Study On The Ponderomotive And Microphonics Instability Of The Superconducting Cavities

The China Initiative Accelerator Driven System(Ci ADS)provides a safe and effective approach for nuclear waste disposal.The target of Ci ADS is to accelerate 5m A continuous wave(CW)proton beam to 500 Me V at the beam power up to 2.5 MW with beam loss limiting of less than 0.1W/m.To achieve this target,a high stability and reliability linac accelerator is required.The experience on Chinese ADS Front-end(CAFe),which is a 25 Me V Demo facility of the Ci ADS,shows that the mechanical instabilities can severely affect the electromagnetic field of the superconducting cavities.Ponderomotive and microphonics effects are the main sources of the mechanical instabilities.The ponderomotive effect is caused by the static or quasi-static(relative to the cavity field building time)mechanical force acting on the superconducting cavity,such as pressure of helium liquid or force of the tuner.This effect may leads to a selfexcited coupling oscillation between electromagnetic field and mechanical deformation of cavity wall via Lorentz force(which is caused by radiation pressure on the cavity walls).Therefore,Ponderomotive effect is a kind of the resonance electro-mechanical.Microphonics effect is the forced oscillation of cavity when cavity absorbs the energy of mechanical wave from the external,which induces the periodic fluctuation of cavity resonant frequency,ultimately leads to periodic amplitude and phase fluctuation on electromagnetic field.Generally,the microphonics slightly disturb the cavity frequency since the mechanical wave usually with energy lower than electromagnetic wave.Many studies related to the coupling instability of cavity electromagnetic field and mechanical were published in other Labs.However,most of those studies focus on the instabilities on the high-? superconducting cavities that operated in pulsed mode but paid less attention on the low-? superconducting cavities that operated in CW mode.In view of this situation,this paper focuses on the evaluation of the electromagnetic and mechanical performance of the superconducting cavities on the current Ci ADS,as well as the rejection of the cavity instabilities in the future beam commissioning.The following studies are carried out: Improvement and complement of physical analysis methods to the interaction between electromagnetic and mechanical;Developed the simulation program of RF system;Simulation and evaluation of ponderomotive and microphonics effect;Study parameters of electromagnetic and mechanical;Measurement instabilities of ponderomotive and microphonics effect.Analysis of electromagnetic and mechanical interaction includes two key issues.The first issue involves the relations between the forces(Lorentz force and mechanical force)and the elastic deformation of cavity,as well as the conversion between the mechanical energy and electromagnetic energy.The second issue is the establishment process of the beam and generator induced electromagnetic field under the time-varying cavity resonance frequency.For the first issue,the current approach is to obtain the correlation between the cavity detuning and its stored energy by utilizing the integral formula of electromagnetic energy.This method is suitable for the qualitative analysis,or solving the of static equilibrium equations;however,it is difficult to calculate the dynamical process quantitatively with this method.For the second issue,it is difficult to deal with the time-varying process by using traditional transfer function-based method.We develop a discretized iterative algorithm derivate from the impulse response model of the RLC parallel resonant circuit,to solve the generator and beam induced field under the time-varying resonance frequency.Furthermore,the elastic deformation of cavity wall is equivalent to the rectilinear motion of the capacitor plate of the RLC parallel equivalent circuit under the spring force.The Lorentz force,the external mechanical force and the elastic resilience on cavity wall,are equivalent to the electromagnetic force between the capacitor plates,the pressure on the plates,and the tension of the spring,respectively.The resonant frequency variation caused by the deformation of cavity wall and the corresponding variation of electromagnetic energy,can be described by the variation of capacitance and stored energy caused by the distance changing between the two plates.Based on the discussion above,this paper,for the first,obtains an iterative equation satisfying the energy conservation equation of electromagnetic-mechanical coupling dynamics.The equation is developed to analyze the time-varying dynamical process of superconducting cavity under the ponderomotive and microphonics effect.In addition,the correlation between the static equilibrium equation of cavity under Lorentz force and mechanical force and potential energy of electromagnetic-mechanical coupling,is deduced based on the model.The numerical solution of the non-steady-state equilibrium pole of cavity with the existence of the ponderomotive effect,is able to obtained as well.This results are consistent with the traditional methods and have been tested on the superconducting cavity at CAFe facility.Base on the discretized iterative algorithm and electromagnetic-mechanical coupling theory,a simulation program is developed to study the ponderomotive and microphonics effects.Phenomena such as field oscillation and sharp amplitude drop that appeared in CAFe facility are reproduced by the program.This program provides a basis for the future study related with ponderomotive effect.Furthermore,other significant issues such as the impact of ponderomotive effects on RF amplitude and phase stabilities,as well as the correlations between mechanical time constant,tuning error and Lorentz force detuning(in resonant state),are studied with the help of the program.According to the simulation results of ponderomotive effect,we calibrate the limitations of mechanical and electrical field strength of superconducting cavities.The limitations require that the ratio of Lorentz force detuning to the cavity half-bandwidth should not exceed the value of 3.Regarding to microphonics effects,we studied the impacts of frequency and strength of microphonics on the stabilities of RF field.The results show that microphonics mainly effect phase stability of superconducting cavity,and the effect depends on the ratio of the oscillation frequency of the microphonics to the cavity resonant frequency,and depends on the ratio of the frequency microphonics to the cavity half-bandwidth.According to the requirements of RF stabilities on Ci ADS(0.1% for amplitude and 0.1 deg for phase),we provide a basis for the requirements of the limits of the microphonics and ponderomotive effects.To clearly understand the characteristic of the cavity,we measure the related parameters such as the loaded quality factor and Lorentz force detuning coefficient.Furthermore,based on the theoretical model in this paper,we developed a novel algorithm to measure the mechanical time constant and the cavity resonant frequency by using the information from the cavity field falling edge.This method is demonstrated on CAFe.Compared with conventional measurement methods of mechanical impulse response,this method is easy and efficient.Compared with conventional resonance criterions of minimal-reflection method or maximum cavity voltage,this method can measure the eigenfrequency more accurate.In summary,a mechanical vibration monitor system in combination with a spectrum measurement system are constructed,to measure the ponderomotive effects and microphonics noise on the SC cavities of CAFe.We detuned the cavity by modulating the frequency of the cavity input,the ponderomotive effects-induced instabilities were observed.In the next step,the correlation among cavity field,cavity detuning and the ponderomotive-induced vibration intensity are obtained.Further,by measuring the mechanical vibration and RF spectrum,we studied the relation between microphonics-induced instabilities and mechanical vibration source;some microphonics sources were therefore located and then eliminated.After a continuous effort,the stabilities of the SC cavity are improved.