Tesla coils are notorious for destroying electrical equipment. The
extreme voltages generated can punch through insulators like they are not
there, shorting out capacitors and transformers. The high frequency output
can also induce currents in nearby devices and burn out sensitive electronics.
Protection is needed to keep this equipment functional. The first line
of defense is physical distance, don't put anything closer to the secondary
than it needs to be. Next is shielding, place a grounded conductor around
any sensitive equipment (this is known as a Faraday cage) or between the
equipment and the secondary (like the strike-ring above the primary).
Safety gaps are set to short out or ground voltages which are high enough
to be damaging. These are particularly important for capacitors and neon
sign transformers (even pole-pigs, which are designed to survive lightning
strikes, have been killed by Tesla coils when used without safety gaps).
Lastly, a band pass filter should be used between the transformer and
the Tesla coil primary. This circuit is meant to allow low frequency AC
from the power supply to pass with little resistance, but present a very
large resistance to the high frequency currents generated by the primary
or tank circuit. A schematic and construction details are shown below (the
transformer connects to the side with the safety gap).