Frequency planning for LISA

The Laser Interferometer Space Antenna (LISA) is poised to revolutionize astrophysics and cosmology in the late 2030's by unlocking unprecedented insights into the most energetic and elusive astrophysical phenomena. The mission envisages three spacecraft, each equipped with two lasers, on a triangular constellation with 2.5 million-kilometer arm-lengths. Six inter-spacecraft laser links are established on a laser-transponder configuration, where five of the six lasers are offset-phase-locked to another. The need to determine a suitable set of transponder offset frequencies precisely, given the constraints imposed by the onboard metrology instrument and the orbital dynamics, poses an interesting technical challenge. In this paper we describe an algorithm that solves this problem via quadratic programming. The algorithm can produce concrete frequency plans for a given orbit and transponder configuration, ensuring that all of the critical interferometric signals stay within the desired frequency range throughout the mission lifetime, and enabling LISA to operate in science mode uninterruptedly.