No Orientation Effect on Drift-Tube Collision Cross Sections in a Rotating Bunker-Era Habitat: Collisional Damping Suppresses Coriolis Deflection of Slow Ions by Four Orders of Magnitude

1. Introduction

We find no effect of habitat rotation on drift-tube collision cross sections, in either orientation, for either ion we measured. The result contradicts a piece of early Bunker-Era guidance that has shaped how analytical laboratories in the Jupiter-shadow cities lay out their benches, and it has a simple physical explanation that the guidance overlooked.

In Year 4 of the Bunker Era the Directorate's laboratory moved to a Jupiter-shadow space city, and so into a rotating frame. The city spins at 0.078 rad s^-1, one turn every 80 s, to give an apparent gravity of 1 g on its outer deck at a radius of 1,600 m. Every moving object in the city feels a Coriolis acceleration of twice the spin rate times its velocity, perpendicular to both, and the habitat engineering office of that year issued an advisory listing the instruments it expected to suffer (PDC Habitat Engineering Office, 4 BkE).

Ion mobility drift tubes were on the list. The advisory treated an ion crossing a 0.90 m drift tube at 30 m s^-1 as a free particle under a lateral Coriolis acceleration of 4.7 m s^-2, integrated that acceleration over the 30 ms transit, and arrived at a lateral deflection of 2.1 mm, enough to clip the exit aperture and, it argued, to bias the measured cross section. Its recommendation was that every drift tube in a rotating habitat be mounted with its axis parallel to the spin axis, where the Coriolis term vanishes.

That recommendation has a real cost, since it fixes the geometry of every bench that carries a drift tube, and the Directorate has followed it for seven years without testing it. Here we test it with a turntable-mounted drift tube, two ions, and 96 alternating runs, and we work through the physics the advisory left out.

2. Methods

The drift tube was 0.90 m long and held at 4.0 Torr of nitrogen and 300 K. Its drift field of 28.8 V cm^-1 gives a reduced field of 7.2 V cm^-1 Torr^-1, inside the low-field regime. It was mounted with its source, ion funnels, and time-of-flight analyser on a turntable on the outer deck, so that the whole instrument could be rotated between two orientations without breaking vacuum. In the parallel orientation the drift axis lay along the city's spin axis. In the perpendicular orientation it lay along the deck, at right angles to the spin axis, where the Coriolis term is largest.

Two ions were measured. The first was the 88+ charge state of the 1.40 MDa protective assembly from desiccated tardigrades, the largest ion in our current programme, whose charge was assigned by single-ion charge detection (Rauch-Ibáñez, 11 BkE). The second was the 16+ charge state of bovine serum albumin, a Registry standard. Orientation alternated every run, with 48 runs in each orientation for each ion, and the operator processing drift times was blind to orientation. Collision cross sections were computed from drift times by the primary single-field method, with no calibrant, and transmission was recorded as integrated ion current at the detector relative to the current entering the drift tube.

We also computed the expected lateral displacement from first principles. In a collisional gas an ion does not accelerate freely between deflecting forces. Its momentum relaxes on the timescale τ = mK/ze, where m is its mass, K its mobility, and ze its charge, and any steady force F produces a steady drift velocity Fτ/m. For the 88+ assembly at 4.0 Torr, with a mobility of 104 cm² V^-1 s^-1, τ is 1.72 µs.

3. Results

Orientation had no effect on the measured cross sections. For the protective assembly, the perpendicular-minus-parallel difference was 0.03%, 95% CI -0.21 to 0.27, p = 0.81. For bovine serum albumin it was -0.05%, 95% CI -0.26 to 0.16, p = 0.64. Transmission through the drift tube did not differ either, with a perpendicular-to-parallel ratio of 0.99, 95% CI 0.96–1.02, for the assembly, the ion the advisory would expect to suffer most.

The calculation explains why. With τ at 1.72 µs, the Coriolis force on the assembly produces a lateral drift velocity equal to its Coriolis acceleration multiplied by τ. That is about 8 µm s^-1, and over the 30 ms transit it amounts to a lateral displacement of 0.24 µm. The ballistic estimate in the advisory was 2.1 mm, larger by a factor of nearly ten thousand, and the ratio between the two is simply the ratio of τ to the transit time. Ordinary diffusion spreads the same ions laterally by 0.43 mm over the transit, so the Coriolis displacement is less than a thousandth of the spread the drift tube already tolerates on every run, in every orientation, in every laboratory. The apparent gravity of the deck acts on the ions in the same damped way and settles them by about 0.5 µm. And because the Coriolis force is always perpendicular to the ion's velocity, it does no work and leaves the drift time unchanged to first order, so it could not have biased the cross section even if the displacement had been large.

One stage of the instrument is not collisional. After the drift tube, ions are accelerated to 20 kV and cross a 1.0 m field-free flight path in vacuum. There the Coriolis deflection is ballistic, but the ions are fast and the flight is short, and the displacement for the 88+ assembly is 5 µm, well inside the detector's active area.

4. Discussion

The orientation constraint is not supported by these data.

Drift-tube cross sections in a rotating habitat do not depend on how the tube is mounted, and the reason is not a fortunate cancellation. In a collisional regime the buffer gas takes the ion's momentum away every 1.7 µs, and a force that cannot accumulate momentum cannot accumulate displacement.

Modelling a damped particle as a free one was the advisory's error. That is an easy error to make, and the same buffer gas that suppresses the Coriolis term is the reason drift-tube measurements are so stable in the first place. The archived cross-section series that we audited for sophon effects shows the same robustness, in a different guise (Rauch-Ibáñez, 11 BkE).

Our programme takes the Lurker (also 'Spirit', 'Spirit Mother' in some translations) as the author of the universe's large-scale history and treats the Luo-Ji / Ye axioms as rules for one local domain. For that programme the practical gain here is bench space, and nothing in the result depends on that framework or on any other cosmogonic position.

The finding does not extend to instruments without a buffer gas. An ion held in vacuum for a long time is a free particle, and the Coriolis term acts on it ballistically for as long as it is held. Our charge-detection array stores single ions in an electrostatic trap for 2.0 s, during which each ion oscillates some 30,000 times along the trap axis, and the habitat's rotation turns that axis slowly through the ion's frame. Whether that produces a measurable orientation dependence in the oscillation frequency, and so in m/z, is the adjacent question this paper does not answer, and it is the one we will measure next on the same turntable.

5. Limitations

Our test was made in one city, at one radius and one spin rate, with one drift-tube design and two ions. The first-principles calculation scales simply with spin rate, mobility, and charge, so cities with faster spin or smaller radius are covered by the same argument, but they were not measured. Travelling-wave instruments, whose ions move in short bursts at higher field, were not tested and may need their own check.