The susceptibility tensor of a homogeneous collisionless magnetized plasma possesses parity-time (PT) symmetry. For a stationary gyrotropic equilibrium, with the wave vector
k and the equilibrium magnetic field
B0 in the
x--
z plane, the kinetic response satisfies
χ(ω∗,k)=Rχ(ω,k)∗R, where
R=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
HVM of the linearized Vlasov--Maxwell system is PT-symmetric, satisfying
PTHVM(PT)−1=HVM. 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.
Two-dimensional topological insulators protected by nonlocal symmetries or with fragile topology usually do not admit robust in-gap edge modes due to the incompatibility between the symmetry and the boundary. Here, we show that in a parity-time (PT) symmetric system robust in-gap topological edge modes can be stably induced by non-Hermitian couplings that spontaneously break the PT symmetry of the eigenstates. The topological edge modes traverse the imaginary spectral gap between a pair of fragile topological bands, which is opened by the presence of the non-Hermitian perturbation. We demonstrate that the net number of resulting in-gap modes is protected by an operator version of anomaly cancellation that extends beyond the Hermitian limit. The results imply that loss and gain can in principle drive fragile topological phenomena to stable topological phenomena.