D. E. Ruiz

Zonal-flow dynamics from a phase-space perspective

The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in the studies of zonal flows (ZFs) emerging from DW turbulence. However, this formulation neglects the exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometrical-optics limit. We derive a modified theory that takes both of these effects into account, while still treating DW quanta (“driftons”) as particles in phase space. The drifton dynamics is described by an equation of the Wigner–Moyal type, which is commonly known in the phase-space formulation of quantum mechanics. In the geometrical-optics limit, this formulation features additional terms missing in the traditional WKE that ensure exact conservation of the total enstrophy of the system, in addition to the total energy, which is the only conserved invariant in previous theories based on the WKE. Numerical simulations are presented to illustrate the importance of these additional terms. The proposed formulation can be considered as a p...

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

Abstract Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the “wave spin”. Both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern–Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler–Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and lead to equations for the wave spin, which happens to be an ( N 2 − 1 ) -dimensional spin vector. As a special case, classical equations for a Dirac particle ( N = 2 ) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann–Michel–Telegdi equations with added Stern–Gerlach force.

Extending geometrical optics: A Lagrangian theory for vector waves

Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and momenta, but vector-wave rays have another degree of freedom, namely, their polarization. The polarization degree of freedom manifests itself as an effective (classical) “wave spin” that can be assigned to rays and can affect the wave dynamics accordingly. A well-known manifestation of polarization dynamics is mode conversion, which is the linear exchange of quanta between different wave modes and can be interpreted as a rotation of the wave spin. Another, less-known polarization effect is the polarization-driven bending of ray trajectories. This work presents an extension and reformulation of GO as a first-principle Lagrangian theory, whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously. As an example, the theory is applied to describe ...

On the correspondence between quantum and classical variational principles

Abstract Classical variational principles can be deduced from quantum variational principles via formal reparameterization of the latter. It is shown that such reparameterization is possible without invoking any assumptions other than classicality and without appealing to dynamical equations. As examples, first principle variational formulations of classical point-particle and cold-fluid motion are derived from their quantum counterparts for Schrodinger, Pauli, and Klein–Gordon particles.

Relativistic ponderomotive Hamiltonian of a Dirac particle in a vacuum laser field

Here, we report a point-particle ponderomotive model of a Dirac electron oscillating in a high-frequency field. Starting from the Dirac Lagrangian density, we derive a reduced phase-space Lagrangian that describes the relativistic time-averaged dynamics of such a particle in a geometrical-optics laser pulse propagating in vacuum. The pulse is allowed to have an arbitrarily large amplitude provided that radiation damping and pair production are negligible. The model captures the Bargmann-Michel-Telegdi (BMT) spin dynamics, the Stern-Gerlach spin-orbital coupling, the conventional ponderomotive forces, and the interaction with large-scale background fields (if any). Agreement with the BMT spin precession equation is shown numerically. The commonly known theory in which ponderomotive effects are incorporated in the particle effective mass is reproduced as a special case when the spin-orbital coupling is negligible. This model could be useful for studying laser-plasma interactions in relativistic spin-1/2 plasmas.

Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics

Abstract Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables. Here, a different approach is proposed. We show that, for a broad class of dissipative systems of practical interest, variational principles can be formulated using constant Lagrange multipliers and Lagrangians nonlocal in time, which allow treating reversible and irreversible dynamics on the same footing. A general variational theory of linear dispersion is formulated as an example. In particular, we present a variational formulation for linear geometrical optics in a general dissipative medium, which is allowed to be nonstationary, inhomogeneous, anisotropic, and exhibit both temporal and spatial dispersion simultaneously.

Photon polarizability and its effect on the dispersion of plasma waves

High-frequency photons traveling in plasma exhibit a linear polarizability that can influence the dispersion of linear plasma waves. We present a detailed calculation of this effect for Langmuir waves as a characteristic example. Two alternative formulations are given. In the first formulation, we calculate the modified dispersion of Langmuir waves by solving the governing equations for the electron fluid, where the photon contribution enters as a ponderomotive force. In the second formulation, we provide a derivation based on the photon polarizability. Then, the calculation of ponderomotive forces is not needed, and the result is more general.