The most promising path towards controlled thermonuclear fusion as a new source of energy makes use of devices, called tokamaks, for the confinement of high temperature hydrogen plasma by means of intense magnetic fields in toroidal configurations. The deuterium-tritium reactions in fusion reactors generate alpha particles with 3.5 MeV energy. These particles are supposed to transfer their energy to the plasma in order to self-sustain the conditions required for thermonuclear burn. Therefore, in order to realize such a fusion burning plasma, alpha particles in the MeV range must also be magnetically confined. However, under these circumstances, instabilities related to resonant interactions between the periodic motions of energetic particles and normal mode fluctuations of the thermal plasma may be excited.