Time-of-Flight Mass Spectrometry - 2D Drift Tube

An ion of mass m and charge q = z e accelerated through a potential difference U gains kinetic energy q U = m v^2 / 2, so v = sqrt(2 z e U / m). It then crosses a field-free drift tube of length L in t = L / v = L sqrt(m / (2 z e U)). Hence t^2 is proportional to m/z: a plot of arrival time squared against m/z is a straight line, which is how real instruments are calibrated with two or more known peaks.

With an acceleration region of length s and uniform field E = U / s, an ion starting at rest at the far plate needs an extra 2 s / v in the field, so t = (2 s + L) / v (the full formula is used here). Ions that start at different depths gain different energies, and ions with an initial velocity away from the detector must turn around first; both broaden the peak. The resolving power is R = m / Delta m = t / (2 Delta t) where Delta t is the peak width at half maximum.

Simplifications: one-dimensional motion, uniform acceleration field, no space-charge repulsion, no detector dead time, no reflectron or delayed extraction, and uniform source depth plus a Gaussian initial-velocity spread. The 3D page shows the instrument; this page measures it. Educational model, not an analysis tool.

• Set source depth and initial energy to zero: the peaks become needles and the resolving power is huge.
• Raise the initial energy to 3 eV and watch each peak broaden and the resolving power drop.
• Pick Protein charge states: one mass with z = 3 to 6 gives peaks at m/z = M/z.