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.