On the Full-range β Dependence of Ion-scale Spectral Break in the Solar Wind Turbulence

The power spectrum of magnetic fluctuations has a break at the high-frequency end of the inertial range. Beyond this break, the spectrum becomes steeper than the Kolmogorov law f ^-5/3. The break frequency was found to be associated with plasma beta (β). However, the full-range β dependence of the ion-scale spectral break has not been presented before in observational studies. Here we show the continuous variation of the break frequency on full-range β in the solar wind turbulence. By using measurements from the WIND and Ulysses spacecraft, we show the break frequency (f _b) normalized, respectively, by the frequencies corresponding to ion inertial length (f _di), ion gyroradius (), and cyclotron resonance scale (f _ri) as a function of β for 1306 intervals. Their β values spread from 0.005 to 20, which nearly covers the full β range of the observed solar wind turbulence. It is found that () generally decreases (increases) with β, while is nearly a constant. We perform a linear fit on the statistical result, and obtain the empirical formulas , , and to describe the relation between f _b and β. We also compare our observations with a numerical simulation and the prediction by ion cyclotron resonance theory. Our result favors the idea that the cyclotron resonance is an important mechanism for energy dissipation at the spectral break. When β ≪ 1 and β ≫ 1, the break at f _di and may also be associated with other processes.