The structure of a microwave gas discharge produced and sustained
by a surface wave (SW) propagating along a cylindrical metal antenna with a
dielectric coating is studied. The SW that produces and sustains
the microwave gas discharge propagates along an external magnetic field
and has an eigenfrequency in the range between the electron cyclotron
and electron plasma
frequencies. The presence of a dielectric (vacuum) sheath region
separating the
antenna from the plasma is assumed. The spatial distributions of
the produced plasma density, electromagnetic fields, energy flow density,
phase velocity and
reverse skin depth of the SW are obtained analytically and numerically.