D.P. Brennan

Dynamics of ion temperature gradient turbulence and transport with a static magnetic island

Understanding the interaction mechanisms between large-scale magnetohydrodynamic instabilities and small-scale drift-wave microturbulence is essential for predicting and optimizing the performance of magnetic confinement based fusion energy experiments. We report progress on understanding these interactions using both analytic theory and numerical simulations performed with the BOUT++ [Dudson et al., Comput. Phys. Commun. 180, 1467 (2009)] framework. This work focuses upon the dynamics of the ion temperature gradient instability in the presence of a background static magnetic island, using a weakly electromagnetic two-dimensional five-field fluid model. It is found that the island width must exceed a threshold size (comparable with the turbulent correlation length in the no-island limit) to significantly impact the turbulence dynamics, with the primary impact being an increase in turbulent fluctuation and heat flux amplitudes. The turbulent radial ion energy flux is shown to localize near the X-point, but...

Adjoint Fokker-Planck equation and runaway electron dynamics

The adjoint Fokker-Planck equation method is applied to study the runaway probability function and the expected slowing-down time for highly relativistic runaway electrons, including the loss of energy due to synchrotron radiation. In direct correspondence to Monte Carlo simulation methods, the runaway probability function has a smooth transition across the runaway separatrix, which can be attributed to effect of the pitch angle scattering term in the kinetic equation. However, for the same numerical accuracy, the adjoint method is more efficient than the Monte Carlo method. The expected slowing-down time gives a novel method to estimate the runaway current decay time in experiments. A new result from this work is that the decay rate of high energy electrons is very slow when E is close to the critical electric field. This effect contributes further to a hysteresis previously found in the runaway electron population.

Thermal island destabilization and the Greenwald limit

Magnetic reconnection is ubiquitous in the magnetosphere, the solar corona, and in toroidal fusion research discharges. In a fusion device, a magnetic island saturates at a width which produces a minimum in the magnetic energy of the configuration. At saturation, the modified current density profile, a function of the flux in the island, is essentially flat, the growth rate proportional to the difference in the current at the O-point and the X-point. Further modification of the current density profile in the island interior causes a change in the island stability and additional growth or contraction of the saturated island. Because field lines in an island are isolated from the outside plasma, an island can heat or cool preferentially depending on the balance of Ohmic heating and radiation loss in the interior, changing the resistivity and hence the current in the island. A simple model of island destabilization due to radiation cooling of the island is constructed, and the effect of modification of the c...

The tokamak density limit: A thermo-resistive disruption mechanism

The behavior of magnetic islands with 3D electron temperature and the corresponding 3D resistivity effects on growth are examined for islands with near-zero net heating in the island interior. We refer to the resulting class of non-linearities as thermo-resistive effects. In particular, the effects of varying impurity mix on the previously proposed local island onset threshold [Gates and Delgado-Aparicio, Phys. Rev. Lett. 108, 165004 (2012)] are examined and shown to be consistent with the well established experimental scalings for tokamaks at the density limit. A surprisingly simple semi-analytic theory is developed which imposes the effects of heating/cooling in the island interior as well as the effects of island geometry. For the class of current profiles considered, it is found that a new term that accounts for the thermal effects of island asymmetry is required in the modified Rutherford equation. The resultant model is shown to exhibit a robust onset of a rapidly growing tearing mode—consistent with the disruption mechanism observed at the density limit in tokamaks. A fully non-linear 3D cylindrical calculation is performed that simulates the effect of net island heating/cooling by raising/suppressing the temperature in the core of the island. In both the analytic theory and the numerical simulation, the sudden threshold for rapid growth is found to be due to an interaction between three distinct thermal non-linearities which affect the islandresistivity, thereby modifying the growth dynamics.

Adjoint method and runaway electron avalanche

The adjoint method for the study of runaway electron dynamics in momentum space Liu et al (2016 Phys. Plasmas 23 010702) is rederived using the Greens function method, for both the runaway probability function (RPF) and the expected loss time (ELT). The RPF and ELT obtained using the adjoint method are presented, both with and without the synchrotron radiation reaction force. The adjoint method is then applied to study the runaway electron avalanche. Both the critical electric field and the growth rate for the avalanche are calculated using this fast and novel approach.

Error field penetration and locking to the backward propagating wave

In this letter, we investigate error field penetration, or locking, behavior in plasmas having stable tearing modes with finite real frequencies ωr in the plasma frame. In particular, we address the fact that locking can drive a significant equilibrium flow. We show that this occurs at a velocity slightly above v=ωr/k, corresponding to the interaction with a backward propagating tearing mode in the plasma frame. Results are discussed for a few typical tearing mode regimes, including a new derivation showing that the existence of real frequencies occurs for viscoresistive tearing modes, in an analysis including the effects of pressure gradient, curvature, and parallel dynamics. The general result of locking to a finite velocity flow is applicable to a wide range of tearing mode regimes, indeed any regime where real frequencies occur.

Control of linear modes in cylindrical resistive magnetohydrodynamics with a resistive wall, plasma rotation, and complex gain

Feedback stabilization of magnetohydrodynamic (MHD) modes in a tokamak is studied in a cylindrical model with a resistive wall, plasma resistivity, viscosity, and toroidal rotation. The control is based on a linear combination of the normal and tangential components of the magnetic field just inside the resistive wall. The feedback includes complex gain, for both the normal and for the tangential components, and it is known that the imaginary part of the feedback for the former is equivalent to plasma rotation [J. M. Finn and L. Chacon, Phys. Plasmas 11, 1866 (2004)]. The work includes (1) analysis with a reduced resistive MHD model for a tokamak with finite β and with stepfunction current density and pressure profiles, and (2) computations with a full compressible visco-resistive MHD model with smooth decreasing profiles of current density and pressure. The equilibria are stable for β = 0 and the marginal stability values βrp,rw < βrp,iw < βip,rw < βip,iw (resistive plasma, resistive wall; resistive plas...

Resolving runaway electron distributions in space, time, and energy

Areas of agreement and disagreement with present-day models of runaway electron (RE) evolution are revealed by measuring MeV-level bremsstrahlung radiation from runaway electrons (REs) with a pinhole camera. Spatially resolved measurements localize the RE beam, reveal energy-dependent RE transport, and can be used to perform full two-dimensional (energy and pitch-angle) inversions of the RE phase-space distribution. Energy-resolved measurements find qualitative agreement with modeling on the role of collisional and synchrotron damping in modifying the RE distribution shape. Measurements are consistent with predictions of phase-space attractors that accumulate REs, with non-monotonic features observed in the distribution. Temporally resolved measurements find qualitative agreement with modeling on the impact of collisional and synchrotron damping in varying the RE growth and decay rate. Anomalous RE loss is observed and found to be largest at low energy. Possible roles for kinetic instability or spatial tr...

A predictive model for the tokamak density limit

We reproduce the Greenwald density limit, in all tokamak experiments by using a phenomenologically correct model with parameters in the range of experiments. A simple model of equilibrium evolution and local power balance inside the island has been implemented to calculate the radiation-driven thermo-resistive tearing mode growth and explain the density limit. Strong destabilization of the tearing mode due to an imbalance of local Ohmic heating and radiative cooling in the island predicts the density limit within a few percent. Furthermore, we found the density limit and it is a local edge limit and weakly dependent on impurity densities. Our results are robust to a substantial variation in model parameters within the range of experiments.

Shaping effects on toroidal magnetohydrodynamic modes in the presence of plasma and wall resistivity

This study explores the effects of plasma shaping on magnetohydrodynamic mode stability and rotational stabilization in a tokamak, including both plasma and wall resistivity. Depending upon the plasma shape, safety factor, and distance from the wall, the β-limit for rotational stabilization is given by either the resistive-plasma ideal-wall (tearing mode) limit or the ideal-plasma resistive-wall (resistive wall mode) limit. In order to explore this broad parameter space, a sharp-boundary model is developed with a realistic geometry, resonant tearing surfaces, and a resistive wall. The β-limit achievable in the presence of stabilization by rigid plasma rotation, or by an equivalent feedback control with imaginary normal-field gain, is shown to peak at specific values of elongation and triangularity. It is shown that the optimal shaping with rotation typically coincides with transitions between tearing-dominated and wall-dominated mode behavior.