## 1 Introduction  
Over the last decade we have witnessed a tremendous progress in the development of regenerative laser amplifiers with repetition rates from 100 kHz up to 1 MHz. These laser systems are widely used as laser material processing tools, where together with a high pulse energy in the Micro-Joule range high pulse repetition-rates are required to minimize production times [1, 2]. A Megahertz repetition rate is also attractive for applications in nuclear, heavy ion and atomic physics enabling synchronization to the round trip times of particle storage rings [3, 4, 5]. Furthermore, high repetition rate picosecond laser systems are routinely used for photo cathode based electron sources seeding linear accelerator driven light sources [6].  
Commonly, \(\beta\)-Barium Borate (BBO), Rubidium Titanyle Phosphate (RTP), Potassium Dihydrogen Phosphate (KDP) or Potassium Dideuterium Phosphate (KD*P) are used for Pockels cells at a wavelength around 1 \(\upmu\)m. As both KD*P and KDP show piezoelectric ringing at repetition rates higher than 10 kHz only RTP and BBO remain. For given apertures and crystal lengths the half wave voltage of BBO is more than five times higher when compared to RTP due to the electro-optic coefficients. Since the average power required for the electronic switch scales linearly with the repetition rate and with the square of the voltage, RTP is often preferred for high repetition rate applications. On the other hand, based on practical experience much higher optical average powers can be realized with BBO since RTP suffers from optically induced birefringence. Furthermore, a much higher polarization contrast ratio can be obtained with BBO. This was observed when comparing BBO and RTP at long term operation in a regenerative Nd:YVO\({}_{4}\) amplifier up to 300 kHz [7].  
Picosecond regenerative amplifiers with high-gain materials such as Nd:YVO\({}_{4}\) have already been demonstrated up to a repetition rate of 850 kHz [8]. Regenerative amplification in broadband gain media such as Yb:CaF\({}_{2}\) and Yb:CAIGO has been shown up to 500 kHz [9] and up to 200 kHz with Yb:YVO\({}_{4}\)[10]. A 100 W picosecond thin-disk Yb:YAG regenerative chirped-pulse amplifier (CPA) system was demonstrated up to 300 kHz [11]. Up to 1.7 MHz has been already achieved with a regenerative Ti:Sapphire amplifier at a shorter wavelength of 800 nm [12]. Complementary to the increase in the repetition rate of regenerative amplifiers, a fast evolution of mode-locked ultra-short pulse oscillators [13,14] with reduced repetition rate down to 1 MHz and with higher single pulse energies up to the \(\upmu\)J-level took place. Recently, a Gd:YVO\({}_{4}\) cavity dumped oscillator with 1 MHz repetition rate using an RTP Pockels cell was reported [15]. However, a more flexible down scale of the repetition rate is possible with regenerative amplifiers compared to mode-locked oscillators.  
Here, we present results of regenerative amplification with a maximum repetition rate of 2 MHz for Yb:YAG and 1 MHz for Yb:CaF\({}_{2}\) using a BBO Pockels cell. These are to our knowledge the highest repetition rates achieved with Ytterbium-doped laser materials. Here, we used active mirrors with a thickness between 1-3 mm which give an adequate thermal management for a high beam quality at laser average powers up to 10 W. The high single-pass gain between 20% and 30% is advantageous for MHz repetition rates compared to 10% usually achieved within thin disk amplifiers [11]. Our work is embedded in HZDR's development of diode-pumped Petawatt laser (PE\(\kappa\)ELOPE) comprising active mirror amplifiers in the front-end up to the 100 mJ level [16].