Beam Dynamics Of Harmonic Cavity In The Electron Storage Ring

In synchrotron light source,the beam lifetime is one of the important beam parameters.In low-emittance storage ring of the third generation light sources,the beam lifetime is usually dominated by Touschek scattering.In the beamline Phase II project of Shanghai synchrotron radiation facility(SSRF),a passive third harmonic cavity is to be installed to the storage ring for bunch-lengthening and instability-suppressing.In this study,the beam dynamics of the harmonic cavity has been investigated.The parameters of both active and passive operation are optimized to cancel the slope of RF voltage and lengthen the bunch.The operation scheme at different harmonic frequencies of the third harmonic,fourth harmonic,and fifth harmonic have been reviewed.The requirement and bunch lengthening effect of harmonic cavity at these three harmonic frequencies have been estimated using analytical model with active mode operation.Even though the third harmonic cavity require the highest harmonic voltage of 1.54 MV,or 35% and 69% more than that the fourth and fifth harmonic case respectively,it can give the highest lifetime improvement factor.In passive operation,the harmonic voltage is generated from the beam itself.The Touschek lifetime increases are estimated for optimum and non-optimum voltage flattening.A tolerance of the operation is studied in case that there is an imperfection on harmonic voltage via shunt impedance or beam current,and also a shift on detuning angle.When the parameters have met flatten potential conditions,the Touschek lifetime consequently improves by the factor of 3.8.When the detuning angle is slightly tuned beyond the detuning angle in the flattened potential condition,the Touschek lifetime rise until reaching the maximum factor of 4.16 with detuning angle of 97.22 degrees.When detuning angle is tuned further,there is a significant distortion on the particle distribution,leading to a drop on the improvement factor.Transient beam loading effect generated by the non-uniform filling pattern causes a variation of harmonic phase and reduces the lengthening effect as well as bunch lengthening effect crucially.The transient loading effects have been investigated using developed tracking code for 3 uniform filling cases and a non-uniform filling case.The tracking result shows the highest average lengthening factor of 4.5 in uniform filling case with 10 bunch trains.While,the non-uniform filling pattern with a long bunch train gives lowest lengthening factor of 1.7.Compared to the result from analytical model with the maximum lengthening factor of 5.3 without considering transient beam loading effect,the lengthening factors in uniform filling case with 2 bunch trains,5 bunch trains,and 10 bunch trains drop 48.0%,32.7%,and 13.5% respectively,moreover,in non-uniform filling case the factor decreases 67.3%.Transient beam loading effect caused by long bunch trains can greatly reduce the bunch lengthening effect of a harmonic cavity.An increase of synchrotron frequency spread due to nonlinearity of the voltage giving to the bunch is found by using tracking simulation.The simulation results the shift and an increase in synchrotron frequency spread after using harmonic cavity.This spread can help in damping coupled bunch instability through Landau damping.The field excited in the passive harmonic cavity depends on the bunch distribution.The effect caused by reduction of harmonic voltage generated by lengthened bunch distribution is also estimated by applying iteration method to both analytical model and tracking code simulation.The result shows a decrease of bunch lengthening effect in both cases of analytical model and tracking code simulation.According to the analytical result,bunch lengthening factor can be regained by adjusting the detuning angle but the bunch lengthening effect occurred from this detuning shift is still less than the maximum factor from using original(short)bunch form factor.However,from tracking code simulation,the detuning cannot be tuned further due to the Robinson instability.The transient beam loading effect combining with the lengthened bunch distribution can greatly reduce the bunch lengthening factor from harmonic cavity.Because in the uniform filling pattern cases,the distribution is much broader,the lengthened bunch could affect the bunch lengthening effect more than that in non-uniform filling with a long bunch train case.However,the eventual factor given by uniform filling is still better than the factor from the non-uniform filling.Siam Photon Source(SPS),located at Nakhon Ratchasima,Thailand,is a 2.5th generation synchrotron light source with the beam energy of 1.2 GeV.Beam lifetime in the SPS storage ring is limited by Touschek scattering and strongly depends on operation conditions,for examples,insertion devices,coupling,chromaticity or cavity voltage.The application of harmonic cavity to increase the beam lifetime in the SPS storage ring is investigated for the third harmonic,fourth harmonic and fifth harmonic cases.The lengthened bunch effect is also estimated using analytical method.The result agrees with SSRF case that the third harmonic cavity shows its advantage of the highest improvement factor.But if there is a limitation of the space,the fourth or fifth harmonic cavity can be the alternative option.