Theoretical Resolution of Magnetic Reconnection in High Energy Plasmas

The formation of macroscopic reconnected magnetic structures (islands) have been observed in advanced experiments on weakly collisional, well confined plasmas while established theories of the drift-tearing modes, which depend strongly on the electron temperature gradient and can describe the formation of these structures, had predicted practically inaccessible excitation thresholds for them in these regimes. The relevant theoretical dilemma is resolved as mesoscopic modes that depend critically on the ratio of the transverse (to the magnetic field) to the longitudinal thermal conductivity{D^e_{\perp}/D^e_{\|}, can produce large scale magnetic reconnection. These modes are envisioned to emerge from a background, which can be coherent, of collisionless microscopic reconnecting modes driven by the electron temperature gradient, that create a sequence of adjacent strings of magnetic islands and increase considerably the ratio {D^e_{\perp}/D^e_{\|} over its classical value. The mesoscopic reconnecting mode is treated by a singular perturbation analysis involving three asymptotic regions and the small parameters ${(D_{\perp }^e\mathrm{/}{D}_{\mathrm{\parallel }}^e)}^{1\mathrm{/}4}$ and ${ϵ}_{\ast }^{1\mathrm{/}4}$, where ${ϵ}_{\ast }\equiv D_m\mathrm{/}{D}_A$, $D_m$ is the magnetic diffusion coefficient, $D_A\sim {\mathtt{\text{v}}}_A^2{r}_{Te}\mathrm{/}(D_B{k}_{\perp })$, $r_{Te}\equiv (-d\mathtt{\text{ln}}{T}_e\mathrm{/}dr{)}^{-1}$, $k_{\perp }$ is the transverse mode number, \texttt{v}^{2}_{A}=B^{2}/(4\pi{nm}_{i})} and $D_B=c{T}_e\mathrm{/}(eB)$.