Collective Modes Associated with Rarefied Populations of Heavy Nuclei

Plasmas in which low density populations of heavier nuclei than those of the main population are a frequent occurrence [1] and an important case is that of ``impurities'' whose cyclotron frequencies, $Omega_I$, differ from that, $Omega_i$, of the main population. $Omega_I$, ``frequency'' modes are found to be sustained by the impurity density gradient. In the limit of ``short'' transverse wavelengths $k_{perp}^{2}d_{i}^{2}>1$ where $d_{i}={c}/{omega_{pi}}$ these modes are nearly electrostatic while in the relatively long wavelength limit $(k_{perp}^{2}d_{i}^{2}ll1)$ they involve significant magnetic field fluctuations [2]. The relevant transverse phase velocities are in the direction of the local impurity diamagnetic velocity and produce a transport of this population across the magnetic field. Growth rates are found which depend on pre-existing thermal energy transport processes for the same population such as those associated with the excitation of the lower frequency ``impurity drift modes'' introduced in Ref. [3].}\

1. C. Mazzotta, et al. Paper IAEA-CN-899 MFE, Fusion Energy Conference (I.A.E.A., Vienna, 2021).\

2. B. Coppi, S. Cowley, R. Kulsrud, P. Detragiache, and F. Pegoraro, Phys. Fluids 29, 4060 (1986).\

3. B. Coppi, H. Furth, M. Rosenbluth and R. Sagdeev, Phys. Rev. Lett. 17, 377 (1966).\