Numerical Simulations of Conversion to Alfvén Waves in Sunspots

Abstract

We study the conversion of fast magneto-acoustic waves to Alfvén waves by means of 2.5D numerical simulations in a sunspot-like magnetic configuration. A fast, essentially acoustic, wave of a given frequency and wave number is generated below the surface and propagates upward though the Alfvén/acoustic equipartition layer where it splits into upgoing slow (acoustic) and fast (magnetic) waves. The fast wave quickly reflects off the steep Alfvén speed gradient, but around and above this reflection height it partially converts to Alfvén waves, depending on the local relative inclinations of the background magnetic field and the wavevector. To measure the efficiency of this conversion to Alfvén waves we calculate acoustic and magnetic energy fluxes. The particular amplitude and phase relations between the magnetic field and velocity oscillations help us to demonstrate that the waves produced are indeed Alfvén waves. We find that the conversion to Alfvén waves is particularly important for strongly inclined fields like those existing in sunspot penumbrae. Equally important is the magnetic field orientation with respect to the vertical plane of wave propagation, which we refer to as "field azimuth". For field azimuth less than 90 • the generated Alfvén waves continue upwards, but above 90 • downgoing Alfvén waves are preferentially produced. This yields negative Alfvén energy flux for azimuths between 90 • and 180 • . Alfvén energy fluxes may be comparable to or exceed acoustic fluxes, depending upon geometry, though computational exigencies limit their magnitude in our simulations.

Benchmarking Fast-to-Alfvén Mode Conversion in a Cold MHD Plasma. Ii. How to Get Alfvén Waves Through the Solar Transition Region

“…The density profile there is linear, though, instead of our exponential. The close correspondence of the results of Paper I, which uses the β = 0 approximation, and the simulations of Khomenko & Cally (2012), which do not, supports the utility and validity of the cold plasma model in this instance.…”

“…These predictions were amply confirmed by numerical simulations in a more realistic model sunspot by Khomenko & Cally (2012).…”

“…There is reason to believe (Parker 1991;Vranjes et al 2008) that the creation of these waves in the photosphere is problematic. Irrespective of that, it appears from Paper I and Khomenko & Cally (2012) that it is easy to generate substantial 4 For completeness, we mention the result from Paper I (see also Ferraro & Plumpton 1958) that the decoupled (k y = 0) fast wave has exact solution ξ ⊥ = a J 2κ (2e −x/h ), with arbitrary complex constant a. This splits into forward and backward traveling wave components:…”

“…Is there some way that the Alfvén transmission coefficient can be increased? 2 We postulate and explore a novel possibility that the Alfvén waves have not propagated as transverse waves (Alfvén or kink) from the photosphere, but that instead they have been generated by local mode conversion from reflecting fast waves high in the chromosphere (Melrose 1977;Melrose & Simpson 1977;Cally & Goossens 2008;Cally & Hansen 2011;Khomenko & Cally 2012), where low-ionization fraction is not an issue for the 3-6 mHz frequency range of most interest here. It will be shown that this greatly increases Alfvén penetration of the TR, thereby opening up a potentially more fruitful source of coronal Alfvén waves.…”

Generation of Magnetohydrodynamic Waves in Low Solar Atmospheric Flux Tubes by Photospheric Motions

“…It is discussed in detail in Bogdan et al (2003), where it is compared to the "true" MHD flux for linear perturbations and found to be generally clearer. It is used in Vigeesh et al (2009Vigeesh et al ( , 2012; and Khomenko & Cally (2012). For a full derivation and discussion relating to timeaveraging, see Leroy (1985).…”