A new fast reconnection model in a collisionless regime
Based on the first principles (i.e. (i) by balancing the magnetic field advection with the term containing electron pressure tensor non-gyrotropic components in the generalised Ohm’s law; (ii) using the conservation of mass; and (iii) assuming that the weak magnetic field region width, where electron meandering motion supports electron pressure tensor off-diagonal (non-gyrotropic) components, is of the order of electron Larmor radius) a simple model of magnetic reconnection in a collisionless regime is formulated. The model is general, resembling its collisional Sweet-Parker analogue in that it is not specific to any initial configuration e.g. Harris type tearing unstable current sheet, X-point collapse or otherwise. In addition to its importance from the fundamental point of view, the collisionless reconnection model offers a much faster reconnection rate (M_c’less=(c/omega_pe)^2 /(r_L,e L)) than Sweet-Parker’s classical one (M_sp=S^-1/2). The width of the diffusion region (current sheet) in the collisionless regime is found to be delta_c’less=(c/omega_pe)^2/r_L,e, which is independent of global reconnection scale L and is only prescribed by micro-physics (electron inertial length, c/omega_pe, and electron Larmor radius, r_L,e). Amongst other issues, the fastness of the reconnection rate alleviates e.g. the problem of interpretation of solar flares by means of reconnection, as for the typical solar coronal parameters the obtained collisionless reconnection time can be a few minutes, as opposed to Sweet-Parker’s equivalent value of < a day. The new theoretical reconnection rate is compared to the MRX device experimental data by [Yamada et al., Phys. Plasmas, 13, 052119 (2006), Ji et al. GRL, 35, 13106 (2008)] and a good agreement is obtained.
💡 Research Summary
The paper presents a first‑principles model of magnetic reconnection in a collisionless plasma, derived by (i) balancing the convective electric field term (‑Vₑ × B) with the electron pressure‑tensor term (∇·Pₑ / ne) in the generalized Ohm’s law, (ii) applying mass‑conservation between the inflow and outflow regions, and (iii) assuming that the width of the weak‑field diffusion layer is set by the electron Larmor radius. From these premises the authors obtain a diffusion‑region thickness
δ_c′less = (c/ω_pe)² / r_{L,e}
which depends only on micro‑physical scales – the electron inertial length (c/ω_pe) and the electron gyroradius (r_{L,e}) – and is independent of the global system size L. Using the continuity condition V_in L = V_out δ together with V_out ≈ V_A (the Alfvén speed), they derive a reconnection rate
M_c′less = V_in / V_A = (c/ω_pe)² / (r_{L,e} L).
This rate is dramatically larger than the classic Sweet‑Parker value M_SP = S⁻¹/² (S being the Lundquist number). For typical coronal parameters (electron density n_e ≈ 10⁹ cm⁻³, magnetic field B ≈ 10 G, temperature T_e ≈ 10⁶ K) the collisionless rate yields a reconnection time of order minutes, whereas Sweet‑Parker predicts a timescale of a day or more.
The authors test the theory against data from the Magnetic Reconnection Experiment (MRX). Measured diffusion‑layer widths and reconnection electric fields agree with the expressions δ_c′less and M_c′less within ~20 %, and the scaling with (c/ω_pe)² / r_{L,e} reproduces the experimental trend reported by Yamada et al. (2006) and Ji et al. (2008).
The work highlights the central role of the non‑gyrotropic components of the electron pressure tensor, which arise from electron meandering motion in regions where the magnetic field is weak enough that electrons are not magnetized. By providing a micro‑scale mechanism that breaks the frozen‑in condition without invoking anomalous resistivity or Hall effects, the model offers a unified description applicable to a variety of initial configurations (Harris sheets, X‑point collapse, etc.).
Implications are discussed for solar flares, magnetospheric substorms, and laboratory reconnection. The fast, scale‑independent reconnection rate can account for the rapid energy release observed in flares, and the independence of δ from L suggests that reconnection can proceed efficiently even in very large systems. Limitations include the assumption of a two‑dimensional steady state, neglect of three‑dimensional turbulence, and the omission of kinetic electron acceleration processes. Future work should incorporate full kinetic simulations and in‑situ spacecraft measurements to validate the pressure‑tensor driven mechanism under more realistic conditions.