LAUSR

Ions and electrons play an important role in various stages of the star formation process. By following the magnetic field of their environment and interacting with neutral species, they slow down the gravitational collapse of the proto-star envelope. This process (known as ambipolar diffusion) depends on the ionisation degree, which can be derived from the \hco abundance. We present a study of \hco and its isotopologues (H$^{13}$CO$^+$, HC$^{18}$O$^+$, DCO$^+$, and H$^{13}$CO$^+$) in the low-mass proto-star IRAS16293$-$2422. The structure of this object is complex, and the HCO$^+$ emission arises from the contribution of a young NW-SE outflow, the proto-stellar envelope and the foreground cloud. We aim at constraining the physical parameters of these structures using all the observed transitions. For the young NW-SE outflow, we derive $T_{\rm kin}=180-220$ K and $n({\rm H_2})=(4-7)\times10^6$ cm$^{-3}$ with an HCO$^+$ abundance of $(3-5)\times10^{-9}$. Following previous studies, we demonstrate that the presence of a cold ($T_{\rm kin}$$\leqslant$30 K) and low density ($n({\rm H_2})\leqslant1\times10^4$ cm$^{-3}$) foreground cloud is also necessary to reproduce the observed line profiles. We have used the gas-grain chemical code \textsc{nautilus} to derive the HCO$^+$ abundance profile across the envelope and the external regions where X(HCO$^+$)$\gtrsim1\times10^{-9}$ dominate the envelope emission. From this, we derive an ionisation degree of $10^{-8.9}\,\lesssim\,x(e)\,\lesssim\,10^{-7.9}$. The ambipolar diffusion timescale is $\sim$5 times the free-fall timescale, indicating that the magnetic field starts to support the source against gravitational collapse and the magnetic field strength is estimated to be $6-46 \mu$G.