Optimization Of The "acceleration-focusing" System Of The Cold Atom Electron Source Based On The Finite Element Method

As is known,the traditional electronic sources are mainly generated by several types of electron guns,namely the hot cathode microwave electron gun,the photocathode microwave electron gun,and the field emission electron gun.Among them,the hot cathode microwave electron gun has the advantages of high average current density,quickly accelerating to relativistic speed,and rapidly shooting out of the cavity.However,the existence of back bombardment will increase the inter-bunch energy spread of the electron beam and reduce the beam quality.Meanwhile,the photocathode microwave electron gun has a series of advantages such as high brightness,high peak current,and fast acceleration,but also has the disadvantages of insufficient transverse coherence and inability to meet the spatial resolution requirements for electron diffraction experiments.The field emission electron gun has the advantages of high average current density and short start-up time,but the electron density in the beam group is not enough,the imaging is too slow,and the time resolution cannot meet the practical requirements.Compared to the conventional electron sources,the prominent advantage of the ultracold electron source lies in its extremely low temperature(10K or lower)achieved through laser cooling and ionization of the plasma.At low temperature,the phase space density of the electron beam is higher,the volume is smaller,and the divergence is several orders of magnitude lower than that of the typical electron beam,showing very small divergence.At the same time,the ultralow temperature can significantly improve the transverse coherence of the electron source.However,the electrons produced by the cold atom electron source need to be extracted and accelerated by the static electric field,and then undergo magnetic focusing to meet certain application requirements.Inevitably,this process will increase the effective electron temperature of the electron beam,thus reducing important qualities such as transverse coherence,brightness,and emittance of the electron beam.Therefore,this paper aims to use the finite element method to numerically simulate the "acceleration-focusing" system of the cold atom electron source in the static electric and magnetic fields,and to optimize the parameters to effectively improve the quality of the electron source,so as to meet the requirements in coherent diffraction imaging and high-resolution transmission electron microscopy experiments.Firstly,in terms of extraction and acceleration of the electron source in the static electric field,we designed a static electric field structure consisting of four electrode plates.Then,through simulation and analysis,we compared the effects of different electromagnetic field boundary conditions,electrode plate parameters,and load voltages.The results showed that the periodic electromagnetic field boundary conditions were more in line with the physical reality of the electron source system in the bounded simulation area.Meanwhile,we found that selecting matching electrode plate spacing and voltage can achieve the "acceleration-drift-acceleration" process of the electron beam in the multi-stage acceleration structure composed of four electrode plates.This is not only conducive to compressing the overall size of the electron beam box and improving its longitudinal coherence,but also beneficial for optimizing the transverse coherence of the electron beam based on the static electric lens effect and reducing the transverse emittance.Additionally,the simulation showed that the thickness of the electrode plate had an important impact on the final quality of the generated electron source,and a smaller thickness should be selected within the range allowed by the experimental conditions.Finally,we compared and analyzed the four-electrode structure used in this paper with the static electric field structure composed of two electrode plates commonly used.The results showed that the multi-stage static electric field based on the four electrode plates can effectively improve the quality of the electron source,i.e.reduce energy spread,emittance,and effective electron temperature.After extracting the electron beam from the static electric field,we analyzed and simulated the magnetic focusing of the electron beam using a solenoid system,and optimized the parameters of the solenoid focusing system.The results showed that the radial magnetic field played a major role at the entrance and exit of the solenoid,while the axial magnetic field played a major role inside the solenoid.The closer the solenoid entrance is to the static electric field exit,the smaller the waist radius of the electron beam after magnetic lens focusing,and the higher the quality of the electron beam.At the same time,the closer the sample is to the solenoid exit,the stronger the magnetic field required for focusing,and the smaller the waist radius of the electron beam when it reaches the sample.Based on the optimization of parameters such as the plate spacing,voltage,outer diameter,thickness of the electrode plates,and magnetic focusing system of the static electric field structure,a high-quality electron beam was obtained with an effective electron temperature of about 8.2K,energy spread of about 10-4,and normalized emittance of about 10-7mm.mrad.