The understanding and predictive capability of transport physics and plasma confinement is reviewed from the perspective of achieving reactor-scale burning plasmas in the ITER tokamak, for both core and edge plasma regions. Very considerable progress has been made in understanding, controlling and predicting tokamak transport across a wide variety of plasma conditions and regimes since the publication of the ITER Physics Basis (IPB) document (1999 Nucl. Fusion 39 2137-2664). Major areas of progress considered here follow. (1) Substantial improvement in the physics content, capability and reliability of transport simulation and modelling codes, leading to much increased theory/experiment interaction as these codes are increasingly used to interpret and predict experiment. (2) Remarkable progress has been made in developing and understanding regimes of improved core confinement. Internal transport barriers and other forms of reduced core transport are now routinely obtained in all the leading tokamak devices worldwide. (3) The importance of controlling the H-mode edge pedestal is now generally recognized. Substantial progress has been made in extending high confinement H-mode operation to the Greenwald density, the demonstration of Type I ELM mitigation and control techniques and systematic explanation of Type I ELM stability. Theory-based predictive capability has also shown progress by integrating the plasma and neutral transport with MHD stability. (4) Transport projections to ITER are now made using three complementary approaches: empirical or global scaling, theory-based transport modelling and dimensionless parameter scaling (previously, empirical scaling was the dominant approach). For the ITER base case or the reference scenario of conventional ELMy H-mode operation, all three techniques predict that ITER will have sufficient confinement to meet its design target of Q = 10 operation, within similar uncertainties.

https://iopscience.iop.org/article/10.1088/0029-5515/47/6/S02/pdf

Chapter 2: Plasma confinement and transport

Significant progress has been made in the area of advanced modes of operation that are candidates for achieving steady state conditions in a fusion reactor. The corresponding parameters, domain of operation, scenarios and integration issues of advanced scenarios are discussed in this chapter. A review of the presently developed scenarios, including discussions on operational space, is given. Significant progress has been made in the domain of heating and current drive in recent years, especially in the domain of off-axis current drive, which is essential for the achievement of the required current profile. The actuators for heating and current drive that are necessary to produce and control the advanced tokamak discharges are discussed, including modelling and predictions for ITER. The specific control issues for steady state operation are discussed, including the already existing experimental results as well as the various strategies and needs (qψ profile control and temperature gradients). Achievable parameters for the ITER steady state and hybrid scenarios with foreseen heating and current drive systems are discussed using modelling including actuators, allowing an assessment of achievable current profiles. Finally, a summary is given in the last section including outstanding issues and recommendations for further research and development.

Chapter 6: Steady state operation

Parametric scalings of the intrinsic (spontaneous, with no external momentum input) toroidal rotation observed on a large number of tokamaks have been combined with an eye towards revealing the underlying mechanism(s) and extrapolation to future devices. The intrinsic rotation velocity has been found to increase with plasma stored energy or pressure in JET, Alcator C-Mod, Tore Supra, DIII-D, JT-60U and TCV, and to decrease with increasing plasma current in some of these cases. Use of dimensionless parameters has led to a roughly unified scaling with M-A alpha beta(N), although a variety of Mach numbers works fairly well; scalings of the intrinsic rotation velocity with normalized gyro-radius or collisionality show no correlation. Whether this suggests the predominant role of MHD phenomena such as ballooning transport over turbulent processes in driving the rotation remains an open question. For an ITER discharge with beta(N) = 2.6, an intrinsic rotation Alfven Mach number of M-A similar or equal to 0.02 may be expected from the above deduced scaling, possibly high enough to stabilize resistive wall modes without external momentum input.

https://iopscience.iop.org/article/10.1088/0029-5515/47/11/025/pdf

Inter-machine comparison of intrinsic toroidal rotation in tokamaks

The first suppression of the important and deleterious m = 2/n = 1 neoclassical tearing mode (NTM) is reported using electron cyclotron current drive (ECCD) to replace the 'missing' bootstrap current in the island O-point. Experiments on the DIII-D tokamak verify that the maximum shrinkage of the m = 2/n = 1 island occurs when the ECCD location coincides with the q = 2 surface. The DIII-D plasma control system is put into a 'search and suppress' mode to make small changes in the toroidal field to find and lock onto the optimum position, based on real time measurements of dB?/dt, for complete m = 2/n = 1 NTM suppression by ECCD. The requirements of the ECCD for complete island suppression are well modelled by the modified Rutherford equation for the DIII-D plasma conditions.

http://iopscience.iop.org/article/10.1088/0029-5515/44/2/004/pdf

Complete suppression of the m = 2/n = 1 neoclassical tearing mode using electron cyclotron current drive in DIII-D

A271 COMPLETE SUPPRESSION OF THE M=2/N-1 NEOCLASSICAL TEARING MODE USING ELECTRON CYCLOTRON CURRENT DRIVE ON DIII-D. The first suppression of the important and deleterious m=2/n=1 neoclassical tearing mode (NTM) is reported using electron cyclotron current drive (ECCD) to replace the ''missing'' bootstrap current in the island O-point. Experiments on the DIII-D tokamak verify the maximum shrinkage of the m=2/n=1 island occurs when the ECCD location coincides with the q = 2 surface. The DIII-D plasma control system is put into search and suppress mode to make small changes in the toroidal field to find and lock onto the optimum position, based on real time measurements of dB{sub {theta}}/dt, for complete m=2/n=1 NTM suppression by ECCD. The requirements on the ECCD for complete island suppression are well modeled by the modified Rutherford equation for the DIII-D plasma conditions.

/pdf/complete-suppression-of-the-m-2-n-1-neoclassical-tearing-5ejl0quuxb.pdf

Complete suppression of the m=2/n-1 neoclassical tearing mode using electron cyclotron current drive on diii-d

Plasma rotational shear is potentially important for controlling the formation and positioning of internal transport barriers that could stabilize tokamak microturbulence and improve plasma confinement. A new physical mechanism capable of inducing plasma rotation and rotational shear via the ion cyclotron resonance frequency (ICRF) heating of minority ion species in a tokamak has been proposed [Perkins, White, Bonoli, and Chan, Phys. Plasmas 8, 2181 (2001)]. The present work evaluates the validity of this mechanism under the realistic condition when fast ions are continuously heated and slowed down in a driven system. Ion dynamics are calculated with a Monte Carlo code in which wave-induced diffusion in velocity space is accounted for by a quasilinear operator. The code follows the drift trajectories of test particles in a tokamak geometry under the influence of given rf fields and collisions with the background plasma. When the heating geometry is such that no net toroidal wave momentum is injected, the ...

Radio-frequency-driven radial current and plasma rotation in a tokamak

The noncanonical Lagrangian theory of guiding center orbits is applied to the coordinate system of White–Chance–Boozer. The result is a generalized set of equations of motion which eliminates certain approximations of the static field and includes the effects of large rotations and high frequency waves. A quasilinear gyrokinetic theory is shown to readily follow from these equations.

Gyrokinetic theory in the White–Chance–Boozer coordinates

Electron cyclotron current drive (ECCD) experiments on the DIII-D tokamak are solidifying the physics basis for localized, off-axis current drive in both standard and advanced operating modes, the goal being to validate a predictive model for ECCD. The measured ECCD efficiency is found to be in agreement with theoretical calculations using the CQL3D Fokker-Planck code over a range of toroidal injection angles, absorption radii, and electron beta. The latter dependence is especially important since the ECCD efficiency is shown to increase with local electron beta, which is favorable for current profile control using off-axis ECCD in high-beta advanced tokamaks.

https://web.gat.com/pubs-ext/RF01/A23698.pdf

Electron cyclotron wave experiments on diii-d

The orbits of particles in the core region of a rotating tokamak plasma are analyzed. It is found that the phase space topologies of finite orbits differ significantly from those of thin orbit considerations. Specifically, in the absence of rotations, the trapped-passing boundary of co-moving particles has a finite extent in energies and disappears above a critical energy; and the pitch angle of the boundary has a rather strong energy dependence. Rotation and rotation shear cause significant shifts of this boundary in phase space so that above certain thresholds this boundary disappears. The finite orbit analysis also leads to improved analytic formulas for orbit averaged quantities of interest.

Finite orbit analysis in tokamak plasmas

Under quasi‐radial interplanetary magnetic fields (IMF), foreshock turbulence can have an impact on the magnetosheath and cusps depending on the location of the quasi‐parallel shock. We perform three‐dimensional simulations of Earth's dayside magnetosphere using the hybrid code HYPERS, and compare northward and southward quasi‐radial IMF configurations. We study the magnetic field configuration, fluctuations in the magnetosheath and the plasma in the regions around the northern cusp. Under northward IMF with Earthward Bx, there is a time‐varying plasma depletion layer immediately outside the northern cusp. In the southward IMF case, the impact of foreshock turbulence and high‐speed jets, together with magnetopause reconnection, can lead to strong density enhancements in the cusp.

Y. A. Omelchenko

Papers

Radio-frequency-driven radial current and plasma rotation in a tokamak

Gyrokinetic theory in the White–Chance–Boozer coordinates

Electron cyclotron wave experiments on diii-d

Finite orbit analysis in tokamak plasmas

Hybrid Simulations of the Cusp and Dayside Magnetosheath Dynamics Under Quasi‐Radial Interplanetary Magnetic Fields