  The classical electromagnetic modes outside a long, straight, superconducting
cosmic string are calculated, assuming the string to be surrounded by a
superconducting cylindric surface of radius R. Thereafter, by use of a
Bogoliubov-type argument, the electromagnetic energy W produced per unit length
in the lowest two modes is calculated when the string is formed "suddenly". The
essential new element in the present analysis as compared with prior work of
Parker [Phys. Rev. Lett. {\bf 59}, 1369 (1987)] and Brevik and Toverud [Phys.
Rev. D {\bf 51}, 691 (1995)], is that the radius {\it a} of the string is
assumed finite, thus necessitating Neumann functions to be included in the
fundamental modes. We find that the theory is changed significantly: W is now
strongly concentrated in the lowest mode $(m,s)=(0,1)$, whereas the
proportionality $W \propto (G\mu /t)^2$ that is characteristic for zero-width
strings is found in the next mode (1,1). Here G is the gravitational constant,
$\mu$ the string mass per unit length, and t the GUT time.
