We perform test particle simulations of nonlinear interaction between energetic protons and EMIC waves. We assume a coherent EMIC waves that have a constant frequency and propagate parallel to the magnetic field. We find that protons can be trapped and accelerated by EMIC waves. We find a very efficient acceleration process of protons in which kinetic energy of protons increases while directions of parallel velocities reverses when we assume parameters in the Jovian magnetosphere. We notice that this phenomenon is very similar to the interaction process between relativistic electrons and whistler-mode waves, which is called Relativistic Turning Acceleration (RTA) . In order to analyze the phenomena, we have developed nonlinear trapping theory of interaction between relativistic protons and EMIC waves. Next, we compare the theory and simulation results. We confirm that the results satisfy the conditions for RTA. Following the trajectories of many resonant protons, we obtain time evolution of the distribution function of relativistic protons as a function of energy and equatorial pitch angle based on the numerical Green’s function method .
 Y. Omura, N. Furuya, D. Summers, Relativistic turning acceleration of resonant electrons by coherent whistler-mode waves in a dipole magnetic field, Journal Geophysical Research, Vol. 112, A06236, doi:10.1029/2006JA012243, 2007.
 Y. Omura, Y. Miyashita, M. Yoshikawa, D. Summers, M. Hikishima, Y. Ebihara, and Y. Kubota (2015), Formation process of relativistic electron flux through interaction with chorus emissions in the Earth’s inner magnetosphere, J. Geophys. Res. Space Physics, 120, 9545–9562, doi:10.1002/2015JA021563, 2015.