[en] Collective lateral oscillations of a circulating proton beam due to the interaction with positive ions formed during the ionization of a residual gas by protons are investigated. Instabilities of various types are interpreted as betatron oscillation resonances caused by the ion field. A dispersion relation has been obtained and solved. It refers to the resonances of any type, including nonlinear and coupling resonances. The equation can be used to analyse some other instabilities, the wall instability, in particular. In a greater detail the resonances of 1 and 2 order, resulting in increasing oscillations of the centre of gravity and lateral sizes of the beam, are studied