1D kappa distributions with various characteristic potentials of radial and angular dependence: positive attractive potential (oscillation-type) ﹩{\rm{\Phi }}(r)/m=k\cdot {r}^{b}﹩ with b = 2, plotted for kappa indices, κ = 1.55 (a), 2.5 (b), and 20 (c); negative attractive potential (gravitational-type) ﹩{\rm{\Phi }}(r)/m=-k\cdot {r}^{-b}﹩ with b = 1, plotted for kappa indices κ = 2 (d), 2.5 (e), and 2.9 (f); and angular potential ﹩{\rm{\Phi }}(\vartheta )=-{\boldsymbol{\mu }}\cdot {\boldsymbol{B}}=-\mu \,B\cos \vartheta ﹩ with ﹩\beta \equiv \mu \,B/({k}_{{\rm{B}}}T)=2﹩, plotted for kappa indices κ = 1.55 (g), 2.5 (h), and 20 (i).