episciences.org_13628_2026051822190987620260518221909876episciences.orgraphael.tournoy+crossrefapi@ccsd.cnrs.frepisciences.orgOpen Plasma Science3076-146810.46298/journals/opshttp://ops.episciences.org10292024Volume 1JeanneBourgeoisÉcole Polytechniquehttps://ror.org/05hy3tk52Kyushu Universityhttps://ror.org/00p4k0j84MaximeLesurInstitut Jean Lamourhttps://ror.org/05k1smh27Institut Universitaire de Francehttps://ror.org/055khg266https://orcid.org/0000-0001-9747-5616Guillermo CuervaLazaroInstitut Jean Lamourhttps://ror.org/05k1smh27YusukeKosugaKyushu Universityhttps://ror.org/00p4k0j84https://orcid.org/0000-0002-4075-5542In magnetized plasmas, a radial gradient of parallel velocity, where parallel refers to the direction of magnetic field, can destabilise an electrostatic mode called Parallel Velocity Gradient (PVG). The theory of PVG has been mainly developed assuming a single species of ions. Here, the role of impurities is investigated based on a linear, local analysis, in a homogeneous, constant magnetic field. To further simplify the analysis, the plasma is assumed to contain only two ion species - main ions and one impurity species - while our methodology can be straightforwardly extended to more species. In the cold-ion limit, retaining polarization drift for both main ions and impurity ions, and assuming Boltzmann electrons, the system is described by 4 fluid equations closed by quasi-neutrality. The linearized equations can be reduced to 2 coupled equations: one for the electric potential, and one for the effective parallel velocity fluctuations, which is a linear combination of main ion and impurity parallel velocity fluctuations. This reduced system can be understood as a generalisation of the Hasegawa-Mima model. With finite radial gradient of impurity parallel flow, the linear dispersion relation then describes a new instability: the impurity-modified PVG (i-PVG). Instability condition is described in terms of either the main ion flow shear, or equivalently, an effective flow shear, which combines main ion and impurity flow shears. Impurities can have a stabilising or destabilising role, depending on the parameters, and in particular the direction of main flow shear against impurity flow shear. Assuming a reasonable value of perpendicular wavenumber, the maximum growth rate is estimated, depending on impurity mass, charge, and concentration.17 pages, 12 figures102920241005202413628French National Research Agency (ANR)ANR-19-CE30-0005https://creativecommons.org/licenses/by/4.0https://creativecommons.org/licenses/by/4.0https://creativecommons.org/licenses/by/4.0arXiv:2405.0847210.48550/arXiv.2405.08472https://arxiv.org/abs/2405.08472v2https://arxiv.org/abs/2405.08472v110.46298/ops.13628http://ops.episciences.org/13628https://arxiv.org/pdf/2405.08472v3https://arxiv.org/pdf/2405.08472v3