Linear stability studies for a quasi-axisymmetric equilibrium including plasma flow, drift and viscosity effects

This study investigates the impact of various impurity species on peeling-ballooning (PB) modes and microturbulence in tokamak plasmas through the extension of traditional twofluid and gyro-Landau-fluid (GLF) models. By incorporating finite Larmor radius (FLR) effects, the analysis provides a comprehensive understanding of impurity-driven impact and its interaction with plasma turbulence. Depending on charge state and local plasma conditions, heavy impurities may exhibit gyro-radii larger than those of main ions, which are captured in the extended GLF model presented. Following the presentation of modified two-fluid equations incorporating impurity effects, we systematically analyze the distinctions between impurity and main ion dynamics and their resultant feedback mechanisms on plasma behavior. Derivation of the linear dispersion relation enables quantification of impurity-mediated modifications to: plasma vorticity, diamagnetic drift and gyroviscous effects, electron Hall physics, and FLR effects. BOUT++ -based linear simulations corroborate this formalism, demonstrating systematic stabilization of peeling-ballooning (PB) modes upon impurity seeding. And then operational implications for practical impurity control strategies in tokamak devices are proposed. The results underscore the necessity of impurity management to maintain stability and optimize plasma confinement, with specific focus on how FLR effects contribute to transport dynamics. This work paves the way for enhanced modeling and simulation efforts, supporting the development of strategies to control impurity-induced turbulence and improve overall reactor performance.

Local helicity injection (LHI) is a non-inductive startup and current drive method via Taylor relaxation for the spherical torus. In achieving Taylor relaxation, it has been suggested that kink instability in 3D helical flux ropes plays an important role. However, the role and occurrence of kink instability during LHI have yet to be validated. Experimentally, determining the kink mode in a flux rope relies on measuring internal information using a probe. However, for LHI, the 3D geometry complicates this measurement process. Here, we propose a new approach for determining the kink modes of 3D helical flux ropes without any internal probe measurements. It is confirmed by this approach that flux ropes exhibit two different kink modes. With increasing plasma current in the flux ropes, a transition from the coherent internal kink mode to the external kink mode is observed. Kink mode properties such as rotating frequency calculated from the kink theory agree well with the magnetic signature driven by the kink mode. During the LHI experiment in the versatile experiment spherical torus, three distinguishable phases are confirmed by the approach, consistent with NIMROD simulation. Before driving the toroidal plasma current, the external kink mode is observed for 3D helical flux ropes. As the toroidal plasma current increases, the external kink mode disappears while generating broadband internal modes instead of coherent internal kink of flux ropes. Decoupling between the toroidal plasma and flux rope results in both decay of toroidal plasma current and re-appearance of the external kink mode in the flux ropes.

The stability with respect to a peeling–ballooning mode (PBM) was investigated numerically with extended MHD simulation codes in JET, JT-60U and future JT-60SA plasmas. The MINERVA-DI code was used to analyze the linear stability, including the effects of rotation and ion diamagnetic drift (), in JET-ILW and JT-60SA plasmas, and the JOREK code was used to simulate nonlinear dynamics with rotation, viscosity and resistivity in JT-60U plasmas. It was validated quantitatively that the ELM trigger condition in JET-ILW plasmas can be reasonably explained by taking into account both the rotation and effects in the numerical analysis. When deuterium poloidal rotation is evaluated based on neoclassical theory, an increase in the effective charge of plasma destabilizes the PBM because of an acceleration of rotation and a decrease in . The difference in the amount of ELM energy loss in JT-60U plasmas rotating in opposite directions was reproduced qualitatively with JOREK. By comparing the ELM affected areas with linear eigenfunctions, it was confirmed that the difference in the linear stability property, due not to the rotation direction but to the plasma density profile, is thought to be responsible for changing the ELM energy loss just after the ELM crash. A predictive study to determine the pedestal profiles in JT-60SA was performed by updating the EPED1 model to include the rotation and effects in the PBM stability analysis. It was shown that the plasma rotation predicted with the neoclassical toroidal viscosity degrades the pedestal performance by about 10% by destabilizing the PBM, but the pressure pedestal height will be high enough to achieve the target parameters required for the ITER-like shape inductive scenario in JT-60SA.

To improve the understanding of mud resuspension and the behaviour of mud flow in estuaries, a parametric stability analysis of a shear flow is carried out with a model of two miscible fluid layers of different properties. The shear layer is modelled by asymmetric erf(z) vertical profiles of the same thickness for each quantities. The upper layer, composed of water, is considered as a Newtonian fluid. The lower layer mud flow is also considered as a Newtonian fluid of high density and high viscosity. A linear stability study, realized with the code LiSa developed at IMFT (Institut de Mecanique des Fluides de Toulouse), explores the influence of the principal control parameters: the Richardson number, the Reynolds number and viscosity ratio between the two fluids. Direct numerical simulations (DNS) performed with the code JADIM of IMFT are used to compute the temporal evolution of these flows and are compared with the linear stability study. Both approaches describe consistently the development of the bidimensional primary instability. The computed critical Richardson number is close to 0.25. Results show that for high Reynolds numbers, evaluated at the interface, there is no influence of the viscosity ratio with respect to the primary instability. For Reynolds number lower than 10, the viscosity has a destabilizing effect: a bigger difference of viscosity leads to a more important growth rate. This property can result in higher instability growth rates for highly viscous mud flows when submitted to a velocity shear in real estuaries. Secondary instabilities and the other processes leading to an eventual three-layer flow are documented through DNS simulations. Different secondary instabilities are observed depending on the Reynolds number at the interface. Likely outcomes of this study are new parameterizations of the bed sediment flux in realistic modelling of estuaries.

The viscosity of whole blood measured at low shear rates is determined partly by shear resistance of the red cell aggregates present, stronger aggregation increasing the viscosity in the absence of other changes. Effects of cell deformability can confound interpretation and comparison in terms of aggregation, however, particularly when the plasma viscosity is high. We illustrate the problem with a comparison of hematocrit‐adjusted blood from type 1 diabetes patients and controls in which it is found the apparent and relative viscosities at a true shear rate of 0.20 s $^{-1}$ are lower in the patient samples than age matched controls, in spite of reports that aggregation is increased in such populations. Because the plasma viscosities of the patients were higher on average than controls, we performed a series of experiments to examine the effect of plasma protein concentration and viscosity on normal blood viscosity. Dilution or concentration by ultrafiltration of autologous plasma and viscosity measurements at low shear on constant hematocrit red cell suspensions showed (a) suspension viscosity at 0.25 and 3 s $^{-1}$ increased monotonically with plasma protein concentration and viscosity but (b) the relative viscosity increased, in concert with the microscopic aggregation grade, up to a viscosity of approximately 1.25 mPa‐s but above this the value the relative viscosity no longer increased as the degree of aggregation increased in concentrated plasmas. It is suggested that in order to reduce cell deformation effects in hyperviscous pathological plasmas, patient and control plasmas should be systematically diluted before hematocrit is adjusted and rheological measurements are made. True shear rates should be calculated. Comparison of relative viscosities at low true shear rates appears to allow the effects of red cell aggregation to be distinguished by variable shear rate viscometry in clinical blood samples.

Kink modes are investigated in pedestal for shaped tokamaks. An analytic combining criterion is presented. It lies on the middle of the sufficient criterion of Lortz and necessary criterion of Mercier giving a more restricted necessary criterion. Growth rates and mode structure are calculated. For large poloidal mode number, the modes are highly localized in both poloidal and radial directions. The modes increase rapidly when they approach to the resonant surface. They are typical of edge localized modes (ELMs). It is assumed that the modes vanish inside the next resonant surface, then, there seems to be a second stable region. Several mitigation methods for controlling ELMs are proposed.

An explanation is provided for the disruptive instability in diverted tokamaks when the safety factor$q$at the 95 % poloidal flux surface,$q_{95}$, is driven below 2.0. The instability is a resistive kink counterpart to the current-driven ideal mode that traditionally explained the corresponding disruption in limited cross-sections (Shafranov,Sov. Phys. Tech. Phys., vol. 15, 1970, p. 175) when$q_{edge}$, the safety factor at the outermost closed flux surface, lies just below a rational value$m/n$. Experimentally, external kink modes are observed in limiter configurations as the current in a tokamak is ramped up and$q_{edge}$decreases through successive rational surfaces. For$q_{edge}<2$, the instability is always encountered and is highly disruptive. However, diverted plasmas, in which$q_{edge}$is formally infinite in the magnetohydrodynamic (MHD) model, have presented a longstanding difficulty since the theory would predict stability, yet, the disruptive limit occurs in practice when$q_{95}$, reaches 2. It is shown from numerical calculations that a resistive kink mode is linearly destabilized by the rapidly increasing resistivity at the plasma edge when$q_{95}<2$, but$q_{edge}\gg 2$. The resistive kink behaves much like the ideal kink with predominantly kink or interchange parity and no real sign of a tearing component. However, the growth rates scale with a fractional power of the resistivity near the$q=2$surface. The results have a direct bearing on the conventional edge cutoff procedures used in most ideal MHD codes, as well as implications for ITER and for future reactor options.

The effect of small viscosity on the ‘‘constant ψ’’ tearing mode in the presence of shear flow is analyzed using the boundary-layer approach. It is found that the influence of viscosity depends upon the parameter G′(0)/F′(0), where G′(0) and F′(0) denote the flow shear and magnetic field shear at the magnetic null plane, respectively. When ‖G′(0)/F′(0)‖≪1, the tearing mode growth rate is suppressed by the viscosity, but not completely stabilized. When ‖G′(0)/F′(0)‖∼𝒪(1) and the viscosity is comparable to the resistivity, the growth rate vanishes as [1−G′(0)2/F′(0)2]1/3, when G′(0)2→F′(0)2 from below. In the case where 1−[G′(0)2/F′(0)2]<0 matching cannot be achieved and the tearing mode vanishes.

The relationship between determinants of blood viscosity and blood pressure (BP) variables was studied in a large sample of a population aged 25 to 64 years. Plasma viscosity, hemoglobin, and total serum protein were examined. Systolic and diastolic BP and the prevalence of hypertension showed a crude positive association with plasma viscosity levels in both sexes. Age, body mass index, and total serum protein appeared to have a confounding effect on this relationship, whereas hemoglobin, smoking behavior, and alcohol consumption did not. A crude positive association was also found between total serum protein levels and the prevalence of hypertension in men and women; however, since total serum protein was treated as a covariable, no further analyses were carried out. In contrast to findings reported in the literature, hemoglobin levels were not correlated with BP variables in either sex. After adjusting for all confounders, a significant main effect of plasma viscosity still was found. However, the magnitude of the effect was not as large as for body mass index, a well-established risk variable for hypertension. These results indicate that BP is positively associated with plasma viscosity. Whether increased plasma viscosity in hypertension constitutes a primary or a secondary phenomenon remains to be answered. Since plasma viscosity is significantly associated with hypertension but any BP variable, increased levels of plasma proteins (particularly fibrinogen as the main determinant of plasma viscosity) may represent the cause for elevated plasma viscosity. This might contribute to persistently increased resistance to blood flow on the microcirculatory level in arterial hypertension.

The roles of a magnetic separatrix and of a steep-edge pressure gradient on finite beta external kink and tearing modes in tokamaks are examined by using a newly developed initial value code. For fixed profiles of current density and pressure, the separatrix is found to have a weak effect on the linear characteristics of the global mode. The presence of a steep pressure gradient at the plasma edge reduces the overall growth rate in a similar fashion for both cases with and without the separatrix.

Fully suppressing edge-localized modes (ELMs), e.g., with resonant magnetic perturbations (RMPs), is essential to reach and sustain high-performance steady-state H-mode plasmas because large ELMs can significantly reduce the lifetime of divertor components in future tokamak reactors. RMP-driven ELM suppression in KSTAR has been modeled by coupling the neoclassical transport code PENTRC to the nonlinear 3D MHD code JOREK. We have found that the radial transport from the combined effects of the kink-peeling, tearing response, and neoclassical toroidal viscosity can explain the pedestal degradation observed in experiments. In addition, it has been found that the RMP response can increase the inter-ELM heat flux on the lower outer divertor by redistributing the heat transport between the divertor plates. In addition to the degraded pedestal, ELM suppression is also attributable to the RMP-induced mode interactions. While the linear stability of peeling-ballooning mode (PBMs) improves owing to the degraded pedestal, the PBM and RMP interaction increases the spectral transfer between edge harmonics, preventing catastrophic growth and the crash of unstable modes. Here, it turns out that the magnetic islands near the pedestal top can play a vital role in mediating the mode interactions.

Magnetohydrodynamic (MHD) stability studies of low-mode-number free-boundary kink modes in a finite-β Large Helical Device (LHD) [A. Ilyoshi, et al. Fusion Technology 17, 169 (1990)] equilibrium series with self-consistent bootstrap current find some serious free-boundary modes. They indicate that care must be taken in the design of high-β experiments. Since the LHD configuration is flexible, with the possibility of introducing or modifying dipole and quadrapole fields, unbalancing the currents in the helical coils, operating with a high-temperature divertor, and changing the collisionality regime by working with different values of temperature and density, paths to high-β operation should exist. Comparison of the experimental results with these theoretical predictions for the studied equilibrium sequence will provide understanding of the MHD stability properties of LHD.

The development of small and no-ELM regimes for ITER is a high priority topic due to the risks associated with type-I ELMs. By considering non-linear extended magnetohydrodynamic (MHD) simulations of the ASDEX Upgrade tokamak with the JOREK code, we probe a regime that avoids type-I ELMs completely, provided that the separatrix density is high enough. The dynamics of the pedestal in this regime are observed to be qualitatively similar to the so-called quasi-continuous exhaust regime in several ways. Repetitive type-I ELMs are substituted by roughly constant levels of outward transport, caused by peeling-ballooning modes (with dominant ballooning characteristics) which are localised in the last 5% of the confined region (in normalised poloidal flux). The simulated low triangularity plasma transitions to a type-I ELMy H-mode if the separatrix density is sufficiently reduced or if the input heating power is sufficiently increased. The stabilising factors that play a role in the suppression of the small ELMs are also investigated by analysing the simulations, and the importance of including diamagnetic effects in the simulations is highlighted. By considering a scan in the pedestal resistivity and by comparing the poloidal velocity of the modes to theoretical estimates for ideal and resistive modes, we identify the underlying instabilities as resistive peeling-ballooning modes. Decreasing the resistivity below experimentally-relevant conditions (i.e. going towards ideal MHD), the peeling-ballooning modes that constrain the pedestal below the type-I ELM stability boundary display sharply decreasing growth rates.

We present the linear simulations of edge plasma instabilities using the 3-field peeling-ballooning model and gyro-Landau-fluid model under the BOUT++ framework. A series of realistic equilibria of shifted circular geometry are generated by a global equilibrium solver CORSICA, where the Shafranov shift, elongation effects, and bootstrap current are included. The linear growth rate spectrum of the peeling-ballooning modes is shown in a wide range of pressure gradient and parallel current density in the pedestal region. The results show that the bootstrap current stabilizes high beta ballooning modes. The simulations with different fractions of bootstrap current indicate a trend for the existence of the high beta peeling-ballooning mode stability region. Taking the kinetic effects into account, the linear simulations of kinetic peeling-ballooning mode using the gyro-Landau-fluid model show that this region can be accessed.

We perform two-dimensional simulations of strongly–driven compressible Rayleigh–Taylor and Kelvin–Helmholtz instabilities with and without plasma transport phenomena, modeling plasma species diffusion, and plasma viscosity in order to determine their effects on the growth of the hydrodynamic instabilities. Simulations are performed in hydrodynamically similar boxes of varying sizes, ranging from 1 μm to 1 cm in order to determine the scale at which plasma effects become important. Our results suggest that these plasma effects become noticeable when the box size is approximately 100 μm, they become significant in the 10 μm box, and dominate when the box size is 1 μm. Results suggest that plasma transport may be important at scales and conditions relevant to inertial confinement fusion, and that a plasma fluid model is capable of representing some of the kinetic transport effects.