A full orbit code is used to compute collisionless losses of fusion particles from three proposed burning plasma tokamaks: the International Tokamak Experimental Reactor ITER; a spherical tokamak power plant (STPP) [T. C. Hender, A. Bond, J. Edwards, P. J. Karditsas, K. G. McClements, J. Mustoe, D. V. Sherwood, G. M. Voss, and H. R. Wilson, Fusion Eng. Des. 48 , 255 2000]; and a spherical tokamak components test facility (CTF) [H. R. Wilson, G. M. Voss, R. J. Akers, L. Appel, A. Dnestrovskij, O. Keating, T. C. Hender, M. J. Hole, G. Huysmans, A. Kirk, P. J. Knight, M. Loughlin, K. G. McClements, M. R. O’Brien, and D. Yu. Sychugov, Proceedings of the 20th IAEA Fusion Energy Conference , Invited Paper FT/3-1Ra]. It has been suggested that particle transport could be enhanced due to cyclotron resonance with the toroidal magnetic field ripple. However, calculations for inductive operation in ITER yield a loss rate that appears to be broadly consistent with the predictions of guiding center theory, falling monotonically as the number of toroidal field coils N is increased (and hence the ripple amplitude is decreased).