Magnetohydrodynamic Kelvin-Helmholtz instability for finite-thickness fluid layers

We have derived the analytical formulas for the Kelvin-Helmholtz instability (KHI) of two superposed finite-thickness fluid layers with the magnetic field effect into consideration. The linear growth rate of KHI will be reduced when the thickness of the fluid with large density is decreased or the thickness of fluid with small density is increased. When the thickness and the magnetic field act together on the KHI, the effect of thickness is more obvious when the magnetic field intensity is weak. The magnetic field transition layer destabilizes (enforces) the KHI, especially in the case of small thickness of the magnetic field transition layer. When considering the effect of magnetic field, the linear growth rate of KHI always decreases after reaching the maximum with the increase of total thickness. The stronger the magnetic field intensity is, the more obvious the growth rate decreases with the total thickness. Thus, it should be included in applications where the effect of fluid thickness on the KHI cannot be ignored, such as in double-cone ignition scheme for inertial confinement fusion.