Laser Field Phase Velocity Distribution Of Laser Acceleration Of Electrons

With the rapid development of ultra-intense laser technologies, there has been much interest in the study of making use of intense laser fields to accelerate electrons in order to develop new type of small sized, high energy laser-driven accelerator. In this thesis, the phase slippage in the laser field, a key problem in vacuum laser accleration, has been investigated deeply. We obtained the distribution of subluminous phase velocity region and its scaling characteristics in widely used paraxial approximation of Gaussian laser field. At the same time, the reason causing the subluminous phase velocity to appear in optical field was investigated. The relationship between subluminous phase velocity and CAS (Capture and Acceleration Scenario) was analyzed. Furthermore, the subluminous phase velocity regions have been deduced and demonstrated in high-order corrected Gaussian field, exact nonparaxial field and more pratical ultra-short pulsed Gaussian laser field, respectively.First, the phase velocity of the widely used paraxial approximation Gaussian field has been studied. The results show that, for a focused laser beam propagaing in vacuum, there exists a subluminous wave phase velocity region surrounding the laser beam axis, which emerges just beyond the beam width and extends along the diffraction angle θ = 1/kw₀ . For example, when kw₀ =60 (k is the wave number, w₀ is the beam width at focus), the maximum difference between the curve of w(z) and V_φm =c is less than 0.01% within a Rayleigh length. In this region, the minimum phase velocity of the wave is lower than the light speed c. The magnitude of the phase velocity scales as V_φm - c(1 + b/(kw₀)²) . Combined with the longitudinal electric field force, it can form ideal acceleration channels for laser-driven acceleration in vacuum, which possess similar characteristics to that of a wave guide tube of conventional accelerators. Relativistic electrons injected into this region can be trapped in the acceleration phase and remain in the phase with the laser field for sufficiently long times, thereby receiving considerable energy from the field.This feature gives a reasonable explanation for the mechanism of CAS. The phase velocity of diffraction fields for uniform plane wave on a circular aperture has been investigated. It is shown that diffraction can result in subluminous phase velocity at certain points of optical field in vacuum. What the Lawson-Woodward theorem states, i.e. an electron will not gain any net energy from a laser field, is not valid, because it is based on the infinite plane wave propagation in free space. What has to be kept in mind is that all actual light beams have finite divergences due to diffraction. The subluminous phase velocity region in Gaussian beam is just caused by the factor kr²/2R{z).With the decreasing of the spot size of a focused laser beam, the error in describing the laser field with the paraxial approximation model will increase. By deriving the higher order corrections to describe a Gaussian laser field, the subluminous phase velocity region is further demonstrated. However the difference of phase velocity between paraxial and high order corrected field will emerge when the beam width kw₀ < 30. By using test particle simulation programs, the electron dynamics obtained using the paraxial approximation, the third-order, the fifth-order, and the seventh-order corrections are compared. The results reveal that, when kw₀≥60, the paraxial approximation field is good enough to reproduce all the electron dynamic characteristics. The above results strongly support the conclusions on CAS from our previous work.For a tightly focused laser beam, which usually appears in ultra-intense laser system, its diameter can be of the order of a few wavelengths, the exact nonparaxial solution of Gaussian beam must be used to describe the physics model. In order to demonstrate the subluminous phase velocity strictly, we use accurate expressions of Gaussian light beams to investigate the phase velocity distributions. These expressions are given in the angular-spectrum approach, therefore are with no any error. The results show there are steady subluminous phase velocity regions in a Gaussian light beam, which has the similar characteristics in essence with that of paraxial model. Especially for kw₀≥30, the results coincide with each other verywell. By expanding the exact solution, it can be seen clearly that the zeroth order term is just the paraxial one, so the paraxial approximation field is good enough to replace the exact field when the beam width is large to some extent. Recent developments in laser technology have yielded ultra-short, ultra-intense laser pulses. The commonly adopted description for a long laser pulse approximation where all the e-m components of the laser beam are multiplied by a common temporal shape factor can not be applied to femtosecond laser pulses because its spatial and temporal characteristics interact with each other during propagation. The phase velocity and wave propagation of such ultra-short laser pulse has been investigated. The results show the pulse correction factor w₀{1-(rδ)²/[ω₀w₀(z)]² would cause the phase velocity get smaller. Here ω₀ represents the central oscillatory frequency, and δ the spectral width. For an ultrashort laser pulse, the basic characteristics of its subluminous phase velocity distribution remain unchanged compared with that of monochromatic field. Furthermore, the area of its subluminous phase velocity region will enlarge due to the expanding of the curve V_φm=c toward the inner side of w(z).Synchronous acceleration is very important for the design of an accelerator. Concerning laser acceleration in vacuum, there existed the following fundamental and long-standing question which had not been satisfactorily answered, that is "Can a free electron get net energy gain or loss with a laser beam in its far field where the interaction length is unlimited". Here the crucial issue is just related to the phase velocity and periodical feature of optical fields. In this thesis, we put emphasis on the research of characteristics of phase velocity in a focused laser beam. This problem is proposed by our group first. It is very meaningful for promoting the development of CAS and other laser-driven acceleration schemes. Also, to study the subluminous phase velocity in optical field is meaningful and fundamental from the view of basic research in optical theory.