gradients vanish at worst polynomially in system size. Here we present a general bound that unifies all these previous cases and that can tackle physically-motivated ansätze that could not be analyzed previously. Concretely, we analytically prove a lower-bound on the variance of the loss that can be used to show that in a non-exponentially narrow region around a point with curvature the loss variance cannot decay exponentially fast. This result is complemented by numerics and an upper-bound that suggest that any loss function with a barren plateau will have exponentially vanishing gradients in any constant radius subregion. Our work thus suggests that while there are hopes to be able to warm-start variational quantum algorithms, any initialization strategy that cannot get increasingly close to the region of attraction with increasing problem size is likely inadequate.
Physics, Quantum PhysicsFeb 11, 2025 - On the relation between trainability and dequantization of variational quantum learning models
Elies Gil-Fuster, Casper Gyurik, Adrián Pérez-Salinas, Vedran Dunjko
The quest for successful variational quantum machine learning (QML) relies on the design of suitable parametrized quantum circuits (PQCs), as analogues to neural networks in classical machine learning. Successful QML models must fulfill the properties of trainability and non-dequantization, among others. Recent works have highlighted an intricate interplay between trainability and dequantization of such models, which is still unresolved. In this work we contribute to this debate from the perspective of machine learning, proving a number of results identifying, among others when trainability and non-dequantization are not mutually exclusive. We begin by providing a number of new somewhat broader definitions of the relevant concepts, compared to what is found in other literature, which are operationally motivated, and consistent with prior art. With these precise definitions given and motivated, we then study the relation between trainability and dequantization of variational QML. Next, we also discuss the degrees of "variationalness" of QML models, where we distinguish between models like the hardware efficient ansatz and quantum kernel methods. Finally, we introduce recipes for building PQC-based QML models which are both trainable and nondequantizable, and corresponding to different degrees of variationalness. We do not address the practical utility for such models. Our work however does point toward a way forward for finding more general constructions, for which finding applications may become feasible.
Physics, Quantum PhysicsJun 11, 2024 - A Weakly Nonlinear Theory of Zonal-Flow Forcing in Gyrokinetic Turbulence
Georgia Acton, Eduardo Rodrìguez, Gareth Roberg-Clark, Alessandro Zocco
The forced generation of zonal flows by microinstability-driven turbulence is investigated within the framework of local gyrokinetic theory far from marginality. We use a numerically and physically informed three-wave truncation scheme, which allows the prediction of the zonal-flow k_ψ-spectrum during the early phase of nonlinear gyrokinetic simulations. The model reproduces the known 2-γgrowth rate resulting from nonlinear beating of linearly unstable primary modes, in line with previous results, without any marginal stability point. The phase-space structure of such zonal flow is strongly constrained by that of the driving fluctuations, which is essential to understand its behaviour in the region of validity. It is shown that this leads to an enhanced residual spectrum compared to the classic Rosenbluth-Hinton calculation.
Physics, Plasma PhysicsJun 26, 2026 - On Phase Transition of ITG Turbulence in the Dimits shift
L. N. Marquant, P. Morel, Ö. D. Gürcan
The transition between turbulent and zonal flow dominated states is investigated by varying the ion temperature gradient in nonlinear gyrokinetic simulations. Independent gradient scans reveal three distinct regimes: a turbulent regime at high gradients, a zonal flow dominated regime with strongly reduced heat transport at low gradients, and an intermediate regime characterized by intermittent switching between these two states. These different regimes can be classified using an order parameter, defined as the fraction of the zonal to total free energy in the system. To assess the memory effects, the temperature gradient is first lowered gradually from high values that result in fully developed turbulence, to lower values in the Dimits shift region that form strong zonal flows, and then is slowly increased back. Once the zonal flows form, and efficiently suppress turbulence, they can persist at higher gradients, leading to an asymmetric response implying a hysteresis loop. It is observed that, in the zonal flow dominated state, the free energy is mostly condensated in the largest radial scale, with a steep slope of the $k_x$ spectrum, while in the turbulent state, it exhibits a wider spectrum with two distinct slopes.
Physics, Plasma PhysicsMay 26, 2026 - A Ritz variational principle for local collisionless gyrokinetic instabilities
Turbulence driven by gyrokinetic instabilities is largely responsible for transport in magnetic fusion devices. To estimate this turbulent transport, integrated modeling codes often use mixing length estimates in conjunction with reduced models of the linearized gyrokinetic equation. One common method of formulating and solving the linearized gyrokinetic eigenvalue problem equation uses a Ritz variational principle, particularly in the local collisionless limit. However, the variational principle as typically stated in the literature is mathematically incorrect. In this work, we derive a mathematically correct form of the variational principle that applies to local linear collisionless gyrokinetics in general geometry with electromagnetic effects. We also explicitly derive a weak form of the gyrokinetic field equations suitable for numerical applications.
Physics, Plasma PhysicsJan 1, 2025 - Eliminating Tokamak Disruptions with Feedback
Many disruptions are caused by resistive wall tearing modes (RWTM). A database of DIII-D locked mode disruptions provides two main disruption criteria, which are shown to be signatures of RWTMs. The first is that the q = 2 rational surface must be sufficiently close the resistive wall surrounding the plasma to interact with it. If active feedback is used, this implies that RWTMs can be prevented from causing major disruptions. This is demonstrated in simulations. The second criterion is that the current profile is sufficiently peaked. This is caused by edge cooling, such as by impurity radiation and turbulence, which suppress edge current and temperature. This implies the disruptions are not caused by neoclassical tearing modes (NTM), because the bootstrap current is also suppressed. The dependence of the critical internal inductance on elongation is given, which suggests that elongation might be used as an actuator to prevent disruptions. At high $β,$ resistive wall modes (RWM) can be stabilized with feedback. Feedback also stabilizes high $β$ RWTMs, as shown in NSTX data and in simulations. These results suggest that RWTM disruptions in ITER might be prevented using the resonant magnetic perturbation (RMP) coils.
Physics, Plasma PhysicsAug 18, 2025 - Quasilinear drift kinetic theory of alpha particle transport by neoclassical tearing modes
Elizabeth A. Tolman, Peter J. Catto
Kinetic theory of particles near resonances is a current topic of discussion in plasma physics and astrophysics. We extend this discussion to the kinetic theory of the interaction between alpha particles (energetic particles predicted to exist in large quantities in next-generation fusion experiments) and a neoclassical tearing mode (NTM), a resistively-driven perturbation that sometimes exists in a tokamak. We develop a quasilinear treatment of the interaction between alphas and an NTM, showing why an NTM can be a source of significant passing alpha particle transport in tokamaks. The limitations on quasilinear theory constrain our theory's applicability to small amplitude NTMs, highlighting the importance of nonlinear studies.
Physics, Plasma PhysicsJun 19, 2024 - Direct prediction of saturated neoclassical tearing modes in slab using an equilibrium approach
Erol Balkovic, Joaquim Loizu, Jonathan P. Graves, Yi-Min Huang, Christopher B. Smiet
We demonstrate for the first time that the nonlinear saturation of neoclassical tearing modes (NTMs) can be found directly using a variational principle based on Taylor relaxation, without needing to simulate the intermediate, resistivity-dependent dynamics. As in previous investigations of classical tearing mode saturation (Loizu et al. 2020; Loizu & Bonfiglio 2023), we make use of SPEC (Hudson et al. 2012), an equilibrium solver based on the variational principle of the Multi-Region relaxed MHD, featuring stepped pressure profiles and arbitrary magnetic topology. We work in slab geometry and employ a simple bootstrap current model $J_\textrm{bs} = C \nabla p$ to study the bootstrap-driven tearing modes, scanning over the asymptotic matching parameter $Δ'$ and the bootstrap current strength. Saturated island widths produced by SPEC agree well with the predictions of an initial value resistive MHD code (Huang & Bhattacharjee 2016) while being orders of magnitude faster to calculate. Additionally, we observe good agreement with a simple analytical Modified Rutherford Equation, without requiring any fitting coefficients. The match is obtained for both linearly unstable classical tearing modes in the presence of bootstrap current, and neoclassical tearing modes, which are linearly stable but nonlinear-unstable due to the effects of the bootstrap current
Physics, Plasma PhysicsJul 4, 2024 - Symmetry-agnostic stellarators for collisionless confinement
W. Sengupta, A. Bhattacharjee, S. Buller
Quasisymmetry, omnigenity and piecewise omnigenity confine trapped particles by making the bounce action independent of the field-line label. Recent optimizations produce mixed-symmetry stellarators that confine alpha particles well without them. We propose a general theory for them. From Whitham modulation theory we define iso-action, which requires only that the drift surface close and allows misalignment with flux surfaces. A solvable model supplies an exact relation between trapped segments while branch actions vary. We develop a proxy $Γ_W$ for the reach that misalignment costs.
Physics, Plasma PhysicsAug 20, 2026 - The High-Order Magnetic Near-Axis Expansion: Ill-Posedness and Regularization
Maximilian Ruth, Rogerio Jorge, David Bindel
When analyzing stellarator configurations, it is common to perform an asymptotic expansion about the magnetic axis. This so-called near-axis expansion is convenient for the same reason asymptotic expansions often are, namely, it reduces the dimension of the problem. This leads to convenient and quickly computed expressions of physical quantities, such as quasisymmetry and stability criteria, which can be used to gain further insight. However, it has been repeatedly found that the expansion diverges at high orders in the distance from axis, limiting the physics the expansion can describe. In this paper, we show that the near-axis expansion diverges in vacuum due to ill-posedness and that it can be regularized to improve its convergence. Then, using realistic stellarator coil sets, we demonstrate numerical convergence of the vacuum magnetic field and flux surfaces to the true values as the order increases. We numerically find that the regularization improves the solutions of the near-axis expansion under perturbation, and we demonstrate that the radius of convergence of the vacuum near-axis expansion is correlated with the distance from the axis to the coils.
Physics, Plasma PhysicsNov 7, 2024 - Characterization of admissible quasisymmetries
J. W. Burby, N. Kallinikos, R. S. MacKay, D. Perrella, D. Pfefferlé
We solve "half" the problem of finding three-dimensional quasisymmetric magnetic fields that do not necessarily satisfy force balance. This involves determining which hidden symmetries are admissible as quasisymmetries, and then showing explicitly how to construct quasisymmetric magnetic fields given an admissible symmetry. The admissibility conditions take the form of a system of overdetermined nonlinear partial differential equations involving second derivatives of the symmetry's infinitesimal generator.
Physics, Plasma PhysicsMar 5, 2024