The mirror mode: A "superconducting'' space plasma analogue

We examine the physics of the magnetic mirror mode in its final state of saturation, the thermodynamic equilibrium, to demonstrate that the mirror mode is the analogue of a superconducting effect in a classical anisotropic-pressure space plasma. Two different spatial scales are identified which control the behaviour of its evolution. These are the ion inertial scale $\lambda_{im}(\tau)$ based on the excess density $N_m(\tau)$ generated in the mirror mode, and a correlation length. This can be either the Debye length, the ion gyro-radius, or a turbulent correlation length. The mirror mode equilibrium structure under saturation is determined by the Landau-Ginzburg ratio of these two length scales. Mirror modes then behave like type II superconductors, naturally giving rise to chains of local depletions of the magnetic field of the kind observed in the mirror mode, providing the plasma a short scale magnetic bubble texture. This might be important in the study of magnetic turbulence in plasmas.Comment: 13 pages, 2 figure, Discussion paper, to appear in Ann. Geophy

A Direct D-Bar Method for Partial Boundary Data Electrical Impedance Tomography With a Priori Information

Electrical Impedance Tomography (EIT) is a non-invasive imaging modality that uses surface electrical measurements to determine the internal conductivity of a body. The mathematical formulation of the EIT problem is a nonlinear and severely ill-posed inverse problem for which direct D-bar methods have proved useful in providing noise-robust conductivity reconstructions. Recent advances in D-bar methods allow for conductivity reconstructions using EIT measurement data from only part of the domain (e.g., a patient lying on their back could be imaged using only data gathered on the accessible part of the body). However, D-bar reconstructions suffer from a loss of sharp edges due to a nonlinear low-pass filtering of the measured data, and this problem becomes especially marked in the case of partial boundary data. Including a priori data directly into the D-bar solution method greatly enhances the spatial resolution, allowing for detection of underlying pathologies or defects, even with no assumption of their presence in the prior. This work combines partial data D-bar with a priori data, allowing for noise-robust conductivity reconstructions with greatly improved spatial resolution. The method is demonstrated to be effective on noisy simulated EIT measurement data simulating both medical and industrial imaging scenarios

Boundary-induced instabilities in coupled oscillators

Published version, minor changesPeer reviewedPublisher PD