Reversed Shear Configuration Research Articles

Core localized alpha-channeling via low frequency Alfvén mode generation in reversed shear scenarios

A novel channel for fuel ions heating in tokamak core plasma is proposed and analyzed using nonlinear gyrokinetic theory. The channel is achieved via spontaneous decay of reversed shear Alfvén eigenmode (RSAE) into low frequency Alfvén modes, which then heat fuel ions via collisionless ion Landau damping. The conditions for RSAE spontaneous decay are investigated, and the saturation level and the consequent fuel ion heating rate are also derived. The channel is expected to be crucial for future reactors operating under reversed shear configurations, where fusion alpha particles are generated in the tokamak core with the magnetic shear being, typically, reversed, and there is a dense RSAE spectrum due to the small alpha particle characteristic dimensionless orbits.

Experimental study of double tearing mode on EAST tokamak

The double tearing mode (DTM) in a high βN (βN > 1.5) discharge with internal transport barrier on EAST was investigated. A 15 kHz tearing mode (TM) (m ≥ 3, n = 3) appears at outer q = 2 surface at first, which is stable in the high βN phase. Then a 2 kHz TM (m = 2, n = 1) occurs at inner q = 2 surface. Soon after, high βN collapsed with the crash of ELM, and DTM formed during the collapse of βN. The positions of the two islands of the DTM are consistent with the q = 2 surface. The temperature fluctuations are the strongest between the two magnetic islands. A statistical analysis of high βN discharges operating with the reversed magnetic shear configuration in the EAST 2015–2018 campaign revealed the existence of the DTM in many discharges. During the DTM phase, all βN are reduced by 10%–30% within 0.1 s. However, there are two different βN behaviors thereafter—with and without βN recovery. Studying the physical mechanism of βN recovery during the DTM phase will benefit steady-state operation with reversed shear configurations in the future.

Heat pulse propagation in chaotic three-dimensional magnetic fields

Heat pulse propagation in three-dimensional chaotic magnetic fields is studied by solving numerically the parallel heat transport equation using a Lagrangian Green's function (LG) method. The LG method provides an efficient and accurate technique that circumvents known limitations of finite elements and finite difference methods. The main two problems addressed are (i) the dependence of the radial transport of heat pulses on the level of magnetic field stochasticity (controlled by the amplitude of the magnetic field perturbation, ϵ), and (ii) the role of reversed shear magnetic field configurations on heat pulse propagation. In all the cases considered there are no magnetic flux surfaces. However, the radial transport of heat pulses is observed to depend strongly on ϵ due to the presence of high-order magnetic islands and Cantori. These structures act as quasi-transport barriers which can actually preclude the radial penetration of heat pulses within physically relevant time scales. The dependence of the magnetic field connection length, ℓB, on ϵ is studied in detail. Regions where ℓB is large, correlate with regions where the radial propagation of the heat pulse slows down or stops. The decay rate of the temperature maximum, 〈T〉max(t), the time delay of the temperature response as function of the radius, τ, and the radial heat flux , are also studied as functions of the magnetic field stochasticity and ℓB. In all cases it is observed that the scaling of 〈T〉max with t transitions from sub-diffusive, 〈T〉max ∼ t−1/4, at short times (χ∥t < 105) to a significantly slower, almost flat scaling at longer times (χ∥t > 105). A strong dependence on ϵ is also observed on τ and . Even in the case when there are no flux surfaces nor magnetic field islands, reversed shear magnetic field configurations exhibit unique transport properties. The radial propagation of heat pulses in fully chaotic fields considerably slows down in the shear reversal region and, as a result, the delay time of the temperature response in reversed shear configurations is about an order of magnitude longer than the one observed in monotonic q-profiles. The role of separatrix reconnection of resonant modes in the shear reversal region, and the role of shearless Cantori in the observed phenomena are also discussed.

Frequencies of the geodesic acoustic mode and Alfvén gap modes in high-q2β plasmas with non-circular cross section

This work generalizes recent results [O. P. Fesenyuk et al., Plasma Phys. Controlled Fusion 54, 085014 (2012)] to plasmas with elongated cross section. It suggests new expressions for the frequencies of the geodesic acoustic mode and Alfvén gap modes in tokamaks, with a large ratio of the plasma pressure to the magnetic field pressure and a large safety factor (q≫1, which takes place in discharges with reversed-shear configuration and, especially, in hollow-current discharges).

Alpha particle-driven toroidal rotation in burning plasmas

The mechanism of a torque intrinsically produced by alpha particles and the subsequent possibility to create significant toroidal rotation and shear are numerically investigated. In steady-state DEMO plasmas, regardless of the magnetic configuration, the orbit-following Monte Carlo code OFMC predicts that co-directed collisional torque and a counter-directed torque always emerge due to the gradient of the source profile of alpha particles and both of them virtually cancel each other out, as analytically predicted earlier. The magnitude of each torque is enhanced in the reversed shear configuration compared with the normal shear configuration, provided that the source gradient is finite and similar in both cases. The resultant rotation velocity estimated by the TASK/TX transport code is far below the threshold to stabilize resistive wall modes (RWMs) through intrinsic alpha-driven torque alone. It is estimated that a neutral beam injection at a moderate power level may be capable of producing toroidal rotation sufficient to stabilize RWMs.

Rotational stabilization of resistive wall modes in ITER advanced tokamak scenarios

Rotational stabilization of n=1 resistive wall modes in ITER advanced scenarios [K. Ikeda, Nucl. Fusion 47 (2007)] is investigated, where n is the toroidal mode number. In particular, we present numerical results for the ITER strongly reversed shear case, in comparison to the weakly reversed shear case. The rotation frequency is assumed to be modestly low. Our investigation employs the adaptive eigenfunction independent solution-kinetic (AEGIS-K) code [L. J. Zheng et al., “AEGIS-K code for linear kinetic analysis of toroidally axisymmetric plasma stability,” J. Comput. Phys. (to be published)], which provides a fully kinetic (nonhybrid) and self-consistent (nonperturbative) description. AEGIS-K includes wave-particle resonances, shear Alfvén continuum damping, trapped particle effects, and parallel electric effects, but not finite Larmor radius effects. In the case without rotation and kinetic effects included, we find that the strongly reversed shear configuration is more favorable for perfectly conducting wall stabilization of resistive wall modes, in that it has a higher conducting wall beta limit than the weakly reversed shear case. With sufficient rotation, the strongly reversed shear case can also achieve a higher beta limit for completely suppressing the resistive wall modes. However, the marginal rotation frequency required for complete resistive wall mode stabilization in the strongly reversed shear case is about twice as high as that required for the weakly reversed shear case.

Non-local turbulent effect on internal transport barrier collapse in reversed shear configuration

The mechanism of transport barrier collapse in reversed shear configuration is investigated using a global ion temperature gradient driven drift wave (ITG) turbulence simulation code. The transport barrier collapse event is explained in the context of non-local meso-scale interaction. It is found that the turbulence evolution and the sustainment of the transport barrier is sensitive to the safety factor profile. However, some common meso-scale modes are excited via various non-linear interaction channels whether or not a meso-scale mode in the vicinity of the q profile minimum has resonant surfaces. The non-linear interaction among these non-local modes makes long range correlation possible and carries energy from the core region to the q minimum region. It was shown that such linkage can lead to the collapse of the transport barrier and the change of the global temperature profile.

Effects of a liquid lithium curtain as the first wall in a fusion reactor plasma

This paper explores the effect of a liquid lithium curtain on fusion reactor plasma, such curtain is utilized as the first wall for the engineering outline design of the Fusion Experimental Breeder (FEB-E). The relationships between the surface temperature of a liquid lithium curtain and the effective plasma charge, fuel dilution and fusion power production have been derived. Results indicate that under normal operation, the evaporation of liquid lithium does not seriously affect the effective plasma charge, but effects on fuel dilution and fusion power are more sensitive. As an example, it has investigated the relationships between the liquid lithium curtain flow velocity and the rise of surface temperature based on operation scenario II of the FEB-E design with reversed shear configuration and high power density. Results show that even if the liquid lithium curtain flow velocity is as low as 0.5 m/s, the effects of evaporation from the liquid lithium curtain on plasma are negligible. In the present design, the sputtering of liquid lithium curtain and the particle removal effects of the divertor are not yet considered in detail. Further studies are in progress, and in this work implication of lithium erosion and divertor physics on fusion reactor operation are discussed.

Chapter 5: Physics of energetic ions

This chapter reviews the progress accomplished since the redaction of the first ITER Physics Basis (1999 Nucl. Fusion 39 2137–664) in the field of energetic ion physics and its possible impact on burning plasma regimes. New schemes to create energetic ions simulating the fusion-produced alphas are introduced, accessing experimental conditions of direct relevance for burning plasmas, in terms of the Alfvénic Mach number and of the normalised pressure gradient of the energetic ions, though orbit characteristics and size cannot always match those of ITER. Based on the experimental and theoretical knowledge of the effects of the toroidal magnetic field ripple on direct fast ion losses, ferritic inserts in ITER are expected to provide a significant reduction of ripple alpha losses in reversed shear configurations. The nonlinear fast ion interaction with kink and tearing modes is qualitatively understood, but quantitative predictions are missing, particularly for the stabilisation of sawteeth by fast particles that can trigger neoclassical tearing modes. A large database on the linear stability properties of the modes interacting with energetic ions, such as the Alfvén eigenmode has been constructed. Comparisons between theoretical predictions and experimental measurements of mode structures and drive/damping rates approach a satisfactory degree of consistency, though systematic measurements and theory comparisons of damping and drive of intermediate and high mode numbers, the most relevant for ITER, still need to be performed. The nonlinear behaviour of Alfvén eigenmodes close to marginal stability is well characterized theoretically and experimentally, which gives the opportunity to extract some information on the particle phase space distribution from the measured instability spectral features. Much less data exists for strongly unstable scenarios, characterised by nonlinear dynamical processes leading to energetic ion redistribution and losses, and identified in nonlinear numerical simulations of Alfvén eigenmodes and energetic particle modes. Comparisons with theoretical and numerical analyses are needed to assess the potential implications of these regimes on burning plasma scenarios, including in the presence of a large number of modes simultaneously driven unstable by the fast ions.

Simulations of Reversed Shear Configuration in EAST

The reversed shear (RS) mode is one of the advanced configurationsbeing considered in EAST. Predictive simulations of EAST reversedshear configuration are carried out using an 1.5D equilibriumevolution code. In order to have the desired monotonic q-profileduring a tokamak discharge, a successful preparation phase isrequired. In our simulation, the plasma current is ramped up from100 kA to a flat-top maximum of 1.0 MA for four seconds. AnICRH power of 1 MW is applied until the plasma shape is formed atthe moment of 4 s, and then the power is raised to 3 MW. ALHCD power of 3.5 MW is applied from 1s to optimize the plasmacurrent density profile. A series of simulations are performed tostudy the influence of the time of applying the auxiliary heating onthe plasma parameters. Based on these simulations, a scheme isproposed and tested for the control of the safety factor profile,which is very useful in real time profile control in tokamakexperiments.

Modelling of advanced plasma configurations in SST-1 tokamak

Predictive simulations investigating steady-state advanced reversed shear configurations for steady state tokamak (SST-1) in LHCD+ECRH/CD operations are carried out using the TSC+LSC+TORAY-GA code package. We also explore in detail current profile control scenarios using ECCD at various frequency ranges. Our simulations suggest that it is possible to attain high-density (up to ∼50% of the Greenwald density limit) operation in LHCD+ECCD plasmas by carefully controlling the density evolution, power and current density profiles and hence the safety factor profile. The reversed shear plasmas are sustained by off-axis lower hybrid current drive (LHCD) and ECCD profiles as well as about 50% bootstrap current fraction which is naturally off-centred. Based on these simulations, we propose and test a novel scheme for control of the safety factor profiles as well as poloidal beta and internal inductance profiles which will be tested in actual SST-1 experiments.

Global profile effects and structure formations in toroidal electron temperature gradient driven turbulence

Using a gyrokinetic toroidal particle code with global profile effects, the toroidal electron temperature gradient driven (ETG) turbulence in positive and reversed shear tokamaks is studied. In the simulation, initial saturation levels of the ETG mode are consistent with the mixing length theory, which shows a Bohm (gyro-Bohm) like ρ*-scaling for a ballooning type (slab like) ETG mode in a positive (reversed) shear configuration, where ρ* is the electron Larmor radius ρte divided by the minor radius a. In a realistic small ρ* positive shear configuration, the ETG mode has a higher saturation level than the large ρ* positive shear configuration and the reversed shear configuration. In the nonlinear turbulent state, the ETG turbulence in the positive and reversed shear configurations shows quite different structure formations. In the positive shear configuration, the ETG turbulence is dominated by streamers which have a ballooning type structure, and the electron temperature Te profile is quickly relaxed by enhanced heat transport in a turbulent time scale. In the reversed shear configuration, quasi-steady zonal flows are produced in the negative shear region, while the positive shear region is characterized by streamers. Accordingly, the electron thermal diffusivity χe has a gap structure across the qmin surface, and the Te gradient is sustained above the critical value for a long time. The results suggest a stiffness of the Te profile in positive shear tokamaks and a possibility of the Te transport barrier in reversed shear tokamaks.

Nonlinear behaviour of collisionless double tearing mode induced by electron inertia

A gyrokinetic particle simulation is executed to clarify the effect of the electron inertia on the MHD phenomena in the reversed shear configuration of a cylindrical tokamak plasma. It is found that the collisionless (kinetic) double tearing modes grow at the Alfvén time scale and nonlinearly induce the internal collapse when the helical flux at the magnetic axis is less than that at the outer resonant surface. After the internal collapse, the secondary reconnection is induced by the current concentration due to the m = 2 convective flow. It is also clarified that a nonlinear dynamics accompanying the elementary processes caused by the m = 2 flow can generate a new reversed shear configuration with resonant surfaces. In the presence of the density gradient, after the full reconnection induced by the m = 2 mode, the radial electric field is found to be generated due to the difference of the E × B motion between ions and electrons. However, the intensity of the radial field is not as large as that induced by the collisionless kink mode.

Global gyrokinetic simulation of ion temperature gradient driven turbulence in plasmas using a canonical Maxwellian distribution

A new gyrokinetic toroidal particle code has been developed to study the ion temperature gradient (ITG) driven turbulence in reactor relevant tokamak parameters. We use a new method based on a canonical Maxwellian distribution FCM(Pφ,ε,μ), which is defined by three constants of motion in the axisymmetric toroidal system—the canonical angular momentum Pφ, the energy ε, and the magnetic moment μ. A quasi-ballooning representation enables linear and nonlinear high-m,n global calculations to be carried out, with a good numerical convergence. Conservation properties are improved by using optimized particle loading. From comprehensive linear global analyses over a wide range of unstable toroidal mode numbers (n = 0–100) in large tokamak parameters (a/ρti = 320–460), it is found that the reversed shear configuration produces an effective stabilizing effect on the ITG mode in the q min region through global effects. In the nonlinear simulation, it is found that the new method based on FCM can simulate a zonal flow damping correctly; and spurious zonal flow oscillations, which are observed in a conventional method based on a local Maxwellian distribution FLM(ψ,ε,μ), do not appear in the nonlinear regime.

Study of the effects of liquid lithium curtain as first wall on plasma

A global model analysis of the effects of a liquid lithium curtain, which is utilized as the first wall for the Engineering outline design of the Fusion Experimental Breeder (FEB-E), on plasma has been performed. The relationships between the surface temperature of a liquid lithium curtain and the mean effective plasma charge, fuel dilution and the produced fusion power have been obtained. Studies indicate that under normal operation circumstances, the evaporation of liquid lithium does not affect the mean effective plasma charge seriously, but the effects on the fuel dilution and fusion power are more sensitive. We have investigated the relationships between the flow velocity of the liquid lithium curtain and the rise of surface temperature based on the operation scenario II of FEB-E design with reversed shear configuration and higher power density. Results show that even if the flow velocity of the liquid lithium curtain is as low as 0.5 m/s, the effects of evaporation from the curtain on plasma are negligible.

Variations of Current Profiles in Tokamaks Steady State Sustainment and Confinement Properties of Reversed Magnetic Shear Configuration

The status of transport simulation in reversed magnetic shear configuration of tokamaks is described. Based on the turbulent transport model of the current diffusive ballooning mode,the formation of internal transport barrier and the sustainment of reversed shear configuration is examined. The issues in developing the steady state sustainment scenarios are also discussed.

Effect of power deposition and current evolution on the formation of internal transport barriers

A model for internal transport barrier formation in tokamak plasmas [Newman et al., Phys. Plasmas 5 (1998) 938] is extended to include the evolution equation of the plasma current and a model of neutral beam injection power/particle deposition. The envelope density fluctuation level is evolved in time and coupled, via the E × B shearing rate, to the ASTRA system of transport equations. As a practical realization of the model, reversed shear configurations in the TFTR tokamak are studied. It is found that, aside from the total input power, the detailed profiles of power deposition and current density play an essential role in the determination of the value of the transition power threshold.

Recent progress in high performance and steady-state experiments on the Japan Atomic Energy Research Institute Tokamak-60 Upgrade with W-shaped divertor

In the Japan Atomic Energy Research Institute (JAERI) Tokamak-60 Upgrade [H. Shirai and the JT-60 Team, Phys. Plasmas 5, 1712 (1998)], high performance and steady-state experiments have been conducted in the W-shaped divertor. The equivalent deuterium-tritium (D-T) fusion multiplication factor, QDTeq, was enhanced transiently up to 1.25 in the reversed shear plasma. The reduction in particle diffusivity in the internal transport barriers (ITB) region of the reversed shear plasma was confirmed as well as the thermal diffusivity. It was also confirmed that the correlation length of density fluctuations is reduced inside the ITB of density. The performance with a confinement-enhancement factor (H-factor, H89) of 2.2 and QDTeq of 0.16 was sustained in a quasi-steady-state in the high-poloidal-beta (βp) and high confinement mode (H-mode) regime. The reversed shear configuration with ITBs was sustained by injecting the lower-hybrid waves combined with neutral beam injection and fully noninductive current drive in the reversed shear plasmas was realized for the first time. The driven current by the negative-ion-based neutral beam (NNB) injection increased up to 0.6 MA. The H-mode transition was triggered with the NNB injection and the H-mode with H89∼1.6–1.8 was sustained. The toroidicity-induced Alfvén eigenmode was excited for a volume-averaged fast ion beta, 〈βh〉, as low as ∼0.1%.

Ion Transport in Tokamak Plasmas with Ion Banana Orbits Squeezed by Alfvén Waves

Kinetic or slow Alfv\'en waves, which can be driven in a tokamak plasma by mode conversion, were earlier shown to be useful for wave current drive and plasma heating, for creating reversed shear configurations, and for the formation and maintenance of edge and internal transport barriers due to their small radial localizations. Kinetic Alfv\'en waves can also induce radial electric fields and provide a mechanism for squeezing the banana orbits of ions in weakly collisional plasmas of tokamaks. It is shown that the radial electric field, induced by Alfv\'en waves, under some conditions has a nonlinear dependence on the radio-frequency absorbed power.

Study of a compact reversed shear Tokamak reactor

A reversed shear configuration, which was observed recently in some Tokamak experiments, might have a possibility to realize compact and cost-competitive Tokamak reactors. In this study, a compact (low cost) commercial reactor based on the shear reversed high beta equilibrium with β N=5.5, is considered, namely the Compact Reversed Shear Tokamak, CREST-1. The CREST-1 is designed with a moderate aspect ratio ( R/a=3.4), which will allow us to experimentally develop this CREST concept by ITER. This will be very advantageous with regard to the fusion development strategy. The current profile for the reversed shear operation is sustained and controlled in steady state by bootstrap (88%), beam and rf driven currents, which are calculated by a neo-classical model code in 3D geometry. The MHD stability has been checked by an ideal MHD stability analysis code (ERATO) and it has been confirmed that the ideal low n kink, ballooning and Mercier modes are stable while a closed conductive shell is required for stability. Such a compact Tokamak can be cost-competitive as an electric power source in the 21st century and it is one possible scenario in realizing a commercial fusion reactor beyond the ITER project.