On the 1/f Spectrum in the Solar Wind and Its Connection with Magnetic Compressibility

We discuss properties of Alfvenic fluctuations with large amplitude in plasmas characterized by low magnetic field compression. We note that in such systems power laws cannot develop with arbitrarily steep slopes at large scales, i.e., when vertical bar delta B vertical bar becomes of the order of the background field vertical bar B vertical bar. In such systems there is a scale l(0) at which the spectrum has to break due to the condition of weak compressibility. A very good example of this dynamics is offered by solar wind fluctuations in Alfvenic fast streams, characterized by the property of constant field magnitude. We show here that the distribution of delta B = vertical bar delta B vertical bar in the fast wind displays a strong cutoff at delta B/vertical bar B vertical bar less than or similar to 2, as expected for fluctuations bounded on a sphere of radius B = vertical bar B vertical bar. This is also associated with a saturation of the rms of the fluctuations at large scales and introduces a specific length l(0), above which the amplitude of the fluctuations becomes independent on the scale l. Consistent with that, the power spectrum at l > l(0) is characterized by a - 1 spectral slope, as expected for fluctuations that are scale-independent. Moreover, we show that the spectral break between the 1/f and inertial range in solar wind spectra indeed corresponds to the scale l(0) at which similar to 1. Such a simple model provides a possible alternative explanation of magnetic spectra observed in interplanetary space, also pointing out the inconsistency for a plasma to simultaneously maintain vertical bar B vertical bar similar to const. at arbitrarily large scales and satisfy a Kolmogorov scaling.