Role of Inertial and Inductive Modes in Magnetic Reconnection Events

Recently, an accurate analysis of the database of magnetic island rotation performed with the JET machine [1] has revealed that, in the frame of zero radial electric field, the island rotation frequency is about 0.9$\omega_{di}$, where $\omega_{di}$ is the ion diamagnetic frequency. The drift-tearing mode theory of reconnection in low collisionality regimes predicts a phase velocity in the opposite direction [2] and, under strictly collisionless conditions, stability in the presence of electron temperature gradients. To explain the observations, a ``mode inductivity'' $L_{\parallel}\equiv(4\pi/c^{2})S_{L}$ has been introduced [3] whose effects replace those of finite resistivity. This has led to a linear instability [4] with $\omega$ close to $\omega_{di}$. The reconnection layer thickness is proportional to the inductivity [4] and the mode has a dissipative growth rate. When considering plasmas with ultrarelativistic energies, the inertial skin depth becomes significant. Thus the width of the reconnection layer can be considered as relevant to realistic theories.\\[4pt] [1] P. Buratti et al., 41st EPS Conference, ECA 38F, paper P1.014.\\[0pt] [2] B. Coppi, Phys. Fluids 8, (1965) 2273.\\[0pt] [3] B. Coppi, Bull. Am. Phys. Soc. 45, (2000) 366.\\[0pt] [4] B. Coppi, et al., Int. Fus. En. Conf. TH-P7/10.