Positive Magnetic Shear Research Articles

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.

Resistive instabilities in general toroidal plasmas with neoclassical bootstrap currents

In this work, linear neoclassical resistive instabilities are investigated in general toroidal plasmas using standard perturbation theory. Using a neoclassical fluid model, we derive the singular layer equations modified by bootstrap currents and also obtain the dispersion relation of the resistive interchange mode and the neoclassical tearing mode (NTM), respectively. Additionally, we determine the stability criteria DRbs and Δcbs for bootstrap current-modified resistive modes. The resistive interchange mode is stable when DRbs<0 and the NTM is stable when Δ′<Δcbs, where Δ′ is the stability index of the tearing mode. It is found that, in tokamak plasmas with a positive magnetic shear, bootstrap currents have a destabilizing effect on resistive interchange modes, which not only increases the value of the stability criterion (DRbs) but also enhances the growth rate. In addition, bootstrap currents have a stabilizing effect on the growth rate of the NTM in a low growth rate region. However, bootstrap currents can also decrease the critical value Δcbs. In plasmas with negative magnetic shear, the opposite holds. Furthermore, the coupling effect between bootstrap currents and Pfirsch–Schlüter currents via magnetic field curvature is determined for the first time in this work. This coupling always has a stabilizing influence on the resistive interchange mode and can increase the value of Δcbs. The coupling is also independent of the sign of the magnetic shear and can be enhanced in low-aspect-ratio tokamaks (such as spherical tokamaks) or in plasma regions with low magnetic shear (as used in ITER hybrid scenarios). Our results are valid for low-n resistive instabilities in toroidal plasmas with arbitrary aspect ratios and β, where n is the toroidal mode number and β represents the ratio of the plasma pressure to the toroidal magnetic pressure. Overall, this investigation has broad parametric applications and deepens our understanding of the physical mechanisms underlying the influence of neoclassical effects on resistive instabilities.

Impurity effects on trapped electron modes in tokamak plasmas with inverted electron density profile

Impurity effects on trapped electron modes (TEMs) in tokamak plasmas with inverted electron density profile (IEDP) are numerically investigated with a gyrokinetic integral eigenmode equation. It is found that different from the negative gradient of normal electron density profile, the positive gradient of the IEDP has a stabilizing effect on TEM in the presence of impurity ions. The electron temperature gradient threshold for TEM excitation increases not only with the increasing absolute value of IEDP but also with increasing impurity content. Furthermore, the effects of different impurity species and different impurity peaking profiles on TEMs with the IEDP are analyzed in detail. It is shown that there is a transition point of impurity density profile, on both sides of which the impurity has opposite effects on TEM. The dependence of such a transition point on electron temperature and density gradients is obtained numerically. Besides, the synergistic effects of ion temperature gradient and impurity density gradient are studied, in which a similar transition point of the ion temperature gradient is also identified in the case of outwardly peaked impurity density profile. In addition, impurity effects on the characteristics of mode structure and on the radial transport coefficients in positive and negative magnetic shear regions are discussed as well based on quasi-linear mixing length estimation.

Quasi-linear heat transport induced by ITG turbulence in the presence of impurities

The impurity effects on turbulent transport induced by ion temperature gradient (ITG) turbulence are numerically studied in tokamak plasmas, using a gyrokinetic quasi-linear model. The characteristics of the instability and heat fluxes in the presence of impurity ions are investigated for a broad parameter regime, including temperature and density gradients of main and impurity ions, concentration, charge and mass numbers of impurity ions, magnetic shear as well as wave vector spectrum. The heat fluxes are demonstrated to depend not only on the saturation amplitude of the instability but also on the phase shift between and . The peaking factor of temperature/density profile, defined as the ratio of major radius to gradient scale length when the total turbulent heat flux equals zero, is fitted with linear/quadratic functions. In addition, the contributions from diagonal and off-diagonal terms to heat fluxes are identified in detail, i.e. the main ion heat diffusion are proved to be dominated by off-diagonal (diagonal) terms for regions of weak (strong) ITG. In general, steep temperature gradients of main ions as well as hollow density profiles of impurity ions significantly enhance instability and heat fluxes. However, it is interesting to find that the effect of impurity ions with positive density gradient may transit from the enhancement to reduction of the quasi-linear heat flux of main ions in regions of steep ITG, corresponding to transport barriers (e.g. pedestal of H-mode and I-mode plasmas). Both strong and weak positive magnetic shear decrease heat transport.

Stability of a tokamak plasma with diffuse toroidal rotation

The present work considers the stability of a high- $\beta$ , large aspect ratio, circular plasma with diffuse profiles for the safety factor and the angular toroidal frequency (López & Guazzotto, Phys. Plasmas, vol. 24, 032501). An application of the Frieman–Rotenberg formalism results in a system of scalar eigenmode equations whose coupling is retained at the plasma–vacuum transition but is disregarded across the plasma column, which is a standard practice. The solution technique consists of a multidimensional shooting method for the poloidal harmonics; robust initial guesses are constructed by solving the dispersion relation in the static scenario with vanishing magnetic shear. Flow shear appears as a high- $\beta$ toroidal contribution, and we illustrate its destabilizing influence on $n=1$ external kink modes in the presence of ideal and resistive walls. Internal resonances are avoided by means of the selection of appropriate equilibrium parameters. The stabilizing influence of a finite positive average magnetic shear is also exemplified.

Effects of trapped electrons on the ion temperature gradient mode in tokamak plasmas with hollow density profiles

The ion temperature gradient (ITG) mode in the presence of impurity ions and trapped electrons (TEs) is numerically investigated in tokamak plasmas with hollow density profiles, using the gyrokinetic integral eigenmode equation. It is found that in the inverted density plasma, the increase of the ITG enhances the growth rate and frequency of the ITG, and the density gradient plays an important role in the ITG modes. For weak density gradient situations, the trapped electron effects increase the instability of the ITG, while the impurity has an obviously stabilizing effect. For the strong density gradient cases, both the impurities and trapped electrons enhance the ITG instabilities. In addition, it is shown that the growth rate of the ITG decreases with positive magnetic shear s while the real frequency increases with positive magnetic shear. The growth rate of the ITG increases with negative magnetic shear s while the real frequency decreases with negative magnetic shear. The length of the calculated mode structure in the positive and negative magnetic shear intervals is also presented.

Scaling study for positive magnetic shear ELMy H-mode plasmas in JT-60U

Scaling of the density peaking for positive magnetic shear ELMy H-mode plasmas in JT-60U has been developed. Although the density peaking generally depends on collisionality, a variation of the density peaking factor for the same collisionality exists, and the variation is different between plasmas with co-directed and ctr-directed toroidal rotation(co-VT plasmas and ctr-VT plasmas). The variation of the co-VT plasmas can be explained by particle source profile. As a result of scaling, the peaking factor of the co-VT plasmas depends on the particle source rate profile from neutral beams (NBs) as much as collisionality. The dataset of the ctr-VT plasmas has a larger variation of the peaking factor compared to that of the co-VT plasmas. The larger variation stems from that the peaking factor of the ctr-VT plasmas also depends on the normalized ion temperature gradient at the edge region. As a result of scaling, the normalized ion temperature gradient influences the peaking factor as much as or a little larger than collisionality. The parameter regime of the ctr-VT plasmas ranges from the trapped electron mode (TEM) to the ion temperature gradient mode (ITG mode). The plasmas with the positive correlation between the normalized density gradient and the normalized ion temperature gradient are dominated by the TEM. On the other hand, the plasmas with the negative correlation are dominated by the ITG mode.

Modeling of chirping toroidal Alfvén eigenmodes in NSTX

Modulation of mode amplitude and frequency of TAE modes, observed experimentally and referred to as chirping, is investigated using a guiding center code and a δf formalism. Chirping is observed as the development in time of Fourier sidebands that move above and below the nominal mode frequency. Subsequent doubling of the sidebands is also sometimes observed. Equilibria with conventional positive magnetic shear are used, as well as NSTX reversed shear cases. The onset of chirping can be triggered by a sudden increase in mode damping, as can occur by the mode contacting the continuum.

Candidate explanation for the mild core oscillations in dominant electron heating scenario on experimental advanced superconducting tokamak

The interchange-like transport is observed between two resonant surfaces (q = 1 and q = 4/3, where q is the safety factor) in a finite small positive magnetic shear regime with mild core oscillations in the experimental advanced superconducting tokamak strong on-axis electron heating H-mode plasmas. It is synchronized with the increasing gradient of the soft X-ray profile and the intensifying electron density fluctuations in the core. The analysis of two-fluid simulations combined with experimental measurements indicates the destabilization of collective resistive interchange modes with several toroidal mode numbers. The overall effect of modes leads to strong perturbations at the two resonant surfaces in contrast to that between them where the anomalous electron flux is low. Their radial displacement is beyond the resistive layer width which satisfies the condition for the nonlinear destabilization of tearing modes [L. Comisso et al., Phys. Plasmas 23, 100702 (2016)]. Evidence and analysis shown in this paper tend to understand the mechanism of mild oscillations in the core.

Transport barriers in bootstrap-driven tokamaks

Experiments have demonstrated improved energy confinement due to the spontaneous formation of an internal transport barrier in high bootstrap fraction discharges. Gyrokinetic analysis, and quasilinear predictive modeling, demonstrates that the observed transport barrier is caused by the suppression of turbulence primarily from the large Shafranov shift. It is shown that the Shafranov shift can produce a bifurcation to improved confinement in regions of positive magnetic shear or a continuous reduction in transport for weak or negative magnetic shear. Operation at high safety factor lowers the pressure gradient threshold for the Shafranov shift-driven barrier formation. Two self-organized states of the internal and edge transport barrier are observed. It is shown that these two states are controlled by the interaction of the bootstrap current with magnetic shear, and the kinetic ballooning mode instability boundary. Election scale energy transport is predicted to be dominant in the inner 60% of the profile. Evidence is presented that energetic particle-driven instabilities could be playing a role in the thermal energy transport in this region.

Suppression of fast-ion-driven MHD instabilities by ECH/ECCD on Heliotron J

Experiments of suppressing fast-ion-driven MHD instabilities such as energetic particle modes (EPMs) and global Alfvén eigenmodes (GAEs) have been made using a second harmonic x-mode electron cyclotron heating and current drive (ECCD) in the helical-axis heliotron device, Heliotron J. ECCD experiments show that the GAEs destabilized by fast ions of neutral beam injection with the observed frequency around 140 kHz are fully stabilized, and the EPMs with the observed frequency around 90 kHz are suppressed when the EC-driven plasma current flowing in the counter direction reaches approximately 0.7 kA. The low magnetic shear under the vacuum condition is modified into positive magnetic shear when counter-ECCD is applied, and the amplitude of GAEs and EPMs decreases with an increase in EC-driven plasma current. These results indicate that magnetic shear plays a key role in controlling GAEs as well as EPMs. The comparison of the calculation of shear Alfvén spectra with experimental results shows that the increasing continuum damping rate with an increase in local magnetic shear by EC-driven current is important for both EPMs and GAEs. Moreover, the increase in plasma current leads to the inward movement of GAEs. This effect would also contribute to suppression of GAEs because the continuum damping rate increases more and more toward the core. Steady ECH is also found experimentally to be effective for controlling the amplitude of both GAEs and EPMs. The amplitude of EPMs, and especially for GAEs, decreases with an increase in the ECH power under fixed density conditions.

Effects of toroidal rotation shear and magnetic shear on thermal and particle transport in plasmas with electron cyclotron heating on JT-60U

Increases in thermal and particle transport with electron cyclotron heating (ECH) that are observed in many tokamaks can be a critical issue in establishing ITER operational scenarios with electron heating. To address the issues, conditions with no increase in the thermal and particle transport with ECH have been experimentally investigated in positive magnetic shear, weak magnetic shear (WS) and reversed magnetic shear plasmas with internal transport barrier in the ion channel. The ion heat diffusivity (χi) around the internal transport barrier in the ion temperature remains constant with ECH when a large negative toroidal rotation shear (|dVφ/dr| > 4 × 105 s−1) is formed before the ECH. On the other hand, χi increases on the condition that the toroidal rotation shear is small or positive. The characteristics do not depend on magnetic shear, the electron to ion temperature ratio (Te/Ti) and ECH power. The electron heat diffusivity stays constant with ECH when the magnetic shear is negative. Effective particle transport remains constant or reduces during ECH under the condition of negative magnetic shear. An observation indicates that there is no threshold of the negative magnetic shear or a very small one for the electron channel sustainment; the electron thermal and particle confinement is maintained during ECH with a small negative magnetic shear in the WS operation.

Non-resonant fishbone instabilities of qmin ≳ 1 in tokamak plasmas with weakly reversed magnetic shear

In this study, we theoretically explore properties of non-resonant fishbone (NRF) instabilities with a safety factor profile slightly above unity (qmin ≳ 1) in tokamak plasmas with reversed magnetic shear configuration. From the dispersion relation of the NRF mode, it is found that the growth rate of the mode in general reversed shear scenarios with qmin ≳ 1 depends on fast ion beta βh in a power law of , different from that of ∼βh in a conventional positive magnetic shear configuration. Meanwhile, due to the slow ion precession and small continuum damping in ITER-like tokamaks with reversed shear, the mode has a lower trigger threshold than those with monotonously positive magnetic shear. In addition, the ion diamagnetic drift has been found to destabilize the fast ion-driven NRF mode. Other effects such as the shape of the q-profile, characterized by values of qmin and q(0), neutral beam energy, magnetohydrodynamic potential energy and the fraction of fast ions on the instability threshold are also discussed. Nonlinear behavior of the mode is further analyzed using a modified model.

Intermittent bursts induced by double tearing mode reconnection

Reversed magnetic shear (RMS) configuration is assumed to be the steady-state operation scenario for the future advanced tokamaks like International Thermonuclear Experimental Reactor. In this work, we numerically discover a phenomenon of violent intermittent bursts induced by self-organized double tearing mode (DTM) reconnection in the RMS configuration during the very long evolution, which may continuously lead to annular sawtooth crashes and thus badly impact the desired steady-state operation of the future advanced RMS tokamaks. The key process of the intermittent bursts in the off-axis region is similar to that of the typical sawtooth relaxation oscillation in the positive magnetic shear configuration. It is interestingly found that in the decay phase of the DTM reconnection, the zonal field significantly counteracts equilibrium field to make the magnetic shear between the two rational surfaces so weak that the residual self-generated vortices of the previous DTM burst are able to trigger a reverse DTM reconnection by curling the field lines.

Global geodesic acoustic mode in a tokamak with positive magnetic shear and a monotonic temperature profile

The analytical solution for global geodesic acoustic modes (GGAMs) in a tokamak with a positive magnetic shear profile and a monotonic temperature profile is found in the framework of magnetohydrodynamic theory. The axisymmetric eigenvalue problem for perturbed pressure and electrostatic potential is formulated as a recurrent set of equations for poloidal Fourier harmonics. The integral condition for the existence of GGAMs is obtained. It is shown that the traditional paradigm of having a off-axis maximum of the local geodesic acoustic frequency is not necessary for the existence of GGAMs; a representative example is designed.

Plasma rotation and transport in MAST spherical tokamak

The formation of internal transport barriers (ITBs) is investigated in MAST spherical tokamak plasmas. The relative importance of equilibrium flow shear and magnetic shear in their formation and evolution is investigated using data from high-resolution kinetic- and q-profile diagnostics. In L-mode plasmas, with co-current directed NBI heating, ITBs in the momentum and ion thermal channels form in the negative shear region just inside qmin. In the ITB region the anomalous ion thermal transport is suppressed, with ion thermal transport close to the neo-classical level, although the electron transport remains anomalous. Linear stability analysis with the gyro-kinetic code GS2 shows that all electrostatic micro-instabilities are stable in the negative magnetic shear region in the core, both with and without flow shear. Outside the ITB, in the region of positive magnetic shear and relatively weak flow shear, electrostatic micro-instabilities become unstable over a wide range of wave numbers. Flow shear reduces the linear growth rates of low-k modes but suppression of ITG modes is incomplete, which is consistent with the observed anomalous ion transport in this region; however, flow shear has little impact on growth rates of high-k, electron-scale modes. With counter-NBI ITBs of greater radial extent form outside qmin due to the broader profile of E × B flow shear produced by the greater prompt fast-ion loss torque.

Self-Consistent Pressure and Current Profiles in High-Beta D-3He Tokamak Reactors

D-3He reactor has a great advantage of neutron-poor operation, but it requires higher-beta value and higher bootstrap current fraction than D-T reactor. In this paper, we investigated self-consistent plasma pressure and current profiles in the case of a positive magnetic shear mode (parabolic temperature profile) and a negative magnetic shear mode (ITB temperature profile) using TOTAL-T code including Cytran module. In a negative magnetic shear mode, toroidal beta value βT ∼ 52.4 % and bootstrap current fraction fbs ∼ 0.93 was obtained in a plasma with aspect ratio 1.77, plasma major radius 6.2 m, toroidal field 4.2 T and plasma current 49.3 MA.

Pressure-gradient-induced Alfvén eigenmodes: II. Kinetic excitation with ion temperature gradient

The kinetic excitation of ideal magnetohydrodynamic (MHD) discrete Alfvén eigenmodes in the second MHD ballooning stable domain is studied in the presence of a thermal ion temperature gradient (ITG), using linear gyrokinetic particle-in-cell simulations of a local flux tube in shifted-circle tokamak geometry. The instabilities are identified as α-induced toroidal Alfvén eigenmodes (αTAE); that is, bound states trapped between pressure-gradient-induced potential barriers of the Schrödinger equation for shear Alfvén waves. Using numerical tools, we examine in detail the effect of kinetic thermal ion compression on αTAEs; both non-resonant coupling to ion sound waves and wave–particle resonances. It is shown that the Alfvénic ITG instability thresholds (e.g., the critical temperature gradient) are determined by two resonant absorption mechanisms: Landau damping and continuum damping. The numerical results are interpreted on the basis of a theoretical framework previously derived from a variational formulation. The present analysis of properties and structures of Alfvénic fluctuations in the presence of steep pressure gradients applies for both positive or negative magnetic shear and can serve as an interpretative framework for experimental observations in (future) high-performance fusion plasmas of reactor relevance.

Overview of JT-60U results towards the establishment of advanced tokamak operation

Recent JT-60U experimental results towards the establishment of advanced tokamak (AT) operation are reviewed. We focused on the further expansion of the operational regime of AT plasmas towards higher βN regime with wall stabilization. After the installation of ferritic steel tiles in 2005, the high power heating in a large plasma cross-section in which the wall stabilization is expected has been possible. In 2007, the modification of power supply of NBIs improved the flexibility of the heating profile in long-pulse plasmas. The investigation of key physics issues for the establishment of steady-state AT operation is also in progress using new diagnostics and improved heating systems. In weak magnetic shear plasma, high βN ∼ 3 exceeding the ideal MHD limit without a conducting wall () is sustained for ∼5 s (∼3τR) with RWM stabilization by a toroidal rotation at the q = 2 surface. External current drivers of negative-ion based NB and lower-hybrid waves together with a large bootstrap current fraction (fBS) of 0.5 can sustain the whole plasma current of 0.8 MA for 2 s (1.5τR). In reversed magnetic shear plasma, high βN ∼ 2.7 (βp ∼ 2.3) exceeding with qmin ∼ 2.4 (q95 ∼ 5.3), HH98(y,2) ∼ 1.7 and fBS ∼ 0.9 is obtained with wall stabilization. These plasma parameters almost satisfy the requirement of ITER steady-state scenario. In long-pulse plasmas with positive magnetic shear, a high βNHH98(y,2) of 2.6 with βN ∼ 2.6 and HH98(y,2) ∼ 1 is sustained for 25 s, significantly longer than the current diffusion time (∼14τR) without neoclassical tearing modes (NTMs). A high G-factor, (a major of fusion gain), of 0.54 and a large fBS > 0.43 are suitable for ITER hybrid operation scenario. Based on the plasma for ITER hybrid operation scenario, the high βN of 2.1 with good thermal plasma confinement of HH98(y,2) > 0.85 is sustained for longer than 12 s at and frad > 0.79. Physics studies for the development of AT plasmas, physics studies of H-mode, pedestal and ELM characteristics and physics studies on impurity transport, SOL/divertor plasmas and plasma–wall interactions are also in progress. The active NTM stabilization system using modulated ECCD, which is synchronized to rotating island, has been developed and the efficiency of modulated ECCD in m/n = 2/1 NTM stabilization has been demonstrated. The intrinsic toroidal rotation driven by the ion pressure gradient and by the ECH is confirmed. The dedicated H-mode and pedestal experiments indicate two scalings, H-factor evaluated for the core plasma as and pedestal width scaling of . New fast diagnostics with high spatial and temporal resolutions reveals the different structures of pedestal pressure between co- and counter-rotating plasma, resulting in different ELM sizes determined by the radial penetration depth of the ELM crash. The tungsten accumulation becomes more significant with increasing toroidal rotation in the counter-direction.

Internal transport barriers in the National Spherical Torus Experiment

In the National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 41, 1435 (2001)], internal transport barriers (ITBs) are observed in reversed (negative) shear discharges where diffusivities for electron and ion thermal channels and momentum are reduced. While neutral beam heating can produce ITBs in both electron and ion channels, high harmonic fast wave heating can also produce electron ITBs (e-ITBs) under reversed magnetic shear conditions without momentum input. Interestingly, the location of the e-ITB does not necessarily match that of the ion ITB (i-ITB). The e-ITB location correlates best with the magnetic shear minima location determined by motional Stark effect constrained equilibria, whereas the i-ITB location better correlates with the location of maximum E×B shearing rate. Measured electron temperature gradients in the e-ITB can exceed critical gradients for the onset of electron thermal gradient microinstabilities calculated by linear gyrokinetic codes. A high-k microwave scattering diagnostic shows locally reduced density fluctuations at wave numbers characteristic of electron turbulence for discharges with strongly negative magnetic shear versus weakly negative or positive magnetic shear. Reductions in fluctuation amplitude are found to be correlated with the local value of magnetic shear. These results are consistent with nonlinear gyrokinetic simulations predicting a reduction in electron turbulence under negative magnetic shear conditions despite exceeding critical gradients.