Kinetic Study On The Electron Positron Pairs Production In Strong Fields

In 1951,Schwinger studied the electron positron pairs production in strong field,and obtained the formula of pair generation rate of exponential suppression behavior,as well as the critical field strength of 10¹⁸V/m(corresponding to the laser intensity of10²⁹W/cm²).This outstanding work,that is,the effect of electron pair production from vacuum in strong field,is also known as Schwinger effect.The Schwinger effect is one of the important ways to explore the vacuum structure.In addition,the research can complement the theoretical module of quantum electrodynamics in strong field,and it is also of great significance for non perturbative calculation.With the development of modern laser technology,it is possible to verify the Schwinger effect.In this paper,we will study the fundamental problem in strong field,the frequency threshold of multiphoton process.At present,the main research point of this problem is the sensitivity dependence of frequency threshold.Recently,effective mass signatures in multiphoton pair production,published in PRL journal,is worthy of attention.This work introduces the concept of effective quality from a new perspective,which well explained that the frequency threshold is slightly larger than the estimated value ofω=2m/n（ωis the frequency threshold,m is the static mass of the electron,n is the integer representing the number of photons）.But the proposed effective mass model is very rough,only two parameters,the field strengthεand the photon number n,and they are not accurate.In this paper,we use quantum kinetic method to calculate and analyze the distribution characteristics of the deviation between the real multiphoton frequency threshold and the predicted value of effective mass formula,and find that it is related to momentum.Then we study the influence of the Gaussian envelope of the electric field on the multiphoton frequency threshold.The results show that the influence is very small and irregular.Later,we get the effective mass formula in momentum space by eliminating the influence factors of momentum.Combined with the calculation results of quantum dynamics method,the difference between them is analyzed,and the results show some regularity.For example,the deviation distribution of multiphoton process shows an approximate normal distribution,while the deviation distribution of single photon process shows a number of peaks,which indicates that there are obvious differences between single photon process and multiphoton process,which is worthy of further study.In addition,we find that two cases lead to the failure of the effective mass formula.One is that in the case of low momentum,there will be a sub peak structure on the left front of the multiphoton peak,With the increase of photon number,the sub peak will be superimposed with the sub multiphoton peak.the other is that in the case of high momentum,the sub peak structure disappears,and with the increase of photon number,the multiphoton peak will appear additional envelope structure.We also analyze the distribution of the deviation with respect to the photon number parameter n.The results show that there is an approximate linear relationship in the low photon number region,and the closer the linear relationship is with the increase of momentum.The above results are of great significance for the further study of the frequency threshold of multiphoton processes.