A. Zeiler

Nonlinear reduced Braginskii equations with ion thermal dynamics in toroidal plasma

Starting from the Braginskii fluid equations, a set of nonlinear reduced equations are derived which describe the low frequency dynamics of electron and ion energy and density in a toroidal plasma. The equations have an energy integral. The equations are appropriate for studying the relation between electron and ion thermal transport and particle transport in low temperature plasma near the edge of plasma confinement devices.

Electron magnetohydrodynamic turbulence

Electron magnetohydrodynamic (EMHD) turbulence is studied in two- and three-dimensional (2D and 3D) systems. Results in 2D are particularly noteworthy. Energy dissipation rates are found to be independent of the diffusion coefficients. The energy spectrum follows a k−5/3 law for kde>1 and k−7/3 for kde<1, which is consistent with a local spectral energy transfer independent of the linear wave properties, contrary to magnetohydrodynamic (MHD) turbulence, where the Alfven effect dominates the transfer dynamics. In 3D spectral properties are similar to those in 2D.

Onset of collisionless magnetic reconnection in thin current sheets: Three-dimensional particle simulations

Three-dimensional (3D) particle-in-cell simulations of collisionless magnetic reconnection are presented. The initial equilibrium is a double Harris-sheet equilibrium and periodic boundary conditions are assumed in all three directions. No magnetic seed island is imposed initially, and no flow conditions are imposed. The current sheet width is assumed to be one ion inertial length calculated with the density in the center of the current sheet. The ion to electron mass ratio is mi/me=150, which suppresses the growth of the drift kink instability. Two different runs have been performed: a simulation with exactly antiparallel magnetic field and a simulation with a constant guide field of the same magnitude as the antiparallel field superimposed. In the antiparallel case the inductive field of the waves excited by the lower hybrid drift instability (LHDI) leads to rapid acceleration of the electrons in the center of the current sheet and subsequently to a current sheet thinning. The current increase in the ce...

Breakup of the electron current layer during 3‐D collisionless magnetic reconnection

The structure of the electron current layer which forms in the dissipation region during magnetic reconnection in a collisionless plasma is explored by advancing the 3 - D electron magnetohydrodynamic (EMHD) equations. The current layer thins down below the electron skin depth c/ωpe and then breaks up into a fully turbulent distribution of swirling vortices, The turbulence is sufficiently strong that current is largely shunted into the plane of the magnetic reconnection. The results are consistent with the absense of electron scale current layers in satellite observations of the magnetosphere.

Three‐dimensional fluid simulations of tokamak edge turbulence

Three‐dimensional (3‐D) simulations of drift‐resistive ballooning turbulence are presented. The turbulence is basically controlled by a parameter α, the ratio of the drift wave frequency to the ideal ballooning growth rate. If this parameter is small [α≤1, corresponding to Ohmic (OH) or low confinement phase (L‐mode) plasmas], the system is dominated by ballooning turbulence, which is strongly peaked at the outside of the torus. If it is large [α≥1, corresponding to high confinement phase (H‐mode) plasmas], field line curvature plays a minor role. The turbulence is nonlinearly sustained even if curvature is removed and all modes are linearly stable due to magnetic shear. In the nonlinear regime without curvature the system obeys a different scaling law compared to the low‐α regime. The transport scaling is discussed in both regimes and the implications for OH, L‐mode, and H‐mode transport are discussed.

Transition from resistive ballooning to eta(i) driven turbulence in tokamaks

The mechanisms of turbulent transport in the collisional tokamak edge plasma are investigated linearly and nonlinearly, focusing specifically on the transition from resistive modes to ion temperature gradient driven (ηi) modes. Linear eigenvalue calculations demonstrate that resistive ballooning and toroidal ηi modes can exist as separate roots with similar growth rates but with differing structure along the magnetic field. While the typical transverse scale length of the resistive modes depends strongly on collisionality, the transverse scales of the ηi mode are essentially independent of the collisionality, even in the absence of any assumption on the adiabaticity of the electrons. Three-dimensional nonlinear simulations quantitatively describe the transition between the resistivity dominated outermost edge and regions with moderately higher temperature where resistive modes are stabilized and the collisionless ηi mode dominates. A significant result is that the ηi modes continue to drive significant pa...

Instability of a Magnetized Plasma Jet

The stability characteristics of a plasma jet V(x)=sech2 x embedded in a parallel magnetic field B(x)=B0 tanh x are investigated. The Kelvin–Helmholtz kink mode, which dominates at small B0, is stabilized at B0=0.46, while the pinch mode remains unstable up to B0=0.96. Contrary to a nonmagnetized jet, for finite B0 the kink mode saturates quasilinearly by broadening the jet, such that B0/Vmax becomes larger than the marginal value 0.46. Including finite resistivity the nonlinear behavior is eventually governed by the tearing mode for all values of B0≠0, consisting of a single plasmoid moving along the jet. Hence the shear flow cannot stabilize the tearing mode, so that the apparent tearing stability of resistive current sheets observed in numerical simulations of magnetic reconnection is only due to finite-length effects.

Nonlocal Simulation of the Transition from Balooning to Ion Temperature Gradient Mode Turbulence in the Tokamak Edge

The transition from resistive ballooning to ion temperature gradient (ITG) mode turbulence in the tokamak edge is studied in three dimensions using the electrostatic reduced Braginskii equations with ion temperature dynamics. In contrast to most previous simulations of plasma edge turbulence, which assume the parameters (density, temperature, collisionality, etc.) to be constant in space and time (local approximation), a realistic spatial variation and the nonlinear dependence of the parameters on the fluctuating quantities is taken into account. The influence of nonlocal effects is studied by a scan in the ratio of profile to turbulence scale length. For a large ratio, good agreement between local and nonlocal results on the ITG mode and ballooning turbulence is found. With increasing nonlocality, however, the anomalous transport is more and more suppressed. For the ITG mode, the turbulence quench is due to a decrease of the linear growth rate, while for the ballooning mode a novel, inherently nonlocal s...

Electron temperature fluctuations in drift-resistive ballooning turbulence

Three-dimensional nonlinear simulations of collisional plasma turbulence are presented to model the behavior of the edge region of tokamak discharges. Previous work is extended by including electron temperature fluctuations Te. The basic paradigm that turbulence and transport are controlled by resistive ballooning modes in low temperature plasma and nonlinearly driven drift wave turbulence in higher temperature regimes persists in the new system. Parallel thermal conduction strongly suppresses the ability of the electron temperature gradient ∇Te to drive the turbulence and transport everywhere except the very low temperature edge of the resistive ballooning regime. As a consequence, over most of the resistive ballooning regime only the density gradient drives the turbulence and the temperature fluctuations are convected as a passive scalar. In the drift wave regime only the density gradient acts to drive the nonlinear instability and the temperature fluctuations have a relatively strong stabilizing influ...

Three-dimensional collisional drift-wave turbulence: Role of magnetic shear

Three‐dimensional (3‐D) nonlinear simulations of collisional drift‐wave turbulence are presented. Results for the Hasegawa–Wakatani equations (without magnetic shear) in 3‐D are compared to former two‐dimensional (2‐D) simulations. In contrast to the 2‐D system the 3‐D situation is completely dominated by a nonlinear drive mechanism. The final state of the system is sensitive to the configuration of the computational grid since the sheared flow develops at the longest scales of the system. When magnetic shear is included, the system is linearly stable but the turbulence is self‐sustained by basically the same nonlinear mechanism. Magnetic shear limits the size of the dominant eddies, so the system evolves to a stationary turbulent state independent of the computational box. Finally, it is shown that the level of turbulence in the system with magnetic shear depends sensitively on the size of the effective Larmor radius ρs compared with the characteristic transverse scale length of the eddies.