Upcoming tokamak experiments fueled with deuterium and tritium are expected to have large alpha particle populations. Such experiments motivate new attention to the theory of alpha particle confinement and transport. A key topic is the interaction of alphas with perturbations to the tokamak fields, including those from ripple and magnetohydrodynamic modes like Alfvén eigenmodes. These perturbations can transport alphas, leading to changed localization of alpha heating, loss of alpha power, and damage to device walls. Alpha interaction with these perturbations is often studied with single particle theory. In contrast, we derive a drift kinetic theory to calculate the alpha heat flux resulting from arbitrary perturbation frequency and periodicity (provided these can be studied drift kinetically). Novel features of the theory include the retention of a large effective collision frequency resulting from the resonant alpha collisional boundary layer, correlated interactions over many poloidal transits, and finite orbit effects. Heat fluxes are considered for the example cases of ripple and the toroidal Alfvén eigenmode (TAE). The ripple heat flux is small. The TAE heat flux is significant and scales with the square of the perturbation amplitude, allowing the derivation of constraints on mode amplitude for avoidance of significant alpha depletion. A simple saturation condition suggests that TAEs in one upcoming experiment will not cause significant alpha transport via the mechanisms in this theory. However, saturation above the level suggested by the simple condition, but within numerical and experimental experience, which could be accompanied by the onset of stochasticity, could cause significant transport.
Drift-reduced plasma fluid models are commonly used in plasma physics for analytics and simulations; however, the validity of such models must be verified for the regions of parameter space in which tokamak plasmas exist. By looking at the linear behaviour of drift-reduced and full-velocity models one can determine that the physics lost through the simplification that the drift-reduction provides is important in the core region of the tokamak. It is more acceptable for the edge-region but one must determine specifically for a given simulation if such a model is appropriate.
The competition between drift wave and interchange physics in general E-cross-B drift turbulence is studied with computations in three dimensional tokamak flux tube geometry. For a given set of background scales, the parameter space can be covered by the plasma beta and drift wave collisionality. At large enough plasma beta the turbulence breaks out into ideal ballooning modes and saturates only by depleting the free energy in the background pressure gradient. At high collisionality it finds a more gradual transition to resistive ballooning. At moderate beta and collisionality it retains drift…
The stochastic advection of low energy deuterium ions is studied in a three dimensional realistic turbulence model in conditions relevant for current tokamak fusion experiments. The diffusion coefficients are calculated starting from the test particles trajectories in the framework of the semi-analitical statistical model called the Decorrelation Trajectory Method. We show that trajectory trapping determined by the space correlation of the velocity field is the main cause for anomalous diffusion and we obtain the transport regimes corresponding to different values of the parameters of the turb…
We present particle-in-cell (PIC) simulations of minority energetic protons in deuterium plasmas, which demonstrate a collective instability responsible for emission near the lower hybrid frequency and its harmonics. The simulations capture the lower hybrid drift instability in a regime relevant to tokamak fusion plasmas, and show further that the excited electromagnetic fields collectively and collisionlessly couple free energy from the protons to directed electron motion. This results in an asymmetric tail antiparallel to the magnetic field. We focus on obliquely propagating modes under cond…
Although lower hybrid waves have been shown to be effective in driving plasma current in present-day tokamaks, they are predicted to strongly interact with the energetic alpha particles born from fusion reactions in eventual tokamak reactors. However, in the presence of the expected steep alpha particle birth gradient, this interaction can produce wave amplification rather than wave damping. Here, we identify the flexibilities and constraints in achieving this amplification effect through a consideration of symmetries in the channeling interaction, in the wave propagation, and in the tokamak f…
We investigate the ExB diffusion of fusion born αparticles in tokamak plasmas. We determine the transport regimes for a realistic model that has the characteristics of the ion temperature gradient (ITG) or of the trapped electron modes (TEM) driven turbulence. It includes a spectrum of potential fluctuations that is modeled using the results of the numerical simulations, the drift of the potential with the effective diamagnetic velocity and the parallel motion. Our semi-analytical statistical approach is based on the decorrelation trajectory method (DTM), which is adapted to the gyrokinetic ap…
Recently-proposed tokamak concepts use magnetic fields up to 12 T, far higher than in conventional devices, to reduce size and cost. Theoretical and computational study of trends in plasma behavior with increasing field strength is critical to such proposed devices. This paper considers trends in Alfvén eigenmode (AE) stability. Energetic particles, including alphas from D-T fusion, can destabilize AEs, possibly causing loss of alpha heat and damage to the device. AEs are sensitive to device magnetic field via the field dependence of resonances, alpha particle beta, and alpha orbit width. We d…
Long-pulse operation of a self-sustained fusion reactor using toroidal magnetic containment requires control over the content of alpha particles produced by D-T fusion reactions. On the one hand, MeV-class alpha particles must stay confined to heat the plasma. On the other hand, decelerated helium ash must be expelled before diluting the fusion fuel. Our kinetic-magnetohydrodynamic hybrid simulations of a large tokamak plasma confirm the existence of a parameter window where such energy-selective confinement can be accomplished by exploiting internal relaxation events known as `sawtooth crashe…
Toroidal torque generated by neoclassical viscosity caused by external non-resonant, non-axisymmetric perturbations has a significant influence on toroidal plasma rotation in tokamaks. In this article, a derivation for the expressions of toroidal torque and radial transport in resonant regimes is provided within quasilinear theory in canonical action-angle variables. The proposed approach treats all low-collisional quasilinear resonant NTV regimes including superbanana plateau and drift-orbit resonances in a unified way and allows for magnetic drift in all regimes. It is valid for perturbation…
The conventional ion temperature gradient or η_i mode is known to propagate in the ion diamagnetic direction. Investigation of a generic drift fluid model with warm ions and adiabatic electrons, reveals that as η_i decreases, the propagation characteristics of the unstable mode may change drastically, the mode frequency first decreases in magnitude, and reaches zero for a critical η_i. But as η_i goes down further, the mode begins to propagate in the electron diamagnetic direction. The lower toroidal mode number perturbations are more prone to reversal in propagation direction. Even for η_i=0,…
We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated …
There are two distinct phases in the evolution of drift wave envelope in the presence of zonal flow. A long-lived standing wave phase, which we call the Caviton, and a short-lived traveling wave phase (in radial direction) we call the Instanton. For drift wave turbulence driven by ion temperature gradient mode (ITG), these two stages of dynamics were displayed in [Zhang Y Z, Liu Z Y, Xie T, Mahajan S M and Liu J 2017 Physics of Plasmas 24 122304]. In this paper we show that the dynamical attributes of ITG turbulence are readily replicated when the turbulence rotates in the electron direction; …
In tokamaks, internal transport barriers, produced by modifications of the plasma current profile, reduce particle transport and improve plasma confinement. The triggering of the internal transport barriers and their dependence on the plasma profiles is a key nonlinear dynamics problem still under investigation. We consider the onset of shearless invariant curves inside the plasma which create internal transport barriers. A non-integrable drift-kinetic model is used to describe particle transport driven by drift waves and to investigate these shearless barriers onset in tokamaks. We show that …
The collisional dynamics of test impurity ions in spherical tokamak plasmas with strongly-sheared radial electric fields is investigated by means of a test particle full orbit simulation code. The strength of the shear is such that the standard drift ordering can no longer be assumed and a full orbit approach is required. The effect of radial electric field shear on neoclassical particle transport is quantified for a range of test particle mass and charge numbers and electric field parameters. It is shown that the effect of a sheared electric field is to enhance the confinement of impurity spe…
A 3D numerical model for the ablation of pellets and shattered pellet injection (SPI) fragments in tokamaks in the plasma disruption mitigation and fueling parameter space has been developed based on the Lagrangian particle code [R. Samulyak, X. Wang, H.-S. Chen, Lagrangian Particle Method for Compressible Fluid Dynamics, J. Comput. Phys., 362 (2018), 1-19]. The pellet code implements the low magnetic Reynolds number MHD equations, kinetic models for the electronic heating, a pellet surface ablation model, an equation of state that supports multiple ionization states, radiation, and a model fo…
Using the recently-installed Fast-Ion Deuterium Alpha (FIDA) spectrometer, the effects of low-frequency (20-50 kHz) chirping energetic particle modes with toroidal mode number n \geq 1 on the fast-ion population in MAST plasmas are considered. Results from the FIDA diagnostic are presented and discussed in the light of the present theoretical understanding of these modes, known as fishbones, in plasmas with reversed shear. Measurements of the fast-ion population reveal strong redistribution of fast ions in both real and velocity space as a result of the fishbones. Time-resolved measurements th…
The interaction of passing-ion drift orbits with spatially-inhomogeneous but purely diffusive radial transport is demonstrated to cause spontaneous toroidal spin-up to experimentally-relevant values in the tokamak edge. Physically, major-radial orbit shifts cause orbit-averaged diffusivities to depend on parallel velocity, including its sign, leading to residual stress. The resulting intrinsic rotation scales with ion temperature over poloidal magnetic field strength, resembling typical experimental scalings. Additionally, an inboard (outboard) X-point is expected to enhance co- (counter-) cur…
The effect of the perturbed ion polarization current on the stability of neoclassical tearing modes is calculated using an improved, neoclassical, four-field, drift-MHD model. The calculation involves the self-consistent determination of the pressure and scalar electric potential profiles in the vicinity of the associated magnetic island chain, which allows the chain's propagation velocity to be fixed. Two regimes are considered. First, a regime in which neoclassical ion poloidal flow damping is not strong enough to enhance the magnitude of the polarization current (relative to that found in s…
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 Alfven eigenmode (RSAE) into low frequency Alfven modes (LFAM), 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 gene…
In-situ, two-dimensional (2D) Langmuir probe measurements across a large part of the TCV divertor are reported in L-mode discharges with and without divertor baffles. This provides detailed insights into time averaged profiles, particle fluxes, and fluctuations behavior in different divertor regimes. The presence of the baffles is shown to substantially increase the divertor neutral pressure for a given upstream density and to facilitate the access to detachment, an effect that increases with plasma current. The detailed, 2D probe measurements allow for a divertor particle balance, including i…
The local intrinsic parallel current density driven by electron drift wave (DW) turbulence including electromagnetic (EM) effects is analytically studied. The scalings of the ratios of intrinsic current density driven by residual turbulent flux and by turbulent source to the bootstrap current density with electron density and temperature are predicted to be $T_e^{3/4}T_i/n_e$ and $T_eT_i/n_e$, respectively. Based on the typical parameters in DIII-D pedestal region, the local intrinsic current density driven by both the residual turbulent flux and the turbulent source is negligible. However, de…
Screening effect of plasma flow on the resonant magnetic perturbation penetration in tokamak based on two-fluid model
Key Laboratory of Materials Modification by Laser, Ion, and Electron Beams (Ministry of Education), School of Physics, Dalian University of Technology（大连理工大学物理学院激光、离子和电子束材料改性教育部重点实验室）；Key Laboratory of Geospace Environment, University of Science and Technology of China（中国科学技术大学空间环境重点实验室）；Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology（大连理工大学电子信息与电气工程学部）
This comment clarifies the relation of the research in a recently published article [Phys. Plasmas 14, 042503 (2007)] to other prior publications addressing the inclusion of electromagnetic and drift-kinetic electron physics in gyrokinetic simulation, raises a concern related to the inclusion of kinetic electrons in a system with magnetic shear, and discusses alternatives in the face of an important limitation on the general applicability of the algorithm described therein.
In this paper we have studied the influence of reversed shear on the improvement of the confinement's quality in the plasma of tokamak and especially in reducing the anomalous transport. For that, we have used a special model for the drift wave fields. Comparison between particles trajectories for normal and reversed shear is carried out in 2 D and 3 D presentation. Also, the diffusion coefficient of particles for the two cases, normal and negative shear, is evaluated.
Three dimensional computations of self consistent three species gyrofluid turbulence are carried out for tokamak edge conditions. Profiles as well as disturbances in dependent variables are followed, running the dynamical system to transport equilibrium. The third species density shows a significant correlation with that of the electrons, regardless of initial conditions and drive mechanisms. For decaying systems the densities evolve toward each other. Companion tests with a simple two dimensional drift wave model show this persists even if the third species is a passively advected test field.…
A process specific to the dynamics of the heavy impurities in turbulent tokamak plasmas is found and analysed. We show that the parallel stochastic acceleration is strongly coupled to the perpendicular transport and generates a radial pinch velocity. The interaction is produced with the hidden drifts, a quasi-coherent component of the motion that consists of a pair of average radial velocities in opposite directions. The parallel acceleration breaks this symmetry and yields a radial average velocity that can be in the inward or outward direction. The transport of the tungsten ions in three-dim…
A long-term energy option that is just approaching the horizon after decades of struggle, is fusion. Recent developments allow us to apply techniques from spin physics to advance its viability. The cross section for the primary fusion fuel in a tokamak reactor, D+T=>alpha+n, would be increased by a factor of 1.5 if the fuels were polarized. Simulations predict further non-linear power gains in large-scale machines such as ITER, due to increased alpha heating. These are significant enhancements that could lower the requirements needed to reach ignition and could be used to extend useful reactor…
In an effort to understand the fundamental physics of turbulent transport of particles and heat in a tokamak, the floating potential fluctuations in the the scrape-off layer plasma of ohmically heated ADITYA tokamak are analysed for self-similarity using distribution function approach. It is observed that the distribution function of a sum of n data points converges to a Levy distribution of scale index, alpha=1.111 for n < 40 and alpha=2.0 for larger n. In both scaling ranges, the edge fluctuation is self-similar. This observation is backed by several supporting evidences. The results indicat…
A 1-D linear gyrokinetic code called AWECS is developed to study the kinetic excitation of Alfvenic instabilities in a high-beta tokamak plasma, with beta being the ratio of thermal to magnetic pressure. It is designed to describe physics associated with a broad range of frequencies and wavelengths. For example, AWECS is capable of simulating kinetic ballooning modes, Alfvenic ion-temperature-gradient-driven modes, as well as Alfven instabilities due to energetic particles. In addition, AWECS may be used to study drift-Alfven instabilities in the low-beta regime. Here, the layout of the code a…
Nonlinear simulation model for radio frequency (RF) waves in fusion plasmas has been developed and verified using fully kinetic ion and drift kinetic electron. Ion cyclotron motion in the toroidal geometry is implemented using Boris push in the Boozer coordinates. Linear dispersion relation and nonlinear particle trapping are verified for the lower hybrid (LH) wave and ion Bernstein wave (IBW). Parametric decay instability is observed where a large amplitude pump wave decays into an IBW sideband and an ion cyclotron quasimode (ICQM). The ICQM induces an ion perpendicular heating with a heating…
Poloidal asymmetries in the impurity density can be generated by radio frequency heating in the core and by neoclassical effects in the edge of tokamak plasmas. In a pedestal case study, using global neoclassical simulations we find that finite orbit width effects can generate significant poloidal variation in the electrostatic potential, which varies on a small radial scale. Gyrokinetic modeling shows that these poloidal asymmetries can be strong enough to significantly modify turbulent impurity peaking. In the pedestal the ExB drift in the radial electric field can give a larger contribution…
We present various techniques that make orbit-following Monte Carlo simulations faster and more reliable when assessing collisionless fast particle losses due to magnetic field perturbations. These techniques are based on identifying various loss channels in constants of motion space using the so-called loss maps. We demonstrate that this allows one to attribute losses quantitatively to different transport mechanisms, increase signal-to-noise ratio when estimating FILD signal and peak power loads, and connect magnetic field structure directly to fast particle losses. Furthermore, we show that …
Recently the drift-reduced Landau fluid six-field turbulence model within the BOUT++ framework has been upgraded. In particular, this new model employs a new normalization, adds a volumetric flux-driven source option, the Landau fluid closure for parallel heat flux and a Laplacian inversion solver which is able to capture n=0 axisymmetric mode evolution in realistic tokamak configurations. These improvements substantially extended model's capability to study a wider range of tokamak edge phenomena, and are essential to build a fully self-consistent edge turbulence model capable of both transie…
The XGC1 edge gyrokinetic code is used for a high fidelity prediction for the width of the heat-flux to divertor plates in attached plasma condition. The simulation results are validated against the empirical scaling $λ_q \propto B_P^{-γ}$ obtained from present tokamak devices, where $λ_q$ is the divertor heat-flux width mapped to the outboard midplane and $γ_q=1.19$ as defined by T. Eich et al. [Nucl. Fusion 53 (2013) 093031], and $B_P$ is the magnitude of the poloidal magnetic field at outboard midplane separatrix surface. This empirical scaling predicts $λ_q \leq 1mm$ when extrapolated to I…
Experimental diagnostics, analysis tools and simulations represent particle distributions in various forms and coordinates. Algorithms to manage these data are needed on platforms like the ITER Integrated Modelling & Analysis Suite (IMAS), performing tasks such as archiving, modeling, conversion and visualization. A method that accomplishes some of the required tasks for distributions of charged particles with arbitrarily large magnetic drifts in axisymmetric tokamak geometry is described here. Given a magnetic configuration, we first construct a database of guiding center orbits, which serves…
Global particle simulations of the lower hybrid waves have been carried out using fully kinetic ions and drift kinetic electrons with a realistic electron-to-ion mass ratio. The lower hybrid wave frequency, mode structure, and electron Landau damping from the electrostatic simulations agree very well with the analytic theory. Linear simulation of the propagation of a lower hybrid wave-packet in the toroidal geometry shows that the wave propagates faster in the high field side than the low field side, in agreement with a ray tracing calculation. Electromagnetic benchmarks of lower hybrid wave d…
