Performance of the KAGRA detector during the first joint observation with GEO 600 (O3GK)

KAGRA, the kilometer-scale underground gravitational-wave detector, is located at Kamioka, Japan. In April 2020, an astrophysics observation was performed at the KAGRA detector in combination with the GEO 600 detector; this observation operation is called O3GK. The optical configuration in O3GK is based on a power recycled Fabry-P\'{e}rot Michelson interferometer; all the mirrors were set at room temperature. The duty factor of the operation was approximately 53%, and the strain sensitivity was $3\times10^{-22}~/\sqrt{\rm{Hz}}$ at 250 Hz. In addition, the binary-neutron-star (BNS) inspiral range was approximately 0.6 Mpc. The contributions of various noise sources to the sensitivity of O3GK were investigated to understand how the observation range could be improved; this study is called a "noise budget". According to our noise budget, the measured sensitivity could be approximated by adding up the effect of each noise. The sensitivity was dominated by noise from the sensors used for local controls of the vibration isolation systems, acoustic noise, shot noise, and laser frequency noise. Further, other noise sources that did not limit the sensitivity were investigated. This paper provides a detailed account of the KAGRA detector in O3GK including interferometer configuration, status, and noise budget. In addition, strategies for future sensitivity improvements such as hardware upgrades, are discussed.