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- Giving to Math

Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, May 29, 2015 - 12:00 to 13:00

Location:

GLK 113

Event Link:

Guest Speaker:

Institution:

Mathematics Graduate Student

Abstract:

In this talk we explore electromagnetic models arising in the context of magnetohydrodynamic (MHD) generators or accelerators (which are analogous to traditional turbo-machinery generators and electric motors). The plasma found in MHD generators is different from more well-understood plasmas in that it is not particularly conductive (called restive plasma), it exhibits the Hall-effect (which is a non-linear dependence of current-densities on the magnetic field), and has low magnetic Reynolds number (meaning that the plasma does not induce much magnetic field). When coupled to the extremely high Reynolds number of the fluid flow these plasmas are very different in character from more traditional astrophysical (i.e. ideal) or liquid metal (Stoke’s type, resistive) MHD flows.

We are particularly interested in heuristic models of arcing, a phenomenon by which intense concentrations of current travel from the boundary of the generator, which is relatively cool and therefore less conducive, to the bulk plasma, which is relatively hot and more conductive. The high current densities in these arcs (perhaps three to ten orders of magnitude more intense than the background plasma currents) causes structural damage, but also creates perturbations in the magnetic field which may be measurable outside of the channel.

It is our long term goal to be able to estimate the location of arcs by their induced fields using parameter estimation techniques. In this talk we derive first approximation models and present the well-posedness results and smoothness in parameter space of these systems.