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Ions and electrons play an important role in various stages of the starformation process. By following the magnetic field of their environment andinteracting with neutral species, they slow down the gravitational collapse ofthe proto-star envelope. This process (known as ambipolar diffusion) depends onthe ionisation degree, which can be derived from the \hco abundance. We presenta study of \hco and its isotopologues (H$^{13}$CO$^+$, HC$^{18}$O$^+$, DCO$^+$,and H$^{13}$CO$^+$) in the low-mass proto-star IRAS16293$-$2422. The structureof this object is complex, and the HCO$^+$ emission arises from thecontribution of a young NW-SE outflow, the proto-stellar envelope and theforeground cloud. We aim at constraining the physical parameters of thesestructures using all the observed transitions. For the young NW-SE outflow, wederive $T_{\rm kin}=180-220$ 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$30 K) andlow density ($n({\rm H_2})\leqslant1\times10^4$ cm$^{-3}$) foreground cloud isalso necessary to reproduce the observed line profiles. We have used thegas-grain chemical code \textsc{nautilus} to derive the HCO$^+$ abundanceprofile across the envelope and the external regions whereX(HCO$^+$)$\gtrsim1\times10^{-9}$ dominate the envelope emission. From this, wederive an ionisation degree of$10^{-8.9}\,\lesssim\,x(e)\,\lesssim\,10^{-7.9}$. The ambipolar diffusiontimescale is $\sim$5 times the free-fall timescale, indicating that themagnetic field starts to support the source against gravitational collapse andthe magnetic field strength is estimated to be $6-46 \mu$G.

3D modelling of HCO$^+$ and its isotopologues in the low-mass proto-star IRAS16293$-$2422