Search

We study the physical origins of parallel guiding center drift and parallel velocity-dependent effective magnetic field (B‖*) appearing in the Hamiltonian formulation of a particle motion in a curved magnetic field. The magnetic twist term is shown to be responsible for both of them. The parallel guiding center drift originates from the change in the effective parallel velocity due to the combined effect of the initial perpendicular motion (v⊥0) and the magnetic twist. The effective magnetic field arises from the collated effect of the change in v⊥0 due to its initial parallel guiding center motion and the conservation of magnetic moment. This understanding clearly shows that the appearance of B‖* is a consequence of magnetic moment conservation in curved magnetic fields.

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 $\boldsymbol{E} \times \boldsymbol{B}$ flow shear generation, where the majority of $\boldsymbol{E} \times \boldsymbol{B}$ 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 $\boldsymbol{E} \times \boldsymbol{B}$ shear on $k_\parallel$ 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.

We investigate the finite Larmor radius (FLR) effects that are associated with an external heat source or a sink in the full-f formulation of plasma dynamics. Specifically, we show that a gyrocenter or an additional vorticity source due to the FLR effect should be replenished in fullf turbulence simulations. A quantitative energetics analysis in particle phase space demonstrates that an additional vorticity source is required to satisfy the total energy conservation. A physics picture is presented to elucidate the mechanism of the vorticity source generation from the FLR effects of a heat source or a sink, which reproduces the main result obtained from the quantitative analysis. The additional vorticity source is expected to considerably enhance the generation of the radial electric field and subsequent E × B flow shear in the off-axis heating case. [ABSTRACT FROM AUTHOR]

We perform a numerical study of linear stability of the ion temperature gradient (ITG) mode and the trapped electron mode (TEM) in tokamak plasmas with inverted density profiles. A local gyrokinetic integral equation is applied for this study. From comprehensive parametric scans, we obtain stability diagrams for ITG modes and TEMs in terms of density and temperature gradient scale lengths. The results show that, for the inverted density profile, there exists a normalized threshold temperature gradient above which the ITG mode and the TEM are either separately or simultaneously unstable. The instability threshold of the TEM for the inverted density profile is substantially different from that for normal and flat density profiles. In addition, deviations are found on the ITG threshold from an early analytic theory in sheared slab geometry with the adiabatic electron response [T. S. Hahm and W. M. Tang, Phys. Fluids B 1, 1185 (1989)]. A possible implication of this work on particle transport in pellet fueled tokamak plasmas is discussed. [ABSTRACT FROM AUTHOR]

From the nonlinear simulations of the two-dimensional forced-damped Hasegawa-Mima equation, we show that a Reynolds number-like parameter, Rew, can represent a power law exponent of the energy spectrum in Hasegawa-Mima turbulence. Rew is defined as the ratio of nonlinear convection to dissipation. For a same value of Rew, the power law exponent in the inertial range is shown to be uniquely determined regardless of the forcing and dissipation conditions. At high Rew, the power law exponent asymptotically converges to -7.2, consistent with a recent theoretical prediction based on the shell model [Gürcan et al., Plasma Phys. Controlled Fusion 52, 045002 (2010)]. [ABSTRACT FROM AUTHOR]

A study is conducted on the impact of plasma compressibility on the stability of drift ballooning modes. The two-fluid and four-field model developed by Hazeltine et al. [Phys. Fluids 28, 2466 (1985)] is employed in this study. Results of linear numerical simulations show that finite compressibility destabilizes ballooning modes which are otherwise stable due to the ion diamagnetic drift effect. A systematic study reveals that the parallel compressibility originating from the two-fluid effect, rather than the drift-acoustic wave coupling suggested by Hastie et al. [Phys. Plasmas 10, 4405 (2003)], plays the most important role in destabilizing the ballooning modes. An analytic evaluation of the dispersion relation underpins the strong sensitivity of this parallel compressibility term in the ballooning mode stability. The potential impact of this new understanding on the physics of small edge localized modes is discussed. [ABSTRACT FROM AUTHOR]

We study the impact of external magnetic perturbations on the stability of ballooning modes. A unique feature of our analysis is the two-step parametric process [Chaturvedi and Kaw, J. Geophys. Res. 81, 3257 (1976)], which enables us to calculate contributions from all the modes with high toroidal mode numbers. The analysis shows that the externally applied magnetic field perturbations can modify the linear dispersion characteristics of the ballooning mode. Specifically, the growth rate spectrum of the ballooning modes becomes broader in poloidal wavenumber (kθ) space, implying the generation of high-k fluctuations. The increase of high-k fluctuations (micro-turbulence) can lead to the mitigation of an edge localized mode crash by increasing turbulent transport in the pedestal. In addition to this, a new nonlinear instability is found even below the threshold of the ballooning mode instability when the amplitude of magnetic perturbation is sufficiently large (i.e., δB=B0 ≥ 1:0 × 10-4). A discussion is given of the implication of this new finding. [ABSTRACT FROM AUTHOR]

We report the results of a gyrokinetic simulation study elucidating the characteristics of the current driven by electron temperature gradient (ETG) turbulence in toroidal geometry. We examined the amount of the ETG turbulence-driven current for different turbulence levels, which were obtained by varying the relative electron gyroradius ρ* = ρe/a. Simulations show that the amount of the ETG turbulence-driven current increases with ρ* due to the gyro-Bohm scaling of turbulence intensity. A perturbation of the equilibrium q-profile by the ETG turbulence-driven current becomes noticeable when ρ* > 1/4000. Even in a small ρ* case, the proportional relation between the ETG turbulence-driven current and turbulence intensity suggests that a considerable intrinsic current can be driven inside an edge pedestal where a steep gradient of the electron temperature profile can excite ETG turbulence in a narrow region. [ABSTRACT FROM AUTHOR]

Numerical studies are made of the effects of resistivity on linear plasma responses to resonant magnetic perturbations (RMPs) in tokamaks based on a reduced magnetohydrodynamic model. From a local two-field model, it is suggested that the ratio of the poloidal electron advection to the resistivity diffusion rate αmαm can be a figure of merit parameter in linear RMP penetration physics. The shielding efficiency is governed by αm, and when αm ≳ 1, RMPs are effectively shielded. Global simulations using a four-field model [Hazeltine and Meiss, Phys. Rep. 121, 1 (1985)] show that there exists an effective threshold of the perpendicular electron flow (Ve,⊥c) beyond which RMPs cannot penetrate. Resistivity is found to determine Ve,⊥c which increases as resistivity becomes higher, making RMP penetration easier. At low resistivity, small Ve,⊥c renders the RMP penetration sensitive to ion collisionality and the change in q 95. The kink response is observed to be closely related to the residual level of RMPs at rational surfaces and can be also strongly affected by resistivity. [ABSTRACT FROM AUTHOR]

We perform an analytic study of the tertiary instability driven by a strong excitation of zonal flows during high density low to high (LH) mode transition. The drift resistive ballooning mode is assumed to be a dominant edge turbulence driver. The analysis reproduces main qualitative features of early computational results [Rogers and Drake, Phys. Rev. Lett. 81, 4396 (1998); Guzdar et al, Phys. Plasmas 14, 020701 (2007)], as well as new characteristics of the maximum edge density due to the onset of the tertiary instability. An analytical scaling indicates that the density scaling of LH transition power may be determined by the onset condition of the tertiary instability when the operating density approaches to the Greenwald density. [ABSTRACT FROM AUTHOR]

We study the impact of impurities on turbulence driven intrinsic rotation (via residual stress) in the context of the quasi-linear theory. A two-fluid formulation for main and impurity ions is employed to study ion temperature gradient modes in sheared slab geometry modified by the presence of impurities. An effective form of the parallel Reynolds stress is derived in the center of mass frame of a coupled main ion-impurity system. Analyses show that the contents and the radial profile of impurities have a strong influence on the residual stress. In particular, an impurity profile aligned with that of main ions is shown to cause a considerable reduction of the residual stress, which may lead to the reduction of turbulence driven intrinsic rotation. [ABSTRACT FROM AUTHOR]

Using three-dimensional nonlinear simulations of tokamak turbulence, we show that an edge transport barrier (ETB) forms naturally once input power exceeds a threshold value. Profiles, turbulence-driven flows, and neoclassical coefficients are evolved self-consistently. A slow power ramp-up simulation shows that ETB transition is triggered by the turbulence-driven flows via an intermediate phase which involves coherent oscillation of turbulence intensity and E×B flow shear. A novel observation of the evolution is that the turbulence collapses and the ETB transition begins when RT > 1 at t = tR (RT: normalized Reynolds power), while the conventional transition criterion (ωE×B>γlin where ωE×B denotes mean flow shear) is satisfied only after t = tC (>tR), when the mean flow shear grows due to positive feedback. [ABSTRACT FROM AUTHOR]

We present a semi-analytic model for low (L) to high (H) mode transition power threshold (Pth). Two main assumptions are made in our study. First, high poloidal mode number drift resistive ballooning modes (high-m DRBM) are assumed to be the dominant turbulence driver in a narrow edge region near to last closed flux surface. Second, the pre-transition edge profile and turbulent diffusivity at the narrow edge region pertain to turbulent equipartition. An edge power balance relation is derived by calculating the dissipated power flux through both turbulent conduction and convection, and radiation in the edge region. Pth is obtained by imposing the turbulence quench rule due to sheared E×B rotation. Evaluation of Pth shows a good agreement with experimental results in existing machines. Increase of Pth at low density (i.e., the existence of roll-over density in Pth vs. density) is shown to originate from the longer scale length of the density profile than that of the temperature profile. [ABSTRACT FROM AUTHOR]

We present an analytic study of momentum transport of tokamak plasmas in the vicinity of minimum safety factor (q) position in reversed magnetic shear configuration. Slab ion temperature gradient modes with an equilibrium flow profile are considered in this study. Quasi-linear calculations of momentum flux clearly show the novel effects of q-curvature on the generation of intrinsic rotation and mean poloidal flow without invoking reflectional symmetry breaking of parallel wavenumber ( k‖ ). This q-curvature effect originates from the inherent asymmetry in k‖ populations with respect to a rational surface due to the quadratic proportionality of k‖ when q-curvature is taken into account. Discussions are made of possible implications of q-curvature induced plasma flows on internal transport barrier formation in reversed shear tokamaks. [ABSTRACT FROM AUTHOR]

We show that strong edge magnetic shear, which is generic to divertor plasmas, makes the E × B shearing of turbulence eddys in toroidal geometry more effective. From calculations of the E × B shearing rates for KSTAR edge parameters, we conclude that the enhanced magnetic shear at the diverted KSTAR plasma edge facilitates E × B shear suppression of turbulence and ensuing H-mode transition. [ABSTRACT FROM AUTHOR]

A study is conducted on the feedback stabilization of resistive wall modes (RWMs) in a tokamak plasma using a toroidal shell model. An analytically tractable form of the RWM dispersion relation is derived in the presence of a set of discrete feedback coil currents. A parametric study is carried out to optimize the feedback system configuration. It is shown that the total toroidal angle of a resistive wall spanned by the feedback coils and the poloidal angular extent of a feedback coil are crucial parameters to determine the efficacy of the feedback system. [ABSTRACT FROM AUTHOR]

Examines a general analytic expression for bootstrap current driven by fusion-born alpha particles obtained in a deuterium-tritium tokamak plasma using a kinetic variational theory. Linearized Coulomb scattering operator used in the study; Prediction of alpha-driven bootstrap current in a reactor condition.

We investigate the effect of externally applied resonant magnetic perturbations (RMPs) on the pedestal collapse, using resistive reduced magnetohydrodynamic simulations. The RMP-mediated nonlinear interaction is shown to enhance the fluctuation level, leading to an increase of convective transport. Further, it also induces a broad coherence and strong energy transfer among poloidal and toroidal harmonics. The enhanced fluctuations, especially at lower (than the most unstable mode) toroidal mode number n, eventually increase the tearing-parity fluctuation distinctively at lower n through a series of tearing-parity generation mechanism. Consequently, RMPs are shown to expedite the magnetic field line stochastization process via the nonlinear energy transfer process. [ABSTRACT FROM AUTHOR]

We present experimental observations suggesting that non-diffusive avalanche-like transport events are a prevalent and universal process in the electron heat transport of tokamak plasmas. They are observed in the low confinement mode and the weak internal transport barrier plasmas in the absence of magnetohydrodynamic instabilities. In addition, the electron temperature profile corrugation, which indicates the existence of the shear flow layers, is clearly demonstrated as well as their dynamical interaction with the avalanche-like events. The measured width of the profile corrugation is around , implying the mesoscale nature of the structure. [ABSTRACT FROM AUTHOR]

We perform a computational study of characteristics of coupled drift wave (DW)-parallel velocity gradient (PVG) driven turbulence. The three-dimensional Hasegawa–Mima equation combined with ion parallel flow dynamics is used for this study. Energetic analyses, both analytic and computational, show the energy equipartition of the parallel Reynolds power (i.e. the free energy due to a gradient in equilibrium parallel velocity) in parallel and perpendicular directions. A considerable portion of the perpendicular energy that is transferred through the parallel coupling generates the perpendicular zonal flow (ZF), implying the increase of the ZF level when an equilibrium PVG is present. A careful analysis of parallel-perpendicular coupling dynamics shows that the vortex stretching-like term in this system plays a significant role in the ZF generation. This is in contrast to the neutral fluid turbulence where it hinders the inverse cascade process. However, the ZF generation from PVG turbulence is found to be less effective in comparison with that of DW turbulence. [ABSTRACT FROM AUTHOR]

From global gyrokinetic simulations of toroidal ion temperature gradient-driven turbulence, we show that the ion parallel compression has a strong influence on the generation and radial profile formation of zonal flows. The kinetic potential vorticity (PV) flux and its fluid expression are used to elucidate the zonal flow generation mechanism. In the absence of sheared equilibrium flow, the dominant contributions to the net PV flux are shown to come from the parallel compression and the grad-B drift, and to largely cancel out each other. With a finite parallel rotation shear, however, the parallel compression-driven flux becomes dominant over the grad-B drift-driven one, leading to a change in the radial zonal flow profile. The imbalance between the parallel compression and the grad-B drifts results in a considerable amplification of the zonal flow and a reduction of turbulence fluctuation levels as compared to the non-rotating plasma. These findings demonstrate an essential role of the parallel compression in the zonal flow generation and confinement improvement for rotating tokamak plasmas. [ABSTRACT FROM AUTHOR]

Dedicated experiments have been performed in KSTAR Ohmic plasmas to investigate the detailed physics of the rotation reversal phenomena. Here we adapt the more general definition of rotation reversal, a large change of the intrinsic toroidal rotation gradient produced by minor changes in the control parameters (Camenen et al 2017 Plasma Phys. Control. Fusion59 034001), which is commonly observed in KSTAR regardless of the operating conditions. The two main phenomenological features of the rotation reversal are the normalized toroidal rotation gradient () change in the gradient region and the existence of an anchor point. For the KSTAR Ohmic plasma database including the experiment results up to the 2016 experimental campaign, both features were investigated. First, the observations show that the locations of the gradient and the anchor point region are dependent on . Second, a strong dependence of on is clearly observed in the gradient region, whereas the dependence on , , and is unclear considering the usual variation of the normalized gradient length in KSTAR. The experimental observations were compared against several theoretical models. The rotation reversal might not occur due to the transition of the dominant turbulence from the trapped electron mode to the ion temperature gradient mode or the neoclassical equilibrium effect in KSTAR. Instead, it seems that the profile shearing effects associated with a finite ballooning tilting well reproduce the experimental observations of both the gradient region and the anchor point; the difference seems to be related to the magnetic shear and the value. Further analysis implies that the increase of in the gradient region with the increase of the collisionality would occur when the reduction of the momentum diffusivity is comparatively larger than the reduction of the residual stress. It is supported by the perturbative analysis of the experiments and the nonlinear gyrokinetic simulations. The absence of the sign change of even when a much lower collisionality is produced by additional electron cyclotron heating brings further experimental support to this interpretation. [ABSTRACT FROM AUTHOR]

We perform a computational study of the role of zonal flows in edge pedestal collapse on the basis of a nonlinear three-field reduced magnetohydrodynamic (MHD) model. A dramatic change of dynamics takes place when ideal ballooning modes are completely stabilized. Analyses show that a new instability is developed due to a strong excitation of zonal vorticity, resulting in a series of secondary crashes. The presence of subsidiary bursts after a main crash increases the effective crash time and energy loss. These simulation results resemble the behavior of compound edge localized modes (ELMs). Analyses in this paper indicate that a complete understanding of ELM crash dynamics requires the self-consistent inclusion of nonlinear zonal flows-MHD interaction and transport physics. [ABSTRACT FROM AUTHOR]

On the basis of three-dimensional nonlinear magnetohydrodynamic simulations, we propose a new dynamical process leading to the stochastization of magnetic fields during an edge pedestal collapse. Primary tearing modes are shown to grow by extracting kinetic energy of unstable ballooning modes, eventually leading to the island overlap. Secondary tearing modes, which are generated through a coherent nonlinear interaction between adjacent ballooning modes, play a key role in this process, mediating the energy transfer between primary ballooning and tearing modes. Calculations show that the parallel energy loss through the stochastic fields, which has been identified in early nonlinear simulations, could be a dominant thermal energy release mechanism during an edge pedestal collapse. [ABSTRACT FROM AUTHOR]

A study of intrinsic rotation and hysteresis in ion thermal internal transport barrier (ITB) is presented. Global flux-driven gyrofluid simulations are performed. It is found that significant co-current intrinsic rotation (0.1 [?] Mth [?] 0.2, where Mth is the thermal Mach number) can be produced in ITB plasmas. Exploration of the relationship between the intrinsic rotation and the ITB temperature gradient leads to a novel scaling of intrinsic rotation in ITB plasmas. Long time power ramp simulations with self-consistently evolving profiles clearly demonstrate the existence of hysteresis in reversed shear ITBs. It is shown that intrinsic rotation plays an important role in ITB dynamics and is responsible for determining unique properties of ITB hysteresis. A negative feedback mechanism based on destruction of E x B shear prevails in barrier back transition, triggered by an outward momentum transport event during the power ramp down. [ABSTRACT FROM AUTHOR]