More Like this

1. Metriplectic foundations of gyrokinetic Vlasov–Maxwell–Landau theory

   https://doi.org/10.1063/5.0091727  

   Hirvijoki, Eero; Burby, Joshua W.; Brizard, Alain J. (June 2022, Physics of Plasmas)

   This Letter reports on a metriplectic formulation of a collisional, nonlinear full- f electromagnetic gyrokinetic theory compliant with energy conservation and monotonic entropy production. In an axisymmetric background magnetic field, the toroidal angular momentum is also conserved. Notably, a new collisional current, contributing to the gyrokinetic Maxwell–Ampère equation and the gyrokinetic charge conservation law, is discovered. 

   more » « less
2. Variational formulation of higher-order guiding-center Vlasov–Maxwell theory

   https://doi.org/10.1063/5.0161171  

   Brizard, Alain J. (October 2023, Physics of Plasmas)

   Extended guiding-center Vlasov–Maxwell equations are derived under the assumption of time-dependent and inhomogeneous electric and magnetic fields that obey the standard guiding-center space-timescale orderings. The guiding-center Vlasov–Maxwell equations are derived up to second order, which contains dipole and quadrupole contributions to the guiding-center polarization and magnetization that include finite-Larmor-radius corrections. Exact energy-momentum conservation laws are derived from the variational formulation of these higher-order guiding-center Vlasov–Maxwell equations. 

   more » « less
3. Action principles and conservation laws for Chew–Goldberger–Low anisotropic plasmas

   https://doi.org/10.1017/S0022377822000642  

   Webb, G.M.; Anco, S.C.; Meleshko, S.V.; Zank, G.P. (August 2022, Journal of Plasma Physics)

   The ideal Chew–Goldberger–Low (CGL) plasma equations, including the double adiabatic conservation laws for the parallel ( $$p_\parallel$$ ) and perpendicular pressure ( $$p_\perp$$ ), are investigated using a Lagrangian variational principle. An Euler–Poincaré variational principle is developed and the non-canonical Poisson bracket is obtained, in which the non-canonical variables consist of the mass flux $${\boldsymbol {M}}$$ , the density $$\rho$$ , the entropy variable $$\sigma =\rho S$$ and the magnetic induction $${\boldsymbol {B}}$$ . Conservation laws of the CGL plasma equations are derived via Noether's theorem. The Galilean group leads to conservation of energy, momentum, centre of mass and angular momentum. Cross-helicity conservation arises from a fluid relabelling symmetry, and is local or non-local depending on whether the gradient of $$S$$ is perpendicular to $${\boldsymbol {B}}$$ or otherwise. The point Lie symmetries of the CGL system are shown to comprise the Galilean transformations and scalings. 

   more » « less
4. Superkicks and momentum density tests via micromanipulation

   https://doi.org/10.1117/12.2633726  

   Afanasev, Andrei; Carlson, Carl E.; Mukherjee, Asmita (October 2022, Proc. SPIE 12198, Optical Trapping and Optical Micromanipulation XIX)

   Dholakia, Kishan; Spalding, Gabriel C. (Ed.)

   There is an unsettled problem in choosing the correct expressions for the local momentum density and angular momentum density of electromagnetic fields (or indeed, of any non-scalar field). If one only examines plane waves, the problem is moot, as the known possible expressions all give the same result. The momentum and angular momentum density expressions are generally obtained from the energy-momentum tensor, in turn obtained from a Lagrangian. The electrodynamic expressions obtained by the canonical procedure are not the same as the symmetric Belinfante reworking. For the interaction of matter with structured light, for example, twisted photons, this is important; there are drastically different predictions for forces and angular momenta induced on small test objects. We show situations where the two predictions can be checked, with numerical estimates of the size of the effects. 

   more » « less
5. Representation and conservation of angular momentum in the Born–Oppenheimer theory of polyatomic molecules

   https://doi.org/10.1063/5.0143809  

   Littlejohn, Robert; Rawlinson, Jonathan; Subotnik, Joseph (March 2023, The Journal of Chemical Physics)

   This paper concerns the representation of angular momentum operators in the Born–Oppenheimer theory of polyatomic molecules and the various forms of the associated conservation laws. Topics addressed include the question of whether these conservation laws are exactly equivalent or only to some order of the Born–Oppenheimer parameter κ = ( m/ M) 1/4 and what the correlation is between angular momentum quantum numbers in the various representations. These questions are addressed in both problems involving a single potential energy surface and those with multiple, strongly coupled surfaces and in both the electrostatic model and those for which fine structure and electron spin are important. The analysis leads to an examination of the transformation laws under rotations of the electronic Hamiltonian; of the basis states, both adiabatic and diabatic, along with their phase conventions; of the potential energy matrix; and of the derivative couplings. These transformation laws are placed in the geometrical context of the structures in the nuclear configuration space that are induced by rotations, which include the rotational orbits or fibers, the surfaces upon which the orientation of the molecule changes but not its shape, and the section, an initial value surface that cuts transversally through the fibers. Finally, it is suggested that the usual Born–Oppenheimer approximation can be replaced by a dressing transformation, that is, a sequence of unitary transformations that block-diagonalize the Hamiltonian. When the dressing transformation is carried out, we find that the angular momentum operator does not change. This is a part of a system of exact equivalences among various representations of angular momentum operators in Born–Oppenheimer theory. Our analysis accommodates large-amplitude motions and is not dependent on small-amplitude expansions about an equilibrium position. Our analysis applies to noncollinear configurations of a polyatomic molecule; this covers all but a subset of measure zero (the collinear configurations) in the nuclear configuration space. 

   more » « less