Toroidal Effects Research Articles

Overview of recent experimental results on the EAST Tokamak

Since the last IAEA-FEC in 2021, significant progress on the development of long pulse steady state scenario and its related key physics and technologies have been achieved, including the reproducible 403 s long-pulse steady-state H-mode plasma with pure radio frequency (RF) power heating. A thousand-second time scale (∼1056 s) fully non-inductive plasma with high injected energy up to 1.73 GJ has also been achieved. The EAST operational regime of high β P has been significantly extended (H 98y2 > 1.3, β P ∼ 4.0, β N ∼ 2.4 and n e/n GW ∼ 1.0) using RF and neutral beam injection (NBI). The full edge localized mode suppression using the n = 4 resonant magnetic perturbations has been achieved in ITER-like standard type-I ELMy H-mode plasmas with q 95 ≈ 3.1 on EAST, extrapolating favorably to the ITER baseline scenario. The sustained large ELM control and stable partial detachment have been achieved with Ne seeding. The underlying physics of plasma-beta effect for error field penetration, where toroidal effect dominates, is disclosed by comparing the results in cylindrical theory and MARS-Q simulation in EAST. Breakdown and plasma initiation at low toroidal electric fields (<0.3 V m−1) with EC pre-ionization is developed. A beneficial role on the lower hybrid wave injection to control the tungsten concentration in the NBI discharge is observed for the first time in EAST suggesting a potential way toward steady-state H-mode NBI operation.

Gyrokinetic simulations of the kinetic electron effects on the electrostatic instabilities on the ITER baseline scenario

The linear and nonlinear simulations are carried out using the gyrokinetic code NLT for the electrostatic instabilities in the core region of a deuterium plasma based on the International Thermonuclear Experimental Reactor (ITER) baseline scenario. The kinetic electron effects on the linear frequency and nonlinear transport are studied by adopting the adiabatic electron model and the fully drift-kinetic electron model in the NLT code, respectively. The linear simulations focus on the dependence of linear frequency on the plasma parameters, such as the ion and electron temperature gradients , the density gradient and the ion–electron temperature ratio . Here, is the major radius, and and denote the electron and ion temperatures, respectively. is the gradient scale length, with denoting the density, the ion and electron temperatures, respectively. In the kinetic electron model, the ion temperature gradient (ITG) instability and the trapped electron mode (TEM) dominate in the small and large region, respectively, where is the poloidal wavenumber. The TEM-dominant region becomes wider by increasing (decreasing) ( ) or by decreasing . For the nominal parameters of the ITER baseline scenario, the maximum growth rate of dominant ITG instability in the kinetic electron model is about three times larger than that in the adiabatic electron model. The normalized linear frequency depends on the value of , rather than the value of or , in both the adiabatic and kinetic electron models. The nonlinear simulation results show that the ion heat diffusivity in the kinetic electron model is quite a lot larger than that in the adiabatic electron model, the radial structure is finer and the time oscillation is more rapid. In addition, the magnitude of the fluctuated potential at the saturated stage peaks in the ITG-dominated region, and contributions from the TEM (dominating in the higher region) to the nonlinear transport can be neglected. In the adiabatic electron model, the zonal radial electric field is found to be mainly driven by the turbulent energy flux, and the contribution of turbulent poloidal Reynolds stress is quite small due to the toroidal shielding effect. However, in the kinetic electron model, the turbulent energy flux is not strong enough to drive the zonal radial electric field in the nonlinear saturated stage. The kinetic electron effects on the mechanism of the turbulence-driven zonal radial electric field should be further investigated.

Fundamental properties of ideal and resistive infernal modes in tokamaks

Infernal modes are unstable in regions of weak magnetic shear and significant pressure gradients. These modes comprise a broad class of instabilities, encompassing interchange modes and kink modes, with both short and long length scales. Toroidal effects and fully electromagnetic fields are of crucial importance for their description. The role of resistive diffusion and compressibility are also critical. In order to investigate this awkward problem while still enabling fundamental physics interpretation, a new resistive MHD eigensolver has been developed. An outcome of this study is the identification of an unstable spectrum of resistive infernal modes in regions of the plasma with weak average curvature, and in regions where the average curvature is destabilising. These fast growing modes may be collectively important for our understanding of global reconnection events, stochastic magnetic fields states, and neighbouring supercritical bifurcations.

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.

Reduction of the external resonant magnetic perturbation threshold for 2/1 locked mode excitation by the pre-excited mode on J-TEXT

A significant reduction of the external resonant magnetic perturbation (RMP) required for exciting the locked mode (LM) has been observed experimentally due to the presence of an existing LM on J-TEXT. In a plasma with edge safety factor q a slightly smaller than 3, 3/1 and 2/1 modes are observed to be destabilized successively by a rotating RMP field. The 3/1 mode is excited first and identified as an external kink mode, whose excitation threshold decreases with the operating q a increasing from 2.67 to 2.8 with the absence of a 3/1 rational surface. Shortly after excitation of the 3/1 external kink mode, 2/1 field penetration occurs and the 2/1 mode is excited, as identified by the phase between the 2/1 magnetic response and the RMP field jumping by π. The 2/1 mode is excited with a dominant kink structure and then converts into tearing mode for a duration of several milliseconds. During the excitation of the 2/1 mode, the phase difference between the 2/1 and 3/1 modes evolves from π to around 0 and the 2/1 mode amplitude grows to a saturation value comparable with that of the 3/1 mode. The presence of the 3/1 mode leads to a remarkable reduction of the external RMP current required for the 2/1 mode excitation, which can be explained by the contribution of a 2/1 resonant field from the 3/1 mode via the toroidal coupling effect. The larger 3/1 mode amplitude can lead to a greater reduction. This work reveals that the mode can be excited more easily with a reduced amplitude of RMP or error field due to the impact of the pre-existing mode and this might be a new consideration for error field correlation predictions and active magnetohydrodynamics control actuator designs.

On equations for ion cyclotron modes in ‘warm’ bounded plasmas

An equation describing eigenmodes in the ion cyclotron frequency range in ‘warm’ bounded plasmas, i.e. eigenmodes which are absent in the two-fluid model but exist in kinetic theory due to finite Larmor radius of the ions, is derived for the first time. It is valid for electrostatic modes but the developed approach is generic. Calculations are carried out for two cases: first, for a homogeneous magnetic field; second, taking into account the effects of toroidicity in tokamaks. It is found that, in general, equations for eigenmodes in warm plasmas do not reduce to second-order differential equations (in contrast to those which are usually used to describe the radial structure of eigenmodes in fusion devices). The study of modes in warm plasmas is of interest, in particular, in connection with the recent observations of superthermal ion cyclotron emission in the NSTX-U spherical torus and DIII-D tokamak, which can be hardly explained by conventional theories employing fast magnetoacoustic modes.

The effect of plasma beta on error-field penetration in radio-frequency wave heated plasmas in EAST

The plasma-beta effect on the n = 1 resonant magnetic perturbation (RMP) field penetration in purely radio-frequency (RF) wave heated discharges has been investigated in EAST. The experimental results show that the dependence of the threshold RMP coil current for field penetration, , on the total absorbed power P tot scales as approximately , indicating that the error-field tolerance is improved with increasing RF power. This is benefited by the increased electron perpendicular flow dominated by a counter-current electron diamagnetic flow with increasing RF power. However, theoretical scaling in cylindrical geometry overestimates the power index. Assuming an additional term for the normalized beta in the scaling, it is shown that the fitted from the experimental observation is around −1, indicating a degradation effect of plasma beta. To clarify the underlying physics of the plasma-beta effect that was not included in the theoretical scaling in cylindrical geometry, the MARS-Q code with full toroidal geometry is employed for simulation of nonlinear field penetration (Liu et al 2013 Phys. Plasmas 20 042503). The MARS-Q simulation results reproduce the dependence well, and hence the P tot scaling of the threshold current in experimental observations. The main reason for this is that the net total torque, which is mainly contributed by the neoclassical toroidal viscosity (NTV), increases with increasing plasma . The results demonstrate that the nonlinear toroidal coupling effect via NTV torque plays an important role in determining field penetration, even in cases with relatively low , which is far less than the no-wall beta limit.

A new method to reduce the toroidal field ripple effect due to the ferromagnetic materials in updated CFETR

The toroidal field ripple (TFR) is one of the critical factors affecting the long-pulse high-performance discharges for the tokamak device. The TFR is not only determined by the toroidal field coils (TFCs) but is also affected by the ferromagnetic materials in the plasma facing components such as diagnostic system and blanket system. In the phase Ⅱ design of the China Fusion Engineering Test Reactor (CFETR), the inner ferromagnetic constituent and the poloidal segmentation of water-cooled ceramic breeder (WCCB) blanket are modified and the diagnostic system also has major change compared with the phase Ⅰ design, therefore it is necessary to investigate and reduce the TFR effect of the updated blanket system and diagnostic system for the phase Ⅱ designed CFETR. Firstly, the effect of the blanket system on the TFR is evaluated systematically, considering the diagnostic shielding modules (DSMs) of the diagnostic system at the equatorial ports (EPs). Moreover, a new TFR reducing method by adjusting the distribution of ferromagnetic materials filling ratios in the toroidal direction is proposed. According to the results, the local TFR nearby the plasma separatrix line already exceeds the design specification limit with the blanket system, and this phenomenon will be worse due to installing the DSMs and the EP. After adjusting the percentage of the ferromagnetic materials in the outboard-side (OBs) segment, the plasma TFR is reduced obviously and within the 0.5% limit.

Neutral Beam Coupling with Plasma in a Compact Fusion Neutron Source

FNS-ST is a fusion neutron source project based on a spherical tokamak (R/a = 0.5 m/0.3 m) with a steady-state neutron generation of ~1018 n/s. Neutral beam injection (NBI) is supposed to maintain steady-state operation, non-inductive current drive and neutron production in FNS-ST plasma. In a low aspect ratio device, the toroidal magnetic field shape is not optimal for fast ions confinement in plasma, and the toroidal effects are more pronounced compared to the conventional tokamak design (with R/a &gt; 2.5). The neutral beam production and the tokamak plasma response to NBI were efficiently modeled by a specialized beam-plasma software package BTR-BTOR, which allowed fast optimization of the neutral beam transport and evolution within the injector unit, as well as the parametric study of NBI induced effects in plasma. The “Lite neutral beam model” (LNB) implements a statistical beam description in 6-dimensional phase space (106–1010 particles), and the beam particle conversions are organized as a data flow pipeline. This parametric study of FNS-ST tokamak is focused on the beam-plasma coupling issue. The main result of the study is a method to achieve steady-state current drive and fusion controllability in beam-driven toroidal plasmas. LNB methods can be also applied to NBI design for conventional tokamaks.

Toroidal tidal effects in microstate geometries

Tidal effects in capped geometries computed in previous literature display no dynamics along internal (toroidal) directions. However, the dual CFT picture suggests otherwise. To resolve this tension, we consider a set of infalling null geodesics in a family of black hole microstate geometries with a smooth cap at the bottom of a long BTZ-like throat. Using the Penrose limit, we show that a string following one of these geodesics feels tidal stresses along all spatial directions, including internal toroidal directions. We find that the tidal effects along the internal directions are of the same order of magnitude as those along other, non-internal, directions. Furthermore, these tidal effects oscillate as a function of the distance from the cap — as a string falls down the throat it alternately experiences compression and stretching. We explain some physical properties of this oscillation and comment on the dual CFT interpretation.

Hybrid gyrokinetic ion/fluid electron simulation of toroidal tearing modes

The effects of toroidicity and kinetic ions on the resistive tearing mode are systematically studied with the gyrokinetic particle-in-cell simulation code GEM [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)] and compared with analytic theory. A new field solver in toroidal geometry has been developed for the simulation of low-n (n = 1, 2) modes in tokamaks. It is found that the toroidal effect significantly reduces the growth rate of the tearing mode. The toroidal effect can also increase the radial width of the tearing mode and change the scaling between the radial mode width and resistivity due to the toroidal pressure term in the electron continuity equation. The kinetic effects of ions can decrease the growth rate of the tearing mode. The plasma flux-surface shaping is found to have significant effect on the tearing mode.

Full-wave 2D modeling of helicons propagation and absorption in thespherical tokamak Globus-M2

Numerical modeling of propagation and absorption of fast waves(helicons) with frequency 200 MHz in 2D inhomogeneous plasma of thespherical tokamak Globus-M2 was carried out with 2D full-wave code. Toroidal effects, poloidal magnetic field and the actual shape of the fluxsurfaces were taken into account. The full wave electric field and RF powerabsorption profiles were computed by solving plasma wave equation withelectron Landau damping term. The modeling demonstrated a fairly highefficiency of helicons absorption in the bulk plasma within a wide range ofexperimental parameters. The waves propagate to the inner regions of theplasma column and are mainly absorbed there; less than 20% of RF energyreturns back to the plasma periphery. Keywords: high temperature plasma, nuclear fusion, tokamak, high frequency plasma waves, helicons, plasma wave equation, full-wave code.\

Full-wave 2D modeling of helicons propagation and absorption in the spherical tokamak Globus-M2

Numerical modeling of propagation and absorption of fast waves (helicons) with frequency 200MHz in 2D inhomogeneous plasma of the spherical tokamak Globus-M2 was carried out with 2D full-wave code. Toroidal effects, poloidal magnetic field and the actual shape of the flux surfaces were taken into account. The full wave electric field and RF power absorption profiles were computed by solving plasma wave equation with electron Landau damping term. The modeling demonstrated a fairly high efficiency of helicons absorption in the bulk plasma within a wide range of experimental parameters. The waves propagate to the inner regions of the plasma column and are mainly absorbed there; less than 20% of RF energy returns back to the plasma periphery. Keywords: high temperature plasma, nuclear fusion, tokamak, high frequency plasma waves, helicons, plasma wave equation, full-wave code.

Полноволновое двумерное моделирование распространения и поглощения геликонов в плазме сферического токамака Глобус-М2

Numerical modeling of propagation and absorption of fast waves (helicons) with frequency 200 MHz in 2D inhomogeneous plasma of the spherical tokamak Globus-M2 was carried out with 2D full-wave code. Toroidal effects, poloidal magnetic field and the actual shape of the flux surfaces were taken into account. The full wave electric field and RF power absorption profiles were computed by solving plasma wave equation with electron Landau damping term. The modeling demonstrated a fairly high efficiency of helicons absorption in the bulk plasma within a wide range of experimental parameters. The waves propagate to the inner regions of the plasma column and are mainly absorbed there; less than 20% of RF energy returns back to the plasma periphery.

Pressure driven long wavelength MHD instabilities in an axisymmetric toroidal resistive plasma

A general set of equations that govern global resistive interchange, resistive internal kink and resistive infernal modes in a toroidal axisymmetric equilibrium are systematically derived in detail. Tractable equations are developed such that resistive effects on the fundamental rational surface can be treated together with resistive effects on the rational surfaces of the sidebands. Resistivity introduces coupling of pressure driven toroidal instabilities with ion acoustic waves, while compression introduces flute-like flows and damping of instabilities, enhanced by toroidal effects. It is shown under which equilibrium conditions global interchange, internal kink modes or infernal modes occur. The m = 1 internal kink is derived for the first time from higher order infernal mode equations, and new resistive infernal modes resonant at the q = 1 surface are reduced analytically. Of particular interest are the competing effects of resistive corrections on the rational surfaces of the fundamental harmonic and on the sidebands, which in this paper is investigated for standard profiles developed for the m = 1 internal kink problem.

Influence of Hall effect and toroidal flow on the plasmoid formation and incomplete reconnection in a low resistivity plasma in tokamak

The nonlinear resistive-kink mode in the low resistivity plasma in tokamak is investigated through the three-dimensional, toroidal, and nonlinear Hall-MHD code CLT. It is found that, without the two-fluid effect and the toroidal flow, the system can evolve into a steady-state with the saturated main m/n = 1/1 magnetic island and the co-existing large secondary island. The main m/n = 1/1 magnetic island cannot push the hot core plasma out of the q = 1 surface as it does in Kadomstev’s model, and the reconnection is incomplete. However, with the two-fluid effect or the toroidal flow, the nonlinear behaviors of the resistive-kink mode could be essentially different. The two-fluid effect and the toroidal flow can break the symmetry during the plasmoid formation, which destroys the balance between the main m/n = 1/1 magnetic island and the large secondary island. The large secondary island is then merged into the main m/n = 1/1 island. After that, the main m/n = 1/1 island finally occupies the whole mix region, and all magnetic flux in the mix region is reconnected. A similar simulation study has been done in periodic cylindrical geometry (Günter et al 2015 Plasma Phys. Control. Fusion 57 014017), while our work is done in tokamak toroidal geometry. The toroidal effect has also been investigated, and we find that the widths of the main 1/1 island and the secondary island slightly increase with increasing aspect ratios.

Gyrokinetic simulations of double tearing modes in toroidal plasma

An investigation of the characteristics of double-tearing modes (DTMs) and the influence of the kinetic effects of ions has been carried out with the gyrokinetic code GTC. A simplified linear fluid and a gyro-kinetic model has been used for the electron and ion dynamics, respectively. It was found that as the separation of the rational surfaces was increased, the growth rates of DTMs were enhanced and the DTM system tended to decouple into a system of two single-tearing modes. When the width between the rational surfaces is larger, the corresponding amplitude of the inner-tearing mode is smaller. We also demonstrate that the existence of thermal ions destabilizes the DTM. The toroidal effect also has a mild destabilizing effect (∼8%) on the growth of DTMs, which is consistent with the theoretical analysis.

Turbulence-driven flow dynamics in general axisymmetric toroidal geometry

This work gives the equations governing the generation of toroidally axisymmetric flows by turbulent Reynolds and Maxwell stresses in finite aspect ratio, general cross section tokamak plasmas. Inclusion of the divergence-free flow constraint in the lowest order changes the timescale for evolution of the poloidal flows driven by turbulence by substantial factors. In the pedestal region for the present-day machines, as compared to earlier cylindrical models, the timescale evaluated using a large aspect ratio circular cross section model can be two orders of magnitude longer, while the present, general geometry result can be about one order of magnitude longer. Inclusion of gyroviscosity in the calculation shows that the only lowest order radial velocity fluctuations that enter the problem are those due to fluctuating E ×B flows. Toroidal and poloidal flow effects on the toroidally axisymmetric flows are inextricably coupled due to the neoclassical poloidal viscosity. Accordingly, the physics is inherently three dimensional and measurements of all three-velocity components are required to obtain the information needed to quantitatively test the theory. The parallel and angular momentum equations for the lowest order, toroidally axisymmetric flows look like radial transport equations when the turbulence is included. The turbulence terms provide the radial transport fluxes. In standard neoclassical theory, the parallel flow equation is local on each flux surface; there is no radial derivative term. However, adding turbulence gives a way, in principle, for radial transport to lead to poloidal flows that deviate from the neoclassical prediction. The inclusion of the Maxwell stress provides a mechanism for MHD fluctuations to alter the toroidally axisymmetric flows.

Effects of radial electric field on ion temperature gradient driven mode stability

The local stability of ion-temperature gradient driven mode (ITG) in the presence of a given radial electric field is investigated using gyrokinetic theory and ballooning mode formalism with toroidal effect accounted for. It is found that zero frequency radial electric field-induced poloidal rotation can significantly stabilize ITG, while the associated density perturbation has little effect on ITG stability due to the modification of finite-orbit-width effect. However, the parallel mode structure is slightly affected due to the evenly symmetric density modulation associated with the zero-frequency radial electric field.

The theoretical study on intermittency and propagation of geodesic acoustic mode in L-mode discharge near tokamak edge

Through a systematically developed theory, we demonstrate that the motion of Instanton identified in Zhang et al (2017 Phys. Plasmas 24 122304) is highly correlated to the intermittent excitation and propagation of geodesic acoustic mode (GAM) that is observed in tokamaks. While many numerical simulations have observed the phenomena, it is the first theory that reveals the physical mechanism behind GAM intermittent excitation and propagation. The preceding work is based on the micro-turbulence associated with toroidal ion temperature gradient mode, and slab-based phenomenological model of zonal flow. When full toroidal effect is introduced into the system, two branches of zonal flow emerge: the torus-modified low frequency zonal flow (TLFZF), and GAM, necessitating a unified exploration of GAM and TLFZF. Indeed, we observe that the transition from the Caviton to Instanton is triggered by a rapid zero-crossing of radial group velocity of drift wave and is found to be strongly correlated with the GAM onset. Many features peculiar to intermittent GAMs, observed in real machines, are thus identified in the numerical experiment. The results will be displayed in figures and in a movie; first for single central rational surface, and then with coupled multiple central rational surfaces. The periodic bursting first shown disappears as being replaced by irregular one, more similar to the intermittent characteristics observed in GAM experiments.