## 1 Introduction  
High power picosecond lasers have attracted widespread attention due to their wide application in nonlinear frequency conversion, precision processing, and bio-medicine. A picosecond laser operating at a repetition rate of a few kHz, with both high peak power and high average power, is an excellent source for optical parametric chirped pulse amplification (OPCPA), an optical parametric oscillator (OPO), optical parametric generation (OPG), and UV light generation [1; 2; 3; 4]. At ELI-Beamlines, two picosecond lasers with 1 kHz, \(>\)100 mJ, were used to pump an OPCPA system as a part of an X-ray pump laser [5]. A laser operating at a 193 nm wavelength could be also realized by mixing the fourth harmonic of 1064 nm (266 nm) and 708 nm, which was obtained by an OPO pumped with a picosecond 532 nm laser [6]. Recently, ultra-short laser pulses, especially picosecond pulses, have been widely used in the field of material processing. To achieve high processing speed and productivity, high average power picosecond lasers operating at repetition rates of hundreds of kHz are preferred. The demand for compact, stable, and low-cost picosecond lasers has increased rapidly. Laser diodes are preferred pumps for high power lasers. Diode-pumped solid-state lasers (DPSSLs) are smaller, more stable, and have a lower cost, thus making them more practical for more applications [7; 8; 9]. In order to achieve high output power, higher power has to be pumped into the gain medium. In this case, excessive heat will be generated in the gain medium due to a finite conversion efficiency. Thus, the key issue in a high power laser system is how to remove the heat from the gain medium effectively. In the past years, several designs of high power picosecond lasers have been studied. Using rod materials, pulses with 1.5 J energy and 110 ps duration at 10 Hz [10], with 130 mJ and 64 ps at 300 Hz [11], with 80 mJ and 50 ps at 1 kHz, and with 145 W average power and 200 ps duration at 3 kHz were demonstrated with Nd-doped YVO\({}_{4}\) and YAG [12,13]; pulses with 1 J and 5 ps at 100 Hz [4], with 115 mJ before compressing at 200 Hz [14], and with 58.5 mJ at 1 kHz were also recently reported with cryogenically cooled bulk Yb:YAG [9]. Using thin-disk technology, a 300 W picosecond laser operating at 10 kHz was demonstrated with 1.6 ps in 2013, and a 1.3 kW thin-disk multi-pass amplifier running at 300 kHz with sub-8 ps was reported in 2014 [15,16]. Recently, the team at ELI-Beamlines presented a 110 mJ picosecond thin-disk amplifier with good beam quality. A 1-kHz-repetition-rate thin-disk regenerative amplifier was reported with a pulse energy of 10 mJ and a pulse duration of 1.29 ps after compression [5,17]. With innoslab and fiber materials, an average power of 250 W at 12.5 kHz was obtained, and 97 W average output power at 5.47 MHz picosecond pulses was generated from a fiber master oscillator power amplifier (MOPA) system, respectively [18,19]. Combining some of the different technologies mentioned above, a hybrid CPA laser system was reported recently. The system consisting of fiber pre-amplifiers, a bulk material-based regenerative amplifier, and multi-pass amplifiers provided 70 mJ pulse energy at the repetition rate of 1 kHz and about 6 ps pulse duration after compression [20]. Although thin-disk and innoslab lasers have the advantage of easy heat dissipation, lasers based on bulk materials generally could have higher efficiencies and simpler structures, making them more attractive. In this paper, the research on high energy and high repetition rate DSPP picosecond amplifier systems with bulk Nd-doped crystals is reported. Nd-doped laser media with large emission cross-sections and long upper level lifetimes are very suitable for laser amplifications. Due to its comparatively short upper state lifetime and broad pumping bandwidth, Nd:YVO\({}_{4}\) is appropriate for efficient oscillators and amplifiers. In addition, the 0.8 nm emission bandwidth of Nd:YVO\({}_{4}\) supports sub-10 or sub-100 pspulses [21].