Light pulses from a Q-switched laser with a peak power of 250 MWatts and 3.5 joules are focussed on carbon and LiH targets in a vacuum chamber. Thereby a rapidly expanding plasma is formed. The expansion velocities of the electrons and ions are nearly equal. By means of an electric field the electrons are drawn out of the plasma; the ions are detected in a FARADAY box. From time of flight measurements particles with a maximum energy of 6.3 keV are found in the case of carbon and 1.7 keV in the case of LiH (average mass number=4). The high values of the ion energies result from an energy transfer from the electrons to the ions during the expansion process. This energy transfer is explained by a simple electrostatic model. If the averaged ion energy is equally distributed to all particles of the plasma (electrons and ions), a mean energy of 340 eV per particle is obtained for a LiH target and 550 eV for a carbon target. These values are 5 times higher than the data previously reported. The number of expanding ions in a solid angle π is determined to be about 2.1015 in the case of LiH. The total kinetic energy of these ions is about 0.3 joules. It is hoped, that by an increase of the energy by a factor 4 and the use of a D—T mixture nuclear fusion reactions will be obtained.