Nonlinear effects in Alfvén resonance

Abstract

A study is made of the influence of nonlinearity upon the structure of a steadystate disturbance brought about by low-frequency (ω ω i ) monochromatic magnetosound propagating in a transversally inhomogeneous low-pressure plasma (β m e /m i ), in the vicinity of the Alfvén resonance point for the case when the principal linear mechanism for forming the transverse structure is provided by magnetic field diffusion due to small plasma resistivity. It is shown that the nonlinear properties of the fundamental harmonic of a disturbance are determined by its self-action through a plasma density variation that it produces. The disturbance structure in the region of the Alfvén resonance is described.

Hybrid simulation of mode conversion at the magnetopause

“…Theoretically, as the amplitude of the driver wave is increased, it is expected that the wave should, indeed, first become nonlinear near the resonance location, where the wave solution is singular in MHD and has large amplitude in a kinetic description consistent with a small group velocity across the magnetic field. Dmitrienko [1997], Clack et al [2009], and Clack and Ballai [2009] have discussed the weakly nonlinear interaction of fast magnetosonic waves in a 1‐D planar plasma using an MHD description. They derived a hierarchy of equations considering the MHD singular variables B y and V y as large and the other components as higher order.…”

“…Based on this hierarchy, they found that the governing equation for the second‐order terms was the same as for the first‐order terms in the singular region with the addition of nonlinear terms involving products of first‐order terms. However, at the resonant surface, the driving forces associated with perpendicular velocity and magnetic field nonlinearly cancel each other [ Dmitrienko , 1997; Clack et al , 2009], suggesting that nonlinear effects would mostly lead to radiation of second‐order compressional waves [ Clack et al , 2009]. However, in a kinetic description the resonant region is broadened by wave dispersion, such that the large‐amplitude second‐order nonlinear perpendicular magnetic field and velocity response associated with the kinetic Alfvén wave does not cancel in the region of small‐scale structure, leading to the generation of second‐order harmonic structure in the dispersive kinetic Alfvén waves seen near resonance.…”

Second-order perturbations in Alfvén waves in cold plasma approximatio

“…Accordingly, in [Pokhotelov et al, 2003[Pokhotelov et al, , 2004Zhao et al, 2012] convection flows are identified, if it is formulated in terms of harmonic decomposition as a zero longitudinalcoordinate harmonic, by corresponding averaging. In this case, the averaged longitudinal ponderomotive force exists only due to small effectsdissipative [Dmitrienko, 1997] or kinetic [Pokhotelov et al, 2003[Pokhotelov et al, , 2004Zhao et al, 2012]. In this paper, we examine the longitudinally localized Alfvén perturbations and correspondingly the second-order flows, which are also longitudinally localized.…”

“…The formation of the flow in Alfvén waves has been explored when studying nonlinear effects in Alfvén waves [Dmitrienko, 1997]. Dmitrienko [2011] considered a monochromatic wave with the time envelope arising from FMS-wave transformation as a source of formation of such a flow.…”

Resonant absorption and heating in a nonlinear dissipative resonance layer

“…is satisfied. Our intent here is to obtain the matching conditions, and to calculate the rate of resonant absorption and heating, based on the technique for analytical investigation of the Alfvén resonance proposed by Dmitrienko (1997Dmitrienko ( , 1999. It relies on the assumption that away from the resonance surface, the nonlinearity and dissipation can be neglected in the input equations.…”