Technical Explanation
Pumpdown ODE and Free-Gas Regime
The pressure evolution in a pumped chamber can be written as V·dp/dt = Q_total − S_eff·p, where V is volume, p pressure, S_eff the effective pumping speed, and Q_total the total gas load (leaks, permeation, outgassing, etc.). When Q_total ≈ 0, the early pumpdown is dominated by removal of free gas and the solution becomes:
p(t) ≈ p₀ · exp [ −(S_eff / V) · t ]
Taking the natural logarithm gives ln p(t) ≈ ln p₀ − (S_eff / V)·t. On a ln(p) vs t plot, the slope in the free-gas region is therefore −S_eff/V.
Estimating S/V and S_eff from Data
This tool performs a linear regression of ln(p) versus time over a user-specified window. The fitted slope d(ln p)/dt gives an estimate of −S/V in that region. If chamber volume V is known, S_eff can be obtained from S_eff ≈ −(d(ln p)/dt)·V. If V is unknown, the result still provides S/V, which is useful for comparing different tools or monitoring changes over time.
Approximating Gas Load Q_total
For a chosen time window, the instantaneous total gas load can be approximated as Q_total(t) ≈ V·dp/dt + S_eff·p. Using finite differences for dp/dt and an estimate of S_eff, the tool reports an average Q_total over the selected region. A region near the tail of the pumpdown curve often reflects leakage and outgassing rather than free-gas removal.
Practical Use & Limitations
Fitted S/V and Q_total values depend strongly on which part of the curve is selected and on measurement noise. Early-time data is best for estimating S/V, while late-time segments are better for characterizing leaks and outgassing. Always interpret results together with knowledge of the system (pump curve, conductance, materials) and repeat measurements where possible.