The tabletop synchrotron light sources MIRRORCLE-6X and MIRRORCLE-20SX, operating at electron energies E(el) = 6 MeV and E(el) = 20 MeV, respectively, can emit powerful transition radiation (TR) in the extreme ultraviolet (EUV) and the soft X-ray regions. To clarify the applicability of these soft X-ray and EUV sources, the total TR power has been determined. A TR experiment was performed using a 385 nm-thick Al foil target in MIRRORCLE-6X. The angular distribution of the emitted power was measured using a detector assembly based on an NE102 scintillator, an optical bundle and a photomultiplier. The maximal measured total TR power for MIRRORCLE-6X is P(max) approximately equal 2.95 mW at full power operation. Introduction of an analytical expression for the lifetime of the electron beam allows calculation of the emitted TR power by a tabletop synchrotron light source. Using the above measurement result, and the theoretically determined ratio between the TR power for MIRRORCLE-6X and MIRRORCLE-20SX, the total TR power for MIRRORCLE-20SX can be obtained. The one-foil TR target thickness is optimized for the 20 MeV electron energy. P(max) approximately equal 810 mW for MIRRORCLE-20SX is obtained with a single foil of 240 nm-thick Be target. The emitted bremsstrahlung is negligible with respect to the emitted TR for optimized TR targets. From a theoretically known TR spectrum it is concluded that MIRRORCLE-20SX can emit 150 mW of photons with E > 500 eV, which makes it applicable as a source for performing X-ray lithography. The average wavelength, \overline\lambda = 13.6 nm, of the TR emission of MIRRORCLE-20SX, with a 200 nm Al target, could provide of the order of 1 W EUV.
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