Julian Hirschfeld

Uniqueness of magnetotomography for fuel cells and fuel cell stacks

The criterion for the applicability of any tomographic method is its ability to construct the desired inner structure of a system from external measurements, i.e. to solve the inverse problem. Magnetotomography applied to fuel cells and fuel cell stacks aims at determining the inner current densities from measurements of the external magnetic field. This is an interesting idea since in those systems the inner electric current densities are large, several hundred mA per cm2and therefore relatively high external magnetic fields can be expected. Still the question remains how uniquely the inverse problem can be solved. Here we present a proof that by exploiting Maxwells equations extensively the inverse problem of magnetotomography becomes unique under rather mild assumptions and we show that these assumptions are fulfilled in fuel cells and fuel cell stacks. Moreover, our proof holds true for any other device fulfilling the assumptions listed here. Admittedly, our proof has one caveat: it does not contain an estimate of the precision requirements the measurements need to fulfil for enabling reconstruction of the inner current densities from external magnetic fields.