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tokens: We thank the referee for an encouraging and incisive report which improved the quality of this paper. We gratefully thank Thierry Foglizzo for fruitful exchanges and the mpi-amrvac development team, in particular Oliver Porth, Rony Keppens and Zakaria Meliani, for useful assistance. We acknowledge the financial support from the UnivEarthS Labex programme of Sorbonne Paris Cité (ANR-10-LABX-0023 and ANR-11-IDEX-0005-02). IEM acknowledges financial support from the ENS of Cachan through a contrat doctoral spécifique pour normaliens and from the University Paris 7 Diderot. The numerical simulations were run on the François Arago Centre facilities in Paris 7 and using the HPC resources from GENCI-CINES (Grant c2015047469).