Ripple-precession resonance of fast ions in DTT

The Divertor Tokamak Test (DTT) [1] is planned to be heated through a mix of 45 MW heating power, including 15 MW negative-ion-based Neutral Beam heating (NNBI) which is currently being developed by Consorzio RFX in Padova, Italy [2]. An issue for DTT is that a Toroidal Field (TF) ripple with a maximum value of about ~ 0.42 % (with respect to the on-axis magnetic field B0) is expected on the low-field side (LFS) [3, 4], and this ripple interacts with fast ions through rather well-known phenomena of ripple-precession resonances [5]. In fact, TF ripple breaks the conservation of the fast ion toroidal canonical momentum, expressed as P? = g?k -?p, where g is the covariant toroidal field component in Boozer coordinates, ?k = vk/B and ?p is the poloidal flux which serves as radial coordinate, in such a way that the decrease of the canonical momentum results in the increase of the radial positions of the particles, which are ultimately lost. Regarding the reference DTT configuration [3, 4], and with the parameters of the NNBI project [2], namely energy E = 400 keV and injection angle of ~ 40o w.r.t. the first wall, it is possible to recognize at least four resonances for trapped ions, of the type ?b-nN?d = 0, ?b and ?d being the bounce and precession frequency, respectively, and N the ripple periodicity. Those resonances are characterized by toroidal wavenumbers 3 <= n <= 6. The resonances seem to be well spaced apart, so that the possibility of stochastic overlapping [6] is remote: this is consistent with the calculated contribution of ripple losses in DTT, which are of the order of less than 0.5 % in the standard single-null scenario, as already published in [2]. Acknowledgement: This work is carried out in the frame of the DTT activity. The authors are very grateful to all the colleagues involved in the DTT project for their precious contribution.