Impact of coherent wiggler radiation impedance in Tau-Charm factories

TL;DR

The paper investigates how coherent wiggler radiation (CWR) contributes to the longitudinal impedance in Tau-Charm factory lattices with damping wigglers and how this affects microwave instability thresholds. It develops and compares analytic CWR impedance models (FS-SS, FS-TR, PP-TR, PP-SS) across low- and high-frequency regimes, and integrates these into generalized threshold formulas alongside CSR effects. Applying these models to the Super Tau-Charm Facility (STCF) design, the study shows that CWR-driven instabilities can dominate at certain wiggler periods, with thresholds around 0.6 mA at 1 GeV for λ_w=0.8 m, and higher thresholds (≈1.4 mA) achievable by reducing λ_w to 0.4 m. The results offer practical guidance for wiggler design and shielding to maintain beam stability, supported by GPU-based single-bunch tracking that aligns with dispersion-relations analyses and existing observational data.

Abstract

Coherent synchrotron radiation (CSR) has long been recognized as a significant source of longitudinal impedance driving microwave instability in electron storage rings. In the pursuit of higher luminosity, next-generation circular $e^+e^-$ colliders operating in the few-GeV energy range, such as B-factories and Tau-Charm factories, are being designed with low-emittance beams and high beam currents. Damping wigglers are commonly introduced to reduce damping times and control beam emittance. In this study, we systematically investigate the impact of coherent wiggler radiation (CWR), a specific form of CSR generated within wigglers, on beam stability in Tau-Charm factories. We revisit the threshold conditions for CWR-induced microwave instability and evaluate its effects under realistic lattice configurations of collider rings. Furthermore, we examine theoretical models of longitudinal CWR impedance and identify improved formulations that better capture its influence. As an illustrative example, the developed CWR impedance models are applied to simulate beam stability in the Super Tau-Charm Facility currently under design in China.

Figures (7)

• Figure 1: Total CWR impedance of the STCF rings calculated with free-space models. Beam and wiggler parameters correspond to the 1 GeV case (see Table \ref{['tab:stcf']} and related discussion). The red curves are obtained from Eq. \ref{['eq:CWR_Impedance_PP-TR']} together with Eq. \ref{['eq:F1']}, while the blue and black curves are calculated from Eq. \ref{['eq:CWR_Impedance_FS-SS']} and Eq. \ref{['eq:CWR_Impedance_FS-SS_large_k']}, respectively.
• Figure 2: Total CWR impedance of the STCF rings calculated with parallel-plates shielding models. Beam and wiggler parameters correspond to the 1 GeV case (see Table \ref{['tab:stcf']} and related discussion). The red curves are computed using Eq. \ref{['eq:CWR_Impedance_PP-TR']} with Eq. \ref{['eq:Fp1']}, while the blue and black curves corresponds to calculations using Eq. \ref{['eq:Fp3']} and Eq. \ref{['eq:Fp7']}, respectively.
• Figure 3: Total CWR impedance of the STCF rings for different wiggler periods, calculated using free-space (left) and parallel-plate shielding (right) models. The total wiggler length and peak field are kept fixed while varying the period length. The legend gives the wiggler period length.
• Figure 4: CWR wake potentials for a Gaussian bunch with $\sigma_z=0.5$ mm, obtained from the impedances in Fig. \ref{['fig:FS-PP-comparison']}. Left: free space (FS-TR). Right: parallel-plates shielding (PP-TR). The legend indicates the wiggler period $\lambda_w$. In the right panel, the dashed cyan curve shows the CSR wake for the same bunch computed with the parallel-plates model.
• Figure 5: Comparison of tracking results between two models with different wiggler period lengths. The left plot shows energy spread as a function of bunch current, while the right plot displays rms bunch length. The legend indicates the period lengths and their corresponding calculation models.