Obviously John F knows his charging systems. I'm gonna add my
comments or revisions on top of or within his, while asking him to
comment on mine if he happens to read this post again.

#1. Most planes have an over-voltage protection that opens the
circuit to the alternator rotor winding. Let's say that while the
alternator stator is delivering about 30amps (lights, avionics, pitot
heat,
etc) - the OVR gets tripped, causing the alternator field to be
dropped immediately to 0 current.

The field is always switching at about 100 Hz between 14 volts and
zero volts. This
is the way the regulator works since the inductance of the field is
used with a flyback diode to
average the switching of the voltage regulator. All modern solid
state
alternator regulators are really switching regulators. The flyback
diode is connected across the rotor circuit to conduct the induced
current when the regulator momentarily switches off.

#2. Assume scenario #1 happens (due to a transient condition - not
an
alternator failure)... It takes the pilot some time to realize the
alternator is offline, so the avionics and lights drain the battery
for several minutes. Anyway, the pilot cycles the alternator field
current to bring the alternator back online. The battery is run-down
a bit, so the current delivered by the alternator spikes from zero to
around 30-40 amps, and then gradually tapers off as the battery is
charged.

This should not be a problem unless the main 60 amp alternator output
circuit breaker is weak and then trips again. When the alternator
stator is delivering current and suddenly disconnected by some
mechanical means (such as that breaker) from the load, there is a
negative inductive voltage pulse induced into the regulator, since it
always remains connected to the alternator output. This pulse is
caused by the collapsing field of the stator. If this happens on some
Cessna's (172M is one) you might possibly fry the regulator, the over
voltage light (cheap) and possibly a stator diode within
milli-seconds. I'd be surprised though if there were no reverse or
flyback diodes in the regulator design to protect against this.

You need to find the reason it is tripping off line.

Question: Can either one of these dramatic swings in the alternator
field voltage/current, and/or the alternator output current damage
the
alternator?

Only possibly if the circuit breaker on the alternator output opens.
If the rotor field remains connected to the regulator, the collapsing
field flux of the rotor will cause a negative voltage spike that
should be handled by the regulator's flyback diode. I'm not sure what
happens to the magnetic energy in the stator if the breaker pops, but
theoretically the stator output voltage should spike in the negative
direction. The regulator will have to absorb this.

Last, does anyone have a link to a good tutorial on the components in
a typical alternator?

Cessna put out a manual on charging systems that is reasonable. Most
are very similar (but not identical) to automotive units. A good text
on automotive
charging systems is good.

Aircraft systems are different in that they add the possibility of the
alternator output breaker dropping the load, which doesn't happen in
cars. Aircraft systems also have a master contactor that, if it
stutters, can create a situation in which the aircraft electronics
become the flyback diode for any current transients in the system. A
low battery for instance will cause the master contactor to possibly
stutter when the starter is engaged. As long as the battery remains
on line, the aircraft electronics are probably able to handle the
voltage transients from the starter or other devices. But if the
battery should momentarily disconnect, there is really no place for
the induced currents to flow other than fry electronics stuff. Solid
state devices are the worlds fastest fuses. They also don't like
reverse voltage transients.

Using a scope and an electric motor to temporarily power the
alternator, we found that the trip setting of the overvoltage sensor
on our 172M had drifted low. We fixed it by replacing it. I recall
there was a screw of a multiturn tweekpot on the side of the old
OVsensor that probably allowed the trip point to be adjusted. We
didn't see it until we had it out of the airplane though. Rather than
mess with it, we replaced the whole unit.