Parity-Time Symmetry of Plasma Waves

Abstract:The susceptibility tensor of a homogeneous collisionless magnetized plasma possesses parity-time (PT) symmetry. For a stationary gyrotropic equilibrium, with the wave vector $\mathbf{k}$ and the equilibrium magnetic field $\mathbf{B}_0$ in the $x$--$z$ plane, the kinetic response satisfies $\chi(\omega^*,\mathbf{k})=R\chi(\omega,\mathbf{k})^*R$, where $R=\operatorname{diag}(1,-1,1)$. We show that the susceptibility PT-symmetry is a reduced-response-space manifestation of PT symmetry of the underpinning kinetic system. We identify parity $P$ and time reversal $T$ on the electromagnetic kinetic eigenmode space and show that the Hamiltonian operator $\mathcal{H}_{\mathrm{VM}}$ of the linearized Vlasov--Maxwell system is PT-symmetric, satisfying $PT\mathcal{H}_{\mathrm{VM}}(PT)^{-1}=\mathcal{H}_{\mathrm{VM}}$. The PT symmetry of the homogeneous magnetized Vlasov--Poisson eigenproblem is also established. Many kinetic instabilities associated with nonmonotonic distributions, rings, loss cones, and resonant energetic-particle populations are fundamentally spontaneous PT-symmetry breaking, which is achieved through and only through Krein collisions. Three examples demonstrate distinct utilities of this analysis. Definite-sign cyclotron residues protect thermal Bernstein modes from spontaneous PT-symmetry breaking. The nonmonotonic Dory--Guest--Harris distribution permits sign-indefinite residues and Krein collisions, for which we derive an analytical instability threshold and growth rate. The recently discovered mode-pole resonance instability provides a distinct realization of spontaneous PT-symmetry breaking and illustrates how PT symmetry can guide the discovery of kinetic instabilities with applications to fusion energy. These results establish PT symmetry as a structural principle of plasma waves and instabilities and open new directions for studying spectral topology in kinetic plasmas.

Plasma Physics (physics.plasm-ph); Mathematical Physics (math-ph); Quantum Physics (quant-ph)

arXiv:2610.03433 [physics.plasm-ph]

(or arXiv:2610.03433v1 [physics.plasm-ph] for this version)

https://doi.org/10.48550/arXiv.2610.03433 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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