gem-lte-core

The QBO as a switched toroidal plasma (2026-10-22)

Figure: qbo_switching_plasma.png (script qbo_switching_plasma.py). The detailed working is in qbo_tokamak.md; this note is the short version.

The claim

The QBO behaves like a ring of conducting fluid driven by a polarity-switching pulsed supply: the flow around the ring reverses every 2.37 cycles of the switch, and each reversal sinks from the top of the ring into its interior. Read with 1 year = 1 second, the equatorial stratosphere is a 73-second discharge whose edge field flips every 2.37 s.

Three ingredients

1. A switch (the Sun). It fires twice per cycle and flips polarity each time (+, −, +, −): the semiannual trigger, signed by which hemisphere the Sun is over.
2. A modulator (the Moon). It sets each pulse’s height: how far the Moon is above or below the Sun’s plane (its ecliptic latitude), which repeats every draconic month, 13.42 times per cycle.
3. A ring that reverses. The ring’s flow (or field) flips sign at its edge once the integrated drive passes a threshold, and each new reversal moves inward.

Why the period is 2.37, with nothing tuned

This is stroboscopic beating, the wagon-wheel effect. Flipping the sign at every pulse shifts the 13.42 modulation to 14.42; sampling it twice per cycle folds 14.42 down to 14.42 − 14 = 0.42 cycles, a 2.37-cycle beat: the QBO’s 28-month period. Two controls fail, which is what makes the result specific:

• without the polarity flip the beat is 1.73;
• with the Moon’s declination (its height above the equator) instead of its latitude it is 2.72.

The switch sets the reference plane, so the modulator has to be measured from the Sun’s plane.

Systems that already do each part

Ingredient	Where it exists
Polarity-switched (AC) drive of a toroidal plasma	AC tokamak operation: the plasma current is reversed from one half-cycle to the next with the plasma sustained. Demonstrated on JET (Tubbing et al., Nucl. Fusion 1992) and on smaller tokamaks (STOR-M, CT-6B, ISTTOK, the last running many AC cycles in a row).
A ring whose edge field reverses by itself past a threshold	Reversed-field pinch (RFX-mod in Padova, MST in Madison): the toroidal field reverses near the edge on its own once the driving current is large enough; the relaxed state is Taylor’s minimum-energy state (Taylor, PRL 1974), with reversal when μa > 2.405.
Sustaining a toroidal plasma with oscillating, sign-reversing voltages	Oscillating-field current drive (OFCD): AC poloidal and toroidal loop voltages, 90° apart, inject magnetic helicity and drive net current. Proposed by Bevir and Gray (1980), tested on ZT-40M and on MST (McCollam et al., PRL 2006).
Descending flow reversals driven by an oscillating boundary	The QBO laboratory analogue: Plumb and McEwan (J. Atmos. Sci. 1978) produced descending, periodically reversing mean flow in a stratified annulus forced by a standing wave; Semin, Garaud and Fauve (PRL 2018) revisited it. This is a fluid, not a plasma, but it is the same ring geometry and the same reversals.

So every element is realized somewhere. What has not been built is the combination: an AC- or OFCD-driven reversed-field pinch whose switching is amplitude-modulated off-resonance, so that the edge reversal follows the stroboscopic beat rather than the switch itself.

What a lab test would look like

• Drive an RFP (or AC tokamak) with a pulsed supply that flips polarity twice per cycle, at, say, 2 Hz.
• Modulate each pulse’s height at 13.42 Hz.
• Expected: edge-probe reversals every 2.37 s, and later at probes further in. Remove the polarity flip and the reversals should come every 1.73 s instead.
• The test is cheap in principle, because only the timing of the supply changes; the plasma is standard.

Limits

• The fit to the real QBO holds its phase from 1953 to 2005 (correlation about 0.6 at 30–70 hPa, descent lag 6–8 months against 7 observed) but not across the 2016 and 2019–20 disruptions (qbo_tokamak.md, section 4).
• In the real QBO the mechanism is usually attributed to upward-propagating waves depositing momentum (Lindzen and Holton 1968; Baldwin et al., Rev. Geophys. 2001). The switched-plasma picture replaces the waves’ timing with the Sun–Moon triggers; it does not show that the waves are absent.
• The details (shoulders from strobed penetration, a fast helical ripple) are in qbo_tokamak.md, sections 7–8.

Phase-locking test (qbo_phase_lock.py, qbo_phase_lock.png)

Reversal dates from the KIT winds at 30, 50 and 70 hPa (3-month mean, ±3 m/s hysteresis), 1953–2024: 59–64 reversals per level. Each reversal’s phase in the 2.370-yr beat (easterly onsets shifted by half a cycle); Rayleigh R measures how tightly they cluster. Null: the same intervals between reversals in random order (same period spread, phase free to wander), 5000 draws.

Level	R at 2.370 yr	Shuffled median (95th pct)	p	Best period in a scan (R)	Scan max, p	R at 1.73 / 2.72 yr
30 hPa	0.61	0.31 (0.57)	0.027	2.345 yr (0.70)	0.041	0.05 / 0.13
50 hPa	0.52	0.19 (0.39)	0.002	2.350 yr (0.57)	0.020	0.09 / 0.09
70 hPa	0.44	0.14 (0.28)	0.0006	2.350 yr (0.48)	0.0008	0.04 / 0.08

• The reversals are phase-locked, beyond what the same reversal intervals in random order give, at all three levels (p from 0.03 at 30 hPa to 0.0006 at 70 hPa). The QBO’s phase is regulated: it does not drift like a free oscillator with its own period spread.
• “2.35 yr” is not a distinct period. Over the record the difference from 2.370 amounts to about a quarter of a cycle (30.4 against 30.7 cycles for 1953–2024; 31.2 against 31.4 to late 2026), comparable to the phase jitter itself, so where the cycle is counted from and to decides it. Restricted to 1953–2005, the best period is 2.356 / 2.363 / 2.362 yr at 30 / 50 / 70 hPa, with R at 2.370 essentially equal to the best (0.71 vs 0.73, 0.66 vs 0.67, 0.57 vs 0.57): no measurable departure from 2.370 over five decades. The pull toward 2.345–2.35 comes entirely from the reversals after 2006, the decade with the 2016 and 2019–20 disruptions, i.e. a phase step, not a different steady period.
• The lock weakens but survives after 2006 at 30 hPa (R 0.70, phase shifted from 0.54 to 0.32 cycles); at 50 and 70 hPa it falls to R 0.44 and 0.33.
• What the controls do and do not show. R at 1.73 and 2.72 yr is near zero, but any oscillator with a period near 2.37 yr would fail those; they rule out those periods, not other mechanisms.
• What this does not yet show. Any phase-regulated oscillator near 2.37 yr would pass this test, including a wave-driven QBO whose phase is regulated by the seasonal cycle. Seasonal regulation with half-year steps and a stroboscopic beat are close relatives: a 2.37-yr average built from half-year steps is exactly what the beat produces. The discriminating test is the absolute phase: with the trigger dates fixed by astronomy (not fitted), the strobe model predicts where in the beat the reversals fall. That prediction, checked against the observed mean phases above, is the next step.

Absolute-phase test (qbo_abs_phase.py, qbo_abs_phase.png)

The drive is fixed by the ephemeris alone: impulses at the June and December solstices, heights from the Moon’s ecliptic latitude, the Sun’s declination and its distance. Nothing is fitted.

1. The astronomical beat is almost a perfect clock. Its phase wobbles by only 0.026 cycles over 1953–2024 (sd 0.006) and its amplitude by ±4%. The observed reversal phase wanders by about 0.2–0.3 cycles. So:

• the lag-independent test (do reversals follow the ephemeris wobble?) has no power: the ephemeris-aligned phase gives R 0.617 / 0.523 / 0.448 at 30 / 50 / 70 hPa, the same as time-shifted ephemerides (34th–52nd percentile);
• the QBO’s phase wander is not astronomical. In the gating picture it is the internal (wave) part: jitter in when the system reaches its threshold.

2. Implied lag. Taking the drive’s beat maximum as the edge trigger, the observed reversals follow it by:

	30 hPa	50 hPa	70 hPa
drive sign as written	21.8 months	27.0	30.1
drive sign reversed	7.6 months	12.8	15.9

(beat = 28.4 months). The lags increase downward, by 5 and 3 months, matching the observed descent. A descent of about 1 km per month puts the trigger near 10 hPa for the reversed sign (7.6 months above 30 hPa) or near 2–3 hPa for the sign as written (22 months). Both are plausible places for a QBO to start, and the drive’s sign is not yet fixed by physics. So the absolute phase is consistent with the strobe, but it does not discriminate: a random phase would also land on a plausible lag with good probability.

3. What would discriminate. A wave-driven QBO regulated by the seasonal cycle and a lunar-gated QBO make the same half-year-stepped pattern and the same spectral images (f₀ ± 1, 2 − f₀). They differ in the long-run mean period: the gated QBO must average exactly 2.3702 yr indefinitely; a wave-driven one has no reason to, and climate models project its period to change. Over the record the difference between 2.370 yr and the best-fitting period is about a quarter of a cycle, all of it from a phase step after 2006; over 1953–2005 the record is indistinguishable from 2.370. Not a contradiction, and not yet a confirmation. Two ways to sharpen it:

• fix the drive’s sign from the physics (which sign of the Moon–Sun product pushes westerly), which turns the lag into a prediction of the trigger altitude;
• every further decade of reversals tightens the mean-period test; a QBO that keeps drifting from 2.370 would rule the strobe out.

The SAO above: the clock made visible (qbo_sao.py, qbo_sao.png)

ERA5 monthly equatorial zonal wind (zonal mean, 5°S–5°N), 1–70 hPa, 1979–2025.

1. The SAO is calendar-locked, so it is forced, not resonant. At 1–3 hPa the mean annual cycle carries 77 / 67 / 48% of the wind variance, and the semiannual harmonic’s phase repeats from year to year with R = 0.98 / 0.97 / 0.94. The lock fades below 5 hPa (0.69) and is gone by 10–30 hPa (0.16–0.24).

2. Its two cycles are unequal, and that inequality is the polarity flip. At 1 hPa the January easterlies reach −39 m/s and the July easterlies −20; the April westerlies +32 and the October westerlies +23. A same-sign semiannual strobe would give a 1.73-yr beat, which the data reject; the inequality between the two half-years is an annual component, and an annual component has opposite sign half a year apart. That is the alternating polarity the 2.37-yr beat needs. Physically it is the hemispheric (and perihelion, January) asymmetry of solar heating, which the drive already carries through sin δ_sun and the solar distance.

3. The 2.37-yr lock is a lower-altitude property. Reversal clustering at the beat (Rayleigh R) by level: 1 hPa 0.03 (none), 2–3 hPa 0.33–0.39, 5–10 hPa 0.44–0.47, 20–70 hPa 0.47–0.58. Above, the calendar dominates; below, the beat. (ERA5’s 47 years give about 40 reversals per level, so the shuffle tests here are weaker, p 0.03–0.19, than for the 71-year KIT record.)

4. Descent and the trigger. Reversal timing relative to 30 hPa (months), continuous from 70 hPa upward:

hPa	2	3	5	7	10	20	30	50	70
months	−16.8	−16.4	−12.2	−9.7	−6.9	−2.8	0	+5.1	+7.5

Reversals first appear at 2–3 hPa, at about the same time at both levels, then descend at roughly 1 km per month. This settles the drive’s sign from the absolute-phase test:

• reversed sign: the trigger would fall 7.6 months above 30 hPa, between 7 and 10 hPa, after the reversals have already appeared above it, so it cannot be the trigger;
• sign as written: the trigger falls 21.8 months before 30 hPa, about 5 months before the reversals first appear at 2–3 hPa, i.e. at or just above the top of the QBO, beneath the SAO layer.

So the data favour the written sign, with the drive’s beat maximum acting at the SAO–QBO interface and the reversal emerging about 5 months later at 2–3 hPa (the integration time of the gated medium) before descending.

5. SAO westerly phases seed QBO westerly onsets. At 5–7 hPa, QBO westerly onsets cluster in April–June (5 of 21 in May at 5 hPa), just after the SAO’s strong April westerly peak above. Easterly onsets cluster less.

Summary. The vertical structure matches the switched-plasma picture: a calendar-locked, solar-driven switch at the top (the SAO, too thin and too strongly damped to integrate anything), its unequal half-cycles supplying the alternating polarity, and below it a medium with memory where the lunar-modulated beat takes hold, enters at 2–3 hPa and descends.