Study On Electron Acceleration Using High-power Laser Beams In Vacuum

Considerable attention has focused on the possibility of using high-powerful laser beams to directly accelerate electrons in vacuum because of the rapid development in ultrashort high-power laser technology. Several methods to accelerate electrons by using laser beams have been proposed, and the main features of laser-accelerated electrons have been reviewed. The ultimate goal of electron acceleration is obviously to reach GeV or even TeV energies, a task that requires the use of interaction between laser fields of extremely high intensity with particles. Such intensities may be produced in the laboratory by focusing over extremely small spatial dimensions, typically a few microns. The very small spot size of laser beams is comparable with the wavelength, for which the paraxial theory is invalid and vectoriality, nonparaxiality of laser beams have to been considered.First, some basic methods to the exact solution of electromagnetic field are introduced, including the vectoral Rayleigh-Sommerfeld diffraction integrals, angular spectrum representation, perturbation power series method, etc. The models of laser particle are expatiated, including the ponderomotive potential and the relativistic electron dynamics. Based on the above theory and methods, the main results obtained in this dissertation are as follows:Starting from the vectorial Rayleigh-Sommerfeld diffraction integrals approach, the focusing and diffraction properties of plane wave propagating through a thin lens followed by a small circular aperture have been studied beyond the paraxial regime. A strict analytical expression for the axial field distribution of plane waves has been derived. Under the condition that R>>λ, the analytical field expressions have been deduced, which permit us to treat the far-field, paraxial field, axial field expressions and the expressions without lens as special cases of our general result. The vectorial approach should be used if the aperture dimension is comparable with the wavelength, or the focusing is strong.The concept of partially coherent vectorial nonparaxial ChG beams has been introduced, where the partial coherence, vectorial property and nonparaxiality of ChG beams have been all taken into consideration. Based on the generalized vectorial Rayleigh diffraction integrals, the closed-form propagation expressions for the cross-spectral density matrix and intensity of partially coherent vectorial nonparaxial ChG beams in free space have been derived. The fully coherent vectorial nonparaxial ChG beams, vectorial nonparaxial GSM beams, and their corresponding scalar paraxial and far-field results have been obtained and treated as special cases of our general expressions. The vectorial property and nonparaxiality of partially coherent ChG beams are mainly determined by the f and f_σparameters, but the decentered parameter also affects their behavior. Only for small values of f and f_σparameters the scalar paraxial approach is allowable. In addition, the generalized vectorial Rayleigh diffraction integrals are a useful tool and applicable not only to vectorial nonparaxial GSM beams, but also to other types of partially coherent vectorial nonparaxial beams like ChG ones, showing general applicable advantages. The propagation of partially coherent vectorial nonparaxial ChG beams can be treated by using the Wigner distribution function matrix and the same results will be obtained because the two approaches are equivalent.Using the relations between the transverse and longitudinal electric-field components, the analytical expression of longitudinal electric field of the LG beam has been derived. The general physical characteristics of acceleration electrons by using LG are studied. It is shown that only the longitudinal electric field of the LG beam with mode indices p and l=1 can be used to accelerate electrons. The linearly-and circularly-polarized LG beams with mode indices p and l=1 play the same role in laser electron acceleration because there is not axial longitudinal electric field of polarized LG beams in y direction. Some physical characteristics, such as phase and group velocities of the axial optical field, the slippage distance, accelerating potential, and energy gain of electrons etc., are discussed. The phase velocity of electric field on the axis is greater than the light velocity c in vacuum. The accelerating potential oscillates with mode index p increasing. The energy gain is dependent on the waist width w₀, mode index p, and the initial phaseφ₀. A finite energy gainΔW takes place over a finite interaction range and is maximized when some conditions are satisfied.The general features of the direct acceleration of electrons by using linearly and circularly polarized BG beams in vacuum have been studied. The linearly and circularly polarized BG beams of order n=1 have non-zero axial electric field on axis and can be used to accelerate electrons. The phase velocity of electric field on the axis is greater than the light velocity c in vacuum. The energy gainΔW depends on the waist width w₀, wave number k and its transversal componentα, acceleration distance z₀ and initial phaseφ₀. For circularly polarized BG beams,ΔW is additionally dependent on the angleθ. If lettingθ=0, the results for accelerating field, accelerating potential, energy gain of circularly polarized BG beams reduce to those of linearly polarized BG beams. For a fixed laser power, z_s increases with w₀ increasing andΔW_max increases with w₀ decreasing.The direct acceleration of electrons by using two linearly polarized and circularly symmetric crossed LG beams with equal frequency is proposed and studied. The resulting transverse and longitudinal electric fields have been derived. The initial phase difference plays a key role. For two linearly polarized crossed LG beams with a phase difference ofÏ€-rad the resulting axial transverse electric field, axial transverse and longitudinal magnetic fields disappear, and the resulting longitudinal electric field reaches a maximum, which can be used to effectively accelerate electrons in vacuum. The slippage distance z_s increases with mode index p decreasing and waist width w₀ increasing. For a fixed laser power, the maximum energy gainΔW_max increases with p and w₀ decreasing.The general characteristics of accelerating electrons by using two polarized crossed BG and Bessel beams with equal frequency has been studied and the analytical expressions for the resulting transverse and longitudinal electric fields of two crossed BG and Bessel beams, the slippage distance z_s, accelerating potential and energy gainΔW have been derived. Two crossed BG or Bessel beams of the same order (w=0 or n=1) have a nonzero resultant longitudinal electric-field in the z-axis and can be used, in principle, to accelerate electrons. The initial phase difference plays a crucial role. For two linearly polarized crossed BG or Bessel beams with aÏ€-rad phase difference, the resultant transverse electric field vanishes, and there exists the non-zero resultant longitudinal field in the z-axis, which can be maximized and used to accelerate electrons. The conditions that the energy gain is maximized have been discussed. In comparison with the case of a single Bessel beam, the larger energy gain and accelerating gradient can be achieved in the interaction distance z_s by using two crossed Bessel beams.Based on the method of the perturbation series expansion, the higher-order field corrections of TEM_1,0-mode H-G beams are derived, and used to study the electron acceleration by a tightly focused H-G beam. The illustrative numerical calculation results show that for the off-axis injection the field contributions of the terms up to order f³ have to be included, and the terms higher than the order f³ may result in a divergent energy gain. In the interaction of the electron and TEM_1,0-mode H-G beam the injection parameters including the injection energyγ₀ and the injection angleθand laser parameters including laser power P, the waist width w₀, and the initial phaseψ₀ both affect the energy gainΔW. The asymmetry of the transverse and longitudinal electric-field components along the electron trajectories results in the electron acceleration. For the small injection energyγ₀ the energy gainΔW is very small due to the reflection of electrons and for the large injection energyγ₀ΔW decreases because electrons penetrate through the LEM_1,0-mode H-G beam over a short time. The initial phaseψ₀ which alters the field distribution affects the final energy gain. The electron on-axis injection can be treated as a special case. For such a case the higher-order corrections can be neglected and the result is consistent with the previous one. The energy gain can be optimized to achieve the GeV energy gain by a suitable choice of injection parameters and the injection parameters.The results obtained in this dissertation may be useful for design and application of electron acceleration. Currently, the theory and application in high-laser acceleration electron are in rapid development. However, there are many problems which deserve a further and deep study.