Abstract
A model describing nonlinear saturated state of Alfvén ion-cyclotron instability is presented. Spirally symmetric exact solutions of Vlasov – Maxwell equations describing nonlinear Alfvén waves in collisionless plasmas are presented. On their basis the equation describing ion distribution function in non-linear equilibrium of a weak-collision plasma with the wave is obtained, taking into account an uniform fast ion injection, ion drag caused by electrons and neglecting ion angle scattering. A solution of this equation and relations of the wave parameters with the injection parameters are obtained analytically in the case of the infinitely narrow velocity distribution of the injected ions
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