The tearing mode instability facilitates the formation of magnetic islands and thereby inhibits the performance of fusion plasmas by increasing the energy fluxes from the plasma core. The growth of magnetic islands is related to currents flowing parallel to the magnetic field and, for long narrow islands (with the width comparable to the ion Larmor radii), the contribution from the polarization current can significantly affect the time evolution. A numerical solution of the gyro-kinetic equations confirms, and extends, previous analytic studies of the effect of the polarization current on the island stability. A new analytic approximation that provides a good match over the full range of Larmor radius is also presented. The effect of perpendicular diffusion on the electron density gradient is simulated by the application of a smoothing function, with the results suggesting that the diffusion will noticeably affect the contribution of the polarization current to the island stability.
