ALBERT

Notes: The propagation of slow sausage surface waves in a multi-layered magnetic configuration is considered. The magnetic configuration consists of a central magnetic slab sandwiched between two identical magnetic slabs (with equilibrium quantities different from those in the central slab) which in turn are embedded between two identical semi-infinite regions. The dispersion equation is obtained in the linear approximation. The nonlinear governing equation describing waves with a characteristic wavelength along the central slab much larger than the slab thickness is derived. Solitary wave solutions to this equation are obtained in the case where these solutions deviate only slightly from the algebraic soliton of the Benjamin–Ono equation. © 2001 American Institute of Physics.

Notes: The problem of transition to the steady state of driven oscillations in a magnetic cavity in a cold resistive plasma is addressed. The foot point driving polarized in the inhomogeneous direction is considered, and it is assumed that the cavity length in the direction of the equilibrium magnetic field is much larger than the cavity width in the inhomogeneous direction. The latter assumption enables one to neglect the variation of the magnetic pressure in the inhomogeneous direction, which strongly simplifies the analysis. The explicit solution describing the nonstationary behavior of the magnetic pressure and the velocity is obtained. This solution is used to study the properties of the transition to the steady state of oscillation. The main conclusion is that, in general, there are two different characteristic transitional times. The first time is inversely proportional to the decrement of the global mode. It characterizes the transition to the steady state of the global motion, which is the coherent oscillation of the cavity in the inhomogeneous direction. The second time is the largest of the two times, the first transitional time and the phase-mixing time, which is proportional to the magnetic Reynolds number in 〈fraction SHAPE="CASE"〉13 power. It characterizes the transition to the steady state of the local motion, which is oscillations at the local Alfvén frequencies, and the saturation of the energy damping rate. An example from solar physics shows that, in applications, the second transitional time can be much larger than the first one. © 2000 American Institute of Physics.

Notes: The author's content that the free electron laser instability is not modify and the operation frequency of the FEL is only slightly affected by the modification suggested by Shouric in the dispersion relation of the pump wave. (AIP)

Notes: The steady state of the driven oscillations of the system consisting of N oscillators coupled by friction is considered. It is shown that for large values of N this state is asymptotically described by the F-function previously introduced in the theory of resonant magnetohydrodynamic (MHD) waves in plasmas. © 1998 American Institute of Physics.

Notes: Linear dissipative magnetohydrodynamics (MHD) shows that driven MHD waves in magnetic plasmas with high Reynolds number exhibit a near resonant behaviour if the frequency of the wave becomes equal to the local Alfvén or slow frequency of a magnetic surface. This near resonant behaviour is confined to a thin dissipative layer which embraces the resonant magnetic surface. Although the driven MHD waves have small amplitudes far away from the resonant magnetic surface, this near-resonant behaviour in the dissipative layer may cause a breakdown of linear theory. In the present paper we deal with the nonlinear behaviour of driven MHD waves in the slow wave dissipative layer. The method of matched asymptotic expansions is used to obtain the nonlinear equation for wave variables inside the dissipative layer. The concept of connection formulae introduced into the theory of linear resonant MHD waves by Sakurai, Goossens, and Hollweg [Sol. Phys. 133, 227 (1991)] is extended to include nonlinear effects in the dissipative layer for slow resonant waves. The absorption of the slow resonant wave in the dissipative layer generates a shear flow parallel to the magnetic surfaces with a characteristic velocity of the order of ε1/2, where ε is the dimensionless amplitude of perturbations far away from the dissipative layer. © 1997 American Institute of Physics.

Notes: The quasi-resonant behavior of linear Alfvén waves in one-dimensional magnetized weakly resistive plasmas with the slightly inclined equilibrium magnetic field is studied. The analysis concentrates on the behavior of the y-component of the velocity, v, which is the component perpendicular both to the inhomogeneity direction and to the equilibrium magnetic field, and the z-component of the velocity, w, which is the component along the inhomogeneity direction. It is shown that the behavior of v and w is described by the functions F(σ;Λ) and G(σ;Λ), where σ is the dimensionless distance along the inhomogeneity direction and the parameter Λ characterizes the relative importance of resistivity and the magnetic field inclination near the quasi-resonant position. The functions F(σ;Λ) and G(σ;Λ) are generalizations of the F and G functions introduced by Goossens, Ruderman, and Hollweg [Sol. Phys. 157, 75 (1995)] and coincide with them for Λ=0. The behavior of F(σ;Λ) and G(σ;Λ) is studied numerically for different values of Λ. It changes from monotonic to oscillatory when Λ is increased. It is shown that the connection formulas giving the jumps of w and the perturbation of the total pressure across the quasi-resonant layer and the rate of energy dissipation in the quasi-resonant layer are independent of the inclination angle. © 1999 American Institute of Physics.

Notes: The nonlinear theory of driven magnetohydrodynamic (MHD) waves in the resonant slow wave dissipative layer developed by Ruderman, Hollweg, and Goossens [Phys. Plasmas 4, 75 (1997)] is used to study the interaction of sound waves with a static one-dimensional planar magnetic plasma configuration. This configuration is a nonhomogeneous magnetic slab (region II) sandwiched by a homogeneous magnetic field free plasma (regions I) and a homogeneous magnetic plasma (region III). The equilibrium magnetic field is unidirectional. An incoming sound wave is launched from region I, and the equilibrium quantities and the parameters of the incoming sound wave are chosen in such a way that the wave is evanescent in region III and resonates with a slow local MHD wave in region II. The analysis is restricted to incoming sound waves with wave vectors in the plane determined by the equilibrium magnetic field and the direction of inhomogeneity, so that there is no resonance with a local Alfvén wave. Partial reflection of the incoming sound wave from region II generates an outgoing sound wave in region I. The nonlinearity parameter introduced by Ruderman et al. is assumed to be small, and a regular perturbation analysis is used to determine the wave solution. The present analysis shows that nonlinearity in the resonant slow wave dissipative layer causes the following new effects in comparison with results obtained on the basis of linear theory: (i) higher harmonic contributions are generated in the wave solution in the dissipative layer and also in the outgoing sound wave in addition to the fundamental harmonic. Outside the dissipative layer the amplitude of each harmonic contribution is of a higher order with respect to the small nonlinearity parameter than inside the dissipative layer. This property reflects the fact that nonlinearity is only taken into account in the dissipative layer, so that the higher harmonic contributions to the outgoing wave are only due to the interaction of the external plasma motions with the plasma motions in the dissipative layer; (ii) the coefficient of wave energy absorption and the absolute value of the jump in the normal velocity are decreased. © 1997 American Institute of Physics.