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The direct generation of high energy pulses with a diode-pumped solid-state laser oscillator is a promising approach to enable the multi-megahertz operation of numerous applications in science and industry. Thin disk lasers enable the required average power with excellent beam quality, such that passive mode locking with a semiconductor saturable absorber mirror (SESAM) can be achieved. Using this concept, the authors have recently been able to reach a pulse energy as high as 5.1 muJ at 12 MHz repetition rate from an Yb:YAG thin disk oscillator. This significant increase over previous results was made possible by realizing the importance of the nonlinearity of air inside a thin disk laser cavity. To eliminate the air's contribution to the nonlinearity, the laser was covered with a box which then was flooded with helium. Here a further increase in pulse energy to 11 muJ is presented. The existing 40.7 MHz laser cavity presented was extended to a total of 37 m, by inserting a 23.4 m long multiple-pass cavity (MPC) and a simple 4f extension using curved mirrors with 5000 mm radius of curvature. This resulted in a repetition rate of 4 MHz, at which we achieved an average power of 45 W when operated in the box flooded with helium. The sech2-shaped pulses had a FWHM-duration of 791 fs and a spectral bandwidth of 1.56 nm, resulting in a time-bandwidth product of 0.35 (Fourier-limit: 0.315). The beam quality was nearly diffraction-limited with an M2-value of 1.1 (measured at 9.4 muJ).