Formation of pressure‐balanced structures and fast waves from nonlinear Alfvén waves

In the solar wind, Alfvénic fluctuations are typically observed in association with small fluctuations of the density (ρ) and magnetic field strength ( B ), which tend to be anticorrelated and in approximate pressure balance. One would not expect any finite δρ and δ B among pure Alfvén waves propagating strictly outward from the Sun. Our paper shows how Alfvén waves can nonlinearly produce structures in pressure balance. We present a second‐order analysis of the pure magnetohydrodynamic equations and hybrid simulations which show that nonlinear Alfvén waves traveling in different directions but with equal group velocity can generate pressure‐balanced structures with wave vectors perpendicular to the background magnetic field B 0 . Homogeneous fast waves are also generated in this direction in order to satisfy initial conditions. They cannot be Landau or transit‐time damped and so cause the values of B and ρ to vary with time as they beat with the pressure‐balanced structures. However, we find δρδ B < 0 is satisfied most of the time, and this can partly explain the tendency for anticorrelation observed in the solar wind. In directions away from the perpendicular one, Alfvén waves produce driven fast waves which give constant B and ρ to second order. Homogeneous fast and slow waves are also produced in these directions but Landau damp away in large β plasmas. Thus an equilibrium or steady propagating waveform at second order can be produced where B and ρ vary only in the perpendicular direction. If transverse magnetic structures with wave vectors perpendicular to B 0 are included at the same order as the initial Alfvén waves, then these evolve to pressure‐balanced structures and can also coexist with the Alfvén waves. However, an equilibrium is obtained generally only when these structures also have velocity fluctuations equivalent of those of the Alfvén waves.