Thermal Force and Flux Motion

Abstract

In addition to the Lorentz force of an electric current, the thermal force of a temperature gradient across the superconductor may also act as a driving force on the magnetic flux structure. Again we assume a flat superconductor with its broad surfaces located in the x-y plane and a magnetic field applied in z-direction such that the plate resides in the mixed or the intermediate state. If a temperature gradient of sufficient magnitude is applied in the x-direction, the magnetic flux structure moves with velocity v _φ in a direction given by the Hall angle θ between the x-axis and v _φ (see Fig.9.1). The forces regulating the flux motion satisfy the equation

$$ - {S_\varphi }grad T - f{n_s}e({\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{v} _\varphi } \times \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\varphi } )/c - \eta {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{v} _\varphi } - {\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{f} _p} = 0$$

(9.1)

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