On the steady state of nonlinear quasiresonant Alfven oscillations in one-dimensional magnetic cavity

Details On the steady state of nonlinear quasiresonant Alfven oscillations in one-dimensional magnetic cavity On the steady state of nonlinear quasiresonant Alfven oscillations in one-dimensional magnetic cavity

Dec 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998a%26a...340..287n&link_type=abstract

Astronomy and Astrophysics, v.340, p.287-299 (1998)

Astronomy and Astrophysics

Astrophysics

3

Mhd, Waves, Sun: Chromosphere, Sun: Corona, Sun: Oscillations

Scientific paper

We study the steady state of nonlinear, small-amplitude, quasiresonant Alfven oscillations in a homogeneous dissipative hydromagnetic cavity which is forced by the shear motion of its boundaries. It is shown that, even in the case of strong nonlinearity, these oscillations can be represented, to leading order, by a sum of two solutions in the form of oppositely propagating waves with permanent shapes. An infinite set of nonlinear equations for the Fourier coefficients of these solutions is derived which, in general, admits multiple solutions, depending on the re-scaled total Reynolds number, R, and mistuning, Delta , between the frequency of the boundary forcing and the first Alfven eigenmode of the cavity. Two types of solutions are found. On the one hand, low-modal solutions set in over the entire parameter range studied, which can be represented, with a remarkable accuracy, by very few Fourier modes even at very large R. For a fixed Delta the time-averaged energy, {cal E}, that can be stored in the cavity is saturated, as R increases, to a value which is approximately proportional to epsilon (2) , epsilon (3) << 1 being the Alfven Mach number of the boundary motions. The time-averaged absorbed power (the Poynting flux {cal S}) scales as 1/R. For suitable values of R and Delta catastrophic transitions occur between these solutions, in which the average power released scales as R, provided R

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