Shear Tokamak 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.

Theoretical studies of low-frequency shear Alfvén waves in reversed shear tokamak plasmas

The low-frequency Alfvénic fluctuations in the kinetic thermal-ion gap frequency range have aroused the interest of researchers since they can interact with background thermal particles and/or energetic particles. In the theoretical framework of the general fishbone-like dispersion relation (GFLDR), we theoretically investigate and delineate the linear wave properties of the low-frequency shear Alfvén wave excited by energetic and/or thermal particles observed in tokamak experiments with reversed magnetic shear. These low-frequency shear Alfvén waves are closely related to the dedicated experiment on energetic ion-driven low-frequency instabilities conducted on DIII-D in 2019. Therefore, adopting the representative experimental equilibrium parameters of DIII-D, in this work we demonstrate that the experimentally observed low-frequency modes and beta-induced Alfvén eigenmodes (BAEs) are, respectively, the reactive-type unstable mode and dissipative-type unstable mode, each with dominant Alfvénic polarization, thus the former being more precisely called low-frequency Alfvén modes (LFAMs). More specifically, due to diamagnetic and trapped particle effects, the LFAM can be coupled with the beta-induced Alfvén-acoustic mode (BAAE) in the low-frequency range (frequency much less than the thermal-ion transit frequency and/or bounce frequency), or with the BAE in the high frequency range (frequency higher than or comparable to the thermal-ion transit frequency), resulting in reactive-type instabilities. Moreover, due to different instability mechanisms, the maximal drive of BAEs occurs in comparison with LFAMs, when the minimum of the safety factor (<inline-formula><tex-math id="M1">\begin{document}$ q_{\rm min} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230255_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230255_M1.png"/></alternatives></inline-formula>) deviates from a rational number. Meanwhile, the BAE eigenfunction peaks at the radial position of the maximum energetic particle pressure gradient, resulting in a large deviation from the <inline-formula><tex-math id="M2">\begin{document}$ q_{\rm min} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230255_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230255_M2.png"/></alternatives></inline-formula> surface. The ascending frequency spectrum patterns of the experimentally observed BAEs and LFAMs can be theoretically reproduced by varying <inline-formula><tex-math id="M3">\begin{document}$ q_{\rm min} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230255_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230255_M3.png"/></alternatives></inline-formula>, and they can also be well explained based on the GFLDR. In particular, it is confirmed that the stability of the BAAE is not affected by energetic ions, which is consistent with the first-principle-based theory predictions and simulation results. The present analysis illustrates the solid predictive capability of the GFLDR and its practical applications in enhancing the ability to explain experimental and numerical simulation results.

Three types of pressure crash in the low magnetic shear tokamaks

Numerical investigations on the pressure crash with a low magnetic shear profile in Tokamaks are carried out through the three-dimensional, toroidal, and nonlinear MHD code CLT. We find that there exist at least three different kinds of pressure crashes. The first type is that one cold bubble forms and merges into the hot core, which is the standard case for the nonlinear evolution of the quasi-interchange mode. The second type is two cold bubbles forming and squeezing the hot core, leading to fast pressure crashes. The third one is similar to that caused by the resistive-kink mode, i.e., an m/n = 1/1 magnetic island grows up and fills up the whole central region. The thresholds for these kinds of pressure crashes are systematically discussed.

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.

Nonlinear evolution and control of neo-classical tearing mode in reversed magnetic shear tokamak plasmas

Nonlinear evolution and control of neo-classical tearing mode in reversed magnetic shear tokamak plasmas

Prevention of electron cyclotron current drive triggering explosive bursts in reversed magnetic shear tokamak plasmas for disruption avoidance

An explosive burst excited by a neoclassical tearing mode (NTM) is one of the possible candidates for disruptive terminations in reversed magnetic shear (RMS) tokamak plasmas. For the purpose of disruption avoidance, numerical investigations have been implemented on the prevention of explosive bursts triggered by the ill-advised application of electron cyclotron current drive (ECCD) in RMS configuration. Under the situation of controlling NTMs by ECCD in RMS tokamak plasmas, a threshold in electron cyclotron driven current has been found. Below the threshold, not only are the NTM islands not effectively suppressed but a deleterious explosive burst could also be triggered, which might contribute to major disruption to tokamak plasmas. In order to prevent this ECCD from triggering explosive bursts, three control strategies have been attempted in this work and two of them have been recognized to be effective. One is to apply differential poloidal plasma rotation in the proximity of outer rational surface during the ECCD control process; the other is to apply two ECCDs to control NTM islands on both rational surfaces at the same time. In the former strategy, the threshold is diminished due to the modification of the classical tearing mode index. In the latter strategy, the prevention is accomplished as a consequence of the reduction of the coupling strength between the two rational surfaces via the stabilization of inner islands. Moreover, the physical mechanism behind the excitation of the explosive burst and the control processes by different control strategies have all been discussed in detail.

Interaction between energetic-ions and internal kink modes in a weak shear tokamak plasma

Based on the conventional tokamak HL-2A-like parameters and profiles, the linear properties and the nonlinear dynamics of non-resonant kink mode (NRK) and non-resonant fishbone instability (NRFB) in reversed shear tokamak plasmas are investigated by using the global hybrid kinetic-magnetohydrodynamic nonlinear code M3D-K. This work mainly focuses on the effect of passing energetic-ions on the NRK and NRFB instabilities, which is different from the previous works. It is demonstrated that the NRFB can be destabilized by the passing energetic-ions when the energetic-ion beta β h exceeds a critical value. The transition from NRK to NRFB occurs when the energetic-ion beta β h increases to above a critical value. The resonance condition responsible for the excitation of NRFB is interestingly found to be satisfied at ω t + ω p ≈ ω, where ω t is the toroidal motion frequency, ω p is the poloidal motion frequency and ω is the mode frequency. The nonlinear evolutions of NRFB’s mode structures and Poincaré plots are also analyzed in this work and it is found that the NRFB can induce evident energetic-ion loss/redistribution, which can degrade the performance of the plasmas. These findings are conducive to understanding the mechanisms of NRFB induced energetic-ion loss/redistribution through nonlinear wave-particle interaction.

Coriolis Force Effect on Suppression of Neo-Classical Tearing Mode Triggered Explosive Burst in Reversed Magnetic Shear Tokamak PlasmasSupported by the National Natural Science Foundation of China (Grant Nos. 11925501, 11875099, and 11575158), the Liaoning Revitalization Talents Program (Grant No. XLYC1802009), and the China Scholarship Council (Grant No. 201806060036).

We numerically investigate the Coriolis force effect on the suppression of an explosive burst, triggered by the neo-classical tearing mode, in reversed magnetic shear configuration tokamak plasmas, using a reduced magnetohydrodynamic model, including bootstrap current. Previous works have shown that applying differential poloidal rotation, with rotation shear located near the outer rational surface, is an effective way to suppress an explosive burst. In comparison with cases where there is no Coriolis force, the amplitude of differential poloidal rotation required to effectively suppress the explosive burst is clearly reduced once the effect of Coriolis force is taken into consideration. Moreover, the effective radial region of the rotation shear location is broadened in cases where the Coriolis force effect is present. Applying rotation with shear located between the radial positions of q min and the outer rational surface always serves to effectively suppress explosive bursts, which we anticipate will reduce operational difficulties in controlling explosive bursts, and will consequently prevent plasma disruption in tokamak experiments.

Tungsten impurity effects on the coupling of TEM and ITG mode in reversed magnetic shear tokamak plasmas

The trapped electron mode (TEM) and ion temperature gradient (ITG) mode may couple into one hybrid mode or coexist simultaneously, depending on the regime of tokamak plasma parameters. A gyrokinetic integral eigenvalue equation is applied to investigate the coupling of TEM and ITG mode in the presence of tungsten (W) impurity in tokamak geometry of reversed magnetic shear (RMS). Systematic analysis of W impurity effects on the mode characteristics and induced quasi-linear particle flux has been performed in a wide regime of plasma parameters such as density gradient , charge concentration , and charge number of impurity ions, and poloidal wave number spectrum. It is found that both RMS and the impurity ions with inwardly peaked density profile and high charge concentration have strongly stabilizing effects on the modes. Furthermore, the increasing tends to decouple the hybrid mode into coexisting modes or dominating TEM/ITG mode in different parameter regions. The significance of the results for the particle transport of impurity and main ions as well as electrons in advanced tokamaks with W components is discussed.

Global gyrokinetic nonlinear simulations of kinetic infernal modes in reversed shear tokamaks

The nonlinear evolution of electromagnetic instabilities in reversed shear plasmas is investigated by means of global gyrokinetic simulations. It is found that the kinetic infernal mode (KIM), which is a pressure-driven instability with low to intermediate toroidal mode number excited in a region of low magnetic shear, is unstable at high β, while the ion temperature gradient mode is unstable at low β, where β is the ratio of the plasma kinetic pressure to the magnetic pressure. The β threshold of the KIM is much lower than that of the kinetic ballooning mode (KBM) appearing in a normal shear plasma, while both the KIM and KBM are strong at the unfavorable curvature region, and the KIM has the same parity as the KBM. Nonlinear simulations show that the KIM gets saturated by exciting strong zonal flows and fluctuations of low toroidal mode number. The amplitude of the KIM turbulence is similar to that of the KBM turbulence in spite of the fact that the linear growth rate of the KIM is much higher than that of the KBM. This is because the excitation of zonal flows and fluctuations at low toroidal mode number is stronger in the reversed shear plasma than that of the normal shear plasma. On the other hand, the energy flux and particle flux due to the KIM turbulence are about two or three times larger than those by the KBM turbulence.

Gyrokinetic studies of fast ion precession driven drift instability in reversed shear plasmas

A new electron drift instability driven by resonance with precession reversed fast trapped ions in reversed magnetic shear tokamak plasmas is identified from gyrokinetic simulations. Results from the initial value GKW code and eigenmode analysis in the ballooning space are in broad agreement with predictions from the local analytic theory [B. J. Kang and T. S. Hahm, Phys. Plasmas 26, 042501 (2019)].

Global geodesic acoustic mode in an ideal magnetohydrodynamic tokamak plasma

A concise and transparent second order ordinary differential equation (ODE) describing the radial structure of the global geodesic acoustic mode (GAM) is analytically presented in a low-β tokamak plasma. The large-aspect-ratio and circular cross section are assumed to linearize the ideal magnetohydrodynamic equations. We show clearly how finite β-dependent terms affect the global GAM frequency and radial mode structure. A typical Wentzel–Kramers–Brillouin form of solution is found for some reversed shear equilibria. For some other equilibria with lower β, even also in a reversed shear tokamak, the GAM continuum is upraised by the high order β-dependent terms so that its maximum is beyond ωG, where ωG is the classical local frequency of GAM. As a result, no self-consistent solution to the ODE can be found.

Control of neoclassical tearing mode by synergetic effects of resonant magnetic perturbation and electron cyclotron current drive in reversed magnetic shear tokamak plasmas

Synergetic effects of resonant magnetic perturbation (RMP) and electron cyclotron current drive (ECCD) on stabilizing neoclassical tearing mode (NTM) in reversed magnetic shear (RMS) tokamak plasmas are numerically investigated based on a set of reduced MHD equations. For the moderate separation, it is found that the explosive burst induced by the fast reconnection of double tearing mode (DTM) in the RMS configuration can be completely suppressed by externally applied RMPs. Zonal flows with strong shear induced by a rotating RMP play an important role in this suppression process. Moreover, turning on ECCD in advance is essential to mitigate the NTM. For the large separation without the explosive burst, two strategies, i.e. a continuous ECCD with static RMP and a modulated ECCD with rotating RMP, are separately investigated. It is shown that when the NTM is decelerated by a relatively slow rotating RMP, the modulated ECCD can have a better stabilizing effect. In addition, the ECCD deposition widths in both radial and helical angle directions, as well as the ECCD on-duty time, are analyzed in detail. The best effectiveness of ECCD is obtained and the relevant physical mechanisms are discussed.

Effects of diamagnetic drift on magnetohydrodynamic explosive bursts in reversed magnetic shear tokamak plasmas

The explosive bursts, induced by self-organized double tearing modes (DTMs) in reversed magnetic shear tokamak plasmas, are numerically investigated based on a set of reduced two-fluid equations. It is found that the diamagnetic drift has a destabilizing effect on the mode in the Rutherford phase but can effectively stabilize the explosive burst of the mode in the following nonlinear phase. The plasma viscosity µ is found to have an important effect on the critical ion skin depth for completely suppressing the explosive bursts. In the low viscosity regime (i.e. , where is the critical viscosity), increases with increasing µ, because the increase of µ can effectively reduce the velocity difference of islands between the two rational surfaces, which mainly result from zonal flow and electron diamagnetic flow. In the high viscosity regime (i.e. ), however, decreases with increasing µ, because the increase of µ can greatly stabilize the DTM instability. In addition, the dependences of critical viscosity on viscosity and resistivity are obtained and the relevant mechanisms are analyzed.

Helical equilibrium magnetohydrodynamic flow effects on the stability properties of low-n ideal external-infernal modes in weak shear tokamak configurations

The impact of equilibrium helical flows on the stability properties of low shear tokamak plasmas is assessed. The corrections due to such helical flow to the equilibrium profiles (mass density, pressure, Shafranov shift, magnetic fluxes) are computed by minimising order by order the generalised Grad–Shafranov equation. By applying the same minimisation procedure, a set of three coupled equations, suitable for the study of magnetohydrodynamic perturbations localised within core or edge transport barriers is derived in circular tokamak geometry. We apply these equations to modelling the impact of strong poloidal flow shear in the edge region caused by a radial electric field on the stability of edge infernal modes retaining vacuum effects. Due to the poloidal flow shearing, the effect of plasma rotation is not simply a Doppler shift of the eigenfrequency. Stabilisation is found even for weak flow amplitude.

Suppression of explosive bursts triggered by neo-classical tearing mode in reversed magnetic shear tokamak plasmas via ECCD

The suppression of explosive bursts, triggered by the neo-classical tearing mode, in the reversed magnetic shear configuration tokamak plasmas by electron cyclotron current drive (ECCD) are numerically studied by making use of a reduced magnetohydrodynamic model including both bootstrap current and self-consistently evolving EC driven current. It is found that the ECCD with appropriate input power and switch-on time can effectively stabilize the neo-classical islands. In comparison with the classical one, it is far more difficult to control the neo-classical island due to the strong zonal magnetic field induced during the nonlinear evolution. This strong zonal field can lead to intense fluctuations of the magnetic surfaces once the ECCD is turned on, which can damage the steady deposition of the driven current. To avoid the strong zonal field, the switch-on time should be put forward, which is proved to be effective. By adopting this scheme, the explosive burst triggered by neo-classical current can also be effectively suppressed. Moreover, the steady-state distributions of driven current are displayed. The influence of the radial misalignment of ECCD is discussed in detail. Based on the numerical results in different fractions of bootstrap current, some suggestions are proposed for the tokamak experiments.

Destabilization of beta-induce Alfvén eigenmodes by energetic trapped ions in low-magnetic-shear plasma

The dispersion relation for high toroidal mode number n beta-induced Alfven eigenmodes (BAEs) excited by magnetically trapped energetic ions generated with ion-cyclotron resonance heating via precessional resonance in low magnetic shear (s) tokamak plasma is investigated analytically and numerically. The dynamics of the energetic particles (EPs) is treated non-perturbatively and finite drift orbit width (FOW) effects are taken into account. It is found that, depending on the plasma parameters, the most unstable mode can be either the BAE mode or the energetic particle mode (EPM). Both modes can resonate with the trapped-particles' magnetic precessional drifts and become unstable. The mode frequencies and growth rates depend strongly on the EP parameters. FOW can stabilize high-n BAE modes by reducing the wave-particle interaction. Magnetic shear has an important effect on the growth rate of the modes. For BAE, the growth rate presents the trend of first increase and following decrease with the increase of...

Control of neo-classical double tearing modes by differential poloidal rotation in reversed magnetic shear tokamak plasmas

The control of neo-classical tearing modes (NTMs) by the differential rotation in the reversed magnetic shear (RMS) configuration with different separations between two rational surfaces is numerically studied by means of reduced magnetohydrodynamic (MHD) simulations. It is found that the differential rotation with a strong shear at the outer resonant surface can effectively suppress the explosive burst of double tearing modes (DTMs)/NTMs. Critical values of the strength of rotation to suppress the burst are also presented for different bootstrap current fractions . Furthermore, a couple of measurable parameters , corresponding respectively to the triangularity and elongation of the magnetic islands at the outer resonant surface, are introduced to characterize the deformation of islands in the nonlinear phase. It is found that the triangularity is more likely to precisely predict the onset of burst than the island width and elongation . For a given , the critical value of triangularity is obtained by scanning different plasma parameters. Establishing such a database of is helpful to effectively control the development of NTMs in the RMS experimental discharges.

Double fishbone instability excited by energetic ions with m = n = 1 in a reversed magnetic shear tokamak plasmas

Double fishbone mode excited by energetic particles at q = 1 rational surfaces is studied, with the minimum of the safety factor qmin<1. The dispersion relation of the mode is derived based on energy principle and the radial displacement structure is calculated by an iterative method self-consistently. It is found that the double fishbone mode has a two-step mode structure similar to that of double kink modes. For qmin→1, the sharp slope of the ξr distribution at the rational surfaces is smoothened. The effects of the magnetic shear, the minimum of safety factor, the fast ion beta, and the precession frequency on the plasma displacement and growth rate are also analyzed, respectively.

Nonlinear evolution of neo-classical tearing modes in reversed magnetic shear tokamak plasmas

Linear and nonlinear neo-classical double tearing modes (NDTMs) in the reversed magnetic shear configuration with different separations Δrs between two same rational surfaces are numerically studied by means of reduced magnetohydrodynamic simulations, taking into account different bootstrap current fractions fb. It is found that in the case of large Δrs, an explosive burst of fast reconnection, which was previously observed only in the intermediate Δrs case with fb = 0 (Ishii Y. et al 2002 Phys. Rev. Lett. 89 205002), can also be induced if the fraction of bootstrap current fb is sufficiently high. In the case of intermediate Δrs, such explosive bursts can effectively be brought forward, since the bootstrap current significantly destabilizes the tearing mode on the outer rational surface. In the case of small Δrs, higher order harmonics of the NDTMs become dominantly unstable in the linear phase, if fb continues increasing. In its nonlinear phase, the local modification of bootstrap current near the magnetic islands makes the islands move inwards, while the recovery of the Ohm current tends to make them move outwards. The different dynamics of complicated motions of magnetic islands (or rational surfaces) determined by these two effects are analysed in detail in the cases of different fb values.