Beam mixing 2026-10-18
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Beam mixing changes sample membership between turns through revolution-time differences. Repeatedly correlated samples and thermal noise limit stochastic cooling.[ref]
Fresh samples help across turns; losing pick-up–kicker correlation hurts. Useful feedback gain therefore depends on bandwidth, delay, beam dynamics and signal-to-noise ratio.
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Stochastic cooling 2026-10-18
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Simon van der Meer's stochastic cooling uses measured beam fluctuations, a pick-up, amplifier and timed kicker. Finite samples supply the signal; other particles and electronic noise contribute unwanted kicks. Delay and oscillation phase must make the correction oppose the sampled deviation.[ref]
This active system dissipates energy; it is no one-particle Maxwell's demon individually tracking antiprotons. The stochastic cooling variance model isolates the tradeoff.
Figure 1.
Measured beam fluctuations drive a delayed kicker, while excessive gain amplifies noise
. Original functional signal path, not a mechanical or scale drawing of a historical ring. Beam flight and electrical signal paths are distinct; phase and delay must make the correction oppose the sampled deviation. The graph is the stipulated scalar model with initial variance one and independent noise variance one quarter; it is not a measured cooling curve. Details.
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