Weak Magnetic Shear Research Articles

Effect of central plasma pressure on high-order harmonics of 1/1 quasi-interchange instability in a central weak magnetic shear tokamak configuration

Abstract Numerical investigations of linear and nonlinear stages of quasi-interchange instability in a cylindrical tokamak geometry with a flat q-profile in the core region are conducted using eigenvalue and initial value codes, respectively. It is found that there exists a dependent relationship between the central plasma pressure p 0 (of the initial pressure profile) and the dominant harmonic of the quasi-interchange instability. As p 0 increases, m = n > 1 mode would be dominant in the linear stage and even in the nonlinear stage, where m and n are the poloidal and toroidal mode number, respectively. In addition, with p 0 increasing, the fast growth of other harmonics is inevitable and will deeply affect the evolution of m = n dominant quasi-interchange instability.

Verification of the kinetic electron role in the microinstabilities in a negative triangularity model equilibrium

Effect of kinetic electrons on negative triangularity plasmas has been investigated and compared against the corresponding positive triangularity plasmas, using the global gyrokinetic code X-point Gyrokinetic Code with scale-separated delta-f option without Coulomb collisions. Our model magnetic equilibria have strong positive and negative triangularities and weak magnetic shear. However, unusually large ρi/a and low density plasmas are chosen to maximize the nonlocal effect to investigate the finite ρi effect and to be clearly away from kinetic ballooning modes. Similar conclusions to previous flux tube and global simulations have been obtained in this highly nonlocal model plasma: it is essential to include kinetic electrons in the micro-instability study of negative triangularity plasmas. Most physics findings agree with existing reports, with some disagreement. We offer a new “effective trapping fraction” concept that can add to the explanation of the growth rate difference between NT and PT plasmas, pointing to the significant variation in trapped particle fractions that have turning points in the mode growth regions.

Fundamental properties of ideal and resistive infernal modes in tokamaks

Infernal modes are unstable in regions of weak magnetic shear and significant pressure gradients. These modes comprise a broad class of instabilities, encompassing interchange modes and kink modes, with both short and long length scales. Toroidal effects and fully electromagnetic fields are of crucial importance for their description. The role of resistive diffusion and compressibility are also critical. In order to investigate this awkward problem while still enabling fundamental physics interpretation, a new resistive MHD eigensolver has been developed. An outcome of this study is the identification of an unstable spectrum of resistive infernal modes in regions of the plasma with weak average curvature, and in regions where the average curvature is destabilising. These fast growing modes may be collectively important for our understanding of global reconnection events, stochastic magnetic fields states, and neighbouring supercritical bifurcations.

Global flux-driven gyrofluid simulations of internal transport barrier formation by external torque in weak magnetic shear configuration

Using a global gyrofluid code, we conduct comprehensive flux-driven simulations incorporating external heat and momentum sources/sinks. They involve an external torque ramp while keeping a heating power constant. Simulations show the formation of internal transport barriers (ITBs) in ion heat and parallel momentum in weak magnetic shear configuration. The ITB formation is attributed to the reduction of turbulent transport accompanied by strong E×B flow shear generation, where the majority of E×B shear arises from plasma rotation shear. In contrast, only a minor confinement improvement is observed in strong magnetic shear configuration. There exists a substantial difference in the rotation shear between the weak and strong magnetic shear cases at the same amount of external torque. Transport analysis implies that the difference comes from intrinsic rotation generated by residual stress. Global linear simulations demonstrate that the effect of E×B shear on k∥ symmetry breaking is enhanced in weak magnetic shear configuration, explaining the origin of the difference in intrinsic rotation. The ITB is not achieved when the external torque is injected in counter-direction to intrinsic rotation. It is also shown that threshold torque for the ITB formation depends on power and the ratio of external torque to heating power should exceed a critical value to attain an ITB.

Plasma beta dependence of turbulent transport suggesting an advantage of weak magnetic shear from local and global gyrokinetic simulations

A higher plasma β is desirable for realizing high performance fusion reactor, in fact, one of the three goals of JT-60SA project is to achieve a high-β regime. We investigate key physical processes that regulate the β dependence of turbulent transport in L-mode plasmas by means of both local and global gyrokinetic simulations. From local simulations, we found that the turbulent transport does not decrease as β increases, because the electromagnetic stabilizing effect is canceled out by the increase of the Shafranov shift. This influence of the Shafranov shift is suppressed when the magnetic shear is weak, and thus the electromagnetic stabilization is prominent in weak shear plasmas, suggesting an advantage of weak magnetic shear plasmas for achieving a high-β regime. In high β regime, local gyrokinetic simulations are suffered from the non-saturation of turbulence level. In global simulations, by contrast, the electromagnetic turbulence gets saturated by the entropy advection in the radial direction to avoid the zonal flow erosion due to magnetic fluctuations. This breakthrough enables us to explore turbulent transport at a higher β regime by gyrokinetic simulations.

Experiment study of m/n = 1/1 mode saturation level in high-βp discharge on the EAST tokamak

The saturated internal kink mode with m/n = 1/1 has been observed in the H-mode discharge of the experimental advanced superconducting tokamak, characterized by high βP and weak magnetic shear in the core. This observation was made using a combination of soft x-ray imaging and electron cyclotron emission diagnostics. It was noted that the repetitive bursting of m/n = 1/1 internal mode (large amplitude, short bursting duration) transitions into a long-lasting continuous one (small amplitude, constant frequency), when βp> 2.2 in H-mode, a much shorter bursting duration, transitioning into a long-lasting continuous one, with smaller amplitude and a constant frequency. Conversely, for typical βp< 1.5 in L/I discharge, the frequency of m/n = 1/1 mode decreases with time, associated with local poloidal electron diamagnetism drift velocity. The benign m/n = 1/1 mode in high βp has an amplitude much smaller than one in L-mode for high βP stabilization effect. By adjusting the power deposition of electron cyclotron resonance heating, it is found that the saturation level of m/n = 1/1 mode is independent of the local electron temperature gradient in H-mode discharge. It underscores that the flat current and, hence, weak magnetic shear are crucial factors influencing the saturation level of the m/n = 1/1 mode for both the off-axis electron cyclotron current driving current-dominant and off-axis bootstrap current-dominant cases. Furthermore, the outward movement with growth of the m/n = 1/1 mode in the process of L-H mode transition and the characteristic time of this process are close to the current diffusion time.

Gyrokinetic analysis of turbulent transport by electromagnetic turbulence in finite β plasmas with weak magnetic shear on HL-2A

Turbulent transport and zonal flow (ZF) dynamics in the mixed kinetic ballooning mode (KBM) and ion temperature gradient (ITG) mode dominated turbulence states are analyzed by gyrokinetic simulations based on the experimental observations of KBMs in the HL-2A Internal Transport Barrier (ITB) plasmas with weak magnetic shear configuration. Results have shown that KBMs and ITGs are the main candidates for turbulent transport and the inclusion of fast ions (FIs) can destabilize both instabilities, which is resulted by the decrease of ballooning parameter αMHD hence reduced Shafranov shift stabilization due to the negative FI density gradient, making them more unstable according to the ŝ-αMHD diagram. In addition, the ITGs are suppressed by both dilution and finite-β stabilization effects caused by FIs. Nonlinear simulations excluding the effects of FIs indicate that the transport is minimum at βe=βeexp as the turbulence predominated by ITGs is strongly suppressed by the nonlinear electromagnetic (EM) stabilization and enhancement of ZFs. However, the transport is further increased with β e although the ZFs become stronger due to the transition from ITG to KBM dominated turbulence state. The presence of FIs can modify the relation between ZF shearing rate and β e. The transport level is insensitive to β e when βe⩽βeexp but increases significantly because of the KBM destabilization. Meanwhile, the ZF amplitude reaches maximum at βe=βeexp whereas it suffers an erosion at higher values, implying that the plasma might be a self-organized critical state owning to the interactions among ZFs, KBMs and FI effects hence setting the plasma β around β exp. The results have also provided a possible explanation that the destabilization of EM turbulence is responsible for the ion heat transport stiffness under weak magnetic shear configurations in the off-axis neutral beam injection heated ITB plasmas on HL-2A.

Nonlinear interaction between double tearing mode and Kelvin–Helmholtz instability with different shear flows

The nonlinear interaction between the double tearing mode (DTM) and Kelvin–Helmholtz (KH) instabilities with different shear flow profiles has been numerically investigated via the use of a compressible magnetohydrodynamics (MHD) model. We focus on KH instabilities in weak and reversed magnetic shear plasmas with strong stabilizing effect of field line bending. Results show that KH instabilities coupled with DTMs occur in these plasmas and the KH mode dominates the instability dynamics, suggesting the crucial role of weak magnetic shear in the formation of high-mode harmonics. For symmetric flows, an asymmetric forced magnetic reconnection configuration is maintained during the growth phase, leading to interlocking of the modes. Additionally, this investigation of the DTM-KH instability interaction contributes to our understanding of the nonlinear reconnection mechanism in the regime of weak and reversed magnetic shear plasmas, which is relevant for astrophysical and fusion studies.

Observation of electron-scale turbulence suppression under weak magnetic shear with neon seeding in EAST plasma

Improved confinement caused by Ne injection is investigated in EAST. The safety factor q profile and electron-scale turbulence are studied with a polarimeter-interferometer system and CO2 laser collective scattering system in a series of Ne injection experiments in EAST. Ne with a suitable injection rate can lead to negative magnetic shear in the plasma core, which promotes electron-scale turbulence suppression. The continuous injection of Ne under the reversed shear condition further reduces the electron-scale turbulence intensity. Core electron temperature increase and confinement improvement are observed. QuaLiKiz is applied to model the influence of an impurity and reversed q on turbulence. The combination of stabilization effects of negative magnetic shear and Ne on turbulence is much stronger than the impurity’s own effect, which could explain the experimentally observed electron temperature (T e) increase and turbulence suppression. Besides, the relationship between pedestal structure induced by Ne injection and lower hybrid wave (LHW)-driven current deposition is discussed. These results provide a new perspective to improve the confinement in the case of Ne injection, i.e. to adjust the Ne injection to modify the ideal plasma equilibrium.

Internal Kink Instabilities Driven by Poloidal Flow via Non-Resonant Excitation in Tokamaks

Non-resonant excitation due to plasma inertia may be dominant in inducing internal kink (IK) instabilities. Poloidal rotation can effectively modify plasma inertia and cause non-resonant excitation to occur. An extended dispersion relation including poloidal rotation is established to study the IK mode and the fishbone (FB) mode. It is found that in rotating plasmas, even for a stable IK mode (i.e., the perturbed potential energy of background plasma δWc is positive) and in the absence of energetic particles (EPs), poloidal rotation can drive the IK mode via non-resonant excitation. Moreover, the IK mode is easy to be driven by poloidal rotation in weak magnetic shear plasmas. Similar to toroidal rotation, when poloidal rotation frequency exceeds a threshold, the FB mode can transform into a branch of a non-resonant mode. The real frequency of the mode, being independent of the precessional frequency of EPs, is just equal to the poloidal rotation frequency. Thus, the non-resonant mode is characterized by the long-lived mode (LLM) observed in toroidal rotating plasmas. The critical gradient of the poloidal rotation profile plays a crucial role in causing the resonant mode to evolve into a non-resonant one; for instance, only for a very peaked poloidal rotation profile can the FB mode transform into the LLM. In addition, the diamagnetic drift frequency of thermal ions can stabilize the FB and the IK modes.

Non-axisymmetric magnetohydrodynamic equilibrium and stability in an axisymmetric toroidal device

This paper is dedicated to studying the radial broadening of helical states embedded in three-dimensional nonlinear magnetohydrodynamic (MHD) equilibria in an axisymmetric toroidal device. The stability of these helical equilibria is estimated by analyzing global MHD stability. An equilibrium bifurcation can develop a non-axisymmetric configuration with a helical core encompassed by an axis-symmetric plasma edge when the amplitude of an innermost magnetic helicity exceeds that of the primary axisymmetric magnetic component. It is found that internal negative magnetic shear drives the increase of the helicity and the decrease of the axisymmetric component via triple-mode nonlinear interactions, which induces the helical core to broaden radially. The helical structure mainly rests within the domain where the helicity is larger than the axisymmetric mode. Meanwhile, chaotic fields are generated outside the region predicted by the multi-region relaxed MHD model. Furthermore, the global stability analysis reveals that the helical equilibria are stabilized with flat or weak negative magnetic shear at the plasma core. As the core negative magnetic shear becomes significant, the helical equilibria become destabilized by kink modes even though the helical structure extends radially further out. This work is of importance and interest for reversed-field pinch plasma to reach steady quasi-single-helicity states.

ITB formation in gyrokinetic flux-driven ITG/TEM turbulence

The formation mechanism of internal transport barriers (ITBs) in flux-driven turbulence is studied by means of the full-f gyrokinetic code GKNET. In the adiabatic electron case with a weak magnetic shear configuration, toroidal momentum injection can change the radial mean electric field through radial force balance, leading to a kind of driven ITB formation in which the ion thermal diffusivity by ion temperature gradient (ITG) turbulence decreases to the neoclassical transport level. Only cocurrent toroidal rotation in the outer core region can benefit the ITB formation, and this mechanism is identified to originate from a positive feedback loop between the radial shear and resultant momentum flux. On the other hand, in the kinetic electron case with a reversed magnetic shear configuration, robust co-intrinsic rotation is driven near the surface in ITG turbulence and sustains the shear through the radial force balance, leading to the spontaneous reduction of ion turbulent thermal diffusivity, while this is not observed in the adiabatic electron case. In the presence of electron heating, counter-intrinsic rotation by trapped electron mode turbulence is selectively driven in the negative magnetic shear region, which provides steeper shear formation and a resultant larger reduction of ion turbulent thermal diffusivity. This indicates that the co-existence of different modes can trigger the ‘discontinuity’ of mode structure, intrinsic rotation, and resultant mean near , leading to spontaneous ITB formation.

Effects of compressibility and guiding field on the Kelvin–Helmholtz instability in weakly reversed magnetic shear configurations

The effects of compressibility and guiding field on the Kelvin–Helmholtz (KH) instability in a double resonant surface system are numerically investigated by using a compressible magnetohydrodynamics model. The linear growth rate and the nonlinear saturation amplitude are analyzed for different parameters. A transition from double tearing modes to the KH instability occurs depending on the compressibility and guiding field with a weak magnetic shear. These results may deepen our understanding of the properties of the KH instability with double resonant surfaces in both space and laboratory plasmas.

Two types of helical-core equilibrium states in tokamak plasmas

Helical distortion in the core region and its formation mechanism in weakly reversed magnetic shear tokamak plasmas are investigated using three-dimensional magnetohydrodynamic (MHD) equilibrium calculations and MHD stability analysis. It is found that there are two different types of helical equilibrium states: one is a rigid-body shift in the core region on a poloidal cross-section, while the other is a local advection only around the magnetic axis. Linear stability analysis of the corresponding axisymmetric equilibrium is carried to understand the origin of these two types of helical equilibrium states. The analysis shows that the former is related to the current-driven internal-kink instability, while the latter is linked to the pressure-driven quasi-interchange instability. The kink-mode-driven helical equilibrium state appears when the minimum value of the safety factor is close to unity, while the quasi-interchange-driven helical equilibrium state appears when is below unity. The appearance of the quasi-interchange state is attributed to the weak magnetic shear at the inner rational surface and finite β.

Rheological properties of magnetic field-assisted thickening fluid and high-efficiency spherical polishing of ZrO2 ceramics

Shear thickening polishing technology using non-Newtonian polishing fluids is a low-cost, low-damage polishing method for the ultra-precision machining of complex curved surfaces. However, the low polishing efficiency and poorly controlled viscosity of traditional shear thickening polishing fluids significantly limit their practical applications. In this study, a novel weak magnetic field-assisted shear thickening polishing fluid (WMFA-STPF) containing carbonyl iron particles, which utilized a weak magnetorheological effect to promote the shear thickening process, was developed, and its rheological characteristics were investigated. The obtained results revealed that WMFA-STPF exhibited good fluidity at low shear rates and enhanced thickening characteristics in the working shear rate range. To verify the high efficiency, high quality, and uniform polishing ability of WMFA-STP technology applied to the spherical surface of a zirconia ceramic workpiece, contrast polishing experiments were performed. After 75 min of polishing, the surface damage was effectively mitigated; the surface quality and uniformity were significantly improved; and the material removal rate increased by 156% up to 7.82 μm/h. Hence, the WMFA-STP method can be successfully utilized for the high-efficiency high-quality polishing of hard and brittle ceramics.

Theoretical study of long-lived mode in tokamaks

Long-lived mode (LLM) in rotating plasmas is studied by using a alternative dispersion relation. This work offers a theoretical interpretation of LLM observed in experiments [Heidbrink, Phys. Rev. Lett. 57, 835 (1986)10.1103/PhysRevLett.57.835; Chapman, Nucl. Fusion 50, 045007 (2010)10.1088/0029-5515/50/4/045007]. It is found that in rotating plasmas, LLM can transform from the fishbone mode. The real frequency of LLM, independent of the characteristic frequency of energetic ions (EIs), is proportional to the on-axis rotation frequency of bulk plasma. The key conditions to cause transition between the fishbone mode and LLM are weak magnetic shear (for both monotonic and nonmonotonic safety factor profile) and plasma rotation. The fishbone mode can evolve into LLM only when rotating speed is bigger than a critical value in low shear plasmas. The critical beta of EIs to induce LLM is very low. LLM is nonresonantly excited by EIs, and the driving sources mainly come from plasma inertia.

Poor confinement in stellarators at high energy

High-energy particle resonances can modify particle distributions and even cause significant particle loss. Resonances can be present in any toroidal confinement device and can easily be found numerically. Many stellarators have weak magnetic shear so that large islands and large chaotic regions can be produced by resonant perturbations with small amplitudes. While the choice of the field line helicity profile in the plasma can limit the presence of resonances at low particle energy, the resonance location is energy-dependent, and they can move into the plasma at higher energy. If resonances match the toroidal variation of the equilibrium, they can produce wide islands in the phase space of orbits even in the absence of perturbations due to instabilities. These islands increase in size with particle energy and can seriously affect the confinement of high-energy ions.

Gyrokinetic simulation of low-n Alfvénic modes in tokamak HL-2A plasmas

The turbulence characteristics of plasmas with internal transport barriers in the HL-2A tokamak are analyzed by means of linear gyrokinetic simulations. It is found that turbulence is dominated by the ion temperature gradient (ITG) mode together with large-scale modes characterized by high-frequency electromagnetic fluctuation, which are destabilized by the steep ion temperature gradient in the weak magnetic shear regime. Comparison with solutions of analytical dispersion relations shows that their linear features match well with the beta-induced Alfvén eigenmode branch of the shear Alfvénic spectrum. It is further clarified that the large population of fast ions in these plasmas plays a stabilization role through the dilution mechanism in high-n ITG mode regimes.

Global kinetic-MHD simulations of downward-sweeping reversed shear Alfvén eigenmodes in tokamak plasmas

Hybrid simulations are performed to investigate the dependence of downward-sweeping reversed shear Alfvén eigenmodes (RSAEs) on key parameters in tokamaks. The investigation mainly focuses on downsweeping RSAEs with toroidal number n = 3. It is found that the occurrence of downward-sweeping RSAEs strongly depends on the bulk plasma profiles, including the pressure profile and the safety factor profile. The influence of bulk plasma pressure value and pressure gradient at q min on downsweeping RSAEs is studied, respectively. It is shown that the excitation of downsweeping RSAEs is more associated with the plasma pressure gradient at q min than with the pressure value. The enhancement of the pressure gradient at q min improves the likelihood of the destabilization of downsweeping RSAEs. Moreover, the downsweeping RSAEs only occur in a weak magnetic shear configuration in our simulations. By increasing the magnetic shear strength of central plasmas, it is numerically verified that the downsweeping RSAE activities are suppressed and eventually replaced by toroidal Alfvén eigenmodes (TAEs). Following this process, the transition region from TAEs to RSAEs is shifted to a region with lower q min values. In this work, the downsweeping RSAE, for which it has been confirmed that the mode is in the nonperturbative regime, has a twisted mode structure in the poloidal plane, while the upsweeping RSAE, which is weakly affected by the energetic ion effects, has a nearly up–down symmetry mode structure. Further, downward-sweeping RSAEs, showing a relatively narrow mode spatial profile, are generally more stable than the upward-sweeping ones, which can be a reason why the downsweeping RSAEs are rare in experiments. Finally, it is found that the kinetic effect of the energetic ion central pitch angle does not affect the excitation of downward-sweeping RSAEs, but affects the mode stability.

Mode spectrum characteristics and onset of the low-shear MHD stability regime

Equilibria with extended regions of weak magnetic shear, including some tokamak scenarios and stellarators, can be susceptible to pressure-driven internal MHD instabilities even though there is no mode rational surface in the plasma. Nonresonant modes, in particular, can have properties that are unattractive for confinement, including displacing substantial volumes of the plasma and leading to more efficient pressure gradient flattening in the nonlinear regime. The onset and linear properties of the low shear stability regime are examined using the initial-value, extended-MHD code M3D-C1. For monotonic q-profiles, we demonstrate a clear correlation between the convergents associated with the continued fraction representation of q0 and the spectrum of unstable modes. Nonresonant modes are observed to be destabilized preferentially to any other resonant instability with the same toroidal mode number when n > 1. Using the observed connection between the spectrum associated with q0 and the overall equilibrium stability properties, we suggest a technique for reducing the uncertainty on both q0 and magnetic shear in the core region, obtained either via measurement or through the analysis and reconstruction of experimental results.