The electric field within high-temperature superconductors: mapping the E-J-B surface

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Abstract
At a single temperature, the macroscopic irreversible magnetic behaviour of a superconductor can be described fully by the relationship between the electric field E, the current density J and the magnetic induction B. We show that this relationship can be readily visualized as a three-dimensional E-J-B surface. The utility of this surface is that it is model and parameter independent, and so obviates the need to define the 'critical current density', and the 'irreversibility' field by arbitrarily imposed criteria. Furthermore, the flux creep rate corresponds directly to a gradient of this surface. Data from magnetic studies can be used to generate the surface, but some care with experimentation is needed to avoid distortion by artefacts, such as self-field effects and anisotropy. Transport studies map the surface too, but in a rather different (and limited) region of E-J-B space. The shape of the surface and its dependence on temperature reflect the underlying physics of vortex behaviour, and we discuss briefly the limitations on theoretical models imposed by its form.