Perturbing an axisymmetric magnetic equilibrium to obtain a quasi-axisymmetric stellarator

It is demonstrated that finite-pressure, approximately quasi-axisymmetric stellarator equilibria can be directly constructed (without numerical optimization) via perturbations of given axisymmetric equilibria. The size of such perturbations is measured in two ways, via the fractional external rotation and, alternatively, via the relative magnetic field strength, i.e. the average size of the perturbed magnetic field, divided by the unperturbed field strength. It is found that significant fractional external rotational transform can be generated by quasi-axisymmetric perturbations, with a similar value of the relative field strength, despite the fact that the former scales more weakly with the perturbation size. High mode number perturbations are identified as a candidate for generating such transform with local current distributions. Implications for the development of a general non-perturbative solver for optimal stellarator equilibria are discussed.

Analytical Solution of the Perturbed Magnetic Fields of Plates Under Tensile Stress

Development of magnetism based nondestructive testing technology and the Microelectronic mechanical system require accurate computation of perturbed magnetic fields generated by mechanical stress. In this paper, based on the linearized magnetoelastic theory, the governing equations and continuity conditions to determine the perturbed magnetic fields were formulated for the case of weak external magnetic fields such as the earth’s magnetic field. Under those weak magnetic fields, the effect of the magnetic fields on mechanical deformation was neglected. As a result, the interaction between the deformation and the magnetic field was simplified. The effect of deformation on the perturbed magnetic field was taken into account by introducing the displacement gradient into the boundary conditions that the perturbed field should satisfy. As examples, analytic solutions of the perturbed magnetic field of infinite plates with and without a round hole, which are subjected to tensile stresses and weak external magnetic fields, were obtained by the approach presented. The results show that the perturbed magnetic fields induced by stress are three orders less in magnitude of intensity than that of magnetic fields without stress, and some prominent local features such as that has more peaks and decays more rapidly in the radial direction than the case of stress free that are predicted by the solutions.

Magneto-thermoelastic waves in a perfectly conducting elastic half-space in thermoelasticity III

The propagation of magneto-thermoelastic disturbances in an elastic half-space caused by the application of a thermal shock on the stress-free bounding surface in contact with vacuum is investigated. The theory of thermoelasticity III proposed by Green and Naghdi is used to study the interaction between elastic, thermal, and magnetic fields. Small-time approximations of solutions for displacement, temperature, stress, perturbed magnetic fields both in the vacuum and in the half-space are derived. The solutions for displacement, temperature, stress, perturbed magnetic field in the solid consist of a dilatational wave front with attenuation depending on magneto-thermoelastic coupling and also consists of a part diffusive in nature due to the damping term present in the heat transport equation, while the perturbed field in vacuum represents a wave front without attenuation traveling with Alfv'en acoustic wave speed. Displacement and temperatures are continuous at the elastic wave front, while both the stress and the perturbed magnetic field in the half-space suffer finite jumps at this location. Numerical results for a copper-like material are presented.