The micro-Resistive WELL detector for the phase-2 upgrade of the LHCb muon detector

The $\mu$-RWELL is a new generation Micro-Pattern Gaseous Detector, composed of two elements: the cathode and the $\mu$-RWELL_PCB including the amplification stage, realized with a polyimide structure micro-patterned with a blind-hole matrix, embedded through a Diamond-Like Carbon (DLC) resistive layer with the readout PCB. Different layouts of the resistive stage have been studied: the simplest one is based on a single DLC layer with edge grounding, suitable for low rate applications (30-40 kHz/cm$^{2}$). More sophisticated schemes are under study for high rate purposes (up to 2-3 MHz/cm$^{2}$).The high-rate versions are still under intense R&D; in order to optimize the performance and the constructive process but this detector seems already a valid candidate to be used for the phase 2 upgrade of the LHCb muon detector. For this upgrade, the experiment is targeting a luminosity of 2x10$^{34}$ cm$^{-2}$ s$^{-1}$, with strong requirements on the robustness and detection efficiency of the muon system. We report on the ongoing R&D;, showing also the latest measured performances of the new high rate versions of the detector.