Introduction Effect on resonant absorption Effect on KHI Conclusions Partial ionization effects on resonant absorption and Kelvin-Helmholtz instability Roberto Soler Solar Physics Group Universitat de les Illes Balears (Spain) Also contributed: J. L. Ballester, D. Mart´ ınez-G´ omez, R. Oliver, J. Terradas ISSI Team Meeting on Coronal Rain Bern, 23–27 February 2015
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Partial ionization effects on resonant absorption and ... · Partial ionization e ects on resonant absorption and Kelvin-Helmholtz instability Roberto Soler Solar Physics Group Universitat
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Introduction Effect on resonant absorption Effect on KHI Conclusions
Partial ionization effects on resonant absorptionand Kelvin-Helmholtz instability
Roberto Soler
Solar Physics GroupUniversitat de les Illes Balears (Spain)
Also contributed: J. L. Ballester, D. Martınez-Gomez, R. Oliver, J. Terradas
ISSI Team Meeting on Coronal RainBern, 23–27 February 2015
Introduction Effect on resonant absorption Effect on KHI Conclusions
Outline
1 Introduction
2 Partial ionization effects on resonant absorption
3 Partial ionization effects on Kelvin-Helmholtz instability
4 Conclusions
Introduction Effect on resonant absorption Effect on KHI Conclusions
Transverse oscillations in the solar corona
First observed with TRACE in 1999Nakariakov et al. (1999); Aschwanden et al. (1999)
After an energetic disturbance (flare), the whole loop displays adamped transverse oscillation ∼ cos (2πt/P + φ) exp (−t/τ)
Image credit: E. Verwichte Nakariakov et al. (1999)
Physical interpretation: Global kink MHD modesee, e.g., Edwin & Roberts (1983)
Rapid attenuation consistent with damping by resonant absorptionsee, e.g., Ruderman & Roberts (2002); Goossens et al. (2002)
Introduction Effect on resonant absorption Effect on KHI Conclusions
Transverse oscillations in the solar corona
First observed with TRACE in 1999Nakariakov et al. (1999); Aschwanden et al. (1999)
After an energetic disturbance (flare), the whole loop displays adamped transverse oscillation ∼ cos (2πt/P + φ) exp (−t/τ)
Image credit: E. Verwichte Nakariakov et al. (1999)
Physical interpretation: Global kink MHD modesee, e.g., Edwin & Roberts (1983)
Rapid attenuation consistent with damping by resonant absorptionsee, e.g., Ruderman & Roberts (2002); Goossens et al. (2002)
Introduction Effect on resonant absorption Effect on KHI Conclusions
Simple model: straight magnetic cylinder
l = 0 → Abrupt density jump
l = 2R → Fully nonuniform tube
Fully ionized plasma
Introduction Effect on resonant absorption Effect on KHI Conclusions
Normal modes for l = 0Edwin & Roberts (1983)
Linear ideal MHD equationsPerturbations: f (r) exp (imϕ+ ikzz − iωt)f (r) → Bessel functions (Jm inside, Km outside)kz =
πL → Fundamental mode
Transverse (fast) modes
Sausage (m = 0)Kink (m = 1)Fluting (m ≥ 2)
Longitudinal (slow) modes
Torsional/Rotational (Alfven)modes
Introduction Effect on resonant absorption Effect on KHI Conclusions
The (boring) kink mode when l = 0
Global transverse (kink) motion of the flux tube
No damping, no change of polarisation
Thin tube(L/R � 1)approximation:
P =L
vA,i
√2 (ρi + ρe)
ρi
Introduction Effect on resonant absorption Effect on KHI Conclusions
The kink mode when l 6= 0: Resonant absorption
When l 6= 0 the kink mode is resonantly coupled to Alfven waves
-r
Loop core Transition Exterior
ωA,i
ωkink
ωA,e
Introduction Effect on resonant absorption Effect on KHI Conclusions
The kink mode when l 6= 0: Resonant absorption
When l 6= 0 the kink mode is resonantly coupled to Alfven waves