Effects of trapped energetic ions on the interchange mode

Highlights: • We examine effects on trapped energetic ions on the ideal interchange mode. • The unstable ideal interchange mode is destabilized by the trapped energetic ions. • We also derive a generalized eigenvalue equation of the ideal interchange mode. • A radial profile of the ideal interchange mode is spread by trapped energetic ions. - Abstract: On the basis of the kinetic energy principle, effects on trapped energetic ions on the ideal interchange mode in helical systems are investigated. Approximating that the spatial profile of the ideal interchange mode is given, we introduce an extended dispersion relation of the ideal interchange mode. Numerical analyses of the dispersion relation show that the unstable ideal interchange mode is destabilized by the trapped energetic ions and has a finite rotation frequency due to the precession drift of the trapped energetic ions. We also derive a generalized eigenvalue equation of the ideal interchange mode in the presence of trapped energetic ions. By numerically solving the eigenvalue equation, it is found that a radial profile of the ideal interchange mode is spread by trapped energetic ions.