In burning plasma experiments, the very energetic alpha (a) particles resulting from deuterium-tritium fusion reaction will be the dominant heating mechanism and will give rise to new physics issues. Recent experiments performed on the Joint European Torus (JET) and aiming to investigate burning plasma physics, are reported in this paper. In the presence of very energetic particles, the Magneto-HydroDynamic (MHD) stability of plasmas is affected. Sawteeth will be strongly stabilised and may lead to the onset of Neo-classical Tearing Modes (NTMs), which are damaging for the plasma confinement. 4He ions injected at 120keV by the Neutral Beam Injection system (NBI) and accelerated by Ion Cyclotron Resonance Frequency (ICRF) waves to the MeV energy range have provided the necessary energetic particles to investigate these effects. New scenarios have been used in order to control the stability of the sawteeth even in the presence of fast particles and to prevent or delay the appearance of NTMs. Finally, in a plasma self-heated by a-particles, the thermal stability is a critical point and a equilibrium will have to be maintained between the a-heating and the transport losses. Experiments have been performed where a fraction of the ICRF heating has been used to simulate the a-heating. A situation of thermal runaway has been demonstrated and successfully controlled.