Investigation of beam self-polarization in the future $e^{+}{e}^{-}$ circular collider

The use of resonant depolarization has been suggested for precise beam energy measurements (better than 100 keV) in the $e^{+}{e}^{-}$ Future Circular Collider (FCC-$e^{+}{e}^{-}$) for $Z$ and $WW$ physics at 45 and 80 GeV beam energy respectively. Longitudinal beam polarization would benefit the $Z$ peak physics program; however it is not essential and therefore it will be not investigated here. In this paper the possibility of self-polarized leptons is considered. Preliminary results of simulations in presence of quadrupole misalignments and beam position monitors (BPMs) errors for a simplified FCC-$e^{+}{e}^{-}$ ring are presented.

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Figure 1

LEP polarization wiggler (figure from [18]).

Figure 2

Parameter values vs. polarization time for one wiggler at 45 GeV for various values of $N$. Top left: $B^{+}$. Top right: Asymptotic polarization. Center: ${\tau }_{10\%}$. Bottom left: Energy spread. Bottom right: Energy lost per turn.

Figure 3

Parameter values vs. polarization time for different numbers of wigglers units at 45 GeV with $N=6$ and $L^{+}=1.3\mathrm{m}$. Top left: $B^{+}$. Top right: Asymptotic polarization. Center: ${\tau }_{10\%}$. Bottom left: Energy spread. Bottom right: Energy lost per turn.

Figure 4

Twiss and dispersion functions in the wiggler section with $B^{+}=0.7\mathrm{T}$. The Twiss functions are practically unchanged; the peak $|D_x|$ (and orbit deviation) is 8 mm.

Figure 5

Polarization vs. spin tune after orbit is corrected by using all 1096 correctors with ${\delta }_y^Q=200\mu \mathrm{m}$, $\mathrm{w}/\mathrm{o}$ BPMs errors and in presence of 4 wigglers with $B^{+}=0.7\mathrm{T}$. $60°/60°$ FODO.

Figure 6

$60°/60°$ FODO. Left: Polarization vs. spin tune after orbit is corrected with 1096 correctors with ${\delta }_y^Q={\delta }_y^M=200\mu \mathrm{m}$ and 10% BPM calibration error; 4 wigglers with $B^{+}=0.7\mathrm{T}$. Right: adding the correction of $\delta {\widehat{n}}_0$ through harmonic bumps.

Figure 7

Polarization vs. spin tune after orbit is corrected with 1096 correctors in presence of BPMs errors with $B^{+}=3.9\mathrm{T}$.

Figure 8

$60°/60°$ FODO. Left: Polarization vs. spin tune after orbit is corrected with 110 correctors with ${\delta }_y^Q={\delta }_y^M=200\mu \mathrm{m}$ and 10% BPM calibration error; 4 wigglers with $B^{+}=0.7\mathrm{T}$. Right: adding the correction of $\delta {\widehat{n}}_0$ through orbit bumps.

Figure 9

$60°/60°$ FODO. Left: Polarization vs. spin tune after orbit is corrected with 1096 correctors with ${\delta }_y^Q=200\mu \mathrm{m}$ and no BPMs errors. Right: adding the correction of $\delta {\widehat{n}}_0$ through orbit bumps.

Figure 10

Vertical closed orbit change due to the 8 3-correctors harmonic bumps for the 80 GeV case.

Figure 11

$60°/60°$ FODO. Polarization vs. spin tune after orbit is corrected with SVD in presence of BPMs errors. $\delta {\widehat{n}}_0$ is corrected by 8 3-correctors harmonic bumps (left) or by 8 dispersion-free 5-correctors harmonic bumps (right).

Figure 12

Polarization vs. spin tune after orbit is corrected with SVD in presence of BPMs errors and $\delta {\widehat{n}}_0$ is corrected with 5-correctors harmonic bumps. Left: $Q_s=0.3$. Right: $Q_s=0.9$.

Figure 13

$90°/90°$ FODO. Left: Polarization vs. spin tune after orbit is corrected with 1096 correctors with ${\delta }_y^Q=200\mu \mathrm{m}$ and $\mathrm{w}/\mathrm{o}$ BPMs errors; 4 wigglers with $B^{+}=0.7\mathrm{T}$. Right: adding the BPMs errors.

Figure 14

$90°/90°$ FODO. Left: Polarization vs. spin tune after orbit and $\delta {\widehat{n}}_0$ correction with ${\delta }_y^Q={\delta }_y^M=200\mu \mathrm{m}$ and 10% BPMs calibration error; 4 wigglers with $B^{+}=0.7\mathrm{T}$ (45 GeV). Right: Polarization vs. spin tune after orbit and $\delta {\widehat{n}}_0$ correction with ${\delta }_y^Q={\delta }_y^M=200\mu \mathrm{m}$ and 10% BPMs calibration error, no wigglers (80 GeV).