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An overview on Vertical Displacement Oscillatory Modes driven by fast ions is presented. These modes have been identified by analytic work in 2022 [1,2] and their existence for realistic tokamak geometry has been confirmed by numerical simulations using the NIMROD code [3]. Together with Global Alfvén Eigenmodes (GAE), VDOM are a candidate to explain the observation of axisymmetric, saturated magnetic fluctuations, with toroidal mode number n=0, in recent JET [4] and TCV [5] experiments. In this presentation, we shall focus on the important differences between GAE and VDOM as clarified by semi-analytic work in the cylindrical (straight tokamak) limit. VDOM are global, external plasma modes whose existence rely on the interaction between the plasma current and the currents induced on the nearby conducting wall when the plasma boundary is perturbed. An analytic dispersion relation that contains both VDOM and ideal-MHD unstable vertical displacements is discussed. While VDOM are generally immune against continuum damping, if the wall is brought very close to the plasma boundary and the plasma density remains relatively large up to the last-closed-flux-surface (as in the case of H-mode discharges), the VDOM oscillation frequency may interact with the Alfvén continuum spectrum, giving rise to continuum damping. Specific types of fast ion distribution functions that can provide an instability drive for n=0 modes are considered. With the fast ion distribution function expressed as f_h (ℇ,Λ,P_φ) (ℇ is the energy, Λ=μB_0/ℇ is a pitch angle variable, where μ is the magnetic momentum, and P_φ is the toroidal angular momentum), the drive of axisymmetric modes requires either a non-monotonic distribution in the energy direction (with Λ and P_φ held constant) or anisotropy, i.e. a variation of f_h with Λ. For fusion alpha particles, it is shown that finite orbit width effects lead to an anisotropy with a peak of (∂f_h)⁄∂Λ in the region of trapped orbits. A possible drive due this anisotropy is discussed. Numerical simulations of n=0 modes obtained with the NIMROD code are shown, including a preliminary assessment of the fast ion instability drive for these modes.
[1] T. Barberis, F. Porcelli, and A. Yolbarsop, Fast ion driven vertical modes in magnetically confined toroidal plasmas, Nuclear Fusion Letter 62, 064002 (2022).
[2] T. Barberis, A. Yolbarsop, and F. Porcelli, Vertical displacement oscillatory modes in tokamak plasma, Journal of Plasma Physics 88, 905880511 (2022).
[3] T. Barberis, C.C. Kim, F. Porcelli, D. Banerjee, N. Hawkes, Ye O. Kazakov, Y.Q. Liu, H.J.C. Oliver, S.E. Sharapov, A. Yolbarsop, NIMROD Team and JET Contributors, Simulations of vertical displacement oscillatory modes and global Alfvén Eigenmodes in JET geometry, Nuclear Fusion 64, 126064 (2024).
[4] H.J.C. Oliver, D. King, Ž. Štancar, S.E. Sharapov, D. Banerjee, T. Barberis, R. Coelho, I. Coffey, M. Dreval, M. Fitzgerald, L. Frassinetti, C. Giroud, N. Hawkes, D. Keeling, C.C. Kim, E. Lerche, F. Porcelli, G. Szepesi, Axisymmetric eigenmodes excited by alpha particle energy gradients in JET D-T plasmas, Physical Review Letters, 136 (2026) 055101.
[5] M. Dreval, S.E. Sharapov, H.J.C. Oliver, M. Fitzgerald, A.N. Karpushov, A. Jansen van Vuuren, J. Poley, M. Podesta, F. Porcelli, the TCV Team and the EUROfusion Tokamak Exploitation Team, Axisymmetric global Alfvén eigenmodes in the TCV tokamak, under review for publication in Nuclear Fusion (2026).