Critical thickness for two‐dimensional tearing instability

Abstract

Dependence of tearing mode saturation state on the current sheet thickness is investigated by two‐dimensional (2‐D) full particle simulations. When the system length L x is taken to be the wavelength of the maximum growth mode L x = λ max = 12D (D: half‐thickness of the current sheet), the instability is found to saturate without producing significant reconnection if D > D cr 1st = 3.5 λ e , where λ e is the electron inertial length. When the system length is doubled L x = 2λ max , only insignificant effects are available for D > D cr 2nd = 2.7λ h , where λ h is the ion‐electron hybrid inertial length. Comparing these 2‐D results with a recent 3‐D result, it is shown clearly that a three‐dimensional effect reduces the current sheet thickness and thus leads to quick production of substantial reconnection even if D > D cr 1st .