  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$_{\rm crit}$ =
$6\times10^4$ cm$^{-3}) and NH$_3$ (n$_{\rm crit}=2\times10^3$ 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.
