Photon plasma--wave interaction via Compton scattering

The Kompaneets theory of photon kinetic evolution due to the Compton effect in the absence of absorption and emission is extended to the case of the Vlasov plasma wave oscillations. Under the assumption that the electron distribution function at equilibrium is perturbed by a solution of the linearised Vlasov equation in the long-wavelength limit, a solution of the Kompaneets kinetic equation for the photon distribution function is found and discussed

Second order nonlinear gyrokinetic theory : From the particle to the gyrocenter

A gyrokinetic reduction is based on a specific ordering of the different small parameters characterizing the background magnetic field and the fluctuating electromagnetic fields. In this tutorial, we consider the following ordering of the small parameters: $\epsilon\_B=\epsilon\_\delta^2$ where $\epsilon\_B$ is the small parameter associated with spatial inhomogeneities of the background magnetic field and $\epsilon\_\delta$ characterizes the small amplitude of the fluctuating fields. In particular, we do not make any assumption on the amplitude of the background magnetic field. Given this choice of ordering, we describe a self-contained and systematic derivation which is particularly well suited for the gyrokinetic reduction, following a two-step procedure. We follow the approach developed in [Sugama, Physics of Plasmas 7, 466 (2000)]:In a first step, using a translation in velocity, we embed the transformation performed on the symplectic part of the gyrocentre reduction in the guiding-centre one. In a second step, using a canonical Lie transform, we eliminate the gyroangle dependence from the Hamiltonian. As a consequence, we explicitly derive the fully electromagnetic gyrokinetic equations at the second order in $\epsilon\_\delta$

Conservative dissipation: How important is the Jacobi identity in the dynamics?

Hamiltonian dynamics are characterized by a function, called the Hamiltonian, and a Poisson bracket. The Hamiltonian is a conserved quantity due to the anti-symmetry of the Poisson bracket. The Poisson bracket satisfies the Jacobi identity which is usually more intricate and more complex to comprehend than the conservation of the Hamiltonian. Here we investigate the importance of the Jacobi identity in the dynamics by considering three different types of conservative flows in R3 : Hamiltonian, almost-Poisson and metriplectic. The comparison of their dynamics reveals the importance of the Jacobi identity in structuring the resulting phase space

Kinematics of fluid particles on the sea surface. Hamiltonian theory

We derive the John-Sclavounos equations describing the motion of a fluid particle on the sea surface from first principles using Lagrangian and Hamiltonian formalisms applied to the motion of a frictionless particle constrained on an unsteady surface. The main result is that vorticity generated on a stress-free surface vanishes at a wave crest when the horizontal particle velocity equals the crest propagation speed, which is the kinematic criterion for wave breaking. If this holds for the largest crest, then the symplectic two-form associated with the Hamiltonian dynamics reduces instantaneously to that associated with the motion of a particle in free flight, as if the surface did not exist. Further, exploiting the conservation of the Hamiltonian function for steady surfaces and traveling waves we show that particle velocities remain bounded at all times, ruling out the possibility of the finite-time blowup of solutions

From recollisions to the knee: A road map for double ionization in intense laser fields

We examine the nature and statistical properties of electron-electron collisions in the recollision process in a strong laser field. The separation of the double ionization yield into sequential and nonsequential components leads to a bell-shaped curve for the nonsequential probability and a monotonically rising one for the sequential process. We identify key features of the nonsequential process and connect our findings in a simplified model which reproduces the knee shape for the probability of double ionization with laser intensity and associated trends

Recollisions and correlated double ionization with circularly polarized light

It is generally believed that the recollision mechanism of atomic nonsequential double ionization is suppressed in circularly polarized laser fields because the returning electron is unlikely to encounter the core. On the contrary, we find that recollision can and does significantly enhance double ionization, even to the extent of forming a "knee", the signature of the nonsequential process. Using a classical model, we explain two apparently contradictory experiments, the absence of a knee for helium and its presence for magnesium

Variational method for locating invariant tori

We formulate a variational fictitious-time flow which drives an initial guess torus to a torus invariant under given dynamics. The method is general and applies in principle to continuous time flows and discrete time maps in arbitrary dimension, and to both Hamiltonian and dissipative systems.Comment: 10 page

Hamiltonian formulation of reduced Vlasov-Maxwell equations

The Hamiltonian formulation of the reduced Vlasov-Maxwell equations is expressed in terms of the macroscopic fields D and H. These macroscopic fields are themselves expressed in terms of the functional Lie-derivative generated by the functional S with the Poisson bracket [.,.] for the exact Vlasov-Maxwell equations. Hence, the polarization vector P= (D-E)/(4pi) and the magnetization vector M=(B-H)/(4pi) are defined in terms of the expressions 4pi P=[S,E]+... and 4pi M =-[S,B]+..., where lowest-order terms yield dipole contributions

Hamiltonian description of a self-consistent interaction between charged particles and electromagnetic waves

The Hamiltonian description of the self-consistent interaction between an electromagnetic plane-wave and a co-propagating beam of charged particles is considered. We show how the motion can be reduced to a one-dimensional Hamiltonian model (in a canonical setting) from the Vlasov-Maxwell Poisson brackets. The reduction to this paradigmatic Hamiltonian model is performed using a Lie algebraic formalism which allows us to remain Hamiltonian at each step of the derivation

Nonlinear dynamics of recollisions in the double ionization processes of atoms in strong fields

Double ionization processes triggered by intense linearly polarized laser fields have revealed the paramount role of electron-electron collisions. It has been shown that the correlated dynamics of such electronic collisions can be modeled by a two dimensional symplectic map which captures the bare essentials of the energy exchange processes occurring during a recollision between the two electrons. We investigate linear and nonlinear properties of this map and connect them to the dynamical organization of phase space and related statistical dat