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In this paper, symmetric spoof surface plasmon (SSP) mode on the doubly corrugated metal surfaces is indentified as long-range spoof surface plasmon (LRSSP) because of its extreme low propagation loss and symmetric dominant field profile so as short-range SSP (SRSSP) for anti-symmetric mode. Based on theoretical calculation and numerical simulation of finite integration method, symmetric and anti-symmetric SSP modes with various gap sizes between these two identical corrugated metal surfaces are investigated in terahertz (THz) regime and good agreement is realized. Besides, the low loss superiority of LRSSP diminishes along with the increased gap size. This work opens up new avenues to utilize this long-range surface mode in far-infrared, THz or lower frequency band and can find many potential applications such as low-loss waveguide, filters and novel electronic sources.

The nonlinear theory of slow-wave electron cyclotron masers (ECM) with an initially straight electron beam is developed. The evolution equation of the nonlinear beam electron energy is derived. The numerical studies of the slow-wave ECM efficiency with inclusion of Gaussian beam velocity spread are presented. It is shown that the velocity spread reduces the interaction efficiency.

We show that a Yangian symmetry, namely, Y ( s u ( 2 ) ) , exists in the Dirac equation with spin symmetry when the potential term takes a Coulomb form. We construct the generators of Y ( s u ( 2 ) ) explicitly and get the energy spectrum of this model from the representation theory for Y ( s u ( 2 ) ) . We also show that this model is integrable, from RTT relations.

Ho doped BiFeO 3 nanoparticles were synthesized by a sol–gel method, and their magnetic and microwave absorption properties were investigated. X-ray diffraction pattern shows that Ho ions occupy the Bi site in BiFeO 3 . The Ho substitution is found to enhance ferromagnetic properties, which attributed to the destruction of spin cycloid structure and the emergence of exchange interaction between Ho 4 f electrons and Fe 3 d electrons. Microwave magnetic loss also shows an obvious increase in the range of 2–18 GHz for high level substitution, caused mainly by the natural ferromagnetic resonance at microwave frequencies. Furthermore, microwave absorbing bandwidth and intensity are greatly improved due to the better electromagnetic match property of BiFeO 3 with Ho substitution.

A general dispersion relation is derived for a relativistic rectilinear electron beam of arbitrary momentum distributions interacting with a dielectric in a guide magnetic field, on the basis of Maxwell equations and the relativistic Vlasov equation. The instability occurs when the beam velocity exceeds the wave phase velocity in the medium. The linear wave dispersion relation, growth rate, spatial growth rate are studied analytically for delta and Lorentzian distributions of beam momentums in detail. The results are of importance for a new kind of high-power microwave generation or amplification devices based on anomalous Doppler effect.

The resonance interaction of a relativistic charged particle in a circularly polarized electromagnetic wave traveling along a uniform magnetic field is considered. The position, momentum and energy of the particle are presented analytically as functions of a free parameter. The results may be of importance for plasma heating, microwave generation or particle acceleration.