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 Lx is taken to be the wavelength of the maximum growth mode Lx = λmax = 12D (D: half‐thickness of the current sheet), the instability is found to saturate without producing significant reconnection if D > Dcr1st = 3.5 λe, where λe is the electron inertial length. When the system length is doubled Lx = 2λmax, only insignificant effects are available for D > Dcr2nd = 2.7λh, where λh 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 > Dcr1st.