Photon Kinetics In The Interaction Of Laser Pulses With Plasmas

It is well known that laser-plasma interaction can be self-consistently described byMaxwell wave theory and hydromechanics. The laser pulse obeys Maxwell’sequations, and the plasma is governed by fluid equations. On the other hand,according to the corpuscular property of light a laser pulse can be regarded as anordered particle system composed of photons with various modes (different energiesand momenta). Therefore, it is reasonable to describe the laser pulse by means of thekinetic theory. In this dissertation some phenomena associated with the interaction ofstrong laser pulses with plasmas are studied based on photon kinetic theory,including the dynamical evolution of a single photon in plasma wave, the collectiveeffect of a photon system to plasma wave, the propagation and evolutioncharacteristics of laser pulse in background plasma wave and energy exchangebetween the laser pulse and the plasma wave. In theory, the evolution characteristicsof a laser pulse in a plasma wave can be analyzed by making statistical summation ofall photon behaviors, where the statistical weight is photon number distributionfunction determined by photon kinetic equation. The research approach in thisdissertation is to solve the photon dynamics in plasma wave first, and then extend toobtain the evolution characteristics of the laser pulse in plasma wave based on thekinetic theory. In the research area of laser-plasma interaction, our research approachis a different method from the traditional Maxwell-fluid theory, and the researchresults are consistent.In addition, the existing research increasingly indicates that the nonlinear QEDvacuum polarization is a non-ignorable phenomenon due to the exciting of strongfields. Furthermore, this vacuum polarization can be coupled with plasma effects toproduce some new physical effects. In this dissertation the possible new frequencyshifting of a laser pulse in plasma wave induced by the coupling of vacuum polarization with plasma effects is investigated by using Maxwell’s equations andplasma fluid model.To summarize, this dissertation includes three parts:In the first part, the dynamical evolution behaviors of photons in a backgroundplasma wave are investigated by means of photon Hamiltonian dynamical theory,including photon evolution trajectory in phase space, photon acceleration andtrapping effects in plasma wave, and photon Landau damping to the plasma wave,etc. The cases of both small-amplitude and large-amplitude plasma waves arediscussed. In small-amplitude plasma waves the perturbation method is applicable.And in large-amplitude plasma waves the photon evolution is discussed by solvingnon-perturbative dynamical equations. These questions will be discussed in detail insecond and third chapters;In the second part, based on photon kinetic theory a one-dimensional solvablekinetic model of photons is established to describe the interaction of a laser pulsewith a plasma wave. By extending the motion behaviors of a photon in plasma waveto the whole laser pulse, the propagation and evolution of the laser pulse in theplasma wave are obtained. Our model is the application and extension to photonkinetic theory, and some results obtained in this dissertation are consistent withearlier publications based on the Maxwell’s equations and fluid model. The detaileddiscussion is presented in the fourth chapter;In the third part, the coupling effects of QED vacuum polarization with plasmaprocess are investigated, which could produce some new physical phenomena. Weanalyze the frequency shifting process of a laser pulse propagating in a plasma wave,and obtain the new frequency shifting induced by the coupling effects of QEDvacuum polarization with plasma process, which can be regarded as theenhancement effect of QED vacuum polarization in plasmas. The detailed discussionis presented in the fifth chapter. The main innovation findings in this dissertation sum up as following several points:1. In the framework of Hamiltonian dynamical theory the photon dynamicalbehaviors in a plasma wave with arbitrary amplitude are investigated. By solvingphoton dynamical equations the photon frequency shifting and evolution trajectoryin phase space are analyzed. The research results show that photons with differentmodes will evolve in different types of trajectories in phase space, which reflect thesituation of photon trapping in plasma waves. The trapped possibility and conditionof photons in a given plasma wave are analyzed in detail;2. A collective resonance phenomenon of a photon system with plasma wave, photonLandau damping, is discussed in this dissertation. We analyze the photon Landaudamping effect by means of the law of energy conservation for the first time. Andthen, the results are extended to the laser pulse, and the Landau damping effectoriginated from the laser pulse to plasma wave is proposed for the first time, whichis a new mechanism of energy exchange between laser pulse and plasma wave. Theresearch results show that the laser pulse can produce Landau growth effect to adriven plasma wave under normal conditions, and this growth effect is non-ignorable.The Landau growth means that the energy is transmitted from the laser pulse to theplasma wave, and an instability is produced. Furthermore, the photon Landaudamping effect is also discussed by using of photon kinetic theory in this dissertation,which is a different theoretical method from the consideration of energyconservation. The same results are obtained under the linear approximation, whichvalidate the rationality and validity of our theory and results;3. Regarding the laser pulse as an ordered photon system with various modes, theevolution of a laser pulse in a plasma wave can be described by the time-dependentphoton number distribution function (i.e. the statistical weight of photons withvarious modes in the entire photon system). Then we construct a one-dimensionalsolvable kinetic model to describe the interaction of the laser pulse with plasmawave. By analytical solving the photon kinetic equation a time-dependent photon number distribution is approximately obtained for the first time, which reveals thepropagation and evolution characteristics of the ultra-short laser pulse. The photonnumber distribution function is the connecting link between the laser pulse andsingle photon;4. By using the photon number distribution function and dynamical behaviors ofphotons in plasma wave, the propagation and evolution of the laser pulse inlarge-amplitude plasma wave are discussed, including the evolution characteristics incoordinate space (the effect of compressing and stretching and the pulse splitting)and frequency domain space (the frequency shift of the entire laser pulse) and theenergy transformation between the laser pulse and the plasma wave. The researchresults are generally consistent with the conclusions analyzed in the framework ofMaxwell’s equations and fluid model in earlier publications;5. The coupling effects of QED vacuum polarization induced by strong laser withplasma effects are investigated, and they can produce some new physical phenomena,for example the frequency shifting of a laser in plasma wave discussed in thisdissertation. These new phenomena must be induced in the presence of plasmas, sothey are enhancement effects of the vacuum polarization in plasmas substantially. Itis shown that the enhancement effect originates in two contributions: the screeningeffect of vacuum polarization on electrons and ions in plasmas, and theponderomotive force of the laser pulse acting on the virtual particles in vacuum.