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Implement spacecraft longitudinal jitters

One of the main noises (that we expect we can suppress almost perfectly) in LISA is the longitudinal motion of the spacecraft (ie., the optical bench) along the line of sight. It is modeled in Markus Otto's and Olaf Hartwig's theses as extra couplings in the optical path length

  • in the distant beams reaching the ISIs
  • in the local beam reaching the TMIs

We will follow the conventions from Olaf's thesis (aligned with what we currently have in our LISA Instrument and LISANode's model for the test-mass displacement).

image

As a consequence, the extra path length couples

  • with a minus sign in the ISI distant beams (image), therefore appears with a plus sign in the phase and frequency
  • with a factor 2 and a plus sign in the TMI local beams (image), therefore appears with a minus sign in the phase and frequency

For a realistic simulation, one would need to simulate in-loop quantities, and therefore the DFACS control systems (similar to 10.1103/PhysRevD.106.022006). We currently don't have closed loop systems in LISA Instrument, and therefore agreed with @ohartwig to implement a first model using out-of-loop jitters (same trick as what we use for the test-mass noise).

We couldn't find any clear specifications on the spectrum of this spacecraft longitudinal jitter (before subtraction in TDI) in the performance model (LISA-LCST-INST-TN-003). However, they give an order of magnitude of nm/sqHz. We suggest to start with a white noise of a few nm/sqHz to begin with.