Plasma processing system and method of supporting plasma ignition

A plasma processing system comprising:

• a plasma processing apparatus including a processing container that accommodates a substrate, and configured to perform a plasma processing on the substrate by generating a plasma in the processing container;
• and
• a control device configured to control the plasma processing apparatus,
• wherein the control device is further configured to:
• collect a measurement value indicating a matching state of impedance between a power supply that supplies a radio-frequency power to the plasma and the plasma, with respect to each value of a variable that is adjustable related to matching of the impedance;
• specify a passing point with a point corresponding to a value of the variable that maximizes a gradient of change of the measurement value with respect to a vector extending from a point corresponding to the variable to a matching point that is a point corresponding to a measurement value in a state where the impedance is matched;
• specify a control start point with a point farther from the matching point than the passing point on a straight line including the passing point and the matching point;
• and
• ignite the plasma in the plasma processing apparatus by controlling the variable such that the measurement value changes from the control start point toward the matching point along the straight line.