Engineering topics

Elder, Todd

Publications and source records attributed to Elder, Todd.

3 records

DOE OSTI2024

Current potential patches

A novel form of the current potential, a mathematical tool for the design of stellarators and stellarator coils, is developed. Specifically, these are current potentials with a finite-element basis, called current potential patches. Current potential patches leverage the relationship between distributions of magnetic dipoles and current potentials to explore limits of the access properties of stellarator coil sets. An example calculation is shown using the Helically Symmetric Experiment (HSX) equilibrium, demonstrating the method's use in coil design and understanding the limits of the access properties of coil sets. Current potential patches have additional desirable properties such as of promoting sparse current sheet solutions and identifying crucial locations of shaping current placement. A result is found for the HSX equilibrium that shaping currents covering only 22% of the winding surface are sufficient to produce the equilibrium to a good accuracy, provided a toroidal field is generated by an exterior coil set.

Elder, Todd↗

DOE OSTI2021

Example of exponentially enhanced magnetic reconnection driven by a spatially bounded and laminar ideal flow

In laboratory and natural plasmas of practical interest, the spatial scale Δ d at which magnetic field lines lose distinguishability differs enormously from the scale a of magnetic reconnection across the field lines. In the solar corona, plasma resistivity gives a/Δ d ~ 10 12 , which is the magnetic Reynold number R m . The traditional resolution of the paradox of disparate scales is for the current density j associated with the reconnecting field Brec to be concentrated by a factor of Rm by the ideal evolution, so j ~ B rec /µ 0 Δ d . A second resolution is for the ideal evolution to increase the ratio of the maximum to minimum separation between pairs of arbitrarily chosen magnetic field lines, Δ max /Δ min , when calculated at various points in time. Reconnection becomes inevitable where Δ max /Δ min ~ R m . A simple model of the solar corona will be used for a numerical illustration that the natural rate of increase in time is linear for the current density but exponential for Δ max /Δ min . Reconnection occurs on a time scale and with a current density enhanced by only ln(a/Δ d ) from the ideal evolution time and from the current density B rec /µ 0 a. In both resolutions, once a sufficiently wide region, Δ r , has undergone reconnection, the magnetic field loses static force balance and evolves on an Alfv´enic time scale. The Alfv´enic evolution is intrinsically ideal but expands the region in which Δ max /Δ min is large.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Magnetic nulls in interacting dipolar fields

The prominence of nulls in reconnection theory is due to the expected singular current density and the indeterminacy of field lines at a magnetic null. Electron inertia changes the implications of both features. Magnetic field lines are distinguishable only when their distance of closest approach exceeds a distance Δ d . Electron inertia ensures Δ d ≳ c/ω pe . The lines that lie within a magnetic flux tube of radius Δ d at the place where the field strength B is strongest are fundamentally indistinguishable. If the tube, somewhere along its length, encloses a point where B = 0 vanishes, then distinguishable lines come no closer to the null than ≈ (a 2 c/ω pe ) 1/3 , where a is a characteristic spatial scale of the magnetic field. Here, the behaviour of the magnetic field lines in the presence of nulls is studied for a dipole embedded in a spatially constant magnetic field. In addition to the implications of distinguishability, a constraint on the current density at a null is obtained, and the time required for thin current sheets to arise is derived.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗