Study Of The Vacuum Electron Positron Pair Production Under Spatially Inhomogeneous Ultra-strong Electric Fields

In 1928,Dirac published the equation of motion for the relativistic quantum mechanics and predicted the existence of positrons.Heisenberg found that the existence of positrons means that the quantum vacuum is unstable,and wrote down the quantum correction to Maxwell's Lagrangian,and predicted many nonlinear quantum effects.Among them,the creation of electron and positron pairs,also known as Schwinger pair production,is one of the most important non-perturbative predictions of quantum electrodynamics.Theoretically,the study of vacuum pair production is not only of great significance in the field of non-perturbative physics,but also provides a simple theoretical model for more complex cases as a combination of classical field and quantum effect.Because the essence of vacuum pair production is a tunneling effect,the required electric field strength is very high,which is called critical field strength:E_cr¹0¹⁶V/cm.Since the last century,the realization of vacuum pair production in experiments has become a challenge,and the development of laser technology in recent decades has brought new possibilities to this field.On the other hand,the cleaver shaping of laser pulse can improve the particle production rate by several orders of magnitude,and it is expected to realize the vacuum pair creaton in the laboratory in the near future.It is very important to consider the spatial dependence of the external field in order to give the distribution of the number of particles produced by the vacuum pair in the laser experiment.In this paper,we use the 1+1 electric field model to study the production of vacuum electron positron pair under the inhomogeneous external electric field.In this thesis,we use numerical method to solve the equations of motion of quantum kinetic theory with spatial inhomogeneity,and consider various temporal pulse electric fields with finite spatial extents.We also use semi-classical approximation to study the effect of the spatial pulse shape on the particle production rate.1.The 1+1 dimensional quantum kinetic equations of motion are solved numerical-ly.The momentum distribution and the total number of created particles are calculated,and the influence of different spatial scales on particle production is analyzed.We find that the electric field can be considered approximately uniform when the spatial size is very large,but there are some differences between the general form of momentum spec-trum and the homogeneous case.In the case of a finite spatial extent where the spatial scale cannot be ignored,the momentum distribution loses the characteristics of the homo-geneous field.When the spatial scale of the external electric field is close to the Compton wavelength of the electron,the momentum of the two symmetrical temporal pulse fields will generate a new oscillation mode.Interestingly,the corresponding temporal pulse can not produce oscillation when the electric field is homogeneous.We also find that in the dynamically assisted case,the fast pulse and the slow pulse are not affected by the finite spatial scale similarly,which leads to the spatial scale dependence of the assistance mechanism.2.We consider the effect of temporal pulse frequency chirp on vacuum pair produc-tion in an electric field with finite spatial scale.For this purpose,we consider two kinds of oscillation frequencies,and calculate the particle number density corresponding to the chirp parameters in different spatial scales by numerical method.It is found that the chirp parameter has an obvious effect on the increase of the total number of created particles.For the fast oscillating electric field,the dependence of the total number of particles on the spatial size will be weakened when the chirp is maximum.When the frequency of the electric field oscillation is small,we find that the envelope phase effect of the exter-nal field can also be reflected in the momentum spectrum when the spatial width of the external field is finite.We find that the local density approximation hold for the electric field modes,so one can use the results of homogeneous field to analyze the results of inhomogeneous fields.3.The problem of vacuum pair production in a inhomogeneous electric field is studied by using the world line instanton approximation.In the case of the combination of the strong field and the weak temporal pulse field,different pulse shapes are selected to obtain the corresponding instanton equation.Since the equations only have analytical solutions for special external field forms,we choose numerical methods to solve them.We find that the generation rate of particles is different in tunneling and dynamically assisted fields when the spatial pulse is in different super Gaussian function forms.When tunneling process dominates,the higher rate of spatial change of the super Gaussian function lowers the particle production rate.In the dynamically assisted case,the particle production rate is consistent for all kinds of super Gaussian pulses.Finally,without changing the shape of the spatially inhomogeneous strong pulse,the dynamical assistance is less significant when the auxiliary weak field is in the oscillation form.However,unlike the previous case,the dynamical assistance is more significant when the frequency of weak field oscillation is large enough.