Parker Solar Probes first encounters with the Sun revealed the presence of ubiquitous localised magnetic deflections in the inner heliosphere; these structures, often called switchbacks, are particularly striking in solar wind streams originating from coronal holes. We report the direct evidence for magnetic reconnection occuring at the boundaries of three switchbacks crossed by Parker Solar Probe (PSP) at a distance of 45 to 48 solar radii of the Sun during its first encounter. We analyse the magnetic field and plasma parameters from the FIELDS and SWEAP instruments. The three structures analysed all show typical signatures of magnetic reconnection. The ion velocity and magnetic field are first correlated and then anti-correlated at the inbound and outbound edges of the bifurcated current sheets with a central ion flow jet. Most of the reconnection events have a strong guide field and moderate magnetic shear but one current sheet shows indications of quasi anti-parallel reconnection in conjunction with a magnetic field magnitude decrease by $90%$. Given the wealth of intense current sheets observed by PSP, reconnection at switchbacks boundaries appears to be rare. However, as the switchback boundaries accomodate currents one can conjecture that the geometry of these boundaries offers favourable conditions for magnetic reconnection to occur. Such a mechanism would thus contribute in reconfiguring the magnetic field of the switchbacks, affecting the dynamics of the solar wind and eventually contributing to the blending of the structures with the regular wind as they propagate away from the Sun.
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