Nathaniel Ferraro: Research

Non-Axisymmetric Equilibria in Tokamaks

The application of non-axisymmetric magnetic fields to tokamak plasmas is observed to influence the confinement and stability properties of these plasmas considerably. In particular, the application of non-axisymmetric fields has been found to lead to enhanced particle transport, torque, and the mitigation or complete suppression of edge localized modes (ELMs).

A primary difficulty of understanding these effects is that the magnetic field present in the plasma may be very different from the field that is applied. Currents arising in the plasma in response to the applied field may themselves generate a magnetic field having a very different spectrum from the applied field. Therefore understanding the magnetic field present in the plasma requires a self-consistent description of this plasma response.

This self-consistent response using MHD codes such as M3D-C1. These calculations have been found to provide a good description of both the perturbed magnetic fields measured outside the plasma, and of the perturbed equilibrium profiles measured in the plasma edge. Ultimately, we seek to use this understanding of the complex perturbed equilibrium geometry as a basis for understanding how applied non-axisymmetric magnetic fields modify particle, thermal, and momentum transport.


A Poincaré section of the calculated magnetic field in the edge of a DIII-D plasma, in which a non-axisymmetric field has been applied using the DIII-D I-coils. Top: The field calculated by neglecting the plasma response currents. Bottom: The field calculated by self-consistently including the plasma response currents.

Macroscopic Stability of Tokamaks

Tokamaks are subject to various macroscopic instabilities. Some of these instabilities may lead to a complete loss of plasma confinement, called a "disruption." These must be avoided in any successful tokamak reactor.

MHD codes such as M3D-C1 may be used to study both the onset of disruptive instabilities, and the dynamics of the ensuing disruption. Instability onset can be calculated using linear perturbation theory, and allow the determination of pressure and current thresholds. The subsequent disruption dynamics involve large deviations from equilibrium, and require a nonlinear modeling approach.

An example of a disruptive instability is a vertical displacement event (VDE), which results when control of the vertical positioning of the plasma is lost. Such an event results in significant induced electromagnetic forces on the conducting structures of the tokamak, as well as large thermal fluxes to the plasma-facing components of the tokamak.


The toroidal current density in an M3D-C1 simulation of a VDE. The plasma has drifted vertically to the point where it rests on the lower divertor. Currents persist in the open field-line region (Halo currents).

Computational Modeling

M3D-C1 is an extended-MHD code that is used for calculating plasma equilibrium and stability using an extended-MHD model.

Fusion-IO (FIO) is a set of libraries providing a common interface to data generated by various fusion codes.