A photon (phonon, plasmon, etc) has a linear polarizability. To see this and to understand why this matters, it helps to set aside Maxwell's equations and quantum mechanics per se and start with the following basic physics. Suppose a rapidly oscillating wave field in a weakly inhomogeneous linear medium. Assuming the dispersion operator for the wave field is known, a reduced operator can be defined that governs just the wave envelope. Using the Weyl calculus, an asymptotic approximation of the reduced operator can then be constructed to any power n in the geometrical-optics (GO) parameter. The corresponding truncations yield GO (n = 0), extended GO (n = 1), and quasioptics (n = 2). Notably, an accurate formulation of the latter for inhomogeneous media has only been given recently [unpublished]. But there is even more to this approach. For waves propagating in modulated media (i.e., interacting with other waves), a reduced operator can be derived similarly for Floquet envelopes. The modulation-dependent term in this operator serves as the ponderomotive Hamiltonian of a wave, and its derivative with respect to the (loosely speaking) modulation intensity serves as the wave polarizability [Phys. Rev. A 95, 032114 (2017)]. When applied to charged particles treated as quantum waves, this gives the conventional particle polarizability. Conversely, when applied to classical waves, this defines an effective linear polarizability of a photon (phonon, plasmon, etc). Using this concept, one can interpret modulational dynamics (MD) of nonlinear electromagnetic waves as linear dispersive dynamics of a polarizable photon gas. This significantly simplifies calculations of MD and makes them less error-prone than the standard Maxwell--Vlasov approach [J. Plasma Phys. 83, 905830201 (2017)]. Even more generally, quasilinear MD of all wave ensembles are governed by Wigner--Moyal-type equations that are identical up to a (generally non-Hermitian) Hamiltonian. Then, for example, the modulational instability in the nonlinear Schrodinger equation, the zonostrophic instability of drift-wave turbulence, and the standard two-stream collisionless-plasma instability formally appear as essentially the same effect. In a broader context, elaborating on this approach seems promising for studying inhomogeneous wave turbulence.
Magneto-Fluid Dynamics Seminar, Courant Institute for Mathematical Sciences, New York U. Metriplectic dynamics -- a framework for plasma kinetic theory and numerics
In dissipationless systems, Hamiltonian mechanics, culminating in a Poisson bracket and a Hamiltonian, provides a convenient framework for both theoretical and numerical studies. In systems that obey both the First and the Second Law of Thermodynamics, the dissipationless dynamics can often be extended with a symmetric bracket and an entropy to account for the dissipation. The resulting, so-called metriplectic framework captures many interesting models, including the Navier-Stokes equations, non-isothermal kinetic polymer models, and the Vlasov-Maxwell-Landau model used in plasma physics. In this talk, we review the basic principles of metriplectic dynamics and discuss some prominent methods for time discretization. We focus on the Vlasov-Maxwell-Landau model and, especially, on the Landau collision operator for which a genuine metriplectic integrator is demonstrated. The gyrokinetic version of the Vlasov-Maxwell-Landau system is briefly visited.
ITER Organization Gyrokinetic Simulation of Pedestal and SOL Transport in Present Experiments and ITER