Requirements on singly ionized lithium concentrations for magnetospheric seeding experiments

Optimum concentrations of singly ionized Li relative to warm protons, η ≡ nLi/np,w, for magnetospheric seeding experiments aimed at enhancing the electromagnetic proton cyclotron instability have been obtained analytically and numerically. This has been done by calculating the absolute maximum growth rates γmaxabs and enhancement F ≡ γmaxabs/γmax(η = 0) for the proton instability branch upon addition of cold lithium ions to an infinite anisotropic proton plasma. A necessary condition for enhancement is P ≡ βpAp²(Ap + 1) ≪ 1, where βp ≡ 8πnpKT∥,p/B0² and Ap ≡ (T⊥/T∥)p − 1. The shape of the linearly unstable spectrum strongly depends on the parameter [Ap/(Ap + 1)]/(mLi/ZLimp)−1. When the condition stated above is satisfied, the growth rate and the extension of the unstable spectrum in k space may increase with η. An optimum η value is found to exist.