Low-to-high confinement transition simulations in divertor geometry

Abstract

Recent results are presented for turbulence in tokamak boundary plasmas and its relationship to the low-to-high confinement (L–H) transition in a realistic divertor geometry. These results are obtained from a three-dimensional (3D) nonlocal electromagnetic turbulence code, which models the boundary plasma using fluid equations for plasma vorticity, density, electron and ion temperatures and parallel momenta. With sources added in the core-edge region and sinks in the scrape-off layer (SOL), the code follows the self-consistent profile evolution together with turbulence. Under DIII-D [Luxon et al., International Conference on Plasma Physics and Controlled Nuclear Fusion (International Atomic Energy Agency, Vienna, 1986), p. 159] tokamak L-mode conditions, the dominant source of turbulence is pressure-gradient-driven resistive X-point modes. These modes are electromagnetic and curvature-driven at the outside mid-plane region but become electrostatic near X-points due to magnetic shear and collisionality. Classical resistive ballooning modes at high toroidal mode number, n, coexist with these modes but are sub-dominant. Results indicate that, as the power is increased, these modes are stabilized by increased turbulence-generated velocity shear, resulting in an abrupt suppression of high-n turbulence and the formation of a pedestal in density and temperature, as is characteristic of the H-mode transition. The sensitivity of the boundary turbulence to the direction of the toroidal field Bt is discussed.

Drift wave versus interchange turbulence in tokamak geometry: Linear versus nonlinear mode structure

“…(3,5) are set to unity. The connection length L becomes 2πqR, with q the standard field line pitch parameter and R the major radius.…”

“…To form the energy theorem we multiply Eqs. (3)(4)(5)(6) by − φ, J , p e , and u , respectively, and integrate over the spatial domain, assuming that total divergences vanish. We find the following, in which the integration operation is denoted by the angle brackets,…”

“…More recently [23], the ballooning paradigm was extended to situations including the two fluid Ohm's law (i.e., the adiabatic response), leading to the ballooning mode approach to edge turbulence [3,4,5], coinciding with the development of the earliest treatments of flux tube geometry, which were originally constructed with ballooning modes specifically in mind [24,25].…”

“…Edge turbulence in tokamak flux tube geometry has been treated by models working from a drift wave [1,2] or resistive ballooning [3,4,5] paradigm. Beyond computing edge transport, the main purpose of these computations is to understand the underlying physical character of the turbulence: drive and saturation mechanisms and free energy transfer channels.…”

A compressible Hamiltonian electromagnetic gyrofluid model

“…2D) equilibrium states is essential for physical applications. In the absence of knowledge of the Hamiltonian structure, however, the existence of such equilibrium states can be difficult to ascertain for physically sophisticated models, such as many of the fluid models that are used to describe the dynamics in fusion plasmas (see, for example, [15][16][17][18][19][20][21]). Even simple models that otherwise appear physically compelling can fail to be Hamiltonian.…”