Early Commissioning of the Luminosity Dither Feedback for SuperKEKB

SuperKEKB is an electron-positron collider, which aims to achieve a peak luminosity of 8×10³⁵ cm⁻² s^{−1} using what is known as the "nano-beam" scheme. This paper reports on the commissioning and performance of a luminosity dither feedback. The system, based on one previously used at SLAC for PEP-II, is employed for collision orbit feedback in the horizontal plane. Twelve air-core Helmholtz coils drive the positron beam sinusoidally at a frequency near 80 Hz, forming a closed bump at the interaction point. A lock-in amplifier detects the amplitude and phase of the corresponding frequency component of the luminosity signal. When the beams are aligned for peak luminosity, the magnitude of the luminosity component at the dithering frequency becomes zero. The magnitude grows as the beams are offset, and the phase shifts by 180 degrees when the direction of the necessary correction reverses. The hardware and algorithm were tested during SuperKEKB Phase II run. The electron beam orbit was successfully adjusted to minimize the amplitude of the dither frequency component of the luminosity signal, and the optimal condition was maintained by continuously adjusting the electron beam orbit.