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We use MERLIN, VLA and VLBA observations of Galactic \HI absorption towards3C~138 to estimate the structure function of the \HI opacity fluctuations at AUscales. Using Monte Carlo simulations, we show that there is likely to be asignificant bias in the estimated structure function at signal-to-noise ratioscharacteristic of our observations, if the structure function is constructed inthe manner most commonly used in the literature. We develop a new estimatorthat is free from this bias and use it to estimate the true underlyingstructure function slope on length scales ranging $5$ to $40$~AU. From a powerlaw fit to the structure function, we derive a slope of $0.81^{+0.14}_{-0.13}$,i.e. similar to the value observed at parsec scales. The estimated upper limitfor the amplitude of the structure function is also consistent with themeasurements carried out at parsec scales. Our measurements are henceconsistent with the \HI opacity fluctuation in the Galaxy being characterizedby a power law structure function over length scales that span six orders ofmagnitude. This result implies that the dissipation scale has to be smallerthan a few AU if the fluctuations are produced by turbulence. This inferredsmaller dissipation scale implies that the dissipation occurs either in (i)regions with densities $\gtrsim 10^3 $cm$^-3$ (i.e. similar to that inferredfor "tiny scale" atomic clouds or (ii) regions with a mix of ionized and atomicgas (i.e. the observed structure in the atomic gas has a magneto-hydrodynamicorigin).

The structure function of Galactic \HI opacity fluctuations on AU scales based on MERLIN, VLA and VLBA data