Title: Demonstration of the length stability requirements for ALPS II with a high finesse 9.2m cavity,
Abstract: Light-shining-through-a-wall experiments represent a new experimental
approach in the search for undiscovered elementary particles not accessible
with accelerator based experiments. The next generation of these experiments,
such as ALPS~II, require high finesse, long baseline optical cavities with fast
length control. In this paper we report on a length stabilization control loop
used to keep a 9.2\,m cavity resonant. It achieves a unity-gain-frequency of
4\,kHz and actuates on a mirror with a diameter of 50.8\,mm. The finesse of
this cavity was measured to be 101,304$\pm$540 for 1064\,nm light. The
differential cavity length noise between 1064\,nm and 532\,nm light was also
measured since 532\,nm light will be used to sense the length of the
regeneration cavity. Out-of-loop noise sources and different control strategies
are discussed, in order to fulfill the length stability requirements for
ALPS~II.