T. S. Hahm

On the dynamics of turbulent transport near marginal stability

A general methodology for describing the dynamics of transport near marginal stability is formulated. Marginal stability is a special case of the more general phenomenon of self‐organized criticality. Simple, one field models of the dynamics of tokamak plasma self‐organized criticality have been constructed, and include relevant features such as sheared mean flow and transport bifurcations. In such models, slow mode (i.e., large‐scale, low‐frequency transport events) correlation times determine the behavior of transport dynamics near marginal stability. To illustrate this, impulse response scaling exponents (z) and turbulent diffusivities (D) have been calculated for the minimal (Burgers’) and sheared flow models. For the minimal model, z=1 (indicating ballistic propagation) and D∼(S20)1/3, where S20 is the noise strength. With an identically structured noise spectrum and flow with shearing rate exceeding the ambient decorrelation rate for the largest‐scale transport events, diffusion is recovered with z=...

Physics of non-diffusive turbulent transport of momentum and the origins of spontaneous rotation in tokamaks

Recent results in the theory of turbulent momentum transport and the origins of intrinsic rotation are summarized. Special attention is focused on aspects of momentum transport critical to intrinsic rotation, namely the residual stress and the edge toroidal flow velocity pinch. Novel results include a systematic decomposition of the physical processes which drive intrinsic rotation, a calculation of the critical external torque necessary to hold the plasma stationary against the intrinsic residual stress, a simple model of net velocity scaling which recovers the salient features of the experimental trends and the elucidation of the impact of the particle flux on the net toroidal velocity pinch. Specific suggestions for future experiments are offered.

Intrinsic rotation and electric field shear

A novel mechanism for the generation and amplification of intrinsic rotation at the low-mode to high-mode transition is presented. The mechanism is one where the net parallel flow is accelerated by turbulence. A preferential direction of acceleration results from the breaking of k‖→−k‖ symmetry by sheared E×B flow. It is shown that the equilibrium pressure gradient contributes a piece of the parallel Reynolds stress, which is nonzero for vanishing parallel flow, and so can accelerate the plasma, driving net intrinsic rotation. Rotation drive, transport, and fluctuation dynamics are treated self-consistently.

Nonlinear gyrokinetic theory of toroidal momentum pinch

The turbulent convective flux of the toroidal angular momentum density is derived using the nonlinear toroidal gyrokinetic equation which conserves phase space density and energy [T. S. Hahm, Phys. Fluids, 31, 2670 (1988)]. A novel pinch mechanism is identified which originates from the symmetry breaking due to the magnetic field curvature. A net parallel momentum transfer from the waves to the ion guiding centers is possible when the fluctuation intensity varies on the flux surface, resulting in imperfect cancellation of the curvature drift contribution to the parallel acceleration. This mechanism is inherently a toroidal effect, and complements the k‖ symmetry breaking mechanism due to the mean E×B shear [O. Gurcan et al., Phys. Plasmas 14, 042306 (2007)] which exists in a simpler geometry. In the absence of ion thermal effects, this pinch velocity of the angular momentum density can also be understood as a manifestation of a tendency to homogenize the profile of “magnetically weighted angular momentum ...

Nonlinear gyrokinetic equations for turbulence in core transport barriers

An energy‐conserving set of the nonlinear electrostatic gyrokinetic Vlasov and Poisson equations is derived for the first time in the presence of equilibrium E×B velocity uE∼vTi, via phase‐space Lagrangian Lie‐perturbation theory. In this general formulation, only the basic small parameter e with ω/Ω∼k∥/k⊥∼e and δn/n0∼1/k⊥L∼e, is used, while no device‐specific expansion has been made. Here, L is the equilibrium scale length. For application to microturbulence in tokamak core transport barriers, an additional small ordering parameter δB≡Bθ/B≪1 is utilized. This leads to a useful form of the nonlinear gyrokinetic system which is applicable to a realistic situation in which the gradient lengths of the equilibrium radial electric field and pressure are of the same order as the ion poloidal gyroradius. The ordering for fluctuations is also modified to δn/n0∼eδB≪1/k⊥L∼δB for a better description of sub‐mixing‐length level fluctuations. uE/vTi∼δB and ρθi∼Lp put the pressure‐gradient contribution to Er and the to...

Secondary instability in drift wave turbulence as a mechanism for zonal flow and avalanche formation

The article reports on recent developments in the theory of secondary instability in drift-ion temperature gradient turbulence. Specifically, the article explores secondary instability as a mechanism for zonal flow generation, transport barrier dynamics and avalanche formation. These in turn are related to the space-time statistics of the drift wave induced flux, the scaling of transport with collisionality and β, and the spatio-temporal evolution of transport barriers.

Transport of parallel momentum by collisionless drift wave turbulence

This paper presents a novel, unified approach to the theory of turbulent transport of parallel momentum by collisionless drift waves. The physics of resonant and nonresonant off-diagonal contributions to the momentum flux is emphasized, and collisionless momentum exchange between waves and particles is accounted for. Two related momentum conservation theorems are derived. These relate the resonant particle momentum flux, the wave momentum flux, and the refractive force. A perturbative calculation, in the spirit of Chapman–Enskog theory, is used to obtain the wave momentum flux, which contributes significantly to the residual stress. A general equation for mean k∥ (⟨k∥⟩) is derived and used to develop a generalized theory of symmetry breaking. The resonant particle momentum flux is calculated, and pinch and residual stress effects are identified. The implications of the theory for intrinsic rotation and momentum transport bifurcations are discussed.

Turbulence spreading and transport scaling in global gyrokinetic particle simulations

An intriguing observation in magnetically confined plasma experiments and in global gyrokinetic particle simulations of toroidal ion temperature gradient turbulence is that the fluctuations are microscopic, while the resulting turbulent transport is not gyro-Bohm [Z. Lin et al., Phys. Rev. Lett. 88, 195004 (2002)]. A possible resolution to this puzzle is identified as turbulence spreading from the linearly active (unstable) region to the linearly inactive (stable) region. Large scale gyrokinetic simulations found that transport driven by microscopic fluctuations is diffusive and local, whereas the fluctuation intensity is determined by nonlocal effects. Fluctuations are found to spread from the linearly active region to the linearly inactive region. This turbulence spreading reduces the fluctuation intensity in the unstable region, especially for a smaller device size, and thus introduces a nonlocal dependence in the fluctuation intensity. The device size dependence of the fluctuation intensity, in turn, ...

Dynamics of turbulence spreading in magnetically confined plasmas

A dynamical theory of turbulence spreading and nonlocal interaction phenomena is presented. The basic model is derived using Fokker–Planck theory, and supported by wave-kinetic and K-ϵ type closures. In the absence of local growth, the model predicts subdiffusive spreading of turbulence. With local growth and saturation via nonlinear damping, ballistic propagation of turbulence intensity fronts is possible. The time asymptotic front speed is set by the geometric mean of local growth and turbulent diffusion. The leading edge of the front progresses as the turbulence comes to local saturation. Studies indicate that turbulence can jump gaps in the local growth rate profile and can penetrate locally marginal or stable regions. In particular, significant fluctuation energy from a turbulent edge can easily spread into the marginally stable core, thus creating an intermediate zone of strong turbulence. This suggests that the traditional distinction between core and edge should be reconsidered.A dynamical theory of turbulence spreading and nonlocal interaction phenomena is presented. The basic model is derived using Fokker–Planck theory, and supported by wave-kinetic and K-ϵ type closures. In the absence of local growth, the model predicts subdiffusive spreading of turbulence. With local growth and saturation via nonlinear damping, ballistic propagation of turbulence intensity fronts is possible. The time asymptotic front speed is set by the geometric mean of local growth and turbulent diffusion. The leading edge of the front progresses as the turbulence comes to local saturation. Studies indicate that turbulence can jump gaps in the local growth rate profile and can penetrate locally marginal or stable regions. In particular, significant fluctuation energy from a turbulent edge can easily spread into the marginally stable core, thus creating an intermediate zone of strong turbulence. This suggests that the traditional distinction between core and edge should be reconsidered.

Three-dimensional hybrid gyrokinetic-magnetohydrodynamics simulation

A three‐dimensional (3‐D) hybrid gyrokinetic‐MHD (magnetohydrodynamic) simulation scheme is presented. To the 3‐D toroidal MHD code, MH3D‐K the energetic particle component is added as gyrokinetic particles. The resulting code, mh3d‐k, is used to study the nonlinear behavior of energetic particle effects in tokamaks, such as the energetic particle stabilization of sawteeth, fishbone oscillations, and alpha‐particle‐driven toroidal Alfven eigenmode (TAE) modes.