Nonlinear two‐fluid hydromagnetic waves in the solar wind: Rotational discontinuity, soliton, and finite‐extent Alfvén wave train solutions

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Abstract
Nonlinear one‐dimensional constant‐profile hydromagnetic wave solutions are obtained in finite‐temperature two‐fluid collisionless plasmas under adiabatic equation of state. The nonlinear wave solutions can be classified according to the wavelength. The long‐wavelength solutions are circularly polarized incompressible oblique Alfvén wave trains with wavelength greater than hundreds of ion inertial length. The oblique wave train solutions can explain the high degree of alignment between the local average magnetic field and the wave normal direction observed in the solar wind. The short‐wavelength solutions include rarefaction fast solitons, compression slow solitons, Alfvén solitons and rotational discontinuities, with wavelength of several tens of ion inertial length, provided that the upstream flow speed is less than the fast‐mode speed. The Alfvén solitons and rotational discontinuities are super‐Alfvénic compression waves if the upstream Alfvén‐mode speed is greater than the sound speed; otherwise, they are sub‐Alfvénic rarefaction waves. The density and magnetic field variations of these short‐wavelength waves are shown to obey the following two rules: (1) all compression waves are left‐hand polarized and all rarefaction waves are right‐hand polarized, due to the ion inertial effect, (2) the density variation and the magnetic field magnitude variation are in phase if the flow is supersonic, but out of phase if the flow is subsonic, which is a consequence of conservation of the momentum flux. The two‐fluid rotational discontinuity solution obtained in this study is highly circularly polarized, with a variable angular rotation rate. The total angle of rotation is limited to less than or equal to 180°, which is consistent with the rotational discontinuity observed in the solar wind. The upstream flow speed of the two‐fluid rotational discontinuity must deviate slightly from the Alfvén‐mode speed; the downstream flow speed is equal to the local sound speed. The formation of the two‐fluid rotational discontinuity depends critically on the dispersion effect which converts the Alfvén mode to the ion acoustic mode.