Relativistic Two-fluid Simulations of Guide Field Magnetic Reconnection

The nonlinear evolution of relativistic magnetic reconnection in sheared magnetic configuration (with a guide field) is investigated by using two-dimensional relativistic two-fluid simulations. Relativistic guide field reconnection features the charge separation and the guide field compression in and around the outflow channel. As the guide field increases, the composition of the outgoing energy changes from enthalpy-dominated to Poynting-dominated. The inertial effects of the two-fluid model play an important role to sustain magnetic reconnection. Implications for the single fluid magnetohydrodynamic approach and the physics models of relativistic reconnection are briefly addressed.

💡 Research Summary

This paper presents a comprehensive study of relativistic magnetic reconnection in a sheared magnetic configuration that includes a guide field, using two‑dimensional relativistic two‑fluid simulations. The authors solve the full set of relativistic continuity, momentum, and energy equations for electrons and positrons separately, coupled with Maxwell’s equations and divergence‑cleaning potentials. The initial configuration is a Harris‑type current sheet with a uniform guide field B_G added in the out‑of‑plane (y) direction; the background density, pressure, and drift velocities are chosen so that the electron inertial length and Larmor radius are much smaller than the sheet thickness L. Simulations are performed on domains up to 240 L × 120 L with point‑symmetry at the X‑point to reduce computational cost, and a localized resistivity (via an inter‑species friction term τ_fr) is employed, giving an effective Reynolds number S ≈ 30 near the reconnection site and S ≈ 3000 in the far field.

Five runs explore guide‑field strengths B_G/B_0 = 0, 0.25, 0.5, 1.0, 1.5, corresponding to magnetization parameters σ_y,in ranging from 0 to 0.09. The authors monitor the reconnection rate R, charge separation, guide‑field compression, and the partition of outgoing energy between plasma enthalpy, bulk kinetic energy, and Poynting flux.

Key findings:

1. Charge separation and guide‑field compression – When a guide field is present, the reconnection outflow drags and piles up B_y at the edges of the plasmoid and within the narrow exhaust. This leads to a strong compression of the guide field and a pronounced charge‑separation layer: positrons dominate the upper half of the exhaust, electrons the lower half, with a charge‑density contrast of order 0.5. The non‑neutral layers extend over a large spatial region, a feature absent in single‑fluid MHD.

2. Composition of the reconnection electric field – By combining the two‑fluid momentum equations, the authors derive a generalized Ohm’s law. Along the inflow line (x = 0) the reconnection electric field E_y is decomposed into four contributions: (i) convection (− hv × B), (ii) advective inertia (terms proportional to ∂(h u_y)/∂z), (iii) inter‑species friction (effective resistivity η_eff = τ_fr/q_p²), and (iv) viscous inertia (artificial viscosity introduced for numerical stability). The analysis shows that outside the diffusion region the convection term dominates, while inside the diffusion region the advective inertia is the largest contributor. The frictional term accounts for only about one‑third to one‑quarter of E_y because the local Lorentz factor γ≈1.6 suppresses it. Viscous inertia replaces advective inertia very close to the neutral plane, suggesting that kinetic effects act quasi‑viscously in that region.

3. Reconnection rate – After an initial ramp‑up (t ≈ 50 τ_c), the normalized reconnection rate R settles to a quasi‑steady value. For the antiparallel case (B_G = 0) R≈0.14; with B_G/B_0 = 0.5, R≈0.10; and for the strongest guide field (B_G/B_0 = 1.5) R≈0.055. The rate decreases modestly with increasing guide field, but remains robust, indicating that the inertial mechanisms identified above sustain reconnection even when the guide field is strong.

4. Energy conversion and flux partition – The total energy flux is split into Poynting flux (further divided into guide‑field and reconnecting‑field contributions) and plasma flux (enthalpy, bulk kinetic, and rest‑mass terms). In the weak‑guide cases the enthalpy flux dominates the plasma energy transport, and the reconnection outflow is primarily heated plasma. As the guide field strengthens, the guide‑field Poynting flux grows and eventually exceeds the enthalpy flux; for σ_y,in≈0.09 the Poynting flux carries more than half of the total outgoing energy. This transition from enthalpy‑dominated to Poynting‑dominated outflows confirms theoretical predictions that a strong guide field can alter the energy budget of relativistic reconnection.

5. Plasma structure – The outflow jet reaches speeds of 0.8–0.85 c, with individual species attaining four‑velocities u_x ≈ 2.1 c. A reverse flow forms downstream of the plasmoid, compressing the ambient magnetic field and generating backward‑flow fronts. The plasmoid exhibits a “crab‑claw” shape and, at later times, the guide‑field B_y develops a weak bifurcation that splits the exhaust into three layers, possibly due to a velocity‑shear instability.

Overall, the study demonstrates that relativistic two‑fluid effects—particularly charge separation and fluid inertia—play a decisive role in sustaining magnetic reconnection and shaping the energy conversion when a guide field is present. These results highlight limitations of single‑fluid relativistic MHD models, which cannot capture the non‑neutral layers and the dominant inertial contributions identified here. The findings have direct implications for high‑energy astrophysical environments (pulsar winds, magnetar flares, GRB jets, AGN coronae) where strong guide fields and relativistic magnetization are expected, suggesting that reconnection in such settings may efficiently convert magnetic energy into Poynting flux rather than purely heating the plasma.