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Astron. Astrophys. 326, 1241-1251 (1997)

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2. The equilibrium configuration

We consider a static 1D planar equilibrium model composed of two semi-infinite uniform plasma layers which embrace a nonuniform plasma layer. We use a system of Cartesian coordinates with the z -axis directed downward. The horizontal planes [FORMULA] and [FORMULA] bound the nonuniform plasma layer from above and from below respectively. The plasma is uniform in the regions [FORMULA] (region 1) and [FORMULA] (region 2). In the nonuniform plasma layer [FORMULA] the equilibrium quantities depend on z only.

The magnetic field is assumed to be constant in the whole space and is oriented along the [FORMULA] axis: [FORMULA]. Gravity is neglected in the present analysis.

Since the magnetic pressure [FORMULA] is constant, the thermal pressure [FORMULA] is also constant and so is the plasma parameter [FORMULA]:

[EQUATION]

In addition we can freely specify either the temperature [FORMULA] or the density [FORMULA].

Of course, [FORMULA] implies that

[EQUATION]

The object of the present paper is to study the absorption of slow and fast magnetosonic waves by coupling to local resonant slow magnetosonic waves. The resonant slow waves are controlled by the local cusp frequency which is determined by the wave vector and the local cusp speed. Hence in the present context it is convenient to prescribe the variation of the square of the local cusp velocity [FORMULA]

[EQUATION]

as a function that is monotonous inside the nonuniform layer [FORMULA] and is constant elsewhere:

[EQUATION]

The expressions for density, local Alfvén speed and local sound speed take the simple forms:

[EQUATION]

where [FORMULA] is prescribed by Eqs (3). The dimensionless Alfvén, sound, and cusp speed as functions of coordinate z are shown in Fig. 1.

[FIGURE] Fig. 1. The characteristic velocity profiles for the considered equilibrium state with [FORMULA] and [FORMULA]

We use this model for studying the resonant absorption of magnetosonic waves in different structures in the solar atmosphere. The incoming wave is launched from the lower uniform layer [FORMULA] with a prescribed frequency [FORMULA] and a prescribed wave vector [FORMULA], and propagates towards the nonuniform layer. At the boundary [FORMULA] the wave is partly reflected and partly transmitted. The energy of the transmitted wave is partly absorbed in the nonuniform plasma due to the resonant excitation of local waves. With our choice of the direction of the z -axis, the incident wave propagates in the negative z -direction and the reflected wave propagates in the positive z -direction. We do not want to consider leaky waves and restrict our analysis to waves that are evanescent in the upper uniform layer.

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© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998
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