Minimizing Conduction Electron Heat Losses at the Peripheries of Spinning, Disc-shaped Magnets
In a previous article it was stated that there are "inescapable" heat losses entailed in injecting/extracting conduction electrons from the rims of spinning disc-shaped magnets in/over which radial currents flow. It was suggested that these losses cannot be "designed away." Further consideration suggests that this may not be entirely true.
Fig. 1 depicts two magnets in contact at their rims. Any rotation of one implies a counter-rotation of the other.
Let us follow the average path of a conduction electron. It travels outward from the lower magnetís center to its rim, creating a torque in the negative x-direction (via innumerable ohmic collisions with lattice atoms) as it does so. At the contact point between the lower and upper magnets the electron has a velocity in the negative z-direction of magnitude wR. Assuming its speed is nominally zero when it enters the lower magnetís center, the net work expended to impart this peripheral velocity is
Note that this requires the magnet to exert a torque in the negative x-direction, and that the reaction torque the electron exerts on the magnet opposes tlower in the figure.
At the contact between the upper and lower magnets, the upper magnet also has a velocity in the negative z-direction, of magnitude wR. Thus there is no change in the electronís kinetic energy when it crosses over from the lower magnet into the upper one.
In the upper magnet the electron moves from the rim to the magnetís center, losing kinetic energy in the amount
In traveling from rim to center the electron imparts an average torque in the same direction as tupper. The net change in kinetic energy, from the center of the lower magnet to the center of the upper magnet, is therefore zero. All other things being equal, counter-rotating magnets in contact at their rims evidently entail minimal heat losses as conduction electrons go from center to center.
Of course there are also kinetic energy changes where electrons enter the bottom, spinning shaft from the bottom brush, and where they exit the top shaft into the top brush. These changes are manifest as heat; they do not cancel one another. Such frictional heat losses decrease as the shaft diameters decrease. On the other hand, smaller shaft diameters may require greater brush/shaft pressures to produce a given current.
The use of counter-rotating magnets suggests a mechanism for minimizing heat losses at the magnet peripheries, where conduction electrons exit one magnet and enter the other. Such a design feature is therefore a matter of interest in the over-unity feasibility question.