We report on new results of a search for a two-photon interaction with axionlike particles (ALPs). The experiment is carried out at a synchrotron radiation facility using a "light shining through a wall (LSW)" technique. For this purpose, we develop a novel pulsed-magnet system, composed of multiple racetrack magnets and a transportable power supply. It produces fields of about 10 T over 0.8 m with a high repetition rate of 0.2 Hz and yields a new method of probing a vacuum with high intensity fields. The data obtained with a total of 27 676 pulses provide a limit on the ALP-two-photon coupling constant that is more stringent by a factor of 5.2 compared to a previous x-ray LSW limit for the ALP mass ≲0.1 eV.