We analyse new ALMA observations of the $^{29}$SiO ($ u$=0, $J$=8$-$7) and SO$_2$($ u$=0, $34_{3,31}$$-$$34_{2,32}$) line emissions of the circumstellar envelope (CSE) of the oxygen-rich AGB star R Dor. With a spatial resolution of $sim$2.3 au, they cover distances below $sim$30 au from the star providing a link between earlier observations and clarifying some open issues. The main conclusions are: 1) Rotation is confined below $sim$15 au from the star, with velocity reaching a maximum below 10 au and morphology showing no significant disc-like flattening. 2) In the south-eastern quadrant, a large Doppler velocity gas stream is studied in more detail than previously possible and its possible association with an evaporating planetary companion is questioned. 3) A crude evaluation of the respective contributions of rotation, expansion and turbulence to the morpho-kinematics is presented. Significant line broadening occurs below $sim$12 au from the star and causes the presence of high Doppler velocity components near the line of sight pointing to the centre of the star. 4) Strong absorption of the continuum emission of the stellar disc and its immediate dusty environment is observed to extend beyond the disc in the form of self-absorption. The presence of a cold SiO layer extending up to some 60 au from the star is shown to be the cause. 5) Line emissions from SO, $^{28}$SiO, CO and HCN molecules are used to probe the CSE up to some 100 au from the star and reveal the presence of two broad back-to-back outflows, the morphology of which is studied in finer detail than in earlier work.
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