Numerical simulation of time delay interferometry for a LISA-like
  mission with the simplification of having only one interferometer
  In order to attain the requisite sensitivity for LISA, laser frequency noise
must be suppressed below the secondary noises such as the optical path noise,
acceleration noise etc. In a previous paper (Dhurandhar et al., Class. Quantum
Grav., 27, 135013, 2010), we have found a large family of second-generation
analytic solutions of time delay interferometry with one arm dysfunctional, and
we also estimated the laser noise due to residual time-delay semi-analytically
from orbit perturbations due to Earth. Since other planets and solar-system
bodies also perturb the orbits of LISA spacecraft and affect the time delay
interferometry (TDI), we simulate the time delay numerically in this paper for
all solutions with the generation number n \leq 3. We have worked out a set of
3-year optimized mission orbits of LISA spacecraft starting at January 1, 2021
using the CGC2.7 ephemeris framework. We then use this numerical solution to
calculate the residual optical path differences in the second-generation
solutions of our previous paper, and compare with the semi-analytic error
estimate. The accuracy of this calculation is better than 1 cm (or 30 ps). The
maximum path length difference, for all configuration calculated, is below 1 m
(3 ns). This is well below the limit under which the laser frequency noise is
required to be suppressed. The numerical simulation in this paper can be
applied to other space-borne interferometers for gravitational wave detection
with the simplification of having only one interferometer.
