1. Solar Physics & Space Plasma Research Center (SP 2 RC) The role of partial ionisation in the stability of prominences structures Istvan Ballai SP 2 RC, School of Mathematics & Statistics, The University of Sheffield (UK)

2. Solar Physics & Space Plasma Research Center (SP 2 RC) RAS Meeting, 21/02/2014, London Berger et al. 2010Courtesy of SDO

3. Solar Physics & Space Plasma Research Center (SP 2 RC) Observations of prominence instability A classical example of RT instability (Ryutova et al. 2010) -cuts 1-2 show regular oscillatory pattern - cuts 3-4 show regions where the RT instability broke into plumes (array of small arrows) and destroyed the regular oscillatory pattern (curved arrow).

4. Solar Physics & Space Plasma Research Center (SP 2 RC) RAS Meeting, 21/02/2014, London Temperatures are not high enough to ensure full ionisation The plasma is composed by +’ve and –’ve ions, neutral atoms (ground-level or excited), e -, photons; the Boltzmann, Saha and Maxwell equations (together with the Planck function) fully describe their equilibrium relations This composition requires a complex mathematical description The components of the plasma might not be in thermodynamical equilibrium, however we assume plasma to be in a local thermodynamical equilibrium (LTE) Transport effects are still achieved through collisions, however the presence of different constituents should be taken into account (Khodachenko et al. 2003)

5. Solar Physics & Space Plasma Research Center (SP 2 RC) A couple of basic and necessary ingredients Prominences are very structured, observations show a clear fibril structure The plasma is always in motion, plasma flows along field lines, waves and oscillations are continuously observed (see, e,g, the review by Arregui, Oliver, Ballester 2012) Prominences are embedded in the solar corona The fate of prominences is very often connected to instabilities RAS Meeting, 21/02/2014, London

6. Solar Physics & Space Plasma Research Center (SP 2 RC) Instabilities in solar prominences Here we discuss 3 particular instabilities and the role of partial ionisation in the development of instabilities –Rayleigh-Taylor instability (RTI) –Kelvin-Helmholtz instability (KHI) –Dissipative instability (DI) RAS Meeting, 21/02/2014, London The RTI develops at gravitationally permeated interfaces, where the medium above the interface is heavier (Diaz et al. 2012) g B0B0 x z ρ1ρ1 ρ2ρ2 ρ 1 >ρ 2 Two unstable modes were found; one related to neutrals and the second one to the the e - -ion fluid Ion-neutral collisions lower the growth-rate The results explain the existence of fine structure with lifetime >30 mins

7. Solar Physics & Space Plasma Research Center (SP 2 RC) Instabilities in solar prominences The KHI appears at interfaces in the presence of shear flows (Jones & Downes 2011; Soler et al. 2012) RAS Meeting, 21/02/2014, London B0B0 prominence plasma dark plume v0v0 Ion-electron collisions are not able to stabilise the instability driven by neutrals The magnetic field has a stabilising effect Ion-neutral coupling brings the instability threshold down to observed flow speeds The growth rate depends on the ratio υ in /ω v KHI cannot be responsible for the thread dissapearance

8. Solar Physics & Space Plasma Research Center (SP 2 RC) Instabilities in solar prominences Very often the explanation of observed instabilities in terms of KHI is difficult given the very high instability threshold But instabilities can arise for lower flows through, e.g. dissipative instabilities (Ballai, Oliver et al. 2014) which can set for lower flow speeds than the corresponding KHI Dissipative instabilities are strongly connected to negative energy waves, i.e. to waves that can grow despite the presence of dissipation. RAS Meeting, 21/02/2014, London B0B0 Case 1: prominence corona Case 2: prominence dark plume Case 1: assume an interface separating the partially ionised prominence plasma and a viscous corona (incompressible media) the prominence is dynamic (v 0 ) in the prominence the dominant transport mechanism is the Cowling resistivity, assume weak damping given the large density ratio, the KH threshold is very high, i.e. the interface is KH stable the interface allows the propagation of two modes in opposite direction. The forward mode follows classical damping, the backward wave can become unstable

9. Solar Physics & Space Plasma Research Center (SP 2 RC) Dissipative instability at the prominence/corona interface RAS Meeting, 21/02/2014, London For typical prominence/coronal values, the dissipative instability sets at a tenth of the KH threshold Due to the very high density contrast (here 2 orders of magnitude) the effect of partial ionisation is very week, the coronal plasma parameters control the stability and the dissipative instability is driven by the coronal viscosity

10. Solar Physics & Space Plasma Research Center (SP 2 RC) Dissipative instability at the prominence/plume interface Now assume the interface separates the partially ionised prominence and dark plumes Dark plumes show turbulent upflows (15-30 km/s) and they are dark in CaII-H line because they are hotter and less dense than the prominence. The ionisation degree varies as T 1/2 RAS Meeting, 21/02/2014, London The prominence-plume interface is always unstable regardless the value of the flow The growth rate is higher for fully ionised plasma, neutrals tend to stabilise the interface and the flow in the plume Obviously these calculations contain many simplifications, in reality they are part of a proof-of- concept study on the appearance of dissipative instability (single fluid MHD, incompressible plasma, field aligned flow, elastic collisions between ions and neutrals, etc.)

11. Solar Physics & Space Plasma Research Center (SP 2 RC) RAS Meeting, 21/02/2014, London