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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 OSTI2020

Magnetic well and Mercier stability of stellarators near the magnetic axis

We have recently demonstrated that by expanding in small distance from the magnetic axis compared with the major radius, stellarator shapes with low neoclassical transport can be generated efficiently. To extend the utility of this new design approach, here we evaluate measures of magnetohydrodynamic interchange stability within the same expansion. In particular, we evaluate the magnetic well, Mercier's criterion, and resistive interchange stability near a magnetic axis of arbitrary shape. In contrast to previous work on interchange stability near the magnetic axis, which used an expansion of the flux coordinates, here we use the ‘inverse expansion’ in which the flux coordinates are the independent variables. Reduced expressions are presented for the magnetic well and stability criterion in the case of quasisymmetry. The analytic results are shown to agree with calculations from the VMEC equilibrium code. Finally, we show that near the axis, Glasser, Greene and Johnson's stability criterion for resistive modes approximately coincides with Mercier's ideal condition.

Physics↗

NASA NTRS2010

Broken Ergodicity in Ideal, Homogeneous, Incompressible Turbulence

We discuss the statistical mechanics of numerical models of ideal homogeneous, incompressible turbulence and their relevance for dissipative fluids and magnetofluids. These numerical models are based on Fourier series and the relevant statistical theory predicts that Fourier coefficients of fluid velocity and magnetic fields (if present) are zero-mean random variables. However, numerical simulations clearly show that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation. We explain this phenomena in terms of broken ergodicity', which is defined to occur when dynamical behavior does not match ensemble predictions on very long time-scales. We review the theoretical basis of broken ergodicity, apply it to 2-D and 3-D fluid and magnetohydrodynamic simulations of homogeneous turbulence, and show new results from simulations using GPU (graphical processing unit) computers.

Morin, Lee↗

DOE OSTI2023

Nonlinear mode coupling and energetics of driven magnetized shear-flow turbulence

To comprehensively understand the saturation of two-dimensional (2D) magnetized Kelvin–Helmholtz-instability-driven turbulence, energy transfer analysis is extended from the traditional interaction between scales to include eigenmode interactions, by using the nonlinear couplings of linear eigenmodes of the ideal instability. While both kinetic and magnetic energies cascade to small scales, a significant fraction of turbulent energy deposited by unstable modes in the fluctuation spectrum is shown to be re-routed to the conjugate-stable modes at the instability scale. They remove energy from the forward cascade at its inception. The remaining cascading energy flux is shown to attenuate exponentially at a small scale, dictated by the large-scale stable modes. Guided by a widely used instability-saturation assumption, a general quasi-linear model of instability is tested by retaining all nonlinear interactions except those that couple to the large-scale stable modes. These complex interactions are analytically removed from the magnetohydrodynamic equations using a novel technique. Observations are an explosive large-scale vortex separation instead of the well-known merger of 2D, a dramatic enhancement in turbulence level and spectral energy fluxes, and a reduced small-scale dissipation length scale. These show the critical role of the stable modes in instability saturation. Possible reduced-order turbulence models are proposed for fusion and astrophysical plasmas, based on eigenmode-expanded energy transfer analyses.

Physics↗

NASA NTRS2001

Fluid Aspects of Solar Wind Disturbances Driven by Coronal Mass Ejections

Transient disturbances in the solar wind initiated by coronal eruptions have been modeled for many years, beginning with the self-similar analytical models of Parker and Simon and Axford. The first numerical computer code (one-dimensional, gas dynamic) to study disturbance propagation in the solar wind was developed in the late 1960s, and a variety of other codes ranging from simple one-dimensional gas dynamic codes through three-dimensional gas dynamic and magnetohydrodynamic codes have been developed in subsequent years. For the most part, these codes have been applied to the problem of disturbances driven by fast CMEs propagating into a structureless solar wind. Pizzo provided an excellent summary of the level of understanding achieved from such simulation studies through about 1984, and other reviews have subsequently become available. More recently, some attention has been focused on disturbances generated by slow CMEs, on disturbances driven by CMEs having high internal pressures, and disturbance propagation effects associated with a structured ambient solar wind. Our purpose here is to provide a brief tutorial on fluid aspects of solar wind disturbances derived from numerical gas dynamic simulations. For the most part we illustrate disturbance evolution by propagating idealized perturbations, mimicking different types of CMEs, into a structureless solar wind using a simple one-dimensional, adiabatic (except at shocks), gas dynamic code. The simulations begin outside the critical point where the solar wind becomes supersonic and thus do not address questions of how the CMEs themselves are initiated. Limited to one dimension (the radial direction), the simulation code predicts too strong an interaction between newly ejected solar material and the ambient wind because it neglects azimuthal and meridional motions of the plasma that help relieve pressure stresses. Moreover, the code ignores magnetic forces and thus also underestimates the speed with which pressure disturbances propagate in the wind.

Gosling, J. T.↗

DOE OSTI2021

Computation of linear MHD instabilities with the multi-region relaxed MHD energy principle

Over the last decade, a variational principle based on a generalisation of Taylor's relaxation, referred to as multi-region relaxed magnetohydrodynamics (MRxMHDs) has been developed. The numerical solutions of the MRxMHD equilibria have been constructed using the Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502). In principle, SPEC could also be established to describe the MRxMHD stability of an equilibrium. In this work, a theoretical framework is developed to relate the second variation of the energy functional to the so-called Hessian matrix, enabling the prediction of MHD linear instabilities of cylindrical plasmas, and is implemented in SPEC. The negative and positive eigenvalues of the Hessian matrix predict the stability of an equilibrium. Verification studies of SPEC stability results with the M3D-C 1 code and the tearing mode $\Delta^{^{\prime}}$ criterion have been conducted for ideal and resistive MHD instabilities, respectively, in a pressureless cylindrical tokamak, and have shown good agreement. Overall, our stability analysis is a critical step towards understanding the MHD stability of three-dimensional MHDs where nested flux surfaces, magnetic islands and stochastic regions co-exist.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1999

Thermodynamic Cycle Analysis of Magnetohydrodynamic-Bypass Airbreathing Hypersonic Engines

Established analyses of conventional ramjet/scramjet performance characteristics indicate that a considerable decrease in efficiency can be expected at off-design flight conditions. This can be explained, in large part, by the deterioration of intake mass flow and limited inlet compression at low flight speeds and by the onset of thrust degradation effects associated with increased burner entry temperature at high flight speeds. In combination, these effects tend to impose lower and upper Mach number limits for practical flight. It has been noted, however, that Magnetohydrodynamic (MHD) energy management techniques represent a possible means for extending the flight Mach number envelope of conventional engines. By transferring enthalpy between different stages of the engine cycle, it appears that the onset of thrust degradation may be delayed to higher flight speeds. Obviously, the introduction of additional process inefficiencies is inevitable with this approach, but it is believed that these losses are more than compensated through optimization of the combustion process. The fundamental idea is to use MHD energy conversion processes to extract and bypass a portion of the intake kinetic energy around the burner. We refer to this general class of propulsion system as an MHD-bypass engine. In this paper, we quantitatively assess the performance potential and scientific feasibility of MHD-bypass airbreathing hypersonic engines using ideal gasdynamics and fundamental thermodynamic principles.

Litchford, Ron J.↗

DOE OSTI2026

A Full-Induction Magnetohydrodynamics Solver for Liquid Metal Fusion Blankets in Vertex-CFD

Multiphysics modeling of liquid metal fusion blankets, which produce tritium and convert energy of neutrons created via fusion reactions into heat, is crucial for predicting performance, ensuring structural integrity, and optimizing energy production. While traditional blanket modeling of liquid metal flows during normal steady operating conditions commonly employs the inductionless approximation of the magnetohydrodynamics (MHD) equations, transient scenarios, when the plasma-confining magnetic field varies on millisecond time scales, require a full-induction MHD approach that dynamically evolves the magnetic field via the time-dependent induction equation. This paper presents the formulation, implementation, and initial verification of a full-induction MHD solver integrated within the open-source Vertex-CFD framework, which aims to achieve tight multiphysics coupling, a flexible software design enabling easy extension and addition of physics models, and performance portability across computing platforms. The solver utilizes finite element spatial discretization, implicit Runge–Kutta time integration, and an inexact Newton method to solve the resulting discrete nonlinear system, leveraging Trilinos packages for efficient computation. Verification against selected benchmark problems demonstrates accuracy and robustness of the solver. Furthermore, when the solver is applied to an idealized blanket model in 2.5D and full 3D, results obtained with Vertex-CFD are in good agreement with recently published quasi-2D simulations. These findings establish a computational foundation for future simulations of transient MHD phenomena in liquid metal blankets with Vertex-CFD, and open avenues for future extensions and performance optimizations.

Endeve, Eirik [ORNL] (ORCID:0000000312519507)↗

DOE OSTI2026

Comprehensive analytical model of the dynamic 𝑍 pinch

In this work we present an analytical 1D axisymmetric model describing the evolution of the dynamic 𝑍 pinch. This model is capable of predicting the trajectories of the imploding sheath's magnetic piston and preceding shock front, along with the velocity, pressure, density, and magnetic field profiles, for any time-dependent current, spatially varying initial density profile, and weak initial axial field. The implosion is divided into stages, with each stage described by a set of coupled ordinary differential equations derived from the ideal MHD equations. Comparisons with experimental data from the COBRA pulsed-power facility are quite promising and imply this model could prove useful in designing and analyzing future pulsed-power experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Closure models for the feedback of energetic particles on plasma turbulence

Energetic particles interact with the plasma surrounding them, resonating with certain types of plasma waves to stabilize them while destabilizing others, and changing the character of the background turbulence in ways that have not been fully quantified or understood. Interaction with the turbulent background plasma is key to the acceleration of many types of energetic particles including high-energy cosmic rays, solar energetic particles, and pick-up ions. The acceleration of particles is a process that would ideally be described by a kinetic model, a type of model that follows a probability distribution function (PDF) for all particles in 7-dimensional (x, y, z, v x , v y , v z , t) space. Because of the high dimensionality of a kinetic model, simulations that solve kinetic equations use the largest computational resources currently available, and are yet unable to simulate a realistic number of particles, reach the large scales necessary for astrophysical problems, and use high-precision numerical methods. Two available alternatives to kinetic plasma models have been explored for this problem, with limited success. One is a multi-fluid model produced by a cumulant discarding closure, which evolves coupled equations for the velocity, magnetic field, and internal energy for both the background plasma and the fluid of energetic particles. However, simulations that solve multi-fluid magnetohydrodynamic (MHD) equations are able to include the interaction with energetic particles only in crude ways, typically as an add-on pressure term. The second alternative is to use a hybrid method to couple a fluid description of the background plasma to a kinetic model or a Fokker–Planck model for the energetic particles. These methods are hampered by the physical modeling of the coupling. In this work, we develop a new model, which follows the PDF for all particles; this can be viewed as a step toward physical realism above a multi-fluid MHD model, while also being more computationally efficient than a kinetic model. The equations we develop model both the background plasma and the energetic particles self-consistently. Over the last decade, similar PDF methods have been developed to a high level of sophistication to model reactive flows and turbulent combustion for engineering applications. For treatment of the feedback of the energetic particles on a background plasma, a PDF closure approach should evaluate the mean characteristics, including the density, with better statistical quality than will particle-sampling procedures.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Radiation Transport Two-temperature GRMHD Simulations of Warped Accretion Disks

In many black hole (BH) systems, the accretion disk is expected to be misaligned with respect to the BH spin axis. If the scale height of the disk is much smaller than the misalignment angle, the spin of the BH can tear the disk into multiple, independently precessing "sub-disks." This is most likely to happen during outbursts in black hole X-Ray binaries (BHXRBs) and in active galactic nuclei (AGNs) accreting above a few percent of the Eddington limit, because the disk becomes razor-thin. Disk tearing has the potential to explain variability phenomena including quasi-periodic oscillations in BHXRBs and changing-look phenomena in AGNs. Here, we present the first radiative two-temperature general relativistic magnetohydrodynamic (GRMHD) simulation of a strongly tilted (65°) accretion disk around an M BH = 10 M ⊙ BH, which tears and precesses. This leads to luminosity swings between a few percent and 50% of the Eddington limit on sub-viscous timescales. Surprisingly, even where the disk is radiation-pressure-dominated, the accretion disk is thermally stable over t ≳ 14,000 r g /c. This suggests warps play an important role in stabilizing the disk against thermal collapse. The disk forms two nozzle shocks perpendicular to the line of nodes where the scale height of the disk decreases tenfold and the electron temperature reaches T e ~ 10 8 –10 9 K. In addition, optically thin gas crossing the tear between the inner and outer disk gets heated to T e ~ 108 K. This suggests that warped disks may emit a Comptonized spectrum that deviates substantially from idealized models.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Predicting resistive wall mode stability in NSTX through balanced random forests and counterfactual explanations

Abstract Recent progress in the disruption event characterization and forecasting framework has shown that machine learning guided by physics theory can be easily implemented as a supporting tool for fast computations of ideal stability properties of spherical tokamak plasmas. In order to extend that idea, a customized random forest (RF) classifier that takes into account imbalances in the training data is hereby employed to predict resistive wall mode (RWM) stability for a set of high beta discharges from the NSTX spherical tokamak. More specifically, with this approach each tree in the forest is trained on samples that are balanced via a user-defined over/under-sampler. The proposed approach outperforms classical cost-sensitive methods for the problem at hand, in particular when used in conjunction with a random under-sampler, while also resulting in a threefold reduction in the training time. In order to further understand the model’s decisions, a diverse set of counterfactual explanations based on determinantal point processes (DPP) is generated and evaluated. Via the use of DPP, the underlying RF model infers that the presence of hypothetical magnetohydrodynamic activity would have prevented the RWM from concurrently going unstable, which is a counterfactual that is indeed expected by prior physics knowledge. Given that this result emerges from the data-driven RF classifier and the use of counterfactuals without hand-crafted embedding of prior physics intuition, it motivates the usage of counterfactuals to simulate real-time control by generating the β N levels that would have kept the RWM stable for a set of unstable discharges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Predicting nonresonant pressure-driven MHD modes in equilibria with low magnetic shear

Nonresonant internal modes can be difficult to anticipate as there is no resonant surface in the plasma. However, equilibria that are unstable to multiple nonresonant magnetohydrodynamic (MHD) modes may be more prone to global loss of confinement since these instabilities generate spatially extended linear displacements, potentially enhancing magnetic field line chaos via nonlinear interactions. Here, we successfully predict the unstable nonresonant pressure-driven modes for equilibria with zero shear in the plasma core, irrational q on axis, and a central pressure gradient, which is consistent with pre-crash profiles in sawtoothing tokamak plasmas in the large-aspect-ratio limit. A criterion for identifying nonresonant modes most likely to be unstable is developed from the convergents of the continued fraction representation of q 0 . A higher-order analysis of the standard Energy Principle reveals the conditions under which these modes are expected to dominate. Linear growth rate spectra, as a function of toroidal mode number (up to n = 30), calculated using the initial-value extended-MHD code, M3D-C1, recover the characteristic dependence observed for ideal infernal modes. Nonresonant modes have also been invoked in some ideal sawtooth crash models. Finally, this work provides a mechanism to predict the mode numbers of infernal modes and, potentially, the width of some post-sawtooth-crash profiles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Modeling of thermal-ion-driven internal kink in DIII-D high- T i plasmas

Toroidal modeling utilizing the non-perturbative magnetohydrodynamic-kinetic hybrid code MARS-K (Liu Y.Q. et al 2008 Phys. Plasmas 15 112503), to a DIII-D high-performance discharge with the core thermal ion temperature of T i ~ 13 keV, finds multiple branches of unstable internal kink (IK) modes triggered by the bounce resonance of trapped thermal ions. The range of the computed mode frequency aligns well with the bounce frequency of trapped thermal ions, confirming the nature of resonance drive for the instability. The computed mode frequency is close to that observed in experiments. Plasma toroidal flow, in particular the fast flow ($ > $10% of Alfvén speed) as in the considered DIII-D discharge, strongly stabilizes the fluid IK branch but not all of the thermal-ion-driven internal kink (TIK) branches, leaving one dominant unstable TIK branch under the experimental conditions. Plasma resistivity also significantly affects stability of the TIKs (but not much on the IK which is ideally strongly unstable) in combination with the drift kinetic drive by thermal ions. High resistivity can drive additional unstable TIK branches. Scanning the on-axis safety factor over a large range confirms robustness of the TIK triggering by thermal ions. The computed TIKs contain both the IK and the tearing components as the dominant contributions to the eigenmode structure. Furthermore, these findings, together with the experimental results reported in reference (Du X.D. et al 2021 Phys. Rev. Lett. 127 025001), strongly suggest the possibility of thermal-ion driven instabilities in ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Low- n stability and plasma response to RMP in various STEP scenarios

The low-n (n is the toroidal mode number) magnetohydrodynamic (MHD) stability and plasma response are numerically investigated for various scenarios designed for STEP, that are relevant for the H-mode pedestal analysis. Control of the edge-localized modes (ELMs) with externally applied resonant magnetic perturbations (RMPs) is considered. Optimization of the ELM control coil current configuration, based on the computed plasma MHD response and well-established figures of merit validated on present-day experiments, finds reasonable robustness of a fixed coil phasing (for a given n-number) to control ELMs in all five STEP plasmas considered. Based on certain semi-empirical criteria, the required coil current to achieve ELM suppression is estimated to be about 10–20 kAt with the n = 1 or 2 RMP configuration and about 100–200 kAt for the n = 4 RMP. Systematic linear stability calculations are used to map out stability windows for the low-n kink-peeling modes, in terms of the ideal-wall location and variation of the edge safety factor q 95 with respect to the target design. The kink-peeling stability boundary is found to be generally sensitive to the q 95 variation, which has implications for achieving the quiescent H-mode regime in STEP. Full toroidal quasilinear initial-value simulations for these STEP plasmas find that generation of the edge-harmonic oscillations (EHOs) depends sensitively on the plasma scenario, the initial linear stability of the kink-peeling modes, the initial plasma toroidal flow and q 95 . In general, it is easier (more robust) to access the EHO-regime for two of the cases considered with smaller plasma volume and higher on-axis safety factor. Finally, quasilinear simulations find robust density pumpout due to applied RMPs in these STEP plasmas, but the effect on the plasma toroidal flow varies among different cases.

EHO↗

NASA NTRS2023

Modeling the Formation and Eruption of Coronal Structures by Linking Data-Driven Magnetofrictional and MHD Simulations for AR 12673

Context .The data-driven and time-dependent modeling of coronal magnetic fields is crucial for understanding solar eruptions. These efforts are complicated by the challenges of finding a balance between physical realism and computing efficiency. One possible technique is to couple two modeling approaches. Aims . Our aim here is to showcase our progress in using time-dependent magnetofrictional model (TMFM) results as input to dynamical magnetohydrodynamic (MHD) simulations. However, due to the different evolution processes in these two models, using TMFM snapshots in an MHD simulation is nontrivial. We address these issues, both physically and numerically, discuss the incompatibility of the TMFM output to serve as the initial condition in MHD simulations, and show our methods of mitigating this. The evolution of the flux systems and the cause of the eruption are investigated. Methods . TMFM is a prevalent approach that has proven to be a very useful tool in the study of the formation of unstable structures in the solar corona. In particular, it is capable of incorporating observational data as initial and boundary conditions and requires shorter computational time compared to MHD simulations. To leverage the efficiency of data-driven TMFM and also to simulate eruptive events in the MHD framework, one can apply TMFM up to a certain time before the expected eruption(s) and then proceed with the simulation in the full or ideal MHD regime in order to more accurately capture the eruption process. Results . We show the results of a benchmark test case with a linked TMFM and MHD simulation to study the evolution of NOAA active region 12673. A rise of a twisted flux bundle through the MHD simulation domain is observed, but we find that the rate of the rise and the altitude reached depends on the time of the TMFM snapshot that was used to initialize the MHD simulation and the helicity injected into the system. The analysis suggested that torus instability and slip-running reconnection could play an important role in the eruption. Conclusions . The results show that the linkage of TMFM and zero-β MHD models can be successfully used to model the eruptive coronal magnetic fields.

F. Daei↗

DOE OSTI2022

Parthenon—a performance portable block-structured adaptive mesh refinement framework

On the path to exascale the landscape of computer device architectures and corresponding programming models has become much more diverse. While various low-level performance portable programming models are available, support at the application level lacks behind. To address this issue, we present the performance portable block-structured adaptive mesh refinement (AMR) framework Parthenon, derived from the well-tested and widely used Athena++ astrophysical magnetohydrodynamics code, but generalized to serve as the foundation for a variety of downstream multi-physics codes. Parthenon adopts the Kokkos programming model, and provides various levels of abstractions from multidimensional variables, to packages defining and separating components, to launching of parallel compute kernels. Parthenon allocates all data in device memory to reduce data movement, supports the logical packing of variables and mesh blocks to reduce kernel launch overhead, and employs one-sided, asynchronous MPI calls to reduce communication overhead in multi-node simulations. Using a hydrodynamics miniapp, we demonstrate weak and strong scaling on various architectures including AMD and NVIDIA GPUs, Intel and AMD x86 CPUs, IBM Power9 CPUs, as well as Fujitsu A64FX CPUs. At the largest scale on Frontier (the first TOP500 exascale machine), the miniapp reaches a total of 1.7 × 10 13 zone-cycles/s on 9216 nodes (73,728 logical GPUs) at [Formula: see text] weak scaling parallel efficiency (starting from a single node). In combination with being an open, collaborative project, this makes Parthenon an ideal framework to target exascale simulations in which the downstream developers can focus on their specific application rather than on the complexity of handling massively-parallel, device-accelerated AMR.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Development of five-moment two-fluid modeling for Z-pinch physics

The Z-pinch m = 0 instability as well as its stabilization by radially sheared axial flow is studied using the nonlinear ideal five-moment twofluid (5M2F) model with an extension of that model to include Braginskii heat and momentum transport. Using the ideal 5M2F model, linear growth rate results are compared with prior work using MHD and Hall MHD. At small normalized wavenumber, 1 < k a < 4 , where a is the effective pinch radius, 5M2F results agree with Hall MHD within 20% in scenarios without radially sheared axial flow. With the sheared flow and focusing on ka = 10/3, agreement with Hall MHD is excellent. In the limit of small ion inertial length, results also match with MHD. A comparison with PIC modeling of shear-free m = 0 stability focuses on a plasma scenario based on recent experimental results. In a scan of mode wavenumber, ideal 5M2F results are qualitatively similar to PIC: the growth rate rises to a peak at a moderate wavenumber and declines at a large wavenumber in contrast to MHD results, which show the saturation of the growth rate with the increasing wavenumber rather than a decline. The peak normalized 5M2F growth rate is γ τ A = 1.5 , where sA is the Alfven transit time across the pinch. The peak occurs at normalized wavenumber ka = 10. For comparison, PIC results have a peak growth of γ τ A = 0.77 at ka = 5. Including Braginskiibased closure of the 5M2F model does not qualitatively change the ideal results in this particular case. Nonlinear saturation is studied using the 5M2F model with the dissipative Braginskii-based closure in cases with pinch-edge sheared-flow speed equal to half the Alfven speed. Nonlinear mixing due to the sheared flow yields a quasi-steady state after modest losses of pinch ion inventory and pinch thermal energy, approximately 30% and 10%, respectively. 5M2F modeling captures the essential physics of m = 0 instability and offers a computationally tractable route to high-fidelity modeling of 3D Z-pinch behavior, including m = 1 instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗