The purpose of our study is to investigate the way particles are accelerated up to supra-thermal energies in the cusp diamagnetic cavities. For this reason we have examined a number of Cluster cusp crossings, originally identified by Zhang et al. (2005), for the years 2001 and 2002 using data from RAPID, STAFF, EFW, CIS, PEACE, and FGM experiments. In the present study we focus on two particular cusp crossings on 25 March 2002 and on 10 April 2002 which demonstrate in a clear way the general characteristics of the events in our survey. Both events exhibit very sharp spatial boundaries seen both in CNO (primarily single-charged oxygen of ionospheric origin based on CIS observations) and H⁺ flux increases within the RAPID energy range with the magnetic field intensity being anti-correlated. Unlike the first event, the second one shows also a moderate electron flux increase. The fact that the duskward electric field E_y has relatively low values <5 mV/m while the local wave activity is very intense provides a strong indication that particle energization is caused primarily by wave-particle interactions. The wave power spectra and propagation parameters during these cusp events are examined in detail. It is concluded that the high ion fluxes and at the same time the presence or absence of any sign of energization in the electrons clearly shows that the particle acceleration depends on the wave power near the local particle gyrofrequency and on the persistence of the wave-particle interaction process before particles escape from cusp region. Furthermore, the continuous existence of energetic O⁺ ions suggests that energetic O⁺ populations are of spatial nature at least for the eight events that we have studied so far.