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The hollow-cathode triggered discharge extreme ultraviolet source is based on the same principle as pseudospark switches. The electrode geometry consists of a planar anode and cathode with central opposing holes, the one on the cathode side being connected to the hollow cathode. Radiation is generated by magnetic compression of the working gas under high-current operation. Essential for the operation is that the pressure and voltage are chosen to be on the left side of the Paschen curve to insure insulation of the gap between the electrodes. However, this insulation of the electrode system needs to be reinstalled after breakdown. Typical recovery times of a xenon-based system are down to 100 μs, depending on the electrode geometry. It will be shown that the decay of the electron density in the hollow cathode is the limiting process. Investigation of the recovery mechanism has led to a design that allows operation above 4 kHz which is close to the required frequency for extreme ultraviolet lithography.