So by slowing down the rate the inverse current decays you get faster decay?

Mike, if you are going to accuse people of re-inventing physics (especially people who have a PhD in physics), the least you should do is work out or look up the physics yourself first.

Your assumption appears to be that putting a resistor in series with the diode slows down the rate of decay. Basic physics tell us it has the reverse effect. If we ignore iron losses and capacitance, we can model the solenoid as a perfect inductor in series with a resistor. The rate of change of current in an inductor is given by V/L. When the transistor or mosfet switches off, the current in the inductor is unable to change instantaneously and the inductor produces enough back EMF to maintain the same current flow (through the diode) just after switch-off as if was (through the transistor) just before switch off. To see what happens next, we solve the equations V = IR (where R is the total resistance in the circuit - in this case, just the resistance of the coil) and dI/dt = -V/L. I'm assuming a perfect flyback diode (no forward voltage drop). Solving these equations, we find that the current decays exponentially with a time constant L/R. So increasing the resistance R at constant inductance L in an L-R circuit

*decreases* the time constant, unlike an R-C network. If R is zero (= superconductor), we get infinite time constant and the current flows for ever.

If we add a resistor in series with the diode, we increase the total R. For example, if we add a resistor in series with the diode equal to the resistance of the solenoid, we double R, so the current decays twice as fast - but we get a peak voltage across the resistor (just after switch-off) equal to the supply voltage. Therefore the peak collector or drain voltage doubles.

Even better is to use a zener diode instead of a resistor. [EDIT: the following sentence is only true if the on-time is short enough for the resistance of the inductor to be ignored.] If we use a zener diode with a voltage rating equal to the supply voltage, then the switch-on and switch-off times will be the same and the waveforms will be similar. Of course, a zener diode is only practical if the current is low enough.

This effect of the diode causing a slow current decay is noticeable with some relays. With a diode connected directly across the relay coil, if you know when the transistor switches on and off, you can often sense the delay between the current switching off and the click of the relay opening.