Hydromagnetic stability
Stability of magnetized plasmas - gravitational instability, effects of finite Larmor radius, frequency, and resistivity
MAGNETOHYDRODYNAMIC STABILITY↗
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Nonlinear stability of solar type 3 radio bursts. 2: Application to observations near 1 AU
A set of rate equations including strong turbulence effects and anomalous resitivity are solved using parmeters which model several solar type 3 bursts. Exciter distributions observed at 1 AU are excitation of the linear bump-in-tail instability, amplifying Langmuir waves above the threshold for the oscillating two stream instability (OTSI). The OTSI, and the attendant anomalous resistivity produce a rapid spectral transfer of Langmuir waves to short wavelengths, out of resonance with the electron exciter. Further energy loss of the beam is thus precluded. The various parameters needed to model the bursts are extrapolated inside 1 AU with similar results. Again, the OTSI is excited and decouples the electron beam from the Langmuir radiation. Reabsorption of the Langmuir waves by the beam is shown to be unimportant in all cases, even at 0.1 AU. The theory provides a natural explanation for the observed realationship between radio flux, and the electron flux.
Goldstein, M. L.↗
A Comparison between Growth Morphology of "Eutectic" Cells/Dendrites and Single-Phase Cells/Dendrites
Directionally solidified (DS) intermetallic and ceramic-based eutectic alloys with an in-situ composite microstructure containing finely distributed, long aspect ratio, fiber, or plate reinforcements are being seriously examined for several advanced aero-propulsion applications. In designing these alloys, additional solutes need to be added to the base eutectic composition in order to improve heir high-temperature strength, and provide for adequate toughness and resistance to environmental degradation. Solute addition, however, promotes instability at the planar liquid-solid interface resulting in the formation of two-phase eutectic "colonies." Because morphology of eutectic colonies is very similar to the single-phase cells and dendrites, the stability analysis of Mullins and Sekerka has been extended to describe their formation. Onset of their formation shows a good agreement with this approach; however, unlike the single-phase cells and dendrites, there is limited examination of their growth speed dependence of spacing, morphology, and spatial distribution. The purpose of this study is to compare the growth speed dependence of the morphology, spacing, and spatial distribution of eutectic cells and dendrites with that for the single-phase cells and dendrites.
Tewari, S. N.↗
Energetics and the resistive tearing mode - Effects of Joule heating and radiation
The contribution of energy flux to the dynamics of magnetic field reconnection is analytically studied in order to determine the influence of Joule heating and radiation on the linear development of the tearing instability in slab geometry. A temperature-dependent Coulomb-like resistivity is used to provide the coupling between the dynamics and the energy equation. Analytical expressions are derived for the growth rates utilizing constant-psi and long-wavelength approximations. The solutions indicate the occurrence of several modes in addition to the usual tearing mode, several of which have relatively slow, complex growth rates. At large values of the magnetic Reynolds number, there are at least two modes with purely exponential growth when the radiative loss decreases with increasing temperature. If the radiation is neglected, the Joule heating alone also results in two modes with real, positive growth at large S. Below a particular value of S, all the modes are generally stabilized.
Steinolfson, R. S.↗
4D electrical resistivity tomography for assessing the influence of vegetation and subsurface moisture on railway cutting condition
Instability of slopes, embankments, and cuttings on the railway network is increasingly prevalent globally. Monitoring vulnerable infrastructure aids in geotechnical asset management, and improvements to transport safety and efficiency. Here, we examine the use of a novel, near-real-time Electrical Resistivity Tomography (ERT) monitoring system for assessing the stability of a railway cutting in Leicestershire, United Kingdom. In 2015, an ERT monitoring system was installed across a relict landslide (grassed) and an area of more stable ground on either side (wooded), to monitor changes in electrical resistivity through time and space, and to assess the influence of different types of vegetation on the stability of transportation infrastructure. Two years of 4-Dimensional ERT monitoring results are presented here, and petrophysical relationships developed in the laboratory are applied to calibrate the resistivity models in order to provide an insight into hydrogeological pathways within a railway cutting. The influence of vegetation type on subsurface moisture pathways and on slope stability is also assessed – here we find that seasonal subsurface changes in moisture content and soil suction are exacerbated by the presence of trees (wooded area). This results in shrink-swell behaviour of the clays comprising the railway cutting, resulting in fissuring and a reduction in shear strength, leading to instability. As such, it is proposed that on slopes comprised of expansive soils, grassed slopes are beneficial for stability. Insights into the use of 4-D ERT for monitoring railway infrastructure gained from this study may be applied to the monitoring of critical geotechnical assets elsewhere.
58 GEOSCIENCES↗
Cohesive instability in elastomers: insights from a crosslinked Van der Waals fluid model
Abstract The resistance to volumetric deformations displayed by polymer networks is largely due to secondary and tertiary interactions between neighboring polymer chains. These interactions are both entropic and enthalpic in nature but are fundamentally different from the entropic forces that resist shearing in these networks. In this paper, we introduce a new depiction of elastomers as a crosslinked Van der Waals fluid. Starting from first principles, we develop constitutive equations that are implemented in a continuum model as well as a discrete network model. Our models predict that the failure of polymer networks may be driven by an instability in the underlying polymer bulk ‘fluid’ or by the breaking of polymer chains, depending on the loading path taken. The results of this study indicate that material failure in elastomers exposed to a purely triaxial state, such as in a poker chip experiment, may be driven by an entirely different mode of instability than those deformed in pure shear, such as in a uniaxial tension experiment.
Lamont, Samuel C.↗
On the study of hydrodynamic instabilities in the presence of background magnetic fields in high-energy-density plasmas
Blast-wave-driven hydrodynamic instabilities are studied in the presence of a background B-field through experiments and simulations in the high-energy-density (HED) physics regime. In experiments conducted at the Laboratoire pour l’utilisation des lasers intenses (LULI), a laser-driven shock-tube platform was used to generate a hydrodynamically unstable interface with a prescribed sinusoidal surface perturbation, and short-pulse x-ray radiography was used to characterize the instability growth with and without a 10-T B-field. The LULI experiments were modeled in FLASH using resistive and ideal magnetohydrodynamics (MHD), and comparing the experiments and simulations suggests that the Spitzer model implemented in FLASH is necessary and sufficient for modeling these planar systems. These results suggest insufficient amplification of the seed B-field, due to resistive diffusion, to alter the hydrodynamic behavior. Although the ideal-MHD simulations did not represent the experiments accurately, they suggest that similar HED systems with dynamic plasma-β (=2μ0ρv2/B2) values of less than ∼100 can reduce the growth of blast-wave-driven Rayleigh–Taylor instabilities. These findings validate the resistive-MHD FLASH modeling that is being used to design future experiments for studying B-field effects in HED plasmas.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Spontaneous Symmetry–Breaking of Nonequilibrium Steady–States Caused by Nonlinear Electrical Transport
Negative differential resistance (NDR) in certain materials has been attributed to spontaneous emergence of symmetry-breaking electrical current density localization from a previously homogeneous distribution, which is postulated to occur due to the nonequilibrium thermodynamic force of minimization of entropy production. However, this phenomenon has not been quantitatively predicted based on intrinsic material properties and an applied electrical stimulus. Herein an instability criterion is derived for localization of current density and temperature from a thermal fluctuation in a parallel conductor model of a thin film that is subject to Newton's law of cooling. The conditions for steady–state electro-thermal localization is predicted, verifying a decrease in entropy production upon localization. Electro-thermal localization accompanied by a decrease of entropy production is confirmed in a multiphysics simulation of current flow in a thin film. The instability criterion predicts conditions for spontaneous current density localization, relating symmetry breaking fundamentally to dynamical instability via Local Activity theory.
36 MATERIALS SCIENCE↗
Variability of MHD instabilities in benign termination of high-current runaway electron beams in the JET and DIII-D tokamaks
Benign termination, in which magnetohydrodynamic (MHD) instabilities deconfine runaway electrons (REs) following hydrogenic injections, is a promising strategy for mitigating dangerous RE loads after disruptions. Recent experiments on the Joint European Torus (JET) have explored this scenario at higher pre-disruptive plasma currents than are achievable on other devices, revealing challenges in obtaining benign terminations at I p ≥2.5 MA. This work analyzes the evolution of these high-current RE beams and their terminating MHD events using fast magnetic sensor measurements and EFIT equilibrium reconstructions for approximately 40 JET and 20 DIII-D tokamak discharges. On JET, unsuccessful non-benign terminations occur at low edge safety factor (q edge ≈ 2), and are preceded by intermittent, non-terminating MHD events at higher rational qedge. Trends in the internal inductance I i indicate more peaked RE current profiles in the high-I p non-benign population, which may hinder successful recombination through re-ionization of the companion plasma. In contrast, benign terminations on JET typically occur at higher q edge ≥3 and exhibit less peaked RE current profiles. DIII-D displays a broader range of terminating edge safety factors, again correlated with the measured values. Across both tokamaks, the RE current peaking is therefore found to determine which MHD instability boundary is encountered, a result confirmed by linear resistive MHD modeling with the CASTOR3D code. Measured growth rates are similar for benign and non-benign cases, indicating that ideal MHD timescales at low density after hydrogenic injection do not alone explain efficient RE deconfinement. Instead, non-benign cases are most readily characterized by their comparably lower overall MHD perturbation amplitudes δB. These observations suggest that the interplay between ideal and resistive dynamics governs the termination process, with implications for extrapolating benign RE termination to high-I p reactor scenarios.
MHD instabilities↗
Double layers in contactor plasmas
The concept of using a hollow cathode to establish a low impedance contact between a spacecraft and the ambient plasma continues to gain in popularity, and is often then referred to as a plasma contactor. A growing number of studies indicate that large contact currents can be supported with small potential difference between the contactor and the ambient plasma. Results will be presented from a simple one-dimensional spherical model that obtains potentials from the solution of Poisson's equation, and particle densities from a turning point formalism that includes particle angular momentum. The neglect of collisions and magnetic field limits the realism. However, the results illustrate the effect of double layers that can form at the interface between contactor and ambient plasmas, when there is any voltage differential between the contactor and the ambient. The I-V characteristic of this model shows the usual space charge depends upon collection when the contactor flux is lower than some threshold; independence of I from variation in V when the flux is slightly greater than that threshold, and (numerical ?) instability for excessive flux suggesting the possibility of negative resistance. Even if a real I-V characteristic does not exhibit negative resistance, flat spots or high resistance regions may still be troublesome (or useful) to the total circuit.
Cooke, David L.↗
Resistive wall tearing mode disruptions in DIII-D and ITER tokamaks
Disruptions are a serious problem in tokamaks, in which thermal and magnetic energy confinement is lost. This paper uses data from the DIII-D experiment, theory, and simulations to demonstrate that resistive wall tearing modes (RWTMs) produce the thermal quench (TQ) in a typical locked mode shot. Analysis of the linear RWTM dispersion relation shows the parameter dependence of the growth rate, particularly on the resistive wall time. Linear simulations of the locked mode equilibrium show that it is unstable with a resistive wall and stable with an ideally conducting wall. Nonlinear simulations demonstrate that the RWTM grows to sufficient amplitude to cause a complete thermal quench. The RWTM growth time is proportional to the thermal quench time. Here, the nonlinearly saturated RWTM magnetic perturbation amplitude agrees with experimental measurements. The onset condition is that the q = 2 rational surface is sufficiently close to the resistive wall. Collectively, this identifies the RWTM as the cause of the TQ. In ITER, RWTMs will produce long TQ times compared to present-day experiments. ITER disruptions may be significantly more benign than previously predicted.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Resistive ballooning modes in line-tied coronal arcades
The equations describing the linear evolution of resistive ballooning modes are obtained by using a modified WKB expansion in the short perpendicular wavelength, while variations of the perturbations along the field are described by a slowly varying amplitude, on which the tying boundary conditions are imposed. In general, given an equilibrium, there are certain ranges of magnetic surfaces for which the system predicts instability even without dissipation. The main conclusion is that within the resistive MHD approximation cylindrically symmetric arcades with pressure falling with radius are unstable to resistive localized modes; the growth rates, close to ideal marginal stability, are large, so that it would appear that energy could be released during 10 to 100 Alfven times. The wavelength of the modes is expected to be limited by the ion gyroradius, when stabilizing drift effects must be taken into account. The nonlinear evolution of resistive ballooning modes should be studied to assess their overall relevance to the violent and rapidly evolving phenomena observed on the sun.
Velli, Marco↗
Magnetic Reconnection in a Sheared Magnetic Flux Tube: Slippage Versus Tearing
The process of magnetic reconnection in a flux tube can occur in a time-stationary fashion as slippage reconnection or in a time-dependent manner based on, for example, the tearing instability. However, it is not well known under which conditions a system can sustain slippage reconnection. Likewise, it is unclear whether systems can exhibit slippage reconnection and time-dependent reconnection simultaneously. In order to investigate these questions, we employ a set of 3D magnetohydrodynamic simulation. Using these simulations, we model a twisted flux tube with a spatially localized resistive region in the center of the simulation box, and an applied driver on one end plane of the simulation box. As a result, the Poynting flux injected at the boundary propagates to the resistive region and dissipates there. If the driver is nearly circular, we find a predominance of slippage reconnection, which decouples the applied driver entirely from one half of the flux tube. Second, a tearing-like instability occurs with slippage reconnection in the resistive region when the resistivity is strong enough and the cross section of the flux tube, as defined by the shape of the applied velocity perturbation, is elliptical enough. In this case we find the surprising feature that magnetic field perturbation generated by the tearing-like instability radiates away from the resistive region to influence the entire flux tube shape.
Hidetaka Kuniyoshi↗
High-frequency instability of the sheath-plasma resonance
Coherent high-frequency oscillations near the electron plasma frequency are generated by electrodes with positive dc bias immersed in a uniform Maxwellian afterglow plasma. The instability occurs at the sheath-plasma resonance and is driven by a negative RF sheath resistance associated with the electron inertia in the diodelike electron-rich sheath. With increasing dc bias, i.e., electron transit time, the instability exhibits a hard threshold, downward frequency pulling, line broadening, and copious harmonics. The fundamental instability is a bounded oscillation caused by wave evanescence, but the harmonics are radiated as electromagnetic waves from the electrodes acting like antennas. Wavelength and polarization measurements confirm the emission process. Electromagnetic waves are excited by electrodes of various geometries (planes, cylinders, spheres), which excludes other radiation mechanisms such as orbitrons or beam-plasma instabilities. The line-broadening mechanism has been identified as a frequency modulation via the electron transit time by dynamic ions. Ion oscillations at the sheath edge give rise to burstlike RF emissions. These laboratory observations of a new instability are important for antennas in space plasmas, generation of coherent beams with diodes, and plasma diagnostics.
Stenzel, R. L.↗
The theory of kinetic effects on resistive wall mode stability in tokamaks
Tokamak fusion plasmas benefit from high pressures but are then susceptible to modes of instability. These magnetohydrodynamic (MHD) modes are macroscopic distortions of the plasma, but certain collective motions of individual particles can provide stabilizing effects opposing them. The presence of a resistive wall slows the mode growth, converting a kink to a resistive wall mode (RWM). A kinetic MHD model includes Maxwell's equations, ideal MHD constraints, and kinetic effects included through the pressure tensor, calculated with the perturbed drift-kinetic distribution function of the particles. The kinetic stabilizing effects on the RWM arise through resonances between the plasma rotation and particle drift motions: precession, bounce, and transit. A match between particle motions and the mode allows efficient transfer of energy that would otherwise drive the growth of the mode, thus damping the growth. The first approach to calculating RWM stability is to write a set of equations for the complex mode frequency in terms of known quantities and then to solve the system. The “energy principle” approach, which has the advantage of clarity in distinguishing the various stabilizing and destabilizing effects, is to change the force balance equation into an equation in terms of changes of kinetic and potential energies, and then to write a dispersion relation for the mode frequency in terms of those quantities. These methods have been used in various benchmarked codes to calculate kinetic effects on RWM stability. Importantly, the theory has illuminated the important roles of plasma rotation, energetic particles, and collisions in RWM stability.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Active control of resistive wall mode via modification of external tearing index
Modification of the external tearing index, Δ ext ′ , by magnetic feedback is analytically investigated for the purpose of controlling the resistive plasma resistive wall mode (RP-RWM). The matching method is pursued by deriving expressions for the close-loop Δ ext ′ and by linking it to the counterpart from the inner layer. Various feedback coil configurations are found to generally reduce Δ ext ′ and stabilize the RWM, with either proportional or derivative control. Feedback modification of Δ ext ′ is found to be generally independent of the inner layer resistive interchange index D R , confirming that feedback action primarily modifies the solution in the outer ideal region for the RP-RWM. Exception occurs when either the inner layer favorable curvature effect becomes sufficiently large or the feedback action is sufficiently strong to introduce a rotating RP-RWM in the static plasma, leading to complex-valued close-loop Δ ext ′ . The perturbed magnetic energy dissipation in the outer region, associated with the eddy current in the resistive wall, is identified as the key physics reason for feedback induced complex Δ ext ′ . Similar results are also obtained for active control of the external kink instability, whose open-loop growth rate is significantly reduced by inclusion of the plasma resistivity. Within the single poloidal harmonic approximation, which is most suitable for the matching approach, external active coils combined with poloidal sensors are often found to be more efficient for feedback stabilization of the mode at large proportional gain values. This counter-intuitive result is explained as the lack of (non-resonant) poloidal harmonics for proper description of the feedback coil geometry.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
High-frequency instability of the sheath-plasma resonance
Coherent high frequency oscillations near the electron plasma frequency (omega approx. less than omega sub p) are generated by electrodes with positive dc bias immersed in a uniform Maxwellian afterglow plasma. The instability occurs at the sheath-plasma resonance and is driven by a negative RF sheath resistance associated with the electron inertia in the diode-like electron-rich sheath. With increasing dc bias, i.e., electron transit time, the instability exhibits a hard threshold, downward frequency pulling, line broadening and copious harmonics. The fundamental instability is a bounded oscillation due to wave evanescence, but the harmonics are radiated as electromagnetic waves from the electrodes acting like antennas. Wavelength and polarization measurements confirm the emission process. Electromagnetic waves are excited by electrodes of various geometries (planes, cylinders, spheres) which excludes other radiation mechanisms such as orbitrons or beam-plasma instabilities. The line broadening mechanism was identified as a frequency modulation via the electron transit time by dynamic ions. Ion oscillations at the sheath edge give rise to burst-like RF emissions. These laboratory observations of a new instability are important for antennas in space plasmas, generation of coherent beams with diodes, and plasma diagnostics.
Stenzel, R. L.↗
Unraveling Grain Boundary Instability in Dense Proton-Conducting Oxides
The long-term stability of protonic ceramic electrolysis cell (PCEC) materials under high-steam operating conditions remains a critical barrier to device commercialization. Here, we investigate the fundamental degradation mechanisms of dense BaCe 0.7 Zr 0.1 Y 0.1 Yb 0.1 O 3-δ (BCZYYb) electrolytes operated at 550 °C, 50% H 2 O in air. Over 1,000 h, the total electrolyte conductivity decreases by 11.1%, driven primarily by a >130% increase in grain-boundary resistivity. Post-mortem analyses reveal that damage is localized to near-surface grain boundaries extending ∼50 μm into the dense electrolyte pellet. This surface localization indicates that degradation is likely to be severe in thin, device-level electrolytes. Degradation is primarily attributed to chemo-mechanical grain-boundary weakening arising from hydration-induced chemical expansion, culminating in the formation of intergranular cracks oriented parallel to the pellet surface. These internal cracks subsequently react with steam and/or CO 2 , leading to the formation of nanoscale insulating phases, including Ba(OH) 2 , nanocrystalline BaCO 3 , and amorphous Ce/Zr/Y/Yb-containing oxides or hydroxycarbonates. After an initial degradation period of approximately 200 h, the overall conductivity stabilizes. Incorporating NiO sintering aids reduces grain-boundary density by an order of magnitude under identical sintering conditions. Although addition of NiO increases the initial resistivity by >160% at 550 °C, it substantially suppresses grain-boundary instability and mitigates chemical degradation. These findings underscore the urgent need for chemical and/or physical stabilization of BCZYYb electrolytes and offer design guidelines to enable durable, high-performance PCECs.
08 HYDROGEN↗