Spinning Magnet

Since a rotating magnet produces an induced electric field roughly parallel to that of a voltage applied to the surface of the magnet, we were anticipating a change in the plasma discharge as we rotated the magnet. We were disappointed to find no change in the plasma dicharge, only in the outgassing aspects of the magnet discharges. In hindsight, this might have been expected for two reasons. First, the induced electric field is parallel to the DC field at the equator, but is far smaller, thus providing little change to the DC driver of the discharge. Second, the field-aligned components of the induced electric field, while different from the DC field, are nonetheless far smaller than the diffusion driven field-aligned field strengths, which themselves are self-limiting so that a large perturbation would be required to modify the discharge from its topology dominated shape.

We can estimate the induced electric field expected on the surface of the magnet by calculating the Lorentz force

$$E = v \times B = \omega r \times B = {\rm rps} * \pi * 0.01 m * 0.5 T$$ (4)

Plugging in for 10 rps, we obtain 0.15 V/m, which is far less than the $\sim$400 V/m applied DC field or the diffusion dominated kV/m sized fields. Nonetheless, as the experience with outgassing demonstrates, wherever massive, nearly neutral particles take part in the dynamics, rotation will have an effect.

$$E = V/m = V_i/\lambda$$ (5)