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Developments in the theory of collisionless reconnection in magnetic configurations with a strong guide field

We review some recent results that have been obtained in the investigation of collisionless reconnection in two dimensional magnetic configurations with a strong guide field in regimes of interest for laboratory plasmas. First we adopt a two-fluid dissipationless plasma model where the plasma evolution is described by the advection of two Lagrangian invariant fields. Then, we show that an analogous formulation in terms of Lagrangian invariants applies to the case where the electron response is obtained from a drift-kinetic model.