Dense cores are the final place where turbulence is dissipated. It has been proposed from theoretical arguments that the non-thermal velocity dispersion should be narrower both for molecular ions (compared to neutrals) and for transitions with higher critical densities. To test these hypotheses, we compare the velocity dispersion of N$_2$H$^+$ (1--0) (n$_{rm crit}$ = $6times10^4$ cm$^{-3}) and NH$_3$ (n$_{rm crit}=2times10^3$ cm$^{-3}), in the dense core Barnard 5. We analyse well resolved and high signal-to-noise observations of NH$_3$ (1,1) and (2,2) obtained with combining GBT and VLA data, and N$_2$H$^+$ (1--0) obtained with GBT Argus, which present a similar morphology. % Surprisingly, the non-thermal velocity dispersion of the ion is systematically higher than that of the neutral by 20%. The derived sonic Mach number, $mathcal{M}_s = sigma_{rm NT}/c_s$, has peak values $mathcal{M}_{s, {rm N_2H^+}} = 0.59$ and $mathcal{M}_{s, {rm NH}_3} = 0.48$ for N$_2$H$^+$ and NH$_3$, respectively. % This observed difference may indicate that the magnetic field even deep within the dense core is still oscillating, as it is in the turbulent region outside the core. The ions should be more strongly dynamically coupled to this oscillating field than the neutrals, thus accounting for their broader linewidth. If corroborated by further observations, this finding would shed additional light on the transition to quiescence in dense cores.
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