Can High-Mode Magnetohydrodynamic Waves Propagating in a Spinning Macrospicule Be Unstable Due to the Kelvin–Helmholtz Instability?

Abstract

We investigate the conditions at which high-mode magnetohydrodynamic (MHD) waves propagating in a spinning solar macrospicule can become unstable with respect to the Kelvin--Helmholtz instability (KHI). We consider the macrospicule as a weakly twisted cylindrical magnetic flux tube moving along and rotating around its axis. Our study is based on the dispersion relation (in complex variables) of MHD waves obtained from the linearized MHD equations of an incompressible plasma for the macrospicule and cool ($\beta = 0$, rate of the plasma to the magnetic pressure) plasma for its environment. This dispersion equation is solved numerically at appropriate input parameters to find out an instability region or window that accommodates suitable unstable wavelengths on the order of the macro\-spicule width. It is established that an $m = 52$ MHD mode propagating in a macro\-spicule with width of $6$~Mm, axial velocity of $75$~km\,s$^{-1}$, and rotating one of $40$~km\,s$^{-1}$ can become unstable against the KHI with instability growth times of $2.2$ and $0.57$~min at $3$ and $5$~Mm unstable wavelengths, respectively. These growth times are much shorter than the macrospicule lifetime, which lasts about $15$~min. An increase or decease in the width of the jet would change the KHI growth times, which remain more or less on the same order when they are evaluated at wavelengths equal to the width or radius of the macrospicule. It is worth noting that the excited MHD modes are super-Alfv\'enic waves. A change in the background magnetic field can lead to another MHD mode number $m$ that ensures the required instability window.