## 2 Probing the Vacuum Process
### Birefringence Induced by a High-Field Magnet  
Magnet-induced birefringence has long been measured in normal media like gas, and is known as the \"Cotton-Mouton effect\" [35]. The application of this measurement scheme to a vacuum provides the current best sensitivity to observe the vacuum process. The most recent result of the PVLAS experiment in 2016 provides sensitivity that is smaller by a factor of 20 with respect to the coefficient of the vacuum refractive index [10]. The signal birefringence increases in proportion to the square of the magnetic field strength, and thus a high field of a pulsed magnet is advantageous. In addition, the temporal variation of the pulsed field is essential to distinguish the signal from large static birefringence produced by cavity mirrors. In this scheme, a racetrack pulsed magnet was first used in the BMV experiment [36].  
To obtain large statistics along with the field strength, we have been developing a pulsed magnet system suited to a high repetition use. While the typical repetition of a pulsed magnet is about 1 mHz, that of our magnet is higher by about two orders of magnitude [37]. Figure 6 shows a photo of the magnet. The coil part is wound with a copper wire and cooled with liquid nitrogen to reduce the electrical resistivity. Stainless steel metal is used to reinforce the outer strength of the coil that is exposed to an expansion force during the generation of pulsed fields. The peak field reaches 12 T at the magnet center. The magnet has a planar shape to enhance the cooling efficiency. In addition to the magnet, we also developed a discharge unit with capacitors providing pulsed current to the magnet with high repetition [37]. Figure 7(left) shows a cycle of the repetition composed of two successive pulses with alternating field directions. The first pulse produces a field of \(+10\) T at the magnet center with a charged voltage of 4 kV. After a portion of the energy converts into Joule heating in the coil, the second pulse produces \(-6\) T. The residual energy returns to the capacitor that is recharged to 4 kV before the next cycle. Figure 7 (right) shows the distribution of the field strength in a continuous operation. Stable fields are repeatedly produced after the magnets relax to thermal equilibrium. The field length linearly increases the signal birefringence. Up to now, we have tested a simultaneous operation of four magnets, giving a total field length of 0.8 m with a repetition rate of 0.2 Hz and a field strength of 10 T (see also Section 3.2 and Figure 10).  
We have made a setup that combines the magnet with an optical system containing a Fabry-Perot cavity with a finesse of 650,000. The continuous data-taking requires a new scheme that the cavity resonance automatically recovers after the measurements of finesse and static birefringence in each cycle. To verify this scheme, we carried out a test run using a single magnet. The results have been described in Reference [38]. A long-term run of a few months will start after improvements of the optics.  
Figure 6: Racetrack pulsed magnet developed for a high-repetition use. The field length is 200 mm.