Twisted magnetic tubes with field aligned flow

Abstract

Aims. We study the equilibrium and stability of twisted magnetic flux tubes with mass flows along the field lines. Then, we focus on the stability and oscillatory modes of magnetic tubes with uniform twist B 0 = B 0 (r/p e ϕ + e z ) in a zero-β plasma, surrounded by a uniform, purely longitudinal field. Methods. First we investigate the possible equilibriums, and then consider the linearised MHD equations and obtain a system of two first-order differential equations. These are solved numerically, while analytical approximations involving confluent hypergeometric functions are found in the thin tube limit. Finally, new appropriate boundary conditions are deduced and the outer solution considered (with the apparition of cut-off frequencies). We use this to derive a dispersion relation, from which the frequencies of the normal modes can be obtained. Results. Regarding the equilibrium, the only value of the flow that satisfies the equations for this magnetic field configuration is a super-Alfvénic one. Then, we consider the normal modes of this configuration. The thin-tube approximation proves accurate for typical values, and it is used to prove that the equilibrium is unstable, unless the pitch is large. The stability criteria for twisted tubes are significantly lowered. Conclusions. The twisted tube is subject to the kink instability unless the pitch is very high, since the Lundquist criterion is significantly lowered. This is caused by the requirement of having a magnetic Mach number greater than 1, so the magnetic pressure balances the magnetic tension and fluid inertia. This type of instability might be observed in some solar atmospheric structures, like surges.

The kinematics of an untwisting solar jet in a polar coronal hole observed bySDO/AIA

“…First, the formation of the MFs might be associated with the successive occurrence of magnetic reconnection at the jet base. Second, the intrinsic (sausage or kink) instability in the mass flow as described in Chen et al (2009b) and Díaz et al(2011) might be another possible candidate. In morphology, the MFs are similar with the plasma blobs observed in coronal streamers (e.g., Sheeley et al 1997;Wang et al 1998b;Wang et al 2000;Song et al 2009).…”

“…And if the stress is constantly applied at the photospheric boundary, this mechanism would generate recurrent untwisting quasi-homologous jets (e.g., Pariat et al 2010;Asai et al 2001;Chen et al 2008;Yang et al 2011b). More recently, the simulations by Díaz et al (2011) indicate that the speed of the flow along the field lines of twisted magnetic flux tubes may be super-Alfvénic and the twisted tube is subject to the kink instability, which could explain the behaviour of super-Alfvénic jets and the disruption of some observed jets.…”

The Nonlinear Evolution of a Twist in a Magnetic Shocktube

“…This means that the mechanism could permanently twist a larger flux tube without the gas-dynamic shock propagating along the entirety of the flux tube. The final state of the shocktube presented is similar to the equilibrium assumed by Zaqarashvili et al (2010) and Díaz et al (2011). They consider a magnetic flux tube with a helical magnetic field and mass flow along the z-axis.…”

“…The end result is a highly twisted magnetic flux tube with a sub-Alfvénic mass flow which pulls the magnetic field structure along the z-axis. This is much like the flux tubes used as a starting point for kink instability studies by Zaqarashvili et al (2010) and Díaz et al (2011).…”

On Modeling the Kelvin–Helmholtz Instability in Solar Atmosphere

“…First, the axial mass flow reduces the threshold of the kink instability in twisted magnetic tubes. Second, the twist of the magnetic field leads to the KH instability of sub-Alfvénic flows for the harmonics with a sufficiently large azimuthal mode number m. Díaz et al (2011) also studied the equilibrium and stability of twisted magnetic flux tubes with mass flows, but for flows along the field lines. The authors focused on the stability and oscillatory modes of magnetic tubes with a uniform twist in a zero-beta plasma surrounded by a uniform cold plasma embedded in a purely longitudinal magnetic filed.…”