Waves in bi-ion plasmas are affected by asymmetry. The kinetic theory of the Maxwellian and Lorentzian/Kappa-distributed bi-ion plasma is ameliorated to incorporate the transfer of orbital angular momentum from the helical electric field to the plasma modes. By operating the Laguerre-Gaussian (LG) function, the perturbed distribution function and helical electric field are decomposed into characteristic axial and azimuthal components. In symmetric bi-ion plasmas, the conventional ion modes/waves are only present if both ions have similar masses and the concentration of the electrons is negligible. An imbalance of the symmetry is considered by the contamination of a small fraction of the heavy immobile ions, which urges the negative ions to become heavier than the positive ions in the bi-ion plasma system. The distinct masses of the positive and negative ions provoke mass-asymmetry in the Kappa-distributed bi-ion plasmas. The signature of the unique acoustic-laden twisted modes in non-Maxwellian asymmetric bi-ion plasma is perceived by the temperature of the lighter positive ions and the dynamics of the heavier negative ion. The deliberated results of Landau damping are displayed for distinct values of the azimuthal wave-number and spectral index, temperature-variation and mass-asymmetry.
