Theory for Resonant Ion Acceleration by Nonlinear Magnetosonic Fast and Slow Waves in Finite β Plasmas

A Korteweg–de Vries equation that is applicable to both the nonlinear magnetosonic fast and slow waves is derived from a two‐fluid model with finite ion and electron pressures. As in the cold plasma theory, the fast wave has a critical angle θc. For propagation angles greater than θc (quasiperpendicular propagation), the fast wave has a positive soliton, whereas for angles smaller than θc, it has a negative soliton. Finite  β effects decrease the value of θc. The slow wave has a positive soliton for all angles of propagation. The magnitude of resonant ion acceleration (the vp×B acceleration) by the nonlinear fast and slow waves is evaluated. In the fast wave, the electron pressure makes the acceleration stronger for all propagation angles. The decrease in θc resulting from finite  β effects results in broadening of the region of strong acceleration. It is also found that fairly strong ion acceleration can occur in the nonlinear slow wave in high  β plasmas. The possibility of unlimited acceleration of ion...