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The solar wind serves as a laboratory for investigating magnetohydrodynamic turbulence under conditions irreproducible on the terra firma. Here we show that the frame work of Hall magnetohydrodynamics (HMHD), which can support three quadratic invariants and allows nonlinear states to depart fundamentally from the Alfvénic, is capable of reproducing in the inertial range the three branches of the observed solar wind magnetic fluctuation spectrum -the Kolmogorov branch f −5/3 steepening to f −α 1doi:10.5194/npg-12-75-2005 fatcat:zdp34qnwfrgeham6n665av5h2q