The control of charged particles at sub micrometer and nanometer length scales presents an intrinsically interesting challenge, as well as being a rich field for the study of trapped ions and plasmas. Motivated by this, we obtain the exact solution for the
vector potential for a wire of finite length and of arbitrary form. Closed form solutions can then be deduced describing the electromagnetic waves propagating from the wire. This allows us to investigate design parameters, so that we may produce spiral wire shapes which, when injected with oscillatory currents, produce effects similar to conventional magnetic mirrors, except at the submicron and nanometre scale.
Nanoscale devices present an added complication: very closely placed surfaces can exchange heat through the tunneling of evanescent radiation modes. This can augment the local heating effect when compared to blackbody emission, so any fabrication defects on the surface of the wire spirals could be problematic. We show that the evanescent contributions scale as a function of separation and dominate the heat exchange process when the spacing is much less than the characteristic wavelength of a given temperature. We expect that excess material might be deposited erroneously during fabrication of the spiral wires, so the transfer of heat from one wire coil to the defect will be higher than the rate due to uniform blackbody radiation. In the case of tungsten, for our typical spiral geometry, the heating rate is enhanced by a factor of 15. In the case of a carbon or other high conductivity composite material this rate can be raised by as much as 106, which is evidently not appropriate.