Low Collisionality Regime Research Articles

ELM-free H-mode phase and decoupling of peeling–ballooning stability boundary in the MAST Upgrade tokamak

Abstract A linear magnetohydrodynamic (MHD) peeling–ballooning stability analysis of the edge-localized mode (ELM)-free phase of a MAST Upgrade (MAST-U) H-mode plasma is presented. In contrast to other similar discharges, #47018 is found to have a significantly higher and wider pedestal during its ELM-free H-mode phase that lasts for approximately 80 ms; this is made possible by the reduced core MHD mode activity on the q = 2 surface. During this period, there is sustained decoupling of peeling and ballooning branches of the stability boundary on J–α space, opening an access channel to the second stability regime with higher peaks in pedestal current density J N , ped and pressure gradient (α). Such decoupling of the stability boundary has not previously been observed in MAST-U H-modes, and if such a condition can be readily reproduced, it opens a wide range of opportunities for MAST-U to explore low-collisionality peeling-limited pedestal regimes as well as advanced scenarios such as quiescent H-modes that are relevant to future reactors such as STEP and ITER.

MCTrans++: a 0-D model for centrifugal mirrors

The centrifugal mirror confinement scheme incorporates supersonic rotation of a plasma into a magnetic mirror device. This concept has been shown experimentally to drastically decrease parallel losses and increase plasma stability as compared with prior axisymmetric mirrors. MCTrans++ is a dimensionless (0-D) scoping tool which rapidly models experimental operating points in the Centrifugal Mirror Fusion Experiment (CMFX) at the University of Maryland. In the low-collisionality regime, parallel losses can be modelled analytically. A confining potential is set up that is partially ambipolar and partially centrifugal. Due to the stabilizing effects of flow shear, the perpendicular losses can be modelled as classical. Radiation losses such as bremsstrahlung and cyclotron emission are taken into account. A neutrals model is included, and, in some circumstances, charge-exchange losses are found to exceed all other loss mechanisms. We use the SUNDIALS ARKODE library to solve the underlying equations of this model; the resulting software is suitable for scanning large parameter spaces, and can also be used to model time-dependent phenomena such as a capacitive discharge. MCTrans++ has been used to verify results from prior centrifugal mirrors, create an experimental plan for CMFX and find configurations for future reactor-scale fusion devices.

Neoclassical transport of impurities in tokamaks with non-axisymmetric perturbations

The effect of resonant magnetic perturbations (RMPs) on neoclassical transport of impurities is calculated in DIII-D and NSTX. The neoclassical fluxes are evaluated using the NEO code with nonlinear one-fluid nonaxisymmetric equilibrium calculated using M3D-C1. Neoclassical fluxes of impurities show significant changes with RMPs if the impurity resides in low-collisionality regime, but are weakly affected by RMPs in the Pfirsch–Schlüter (P–S) regime. Charge number (Z) of the impurity affects the collisionality of impurity species, which then determines the effect of 3D fields on neoclassical impurity transport. This suggests that RMPs can be possibly used for exhaust of low-Z impurities in these facilities, but have little effect for impurities with charge number greater than 10 or so. Additionally, it is shown that it is the change in the convective fluxes which is a main contributor in modifying the neoclassical impurity fluxes in the presence of RMPs.

Long-wavelength closures for collisional and neutral interaction terms in gyro-fluid models

A collisional gyro-fluid model is presented. The goal of the model is edge and scrape-off layer turbulence. The emphasize in the model derivation heavily lies on ”implementability” with today’s numerical methods. This translates to an avoidance of infinite sums, strongly coupled equations in time and intricate elliptic operator functions. The resulting model contains the four moments density, parallel momentum, perpendicular pressure and parallel energy and is closed by a polarisation equation and parallel Ampere law. The central ingredient is a collisional long-wavelength closure that relies on a drift-fluid gyro-fluid correspondence principle. In this way the extensive literature on fluid collisions can be incorporated into the model including sources, plasma-neutral interactions and scattering collisions. Even though this disregards the characteristic finite Larmor radius terms in the collisional terms the resulting model is at least as accurate as the corresponding drift-fluid model in these terms. Furthermore, the model does enjoy the benefits of an underlying variational principle in an energy-momentum theorem and an inherent symmetry in moment equations with regards to multiple ion species. Consistent particle drifts as well as finite Larmor radius corrections and high amplitude effects in the advection and polarization terms are further characteristics of the model. Extensions and improvements like short-wavelength expressions, a trans-collisional closure scheme for the low-collisionality regime or zeroth order potential must be added at a later stage.

ASCOT5 simulations of neutral beam heating and current drive in the TJ-II stellarator

The TJ-II stellarator neutral-beam injection (NBI) system, vacuum vessel and magnetic configuration have been included in the orbit-following Monte Carlo code ASCOT5 to simulate neutral-beam heating and current drive for high-density NBI plasmas. Co- and counter-injection beams are simulated separately. A scan in both electron density and temperature is carried out within the range of values corresponding to realistic high-density NBI plasmas, for which a low level of fast-ion losses due to charge-exchange reactions is expected, since the version of ASCOT5 used in the paper does not include such processes. The rest of the kinetic profiles (ion temperature, radial electric field and effective charge) are kept fixed. The initial distribution of markers shows that the amount of available power in the plasma carried by the beam ions depends slightly on the electron temperature and on the injection direction (co/counter). The steady-state fast-ion distribution function is obtained and used to calculate the three-dimensional fast-ion density, the neutral-beam driven current and the amount of power deposited to the plasma in the two injection scenarios. These three quantities are higher in the counter-injected case due to a lower amount of promptly lost particles. The neutral-beam current drive (NBCD) has been calculated using the fast-ion beam current given by ASCOT5 and the electron return current, which is computed with the analytic solution of the drift kinetic equation for electrons in the presence of fast ions in the low-collisionality regime. Neither the calculated fast-ion density nor the NBCD are flux functions, in consistency with the fact that fast-ion drift surfaces and flux surfaces are generally not aligned.

Understanding of neoclassical offset rotation based on DIII-D experiments

Neoclassical offset rotation induced by non-axisymmetric magnetic perturbations in tokamaks is investigated using NTVTOK model based on plasma profiles in one DIII-D discharge. The calculated counter-Ip (Ip indicates plasma current) ion root of neoclassical offset rotation is found to be consistent with DIII-D experimental observations. The modeling results predict that this DIII-D plasma regime is close to the marginal condition for the co-Ip electron root to exist. The importance of bounce–drift resonance is highlighted in the calculation, which affects the neoclassical offset rotation, especially the electron root. The ion root usually exists for various parameter regimes, while the electron root is only possible in low collisionality (e.g., high temperature and/or low density) regimes. The magnetic perturbation spectrum is found to influence the existence of electron roots when electrons are closer to resonant superbanana plateau regime than ions. By adjusting the plasma collisionality and tuning the spectrum of magnetic perturbations, it is possible to control the plasma rotation and hence to optimize the plasma confinement.

Modeling the dominance of the gradient drift or Kelvin–Helmholtz instability in sheared ionospheric E × B flows

Studies have shown that in sheared E×B flows in an inhomogeneous ionospheric plasma, the gradient drift (GDI) or the Kelvin–Helmholtz (KHI) instability may grow. This work examines the conditions that cause one of these instabilities to dominate over the other using a novel model to study localized ionospheric instabilities. The effect of collisions with neutral particles plays an important role in the instability development. It is found that the KHI is dominant in low collisionality regimes, the GDI is dominant in high collisionality regimes, and there exists an intermediate region in which both instabilities exist in tandem. For low collisionality cases in which the velocity shear is sufficiently far from the density gradient, the GDI is found to grow as a secondary instability extending from the KHI vortices. The inclusion of a neutral wind-driven electric field in the direction of the velocity shear does not impact the dominance of either instability. Using data from empirical ionospheric models, two altitude limits are found. For altitudes above the higher limit, the KHI is dominant. For altitudes below the lower limit, the GDI is dominant. In the intermediate region, both instabilities grow together. Increasing the velocity shear causes both limits to be lower in altitude. This implies that for ionospheric phenomena whose density and velocity gradients span large altitude ranges, such as subauroral polarization streams, the instabilities observed by space-based and ground-based observation instruments could be significantly different.

Impact of ion temperature anisotropy on 2D edge-plasma transport

Abstract A model of ion temperature anisotropy for 2D plasma transport in the scrape-off layer (SOL) of tokamaks is described and implemented in the UEDGE fluid transport code. Two ion energy equations are used to describe the evolution of the separate parallel and perpendicular ion temperatures. The temperature anisotropy generates viscous forces in both parallel and perpendicular directions that modify the parallel force balance equation and add an additional cross-magnetic-field drift velocity. Using the full set of UEDGE plasma and neutral equations (particle continuity, momentum, and energy), simulations are performed for both a 1D poloidal case and a 2D (radial and poloidal) single-null tokamak geometry case to highlight the 2D effects. The results show that ion parallel flows near the magnetic X-point in a comparatively low collisionality regime can be overestimated by the standard isotropic Braginskii model. The 2D ion temperature anisotropy varies substantially near the X-point and also near the divertor target plates, due to ionization sources. Moving radially outwards at the outer midplane, the anisotropy decreases between the core boundary and the magnetic separatrix and then it increases while moving across the SOL to the chamber wall.

Incorporating nonlocal parallel thermal transport in 1D ITER SOL modelling

Accurate modelling of the thermal transport in the ‘scrape-off-layer’ (SOL) is of great importance for assessing the divertor exhaust power handling in future high-power tokamak devices. In conditions of low collisionality and/or steep temperature gradients that will be characteristic of such devices, classical local diffusive transport theory breaks down, and the thermal transport becomes nonlocal, depending on conditions in distant regions of the plasma. An advanced nonlocal thermal transport model is implemented into a 1D SOL code ‘SD1D’ to create ‘SD1D-nonlocal’, for the study of nonlocal transport in tokamak SOL plasmas. The code is applied to study typical ITER steady-state conditions, to assess the relevance of nonlocality for ITER operating scenarios. Results suggest that nonlocal effects will be present in the ITER SOL, with strong sensitivity in simulation outputs observed for small changes in upstream density conditions, and drastically different temperature profiles predicted using local/nonlocal transport models in some cases. Global flux limiters are shown to be inadequate to capture the spatially and temporally changing SOL conditions. Introducing impurity seeding, under conditions where detached divertor operation is achieved using the flux-limited Spitzer-Härm models used in standard SOL codes, simulations using the nonlocal thermal transport model under equivalent conditions were found to not reach detachment. An analysis of the connection between SOL collisionality and nonlocality suggests that nonlocal effects will be significant for future devices such as DEMO as well. The results motivate further work using nonlocal transport models to study disruption events and low collisionality regimes for ITER, to further improve accuracy of the nonlocal models employed in comparison to kinetic codes, and to identify more appropriate boundary conditions for a nonlocal SOL model.

Extended investigations of isotope effects on ECRH plasma in LHD

Isotope effects of ECRH plasma in LHD were investigated in detail. A clear difference of transport and turbulence characteristics in H and D plasmas was found in the core region, with normalized radius ρ < 0.8 in high collisionality regime. On the other hand, differences of transport and turbulence were relatively small in low collisionality regime. Power balance analysis and neoclassical calculation showed a reduction of the anomalous contribution to electron and ion transport in D plasma compared with H plasma in the high collisionality regime. In core region, density modulation experiments also showed more reduced particle diffusion in D plasma than in H plasma, in the high collisionality regime. Ion scale turbulence was clearly reduced at ρ < 0.8 in high collisionality regime in D plasma compared with H plasma. The gyrokinetic linear analyses showed that the dominant instability ρ = 0.5 and 0.8 were ion temperature gradient mode (ITG). The linear growth rate of ITG was reduced in D plasma than in H plasma in high collisionality regime. This is due to the lower normalized ITG and density gradient. More hollowed density profile in D plasma is likely to be the key control parameter. Present analyses suggest that anomalous process play a role to make hollower density profiles in D plasma rather than neoclassical process. Electron scale turbulence were also investigated from the measurements and linear gyrokinetic simulations.

Observation of the current driving due to electron temperature redistribution by anomalous Doppler instability in the Experimental Advanced Superconducting Tokamak

Density sweeping-down experiments have been performed in order to investigate the electron dynamics and the effects on instabilities such as magnetohydrodynamics (MHD) in the low collisionality regime in the Experimental Advanced Superconducting Tokamak (EAST). It is found that an electrostatic instability is always excited which is recognized as the anomalous Doppler instability (ADI). The ADI is characterized by the stair-stepping electron cyclotron emission (ECE), converting the parallel energy to the perpendicular component of energetic electrons in the direction of the magnetic field. The background electron temperature profile is redistributed which results in the gradient change in the core. Non-negligible bootstrap current causes the loop voltage decrease. The bootstrap current is dissipated by the bursting MHD instability which is explained as the Alfvén-acoustic mode. Analysis indicates that bulk electrons are easily trapped in the steepened temperature gradient region, intensifying the asymmetry of electron velocity distribution in the parallel direction and creating the bootstrap current in the low-collisionality regime. In particular, it is shown that the global Alfvén-acoustic mode dramatically removes trapped electrons and quenches the bootstrap current, which is the main limit for the bootstrap current life.

Isotope effects on energy, particle transport and turbulence in electron cyclotron resonant heating plasma of the Large Helical Device

Positive isotope effects have been found in electron cyclotron resonant heating plasma of the Large Helical Device (LHD). The global energy confinement time (τE) in deuterium (D) plasma is 16% better than in hydrogen (H) plasma for the same line-averaged density and absorption power. The power balance analyses showed a clear reduction in ion energy transport, while electron energy transport does not change dramatically. The global particle confinement time (τp) is degraded in D plasma; τp in D plasma is 20% worse than in H plasma for the same line-averaged density and absorption power. The difference in the density profile was not due to the neutral or impurity sources, but rather was due to the difference in the transport. Ion scale turbulence levels show isotope effects. The core turbulence (ρ = 0.5–0.8) level is higher in D plasma than in H plasma in the low collisionality regime and is lower in D plasma than in H plasma. The density gradient and collisionality play a role in the core turbulence level.

Simulation of edge localized mode heat pulse using drift-kinetic ions and Boltzmann electrons

Abstract This article reports on 1D+2V heat pulse propagation studies using the COGENT guiding center kinetic code. The model uses magnetized kinetic ions and a simple Boltzmann electron model. Results agree with previous kinetic and fluid modeling benchmark studies that correspond to the parameters of edge localized modes (ELMs) observed on the JET tokamak. The plasma parameters for the edge pedestal and ensuing ELM dynamics are in the low collisionality regime. Hence, the dominant balance between the assumed Maxwellian ELM source and collisionless parallel advection causes the ion PDF to develop a significantly anisotropic velocity distribution. Adding nonlinear Coulomb ion-ion collisions to the model acts to smooth the sharp features of the ion distribution function, but the anisotropy remains robust due to the low collisionality.

The plasma-wall transition with collisions and an oblique magnetic field: Reversal of potential drops at grazing incidences

The plasma-wall transition is studied by using 1d3V particle-in-cell simulations in the case of a one dimensional plasma bounded by two absorbing walls separated by 200 Debye lengths (λd). A constant and oblique magnetic field is applied to the system, with an amplitude such that r &amp;lt; λd &amp;lt; R, where r and R are the electron and ion Larmor radii, respectively. Collisions with neutrals are taken into account and modelled by an energy conservative operator, which randomly reorients ion and electron velocities. The plasma-wall transition (PWT) is shown to depend on both the angle of incidence of the magnetic field with respect to the wall, θ, and on the ion mean-free-path to Larmor radius ratio, λci/R. In the very low collisionality regime (λci≫R) and for a large angle of incidence, the PWT consists of the classical tri-layer structure (Debye sheath/Chodura sheath/pre-sheath) from the wall towards the center of the plasma. The drops of potential within different regions are well consistent with already published models. However, when sin θ≤R/λci or with the ordering λci&amp;lt;R, collisions cannot be neglected, leading to the disappearance of the Chodura sheath. In this case, a collisional model yields analytic expressions for the potential drop in the quasi-neutral region and explains, in qualitative and quantitative agreement with the simulation results, its reversal below a critical angle derived in this paper, a regime possibly met in the scrape-off layers of tokamaks. It is further shown that the potential drop in the Debye sheath slightly varies with the collisionality for λci≫R. However, it tends to decrease with λci in the high collisionality regime, until the Debye sheath finally vanishes.

Electrostatic potential variations on stellarator magnetic surfaces in low collisionality regimes

The component of the neoclassical electrostatic potential that is non-constant on the magnetic surface, that we denote by$\tilde{\unicode[STIX]{x1D711}}$, can affect radial transport of highly charged impurities, and this has motivated its inclusion in some modern neoclassical codes. The number of neoclassical simulations in which$\tilde{\unicode[STIX]{x1D711}}$is calculated is still scarce, partly because they are usually demanding in terms of computational resources, especially at low collisionality. In this paper the size, the scaling with collisionality and with aspect ratio and the structure of$\tilde{\unicode[STIX]{x1D711}}$on the magnetic surface are analytically derived in the$1/\unicode[STIX]{x1D708}$,$\sqrt{\unicode[STIX]{x1D708}}$and superbanana-plateau regimes of stellarators close to omnigeneity; i.e. stellarators that have been optimized for neoclassical transport. It is found that the largest$\tilde{\unicode[STIX]{x1D711}}$that the neoclassical equations admit scales linearly with the inverse aspect ratio and with the size of the deviation from omnigeneity. Using a model for a perturbed omnigenous configuration, the analytical results are verified and illustrated with calculations by the codeKNOSOS. The techniques, results and numerical tools employed in this paper can be applied to neoclassical transport problems in tokamaks with broken axisymmetry.

Dynamic divertor control using resonant mixed toroidal harmonic magnetic fields during ELM suppression in DIII-D

Experiments using Resonant Magnetic Perturbations (RMPs), with a rotating n = 2 toroidal harmonic combined with a stationary n = 3 toroidal harmonic, have validated predictions that divertor heat and particle flux can be dynamically controlled while maintaining Edge Localized Mode (ELM) suppression in the DIII-D tokamak. Here, n is the toroidal mode number. ELM suppression over one full cycle of a rotating n = 2 RMP that was mixed with a static n = 3 RMP field has been achieved. Prominent heat flux splitting on the outer divertor has been observed during ELM suppression by RMPs in low collisionality regime in DIII-D. Strong changes in the three dimensional heat and particle flux footprint in the divertor were observed during the application of the mixed toroidal harmonic magnetic perturbations. These results agree well with modeling of the edge magnetic field structure using the TOP2D code, which takes into account the plasma response from the MARS-F code. These results expand the potential effectiveness of the RMP ELM suppression technique for the simultaneous control of divertor heat and particle load required in ITER.

Electromagnetic banana kinetic equation and its applications in tokamaks

A banana kinetic equation in tokamaks that includes effects of the finite banana width is derived for the electromagnetic waves with frequencies lower than the gyro-frequency and the bounce frequency of the trapped particles. The radial wavelengths are assumed to be either comparable to or shorter than the banana width, but much wider than the gyro-radius. One of the consequences of the banana kinetics is that the parallel component of the vector potential is not annihilated by the orbit averaging process and appears in the banana kinetic equation. The equation is solved to calculate the neoclassical quasilinear transport fluxes in the superbanana plateau regime caused by electromagnetic waves. The transport fluxes can be used to model electromagnetic wave and the chaotic magnetic field induced thermal particle or energetic alpha particle losses in tokamaks. It is shown that the parallel component of the vector potential enhances losses when it is the sole transport mechanism. In particular, the fact that the drift resonance can cause significant transport losses in the chaotic magnetic field in the hitherto unknown low collisionality regimes is emphasized.

The build-up of energetic electrons triggering electron cyclotron emission bursts due to a magnetohydrodynamic mode at the edge of tokamaks

Intense bursts of electron cyclotron emission (ECE) triggered by magnetohydrodynamic (MHD) instabilities such as edge localized modes have been observed on many tokamaks. On the DIII-D tokamak, it is found that a MHD mode is necessary in order to trigger the ECE bursts in the low collisionality regime at the plasma edge. ORBIT-code simulations have shown that energetic electrons build up due to an interaction between barely trapped electrons with a MHD mode (f = 50 kHz for the current case). The energetic tail of the electron distribution function develops a bump within several microseconds for this collisionless case. This behavior depends on the competition between the perturbing MHD mode and slowing down and pitch angle scattering due to collisions. For typical DIII-D parameters, the calculated ECE radiation transport predicted by ORBIT is in excellent agreement with ECE measurements, clarifying the electron dynamics of the ECE bursts for the first time.

Extension of high-beta plasma operation to low-collisionality regime

In the large helical device, plasma with more than 4% average beta was successfully produced by multi-pellet injections in a regime with a collisionality one order of magnitude lower than that in previous high-beta operations. An improvement in particle confinement was observed during a high-beta discharge produced by a gas puff, and particle flux to the divertor was reduced by more than 40%. High instabilities at the plasma edge occurred and suppressed the increment of the average beta to 3.4%. A spontaneous change in the magnetic topology contributes to an increase in the average beta value while triggering the excitation of edge MHD instabilities.

Stellarator bootstrap current and plasma flow velocity at low collisionality

The bootstrap current and flow velocity of a low-collisionality stellarator plasma are calculated. As far as possible, the analysis is carried out in a uniform way across all low-collisionality regimes in general stellarator geometry, assuming only that the confinement is good enough that the plasma is approximately in local thermodynamic equilibrium. It is found that conventional expressions for the ion flow speed and bootstrap current in the low-collisionality limit are accurate only in the $1/\unicode[STIX]{x1D708}$-collisionality regime and need to be modified in the $\sqrt{\unicode[STIX]{x1D708}}$-regime. The correction due to finite collisionality is also discussed and is found to scale as $\unicode[STIX]{x1D708}^{2/5}$.