On the laser frequency stabilization by locking to a LISA arm

LISA is an array of three spacecraft flying in an approximately equilateral triangle configuration, which will be used as a low-frequency detector of gravitational waves. Recently a technique has been proposed for suppressing the phase noise of the onboard lasers by locking them to the LISA arms. In this paper we show that the delay-induced effects substantially modify the performance of this technique, making it different from the conventional locking of lasers to optical resonators. We analyze these delay-induced effects in both transient and steady-state regimes and discuss their implications for the implementation of this technique on LISA.