  The thermal and field emission of electrons from protrusions on metal
surfaces is a possible limiting factor on the performance and operation of
high-gradient room temperature accelerator structures. We present here the
results of extensive numerical simulations of electrical and thermal behavior
of protrusions. We unify the thermal and field emission in the same numerical
framework, describe bounds for the emission current and geometric enhancement,
then we calculate the Nottingham and Joule heating terms and solve the heat
equation to characterize the thermal evolution of emitters under RF electric
field. Our findings suggest that, heating is entirely due to the Nottingham
effect, that thermal runaway scenarios are not likely, and that high RF
frequency causes smaller swings in temperature and cooler tips. We build a
phenomenological model to account for the effect of space charge and show that
space charge eliminates the possibility of tip melting, although near melting
temperatures reached.
