Electrostatic modes are shown to be excited, in two‐dimensional plasma equilibrium configurations, with frequency and parity characteristics such as to significantly affect the orbits of trapped ions by proper mode‐particle resonances in regimes where the single‐particle collision mean free paths are considerably longer than the periodic particle excursions. In particular, new modes driven by the ion temperature gradient are shown to become unstable in the presence of trapped particles under less restrictive conditions and with considerably larger transverse wavelengths than the ion temperature gradient driven modes arising in a one‐dimensional equilibrium configuration. The resulting enhancement in the transport of ion thermal energy across the magnetic field is discussed.