Toroidal Code Research Articles

Influence of electron cyclotron current drive on the pressure crashes caused by the 2/1 double tearing modes

Abstract A module with self-consistent evolution of driven current is developed and coupled with the resistive-MHD equations in the three-dimensional, toroidal, and nonlinear simulation code (CLT). The driven current equation is solved with a second-order accuracy symmetric scheme, which exhibits good conservation properties. With the new module, we find that the driven current can self-consistently concentrate inside the magnetic island when the parallel diffusion of the driven current is sufficiently large. The efficiency of the driven current on tearing mode suppression will then be much higher than those with stationary distributions. With the new module, the influence of electron cyclotron current drive (ECCD) on the nonlinear evolution of the 2/1 double tearing modes (DTMs) is investigated. When co-ECCD deposits on the outer resonant surface, the local magnetic shear is reduced, and the growth rates of the DTMs decrease; if ctr-ECCD deposits on the outer resonant surface, the local magnetic shear increases, and the DTMs become more unstable. However, things will be different if ECCD deposits on the inner resonant surface since the local magnetic shear is negative. The co-ECCD deposited on the inner resonant surface increases the negative shear and then promotes the growth of the DTMs; while the ctr-ECCD suppresses the DTMs. It is also found that the off-axis and central pressure crashes associated with the 2/1 DTMs can be converted to each other by properly depositing the driven current. To convert a central crash to an off-axis crash, the co-ECCD should be deposited on the outer resonant surface, or the ctr-ECCD deposited on the inner resonant surface. While, the co-ECCD should be deposited on the inner rational surface, or the ctr-ECCD deposited on the outer rational surface to convert an off-axis crash to a central crash. The co- or ctr-ECCD should be larger than a threshold for such transitions, and the threshold value is mainly determined by the location of the inner resonant surface.

Verification and validation of electrostatic turbulence simulation for numerical Lie transform code

Abstract This paper reports the verification and validation of a new gyrokinetic (GK) code, numerical Lie transform (NLT), for electrostatic turbulence simulation in tokamak plasmas. Based on the standard cyclone base case (CBC), NLT has been verified against two typical GK codes, GK toroidal code (GTC) and GK numerical experiment of tokamak, by simulating the ion temperature gradient mode and trapped electron mode. The linear dispersion relation and mode structure agree well among all these codes. In nonlinear simulation, the time evolution of ion heat diffusivity obtained from NLT is consistent with the GTC results. Furthermore, utilizing experimental equilibria with obvious turbulence features from HL-2A shot #22388, the validation of NLT for real tokamak simulation has been carried out. The profiles of ion turbulent thermal diffusivity calculated by NLT match well with experimental results.

Numerical eigenanalysis of continuum geodesic acoustic mode by ideal magnetohydrodynamic model

In this study, we have developed a new eigenvalue code to solve the three-variables ideal magnetohydrodynamic (MHD) equation in flux coordinate system with the help of a symbolic vector analysis module and an automatic numerical discretization module, which were developed with the use of symbolic computation technique and were greatly facilitated the development of toroidal full MHD eigenvalue code SCELT. It has been used to solve for unstable modes and the present work is dedicated to the more difficult challenge of MHD continua, which ordinarily come with spatial singularities. With this new code, we were able to perform numerical calculations to determine the continuum spectrum of geodesic acoustic modes (GAMs), as well as obtain eigenfunctions for both the perturbed plasma displacement and perturbed magnetic field, incorporating a sufficient number of components. Through our global calculations, we have provided numerical evidence of singularities in the eigenfunctions, characterized by the type s−s0−1 and Ins−s0 . Moreover, we have examined the spatial variations of GAM fluctuations in regions both near and far from the singular surface. Here s represents a flux function that characterizes the magnetic flux surfaces and s=s0 defines the singular surface. Additionally, we have investigated the effects of finite aspect ratio, non-circular cross sections as well as the asymmetry on the frequency and eigenfunction of continuum GAMs through numerical analysis.

The effect of plasma toroidal rotation on n = 1 resonant magnetic perturbation field penetration under low neutral beam injection torque in EAST

An experiment was conducted to study the mode penetration of n=1 resonant magnetic perturbation (RMP) in EAST under low neutral beam injection torque in the co-current direction (Co-NBI). The experimental results indicate that the threshold current IRMP,th for field penetration decreases with higher input torque TNBI . Furthermore, it is observed that the plasma mode frequency |fMHD| at counter-current direction is greatly reduced when the plasma toroidal rotation frequency fϕ increases. The theoretical scaling of mode frequency (IRMP,th∝|fMHD|0.70) predicted by the field penetration theory is in good agreement with the experimental observation ( IRMP,th∝|fMHD|0.53 ). The role of |fMHD| and fϕ on the mode onset threshold was separately investigated using the full toroidal geometry initial value code MARS-Q (Liu et al 2013 Phys. Plasmas 20 042503). The numerical scaling based on the experimental mode frequency is consistent with the experimental and theoretical ones. Numerical results suggest that evaluating the total mode frequency |fMHD| is crucial in field penetration analysis, in contrast to toroidal rotation frequency fϕ . With the increase of TNBI , the decreasing |fMHD| leads to a reduction in the field penetration threshold. This suggests that more attention should be paid to error field tolerance in low Co-NBI torque scenarios, where the electron diamagnetic frequency may be canceled out by NBI-driven toroidal plasma rotation.

Global simulations of kinetic-magnetohydrodynamic processes with energetic electrons in tokamak plasmas

The energetic electrons (EEs) produced from auxiliary heatings have been found to destabilize various Alfven eigenmodes (AEs) in recent experiments. To investigate EE relevant kinetic-magnetohydrodynamic (MHD) processes, a global fluid-kinetic hybrid model is formulated and verified in this work, which consists of Landau-fluid bulk plasmas and drift-kinetic EEs that incorporates the dominant damping and drive mechanisms, respectively. The numerical capability of Landau-fluid bulk plasmas is obtained based on a well-benchmarked eigenvalue code multiscale analysis for plasma stability (MAS) using general geometry (Bao et al 2023 Nucl. Fusion 63 076021), and the comprehensive EE responses to the low frequency ( ω≪Ωci ) MHD fluctuations are analytically derived and implemented in MAS, which not only cover contributions from trapped and passing particles, but also take into account the effects of adiabatic fluid convection and non-adiabatic kinetic compression. The linear properties of EE-driven beta-induced AEs (e-BAEs) are systematically studied using both MAS model and gyrokinetic toroidal code (GTC) particle-in-cell simulations. Building on the good agreements on the mode structure and dispersion relation, several key issues of e-BAE physics are analyzed and discussed, including the parametric dependences of e-BAE stability on EE mass, temperature and density with corresponding phase space dynamics, EE non-perturbative effects on the symmetry breaking of mode structure, and the EE density and temperature thresholds for e-BAE excitation that overcome bulk plasma damping. With these efforts, the upgraded MAS model is superior than initial-value simulations restricted by stringent electron Courant condition for fast linear analyses of most EE-AE problems with ω≪Ωci , of which wave–particle resonance can be used to analyze the analogous effect of alpha particle driven AEs in future fusion reactor.

Numerical investigation of the 2/1 double tearing mode in EAST with the CLT code

The pressure crashes observed in shot No. 71326 in the Experimental Advanced Superconducting Tokamak are numerically investigated with the three-dimensional, toroidal, and full resistive-magnetohydrodynamics code (CLT). Based on the experimental observations, the pressure crash is caused by the nonlinear evolution of the m/n = 2/1 double tearing mode (DTM), where n and m are the toroidal and poloidal mode numbers, respectively. However, we find that the m/n = 2/1 DTM is stable based on the safety factor (q) profile from the equilibrium code EFIT, which indicates that the original q profile is somewhat inconsistent with the actual profile due to q measurement uncertainty. Since there is no motional Stark effect diagnostic for this shot, the local information of the magnetic field is missing, which leads to the largest contribution to the discrepancy. If other information is perfectly known and the q profile is the only uncertainty, then we could provide some information for the EFIT reconstruction by comparing our simulation results with electron cyclotron emission signals to constrain the uncertainty of the q profile to a much smaller region. The influence of plasma rotation and the two-fluids effect is also discussed.

Verification of gyrokinetic particle simulations of neoclassical tearing modes in fusion plasmas

The ability to simulate neoclassical tearing modes (NTMs) in the gyrokinetic toroidal code (GTC) has been developed and verified, in which ions are treated with a gyrokinetic model and electrons are treated as a resistive fluid. The simulation results demonstrate that the neoclassical bootstrap current effect can destabilize an otherwise stable classical tearing mode. In the cylindrical geometry, GTC simulations in the magnetohydrodynamic limit show quantitative agreement with the modified Rutherford theory, both in terms of the scaling law in the small island limit and in terms of the saturation level and pressure flattening effect in the large island limit. The toroidal effects are slightly destabilizing for the NTM, while the kinetic effects of thermal ions are stabilizing for the NTM and increase its excitation threshold.

Gyrokinetic simulation of electromagnetic instabilities in the high β p scenario on EAST

High poloidal beta scenarios with favorable plasma performance () have be achieved on Experimental Advanced Superconducting Tokamak (EAST) since the 2018 international atomic energy agency (IAEA). Linear electromagnetic gyrokinetic simulations using gyrokinetic toroidal code (GTC) code are performed based on the experimental data of a typical high discharge on EAST. In the core region of plasma, an electromagnetic instability with similar dependence and mode structure with kinetic ballooning mode (KBM) but exhibits positive or nearly zero frequency is observed. This instability is referred as unconventional KBM (UKBM). Simulation results demonstrate that UKBM occurs in low ion–electron temperature ratio conditions and UKBM will transit to KBM when ion–electron temperature is high. Further investigation shows the driven mechanism of UKBM differs at different electron beta region. When the electron beta exceeds the threshold of electrostatic instability to UKBM, UKBM is driven by electron pressure gradient. When electron beta is close to the beta threshold of UKBM, the main driven mechanism is . Reversed magnetic shear is found to have a significant stabilize effect on UKBM.

Observations of mode frequency increase and the appearance of ITB during the m/n = 1/1 kink mode in EAST high electron temperature long pulse operation

A new long-pulse high electron temperature () regime has been achieved on experimental advanced superconducting tokamak by pure radio frequency heating. In this new scenario, there are mainly two confinement states involving two magneto-hydrodynamic (MHD) modes, one of which is identified as m/n = 1/1 kink mode (where m and n are the poloidal and toroidal mode numbers, respectively). The frequency evolution of the kink mode is investigated through the three-dimensional, toroidal, and nonlinear Hall-MHD code CLT. We firstly find that the frequency of the m/n = 1/1 kink mode significantly increases during each sawtooth crash and then confirmed it through the experimental data. The simulation results indicate that the increase of the mode frequency is mainly due to the significant increase of the electron diamagnetic frequency nearby the reconnection region. We have also observed the internal transport barrier (ITB) during the m/n = 1/1 kink mode. To further investigate this m/n = 1/1 kink mode in this new regime, the multi-scale interactions between the m/n = 1/1 kink mode and turbulence are discussed.

Characteristics of constrained turbulent transport in flux-driven toroidal plasmas.

We study the dynamics of turbulence transport subject to a constraint on the profile formation and relaxation, dominated by the ion temperature gradient modes, within the framework of adiabatic electron response using a flux-driven global gyro-kinetic toroidal code, GKNET. We observe exponentially constrained profiles, with two different scale lengths, that are spatially constant in each region in higher input power regimes. The profiles are smoothly connected in the knee region located at [Formula: see text] of the minor radius, outside which the gradient is steepened and shows a weak confinement improvement. Based on the probability density function analysis of heat flux eddies, the power law demonstrates a dependence on the eddy size S, as [Formula: see text], which distinguishes events into diffusive and non-diffusive parts including the validation of quasi-linear hypotheses. Radially localized avalanches and global bursts, which exhibit different spatial scales, play central roles in giving rise to constrained profiles on an equal footing. It is also found that the [Formula: see text] shear layers are initiated by the global bursts, which evolve downward on a slow time scale across the knee region and play a role in adjusting the profile by increasing the gradient. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

Influence of toroidal rotation on nonlinear evolution of tearing mode in tokamak plasmas

The nonlinear evolution of the tearing mode instability with toroidal rotation is investigated using a three-dimensional toroidal geometry magnetohydrodynamic code (M3D). It is found that toroidal rotation plays a significantly stable role in reducing the width of magnetic island, which is independent of the direction of toroidal rotation. Compared with the stabilizing effect in the linear phase, the stabilizing effect of toroidal rotation is much stronger in the nonlinear phase. The magnetic island is almost suppressed by large enough rotation, even though the linear growth rate is weakly reduced in the linear phase. It is observed that the flow shear has a stabilizing effect, which is significant when the rotation frequency is large. However, it is shown that the magnitude of rotation plays a dominant role in stabilizing the magnetic island when the rotation frequency is small. The Coriolis force, rather than the centrifugal force, is found to play a dominant role in stabilizing the tearing mode in the nonlinear phase. When and tearing modes exist simultaneously, the sheared toroidal rotation is shown to effectively suppress the overlap of magnetic islands and field stochasticity caused by the coupling of neighboring islands.

Influence of two simultaneous driven currents on multiple tearing modes in tokamak plasmas

The influence of two driven currents simultaneously and respectively imposed on the m/n = 2/1 and 3/2 resistive tearing modes in tokamak plasmas is researched by using a three-dimensional toroidal magnetohydrodynamic code CLT. The simulation results show that using two suitable driven currents can better suppress multiple tearing modes than using only one of the two driven currents. When the two suitable driven currents are simultaneously imposed on both the m/n = 2/1 and 3/2 modes, respectively, the two modes may be well suppressed. If only one of the driven currents is imposed on the m/n = 2/1 mode, then the m/n = 2/1 mode may be well suppressed but the m/n = 3/2 mode may be not. Conversely, if only the other of the two driven currents is imposed on the m/n = 3/2 mode, both the two modes may be not suppressed. Moreover, it should be noted that the parameters of using two driven currents to suppress multiple tearing modes must be appropriate; otherwise, some new modes (such as m/n = 5/3 mode) may be excited and grown due to the interaction among the driven currents and multiple modes.

Global gyrokinetic simulations of electrostatic microturbulent transport using kinetic electrons in LHD stellarator

Global gyrokinetic simulations of ion temperature gradient (ITG) and trapped electron mode (TEM) in the LHD stellarator are carried out using the gyrokinetic toroidal code (GTC) with kinetic electrons. ITG simulations show that kinetic electron effects increase the growth rate by more than 50% and more than double the turbulent transport levels compared with simulations using adiabatic electrons. Zonal flow dominates the saturation mechanism in the ITG turbulence. Nonlinear simulations of the TEM turbulence show that the main saturation mechanism is not the zonal flow but the inverse cascade of high to low toroidal harmonics. Further nonlinear simulations with various pressure profiles indicate that the ITG turbulence is more effective in driving heat conductivity whereas the TEM turbulence is more effective for particle diffusivity.

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.

Verification of a fully kinetic ion model for electromagnetic simulations of high-frequency waves in toroidal geometry

For the study of high-frequency electromagnetic waves in tokamaks, an electromagnetic simulation model, in which the ion dynamics is described by a six-dimensional Vlasov equation and the electron dynamics is described by a drift kinetic equation, is formulated and implemented in the global gyrokinetic toroidal code (GTC). Analytic dispersion relations are derived in reduced systems and compared with various theories to verify the model. Linear simulations of a generalized ion Bernstein wave and ion cyclotron emission are verified by comparing the GTC simulation results with analytic dispersion relation theory and magnetoacoustic cyclotron instability theory, respectively, in cylindrical geometry.

Effects of plasma boundary shape on the βN threshold in the suppression of tearing mode in toroidal tokamak plasmas with reversed magnetic shear

The toroidal magnetohydrodynamic code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) is adopted to investigate the plasma boundary shape effect on the threshold ( is the normalized plasma pressure) reported in (Liu et al 2017 Plasma Phys. Control. Fusion 59 065009) in reversed magnetic shear toroidal tokamak plasmas under different separations between the two rational surfaces of the same helicity. The boundary shape effect is modeled via elongation and triangularity . Here, the study focuses on cases ( is the toroidal mode number). In the small regime, the critical value increases as increases (without triangularity), and barely changes with triangularity (at small elongation). On the other hand, at large elongation (e.g. ), the critical value of decreases with increasing . The change in the may be due to a change in the coupling strength between different poloidal harmonics, due to the fact that, besides toroidal coupling ( is the poloidal mode number), a large elongation (or triangularity ) can result in the () equilibrium component and thus enhances the coupling between the and (). In the large regime, with increasing (without triangularity), first slightly increases followed by a quick reduction. Moreover, as increases, the critical value decreases at small elongation, and first increases followed by a decrease at large elongation (e.g. ). Besides the change in the coupling strength between different poloidal harmonics, the change in the in the large regime is also related to the mode transition. The corresponding physics mechanisms underlying the shift of due to the plasma boundary shape are all discussed in detail.

Study of turbulence in the high β P discharge using only RF heating on EAST

High poloidal beta scenarios with a favorable energy confinement (, have been achieved on the Experimental Advanced Superconducting Tokamak using only radio frequency wave heating. Gyrokinetic simulations are carried out with experimental plasma parameters and tokamak equilibrium data of a typical high discharge using the gyrokinetic toroidal code. Linear simulations show that electron-temperature scale length and electron-density scale length destabilize the turbulence, collision effects stabilize the turbulence, and the instability propagates in the electron diamagnetic direction. These properties indicate that the dominant instability in the core of high plasma is a collisionless trapped electron mode. Ion thermal diffusivity, calculated by nonlinear gyrokinetic simulations, is consistent with the experimental value, in which the electron collision effects play an important role. Further analyses show that instabilities with are suppressed by collision effects and collision effects reduce the radial correlation length of turbulence, resulting in the suppression of the turbulence.

Gyro-average method for global gyrokinetic particle simulation in realistic tokamak geometry

Gyro-average is a crucial operation to capturing the essential finite Larmor radius (FLR) effect in gyrokinetic simulation. In order to simulate strongly shaped plasmas, an innovative multi-point average method based on non-orthogonal coordinates has been developed to improve the accuracy of the original multi-point average method in gyrokinetic particle simulation. This new gyro-average method has been implemented in the gyrokinetic toroidal code (GTC). Benchmarks have been carried out to prove the accuracy of this new method. In the limit of concircular tokamak, ion temperature gradient (ITG) instability is accurately recovered for this new method and consistency is achieved. The new gyro-average method is also used to solve the gyrokinetic Poisson equation, and its correctness is confirmed in the long-wavelength limit for realistically shaped plasmas. The improved GTC code with the new gyro-average method is used to investigate the ITG instability with EAST magnetic geometry. The simulation results show that the correction induced by this new method in the linear growth rate is more significant for short-wavelength modes where the FLR effect becomes important. Due to its simplicity and accuracy, this new gyro-average method can find broader applications in simulating shaped plasmas in realistic tokamaks.

Control of radiation-driven tearing mode by externally driven current in tokamaks

The radiation-driven tearing mode (RTM) in tokamaks was numerically studied in our previous investigation (Xu et al 2020 Plasma Phys. Control. Fusion 62 105009), and it was noticed that radiation cooling could drive magnetic island growth and could even cause disruption due to the nonlinear mode coupling. In this work, the suppression of the radiation-driven tearing mode by an externally driven current is investigated numerically by using a three-dimensional toroidal code CLT (Ci-Liu-Ti means magnetohydrodynamics in Chinese) based on a full set of resistive magnetohydrodynamic equations. It is found that an externally driven current with appropriate turn-on time and strength can effectively stabilize the RTM. The effects of the asymmetry current and multi-mode coupling can be stabilized effectively by the externally driven current. In the nonlinear stage, under the influence of the radiation, a strong mode is generated due to the hot-core shift caused by the decrease of the core thermal pressure, which is irreversible even if the magnetic island could be effectively controlled by the externally driven current. When the externally driven current is turned on in the linear stage, it very efficiently and quickly suppresses the dominant modes, and the hot-core shift effect also becomes weaker because of the smaller mode. Moreover, it is found that external auxiliary heating with appropriate intensity in the core region can effectively balance the reduced pressure and can further control the hot-core shift caused by radiative cooling.

Numerical study on nonlinear double tearing mode in ITER

The nonlinear dynamics of the m/n = 2/1 double tearing mode (DTM) in ITER are systematically studied using the three-dimensional toroidal magnetohydrodynamic code, CLT. We carefully investigate the effects of the radial locations and magnetic shear strengths of the inner and outer rational surfaces r 1, r 2, s 1 and s 2, as well as the safety factor at the magnetic axis q 0 on DTM. It is found that the explosive burst takes place only with the moderate separation of the two rational surfaces or the stronger magnetic shear strength in which the strong interaction of magnetic islands in the two rational surfaces happens in the early nonlinear phase of the island development. The explosive burst can result from either the direct mutual driving associated with the fast growth island in the two rational surfaces or a strong nonlinear mode–mode coupling. For a large separation and a weak shear strength of the two rational surfaces, the magnetic islands saturate without strong interaction with each other, and (w in + w out)/2 is always below the separation Δr s. For a small separation, the kinetic evolution of DTM only exhibits an oscillation with a very low level and then decreases.