The plasma modes are significantly influenced by the simple or/and molecular anions. The reciprocity of beam and tri-ion electron (TIE) plasmas is modeled by the kinetic theory. The set of Vlasov–Poisson equation is solved and decomposed by the Laguerre–Gaussian function under paraxial approximation. The beam plasma expedites unstable twisted modes (UTMs) in the TIE plasma. The UTM or instability is calibrated via axial and azimuthal wave numbers, wind speed, and its growth essence. The qualitative and quantitative anatomy of the instability threshold is also predicted. Our model is eminently applicable to the space plasmas and has been applied to the Ar+–F−–[Formula: see text] and Xe+–F−–[Formula: see text] electron plasmas, specifically.