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The Spallation Neutron Source H- ion source is operated with a pulsed 2-MHz RF (50-60 kW) to produce the 1-ms long, ~50 mA H- beams at 60 Hz. A continuous low power (~300 W) 13.56-MHz RF plasma, which is initially ignited with a H2 pressure bump, serves as starter plasma for the pulsed high power 2-MHz RF discharges. To reduce the risk of plasma outages at lower H2 flow rates which is desired for improved performance of the following radio frequency quadrupole, the 13.56-MHz RF matching network was characterized over a broad range of its two tuning capacitors. The H-α line intensity of the 13.56-MHz RF plasma and the reflected power of the 13.56-MHz RF were mapped against the capacitor settings. Optimal tunes for the maximum H-α intensity are consistent with the optimal tunes for minimum reflected power. Low limits of the H2 flow rate not causing plasma outages were explored within the range of the map. A tune region that allows lower H2 flow rate has been identified, which differs from the optimal tune for global minimum reflected power that was mostly used in the past. [ABSTRACT FROM AUTHOR]