  It is known that high-gradient operation in metallic accelerating structures
causes significant deterioration of structure surfaces that, in turn, greatly
increases the probability of microwave breakdown. At the same time, the
physical reason for this deterioration so far is not well understood. In the
present paper, the role of two effects is analyzed, viz. (a) the microwave
heating caused by penetration of the rf magnetic field into microprotrusion of
a radius on the order of the skin depth and (b) the Joule heating caused by the
field emitted current, i.e. the effect of the rf electric field magnified by a
sharp protrusion. Corresponding expressions for the power densities of both
effects are derived and the criterion for evaluating the dominance of one of
these two is formulated. This criterion is analyzed and illustrated by the
discussion of an example with parameters typical for recent experiments at the
Stanford Linear Accelerator Center (SLAC) National Accelerator Laboratory.
