Numerical study of collisionless q = 1 double tearing instability in a cylindrical plasma

The double tearing mode (DTM) instability with two q _s = 1 rational surfaces is investigated by taking into account the collisionless effects, including electron inertia and electron viscosity in a cylindrical geometry. The calculations show that for q-profile with a small distance between two rational surfaces, Δr _s, there exists a broad linear spectrum of collisionless DTMs. The collisionless effects not only can significantly increase the linear growth rate of DTMs but can also enlarge the width of spectrum of unstable modes. For the q-profile with fixed Δr _s and fixed magnetic shears at two rational surfaces, the high-order harmonics with smaller wavelength, such as the m/n = 2/2, 3/3 and 4/4 modes, can be easily excited to have larger growth rates than the m/n = 1/1 mode by `lifting' the safety factor value between two rational surfaces. The characteristics of eigenmode structures of the most unstable and secondly unstable DTMs with various mode numbers are analyzed in detail and the corresponding collisionless scalings are numerically obtained and verified theoretically based on the previous relevant analytical theories. In addition, the synergetic effects of plasma resistivity, electron inertia and electron viscosity on the linear growth rates of DTMs are analyzed.