In burning plasma experiments, the very energetic alpha (alpha) particles resulting from a 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 [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)] and aiming to investigate burning plasma physics are reported in this paper. In the presence of very energetic particles, the magnetohydrodynamic stability of plasmas is affected. Sawteeth will be strongly stabilized and may lead to the onset of neoclassical tearing modes (NTMs), which are damaging for the plasma confinement. He-4 ions injected at 120 keV by the neutral beam injection system 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 alpha-particles, the thermal stability is a critical point and equilibrium will have to be maintained between the alpha-heating and the transport losses. Experiments have been performed where a fraction of the ICRF heating has been used to simulate the alpha-heating. A situation of thermal runaway has been demonstrated and successfully controlled. (C) 2004 American Institute of Physics.