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DOE OSTI2024

Asymptotic quasisymmetric high-beta three-dimensional magnetohydrodynamic equilibria near axisymmetry

Quasisymmetry (QS), a hidden symmetry of the magnetic field strength, is known to support nested flux surfaces and provide superior particle confinement in stellarators. In this work, we study the ideal magnetohydrodynamic (MHD) equilibrium and stability of high-beta plasma in a large-aspect-ratio stellarator. In particular, we show that the lowest-order description of a near-axisymmetric equilibrium vastly simplifies the problem of three-dimensional quasisymmetric MHD equilibria, which can be reduced to a standard elliptic Grad–Shafranov equation for the flux function. We show that any large-aspect-ratio tokamak, deformed periodically in the vertical direction, is a stellarator with approximate volumetric QS. We discuss exact analytical solutions and numerical benchmarks. Finally, we discuss the ideal ballooning and interchange stability of some of our equilibrium configurations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Effect of insulator end cap thickness on time-dependent Hartmann flow in a rotating mirror

We present a framework for analysing plasma flow in a rotating mirror. By making a series of physical assumptions, we reduce the magnetohydrodynamic (MHD) equations in a three-dimensional cylindrical system to a one-dimensional system in a shallow, cuboidal channel within a transverse magnetic field, similar to the Hartmann flow in ducts. We then solve the system both numerically and analytically for a range of values of the Hartmann number and calculate the dependence of the plasma flow speed on the thickness of the insulating end cap. We observe that the mean flow overshoots and decelerates before achieving a steady-state value, a phenomenon that the analytical model cannot capture. This overshoot is directly proportional to the thickness of the insulating end cap and the external electric field, with a weak dependence on the external magnetic field. Our simplified model can act as a benchmark for future simulations of the supersonic mirror device CMFX (centrifugal magnetic fusion experiment), which will employ more sophisticated physics and realistic magnetic field geometries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Self-organization in collisionless, high- β turbulence

The magnetohydrodynamic (MHD) equations, as a collisional fluid model that remains in local thermodynamic equilibrium (LTE), have long been used to describe turbulence in myriad space and astrophysical plasmas. Yet, the vast majority of these plasmas, from the solar wind to the intracluster medium (ICM) of galaxy clusters, are only weakly collisional at best, meaning that significant deviations from LTE are not only possible but common. Recent studies have demonstrated that the kinetic physics inherent to this weakly collisional regime can fundamentally transform the evolution of such plasmas across a wide range of scales. Here, we explore the consequences of pressure anisotropy and Larmor-scale instabilities for collisionless, β $\gg$ 1, turbulence, focusing on the role of a self-organizational effect known as ‘magneto-immutability’. We describe this self-organization analytically through a high-β, reduced ordering of the Chew–Goldberger–Low-MHD (CGL-MHD) equations, finding that it is a robust inertial-range effect that dynamically suppresses magnetic-field-strength fluctuations, anisotropic-pressure stresses and dissipation due to heat fluxes. As a result, the turbulent cascade of Alfvénic fluctuations continues below the putative viscous scale to form a robust, nearly conservative, MHD-like inertial range. These findings are confirmed numerically via Landau-fluid CGL-MHD turbulence simulations that employ a collisional closure to mimic the effects of microinstabilities. We find that microinstabilities occupy a small (~5%) volume-filling fraction of the plasma, even when the pressure anisotropy is driven strongly towards its instability thresholds. We discuss these results in the context of recent predictions for ion-vs-electron heating in low-luminosity accretion flows and observations implying suppressed viscosity in ICM turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

On reduced modelling of the modulational dynamics in magnetohydrodynamics

This paper explores structure formation in two-dimensional magnetohydrodynamic (MHD) turbulence as a modulational instability (MI) of turbulent fluctuations. We focus on the early stages of structure formation and consider simple backgrounds that allow for a tractable model of the MI while retaining the full chain of modulational harmonics. This approach allows us to systematically examine the validity of popular closures such as the quasilinear approximation and other low-order truncations. We find that, although such simple closures can provide quantitatively accurate approximations of the MI growth rates in some regimes, they can fail to capture the modulational dynamics in adjacent regimes even qualitatively, falsely predicting MI when the system is actually stable. We find that this discrepancy is due to the excitation of propagating spectral waves (PSWs) which can ballistically transport energy along the modulational spectrum, unimpeded until dissipative scales, thereby breaking the feedback loops that would otherwise sustain MIs. The PSWs can be self-maintained as global modes with real frequencies and drain energy from the primary structure at a constant rate until the primary structure is depleted. To describe these waves within a reduced model, we propose an approximate spectral closure that captures them and MIs on the same footing. We also find that introducing corrections to ideal MHD, conservative or dissipative, can suppress PSWs and reinstate the accuracy of the quasilinear approximation. In this sense, ideal MHD is a ‘singular’ system that is particularly sensitive to the accuracy of the closure within mean-field models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Mean-field dynamo as a quantum-like modulational instability

Presented here is a novel formulation of the mean-field dynamo as a modulational instability of magnetohydrodynamic (MHD) turbulence. This formulation, termed mean-field wave kinetics (MFWK), is based on the Weyl symbol calculus and allows describing the interaction between the mean fields (magnetic field and fluid velocity) and turbulence without requiring scale separation that is commonly assumed in the literature. The turbulence is described by the Wigner–Moyal equation for the spectrum of the two-point correlation matrix (Wigner matrix) of magnetic-field and velocity fluctuations and depicts the turbulence as an effective plasma of quantum-like particles that interact via the mean fields. Eddy–eddy interactions, which serve as ‘collisions’ in this effective plasma, are modelled within the standard minimal tau approximation to aid comparison with existing theories. Using MFWK, the non-local electromotive force is calculated for generic turbulence from first principles, modulo the limitations of MFWK. This result is then used to study, both analytically and numerically, the modulational modes of MHD turbulence, which appear as linear instabilities of the said effective quantum-like plasma of fluctuations. The standard α 2 -dynamo and other known results are reproduced as special cases. A new dynamo effect is predicted that is driven by correlations between the turbulent flow velocity and the turbulent current.

astrophysical plasmas↗
DOE OSTI2025

Bootstrap current modeling in M3D-C1

Bootstrap current plays a crucial role in the equilibrium of magnetically confined plasmas, particularly in quasi-symmetric stellarators and in tokamaks, where it can represent bulk of the electric current density. Accurate modeling of this current is essential for understanding the magnetohydrodynamic (MHD) equilibrium and stability of these configurations. This study expands the modeling capabilities of M3D-C1, an extended-MHD code, by implementing self-consistent physics models for bootstrap current. It employs two analytical frameworks: a generalized Sauter model (Sauter et al. 1999 Phys. Plasmas vol. 6, no. 7, pp. 2834–2839), and a revised Sauter-like model (Redl et al. 2021 Phys. Plasmas vol. 28, no. 2, pp. 022502). The isomorphism described by Landreman et al. (2022 Phys. Rev. Lett. vol. 128, pp. 035001) is employed to apply these models to quasi-symmetric stellarators. The implementation in M3D-C1 is benchmarked against neoclassical codes, including NEO, XGCa and SFINCS, showing excellent agreement. These improvements allow M3D-C1 to self-consistently calculate the neoclassical contributions to plasma current in axisymmetric and quasi-symmetric configurations, providing a more accurate representation of the plasma behavior in these configurations. A workflow for evaluating the neoclassical transport using SFINCS with arbitrary toroidal equilibria calculated using M3D-C1 is also presented. This workflow enables a quantitative evaluation of the error in the Sauter-like model in cases that deviate from axi- or quasi-symmetry (e.g. through the development of an MHD instability).

fusion plasma↗
DOE OSTI2026

ARC physics basis–magnetohydrodynamics

ARC is designed to produce 400 ⁢MW of net electricity and prove the commercial feasibility of a fusion power plant. In order to achieve this goal ARC has to operate with optimal core performance in a stationary scenario that minimises wear on the first wall and divertor. This requires avoiding or mitigating magnetohydrodynamic (MHD) instabilities which have the potential to not only degrade the plasma core but also lead to deleterious transient heat loads on plasma facing components. Therefore, this work aims at characterising the MHD stability of the high performance ARC scenario and inform the design of error field correction coils. Firstly, simulations of vertical displacement events show that an in-vessel coil is not needed and instead the poloidal shaping coils can be used to control vertical stability. These simulations also inform the demands on the corresponding coil power supplies. Stability analysis of the ideal kink mode with or without a conducting wall and kinetic effects suggests that the ARC baseline scenario operates deeply in the stable region. Using RDCON, tearing modes at the 𝑚/𝑛 =2/1 and 3/2 surfaces (with poloidal mode number 𝑚, and toroidal mode number 𝑛) are shown to be linearly stable, and including thermal transport effects in the rational surfaces lead to further stabilisation. However, other transient plasma instabilities can seed neoclassical tearing modes (NTMs). The marginally stable width of NTMs in ARC strongly depends on the internal inductance and can fall below 0.1% of the normalised poloidal flux. Furthermore, an empirical cross-machine model of the 𝑛 =1 error field leading to a disruption predicts a critical error field larger than SPARC but smaller than ITER. Three-dimensional coils can be designed with the Generalised Purturbed Equilbium Code based on a simple model that calculates the maximum correctable error field that is limited by the neoclassical toroidal viscosity torque. Broad scans of different coil geometries identify a set of 2 rows of off-midplane coils to be a suitable solution. It is also determined that such a set of three-dimensional coils is capable of correcting 𝑛 =2 error fields to some degree and creating strong enough 𝑛 =2 or 𝑛 =3 edge resonant perturbation fields for the suppression of edge-localised modes at reasonable coil currents. The final design of the first ARC will be further informed by results from SPARC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Narrow operator models of stellarator equilibria in Fourier Zernike basis

Numerical computation of the ideal magnetohydrodynamic (MHD) equilibrium magnetic field is at the base of stellarator optimisation and provides the starting point for solving more sophisticated partial differential equations like transport or turbulence models. Conventional approaches solve for a single stationary point of the ideal MHD equations, which is fully defined by three invariants and the numerical scheme employed by the solver. We present the first numerical approach that can solve for a continuous distribution of equilibria with fixed boundary and rotational transform, varying only the pressure invariant. This approach minimises the force residual by optimising parameters of multilayer perceptrons that map from a scalar pressure multiplier to the Fourier Zernike basis as implemented in the modern stellarator equilibrium solver DESC.

fusion plasma↗
DOE OSTI2020

Using Multiple Signatures to Improve Accuracy of Substorm Identification

Abstract We have developed a new procedure for combining lists of substorm onset times from multiple sources. We apply this procedure to observational data and to magnetohydrodynamic (MHD) model output from 1–31 January 2005. We show that this procedure is capable of rejecting false positive identifications and filling data gaps that appear in individual lists. The resulting combined onset lists produce a waiting time distribution that is comparable to previously published results, and superposed epoch analyses of the solar wind driving conditions and magnetospheric response during the resulting onset times are also comparable to previous results. Comparison of the substorm onset list from the MHD model to that obtained from observational data reveals that the MHD model reproduces many of the characteristic features of the observed substorms, in terms of solar wind driving, magnetospheric response, and waiting time distribution. Heidke skill scores show that the MHD model has statistically significant skill in predicting substorm onset times.

Haiducek, John D.↗
DOE OSTI2020

Characterizing Mars's Magnetotail Topology With Respect to the Upstream Interplanetary Magnetic Fields

The canonical picture of the magnetotail of unmagnetized planets consists of draped interplanetary magnetic fields (IMFs) forming opposite-directed lobes, separated by the current sheet. DiBraccio et al. (2018, https://doi.org/10.1029/2018GL077251) showed that Mars's magnetotail has a twist departing from this picture. Magnetohydrodynamic (MHD) results suggest that the asymmetry in how open field lines connected to the planet populate the tail causes the apparent twist. To validate this interpretation, we compare the tail topology determined from MHD simulations to that inferred from data collected by the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft, in particular, how each topology responds to the upstream IMF orientation. The occurrence rates for open topology from both data and MHD vary with IMF polarities in a similar fashion as the tail twisting. This suggests that Mars's crustal fields have a global effect on the magnetosphere configuration, supporting the picture of a “hybrid” magnetotail that is partly induced/draped and partly intrinsic/planetary in origin.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Plasma Properties in the Earth's Magnetosheath Near the Subsolar Magnetopause: Implications for Geocoronal Density Estimates

Combined in situ ion measurements and remote sensing of energetic neutral atoms are used to determine the geocoronal Hydrogen density at large (∼10 R E ) distances from the Earth. This method for determining the geocoronal density requires global magnetospheric modeling. Observations in the Earth's subsolar magnetosheath from the Magnetospheric Multiscale mission are used to determine the accuracy of using global models to predict the geocoronal density. On average, gas dynamic and magnetohydrodynamic (MHD) models and observations are in reasonable agreement, with differences <25%. In addition, the MHD model subsolar magnetopause is about 0.5 R E sunward of the observed location. However, variations around averages are large (up to a factor of 2), indicating that global models introduce relatively large uncertainties in geocoronal density estimates. Finally, the critical ion flux in the Interstellar Boundary Explorer IBEX‐Hi energy range is often minimally affected by fluctuations of a factor of 2 in the density.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Identification of a non-axisymmetric mode in laboratory experiments searching for standard magnetorotational instability

Abstract The standard magnetorotational instability (SMRI) is a promising mechanism for turbulence and rapid accretion in astrophysical disks. It is a magnetohydrodynamic (MHD) instability that destabilizes otherwise hydrodynamically stable disk flow. Due to its microscopic nature at astronomical distances and stringent requirements in laboratory experiments, SMRI has remained unconfirmed since its proposal, despite its astrophysical importance. Here we report a nonaxisymmetric MHD instability in a modified Taylor-Couette experiment. To search for SMRI, a uniform magnetic field is imposed along the rotation axis of a swirling liquid-metal flow. The instability initially grows exponentially, becoming prominent only for sufficient flow shear and moderate magnetic field. These conditions for instability are qualitatively consistent with SMRI, but at magnetic Reynolds numbers below the predictions of linear analyses with periodic axial boundaries. Three-dimensional numerical simulations, however, reproduce the observed instability, indicating that it grows linearly from the primary axisymmetric flow modified by the applied magnetic field.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Identification of the weak-to-strong transition in Alfvénic turbulence from space plasma

Abstract Plasma turbulence is a ubiquitous dynamical process that transfers energy across many spatial and temporal scales in astrophysical and space plasma systems. Although the theory of anisotropic magnetohydrodynamic (MHD) turbulence has successfully described natural phenomena, its core prediction of an Alfvénic transition from weak to strong MHD turbulence when energy cascades from large to small scales has not been observationally confirmed. Here we report evidence for the Alfvénic weak-to-strong transition in small-amplitude, turbulent MHD fluctuations in Earth’s magnetosheath using data from four Cluster spacecraft. Our observations demonstrate the universal existence of strong turbulence accompanied by weak turbulent fluctuations on large scales. Moreover, we find that the nonlinear interactions of MHD turbulence are crucial to the energy cascade, as they broaden the cascade directions and fluctuating frequencies. The observed connection between weak and strong MHD turbulence systems may be present in many astrophysical environments, such as star formation, energetic particle transport, turbulent dynamos, and solar corona or solar wind heating.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Hints of primordial magnetic fields at recombination and implications for the Hubble tension

Primordial Magnetic Fields (PMFs), long studied as relics of the early Universe, accelerate recombination and have been proposed as a way to relieve the Hubble tension. However, previous studies relied on simplified toy models. Here, in this study, we use recent evaluations of recombination with PMFs, incorporating full magnetohydrodynamic (MHD) simulations and detailed Lyman-alpha radiative transfer, to test PMF-enhanced recombination (bΛCDM) against observational data from the cosmic microwave background (CMB), baryon acoustic oscillations (BAO), and Type Ia supernovae (SN). Focusing on non-helical PMFs with a Batchelor spectrum, we find a preference for presentday total field strengths of approximately 5-10 pico-Gauss. Depending on the dataset combination, this preference ranges from mild (∼ 1.8σ with Planck + DESI) to moderate (∼ 3σ with Planck + DESI + SH0ES-calibrated SN) significance. The bΛCDM has Planck + DESI χ 2 values equal to or better than ΛCDM while predicting a higher Hubble constant. Future high-resolution CMB temperature and polarization measurements will be crucial for confirming or further constraining PMFs at recombination. Field strengths of 5-10 pico-Gauss align closely with those required for cluster magnetic fields to originate entirely from primordial sources, without the need for additional dynamo amplification.

Jedamzik, Karsten [Centre National de la Recherche↗
DOE OSTI2026

Nature of transonic sub-Alfvénic turbulence and density fluctuations in the near-Sun solar wind

Context. Recent Parker Solar Probe (PSP) measurements have revealed that solar wind (SW) turbulence transits from a subsonic to a transonic regime near the Sun, while remaining sub-Alfvénic. These observations call for a revision of the existing SW models, where turbulence is considered to be both subsonic and sub-Alfvénic. Aims. In this work, we introduce a new magnetohydrodynamic (MHD) model of transonic sub-Alfvénic turbulence (TsAT). Methods. We used 3D MHD simulations initialized with parameters measured by PSP to investigate the properties of the new near-Sun SW transonic turbulent regime. We then derived a reduced set of MHD equations in the transonic sub-Alfvénic limit to interpret our numerical results. Results. Our TsAT model shows that turbulence is effectively nearly incompressible (NI) and has a 2D + slab (quasi-2D) geometry not only in the subsonic limit, but also in the transonic regime, as long as it remains sub-Alfvénic, a condition essentially enforced everywhere in the heliosphere by the strong local magnetic field. These predictions are consistent with 3D MHD simulations, showing that transonic turbulence is dominated by low-frequency quasi-2D incompressible structures, while compressible fluctuations are a minor component corresponding to low-frequency slow modes and high-frequency fast modes. Conclusions. Our new TsAT model extends existing NI theories of turbulence, and is potentially relevant for the theoretical and numerical modeling of space and astrophysical plasmas, including the near-Sun SW, the solar corona, and the interstellar medium.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Determination of a macro- to micro-scale progression leading to a magnetized plasma disruption

We report here the observations of a plasma jet evolving through a macro- to micro-scale progression sequence. This leads to a fast magnetic reconnection that results in the jet breaking off from its originating electrode and forming a force-free state. A sausage-like pinching occurs first and squeezes an initially fat, short magnetized jet so that it becomes thin. The thin jet then becomes kink unstable. The lengthening of the jet by the kinking thins the jet even more since the kink is an incompressible instability. When the jet radius becomes comparable to the ion-skin depth, Hall and electron inertial physics become important and establish the environment for a fast magnetic reconnection. This fast reconnection occurs, disrupting the jet and establishing a force-free state. X-ray bursts and whistler waves, evidence of a magnetic reconnection, are observed when the plasma jet breaks off from the electrode. This experimentally confirmed sequence of successive thinning from pinching followed by kinking is reproduced in a three-dimensional ideal Magnetohydrodynamic (MHD) numerical simulation. The results of the experiment and the numerical simulation, together demonstrate a viable path from macro-scale MHD physics to micro-scale non-MHD physics where fast reconnection occurs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Necessary and sufficient conditions for quasisymmetry

A necessary and sufficient set of conditions for a quasisymmetric magnetic field in the form of constraint equations is derived from first principles. Without any assumption regarding the magnetohydrodynamic (MHD) equilibrium of the plasma, conditions for quasisymmetry are constructed starting from the single-particle Lagrangian to the leading order. The conditions presented in the paper are less restrictive than the set recently obtained by Burby et al. [“Some mathematics for quasi-symmetry,” arXiv:1912.06468 (2019)], and could facilitate ongoing efforts toward investigating the existence of global quasisymmetric MHD equilibria. Finally, it is also shown that quasisymmetry implies the existence of flux surfaces, regardless of whether the field corresponds to an MHD equilibrium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Eigenmode analysis of the sheared-flow Z-pinch

Experiments have demonstrated that a Z-pinch can persist for thousands of times longer than the growth time of global magnetohydrodynamic (MHD) instabilities such as the m=0 sausage and m=1 kink modes. These modes have growth times on the order of ta=a/vi, where vi is the ion thermal speed and a is the pinch radius. Axial flows with duz/dr ≲ vi/a have been measured during the stable period, and the commonly accepted theory is that this amount of shear is sufficient to stabilize these modes as predicted by numerical studies using the ideal MHD equations. However, these studies only consider specific equilibrium profiles that typically have a modest magnitude for the logarithmic pressure gradient, qP≡d ln P/d ln r, and may not represent experimental conditions. Linear stability of the sheared-flow Z-pinch is studied here via a direct eigen-decomposition of the matrix operator obtained from the linear ideal MHD equations. Several equilibrium profiles with a large variation of qP are examined. Considering a practical range of k, 1/3 ≲ ka ≲ 10, it is shown that the shear required to stabilize m=0 modes can be expressed as duz/dr≥Cγ0/(ka)α. Here, γ0=γ0(ka) is the profile-specific growth rate in the absence of shear, which scales approximately with |qP|. Both C and α are profile-specific constants, but C is order unity and α≈1. It is further demonstrated that even a large value of shear, duz/dr=3vi/a, is not sufficient to provide linear stabilization of the m=1 kink mode for all profiles considered. This result is in contrast to the currently accepted theory predicting stabilization at much lower shear, duz/dr=0.1vi/a, and suggests that the experimentally observed stability cannot be explained within the linear ideal-MHD model.

Angus, J. R. (ORCID:0000000314740002)↗