A water-window soft X-ray source using laser plasma from a cryogenic solid Ar target has demonstrated an average output power of 0.5 W with continuously repeated pulses at 3.3 Hz. A higher output power of up to 1 W at 10 Hz can be achieved by simply improving the target system. The characteristics of the Ar ion debris from the plasma were also studied and the kinetic energies of the main ions were found to be less than 2 keV. Using the measured ion spectrum, the erosion damage sputtered by Ar ions on the silicon nitride membrane was studied and the results indicated that the damage should cause no problems in the application of a contact soft X-ray microscope. Our laser plasma X-ray source will provide a compact and convenient source suitable for the soft X-ray microscopy in place of conventional synchrotron facilities.