[Paper Review] Investigations of Slow Motions of the SLAC Linac Tunnel

F. Massimo|ArXiv.org|Aug 20, 2000

Particle Accelerators and Free-Electron Lasers3 citations

TL;DR

This study investigates slow transverse ground motions in the SLAC linac tunnel using a laser alignment system with a quadrant photodetector, achieving submicron resolution. The key finding is that atmospheric pressure variations are the dominant cause of short-wavelength tunnel motion, while tidal effects drive long-wavelength components, with amplitudes up to 10 µm; these results are critical for designing feedback systems for the Next Linear Collider to minimize emittance dilution.

ABSTRACT

Investigations of slow transverse motion of the linac tunnel of the Stanford Linear Collider have been performed over period of about one month in December 1999 -- January 2000. The linac laser alignment system, equipped with a quadrant photodetector, allowed submicron resolution measurement of the motion of the middle of the linac tunnel with respect to its ends. Measurements revealed two major sources responsible for the observed relative motion. Variation of the external atmospheric pressure was found to be the most significant cause of short wavelength transverse motion of the tunnel. The long wavelength component of the motion has been also observed to have a large contribution from tidal effects. The measured data are essential for determination of parameters for the Next Linear Collider.

Motivation & Objective

• To measure slow transverse ground motion in the SLAC linac tunnel with submicron resolution to assess its impact on beam stability.
• To identify the dominant environmental drivers of slow ground motion, particularly atmospheric pressure and tidal forces.
• To provide data for determining feedback system requirements and estimating residual emittance dilution in the Next Linear Collider.
• To evaluate the influence of temperature, RF power, and vacuum conditions on tunnel motion, ruling out these factors as major contributors.

Proposed method

• A laser alignment system with a quadrant photodetector was used to measure transverse displacement of the tunnel at the midpoint of the 3050 m linac.
• The system measured the position of a laser beam reflected from a target using the difference in quadrant signals: X ∝ [(u₁+u₂)−(u₃+u₄)]/Σuᵢ, enabling submicron resolution.
• Measurements were conducted over 30 days (Dec 8, 1999 – Jan 7, 2000) with a single fixed target to ensure accuracy and repeatability.
• The data were analyzed using spectral analysis, including tidal harmonic fitting (e.g., M2, N2, J1) and power spectral density estimation with f⁻² behavior.
• Noise levels were assessed by direct illumination of the photodetector with a calibrated light source, and coherence with a broadband seismometer (STS-2) was measured.
• The ATL-law model (P(ω) = 4AL/ω²) was applied to fit the measured spectra, with A derived from data in the 2.44×10⁻⁴ to 1.53×10⁻² Hz band.

Experimental results

Research questions

• RQ1 What environmental factors are primarily responsible for slow transverse motion in the SLAC linac tunnel?
• RQ2 How do atmospheric pressure variations correlate with observed tunnel displacement at submicron resolution?
• RQ3 To what extent do tidal forces contribute to long-wavelength tunnel motion, and can they be modeled accurately?
• RQ4 How does the spectral behavior of tunnel motion (e.g., f⁻² dependence) compare with theoretical models like the ATL-law?
• RQ5 What is the coherence between tunnel motion and absolute ground motion measured by a seismometer during seismic events?

Key findings

• Atmospheric pressure variations were identified as the dominant cause of short-wavelength transverse motion, with a sensitivity of approximately 2 µm/mbar in the horizontal plane and 6 µm/mbar in the vertical plane.
• Tidal effects produced a pronounced long-wavelength component with a peak amplitude of about 10 µm, primarily driven by the M2, N2, and J1 tidal harmonics.
• The effective tidal deformation radius at SLAC was estimated to be ~500 km, indicating a local geological anomaly due to coastal loading from ocean tides.
• The tunnel motion spectrum exhibited a 1/f² behavior over a broad frequency band (down to ~10⁻⁵ Hz), consistent with the ATL-law model, with the parameter A ranging from 10⁻⁷ to 2×10⁻⁶ µm/(m·s).
• Spectral analysis revealed that the parameter A varied over time, and this variation strongly correlated with atmospheric pressure fluctuations, suggesting pressure as a primary driver of the f⁻² motion.
• During a remote earthquake (Alaska, 5.8 Mw), the tunnel motion and seismometer data showed a coherence of ~0.5 at frequencies above 0.2 Hz, with a phase velocity of ~2.5 km/s consistent with prior SLAC measurements.