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摘要: 高次谐波腔在电子储存环中被广泛应用，他可以拉伸电子束团长度、降低束团峰值电流，从而减弱束内散射（IBS）效应、提高Touschek寿命，并提供Landau阻尼，这对于运行在超低发射度或低能区的储存环尤为重要。为了在不增加额外硬件成本的情况下进一步展拉伸团长度，研究在双高频系统中的相位调制方案。进行了逐圈模拟跟踪，跟踪程序包含了纵向运动逐圈迭代（包括相位调制）和同步辐射激发效应，并给出了相位调制引起束团展宽机理的简要理论分析。模拟结果表明，束团峰值电流可以在高次谐波腔作用后，经相位调制后进一步降低，从而减弱IBS效应并提高Touschek寿命。尽管调制会引起能散增加，导致来波荡器辐射的高次谐波辐射亮度降低，但基波辐射的亮度得到了提升。Abstract:
Background High harmonic cavities are widely used in electron storage rings to lengthen the bunch, lower the bunch peak current, thereby reducing the IBS effect, enhancing the Touschek lifetime, as well as providing Landau damping, which is particularly important for storage rings operating with ultra-low emittance or at low beam energy.Purpose To further increase the bunch length without additional hardware costs, the phase modulation in a dual-RF system is considered.Methods In this paper, turn-by-turn simulations incorporating random synchrotron radiation excitation are conducted, and a brief analysis is presented to explain the bunch lengthening mechanism.Results Simulation results reveal that the peak current can be further reduced, thereby mitigating IBS effects and enhancing the Touschek lifetime. Although the energy spread increases, which tends to reduce the brightness of higher-harmonic radiation from the undulator, the brightness of the fundamental harmonic can, in fact, be improved. -
Figure 1. RMS bunch length, energy spread and particle distribution in longitudinal coordinate
Figure 3. Third-harmonic cavity working in an overstretched status. The electrons plotted in magenta and red dot in (b) have the frequency indicated by the color bar in (c)
Figure 4. Beam current profile and phase space for the dual RF over stretched case with RF phase modulation
Figure 8. Electron trajectories in phase space without radiation damping and quantum excitation
Table 1. Beam parameters for simulation
beam energy/GeV ring circumference/m momentum compaction energy loss per turn/keV initial energy spread/% 0.5 76.78 8.15×10−3 4.34 0.038 initial bunch length/mm main RF frequency/MHz main RF voltage/kV longitudinal damping time/ms bending magnet field/T 2.4 499.8 750 29.5 1.31 
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Table 2. Parameters for Touschek lifetime calculation and undulator parameters used for radiation calculation
natural emittance/(nm·rad) transverse coupling βx/m βy/m beam current/mA bunches undulator periods/mm undulator length/m 8.5 10% 7.5 4 500 100 20 3
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emittance counting IBS/(nm·rad) energy spread counting IBS/10−4 touschek lifetime/h single
RFdual
RFdual RF with
RF modulationsingle
RFdual
RFdual RF with
RF modulationsingle
RFdual
RFdual RF with
RF modulation16.2 10.7 8.9 5.6 4.5 9.6 1.4 7.1 20.7
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