Kink instability of a cylindrical current sheet

The paper is dedicated to studying the kink instability of one-dimensional cylindrical current sheet. A model of the self-consistent θ-pinch with constant drift frequencies of ions and electrons is chosen as the initial equilibrium. It is shown that the kink instability can develop in this equilibrium configuration. The dependences of growth rates and real parts of the instability frequency on the mode number are derived. The found dependences show that the wavelength of the unstable mode with the largest growth rate grows proportionally to the thickness of the current sheet, while the value of the growth rate decreases at the same time. Unstable modes develop only within a narrow range of wavelengths determined by the relative thickness of the current sheet. The instability growth rate and the number of unstable mode grow with increasing radius of the cylindrical current sheet. A possibility of application of the obtained results to description of the dynamics of current sheets in the magnetospheres of Uranus and Neptune is discussed in the paper.