Threshold and bursting dynamics of the CSR instability in electron rings
In plain words
In storage rings run with very short bunches, above a certain current the bunch breaks into ripples and emits bursts of far-infrared light; the threshold and the bursting pattern are only partly predicted.
Precise statement
For a Gaussian bunch in an electron ring with the shielded steady-state CSR impedance, Vlasov-Fokker-Planck calculations give a threshold in the dimensionless current $S_{\mathrm{csr}}$ of approximately S_csr,th = 0.5 + 0.12 $\Pi$, with Pi the shielding parameter, plus a narrow low-threshold region near $\Pi \sim 0.7$ (2010). Determine whether the threshold and the period and amplitude of sawtooth bursting above it are predicted within 20 percent once the full ring impedance, potential-well distortion and finite chamber geometry are included, in low-momentum-compaction operation of several rings.
What would settle it
Bunch-by-bunch measurements of threshold current and burst spectra versus Pi in two or more rings, compared with Vlasov-Fokker-Planck solutions that use independently measured impedances.
Status in the literature
Unverified note
Measured thresholds in low-momentum-compaction modes of several rings in the 2010s were broadly consistent with the scaling law; bursting dynamics above threshold are reproduced only qualitatively (moderate confidence, not rechecked for 2024-2026).