Spectrum of kinetic plasma turbulence at 0.3–0.9 astronomical units from the Sun

We investigate spectral properties of turbulence in the solar wind that is a weakly collisional astrophysical plasma, accessible to in situ observations. Using the Helios search coil magnetometer measurements in the fast solar wind, in the inner heliosphere, we focus on properties of the turbulent magnetic fluctuations at scales smaller than the ion characteristic scales, the so-called kinetic plasma turbulence. At such small scales, we show that magnetic power spectra between 0.3 and 0.9 AU from the Sun have a generic shape $\sim f^{-8/3}exp(-f/f_d)$, where the dissipation frequency $f_d$ is correlated with the Doppler shifted frequency $f_{\rho e}$ of the electron Larmor radius. This behavior is statistically significant: all the observed kinetic spectra are well described by this model, with $f_d=f_{\rho e}/1.8$. Our results indicate that the electron gyroradius plays the role of the dissipation scale and marks the end of the electromagnetic cascade in the solar wind.

Figure 1

Examples of the most intense Helios-SCM spectra of $B_y$ component, as functions of the spacecraft-frame frequency $f$ at (a) 0.3, (b) 0.6, and (c) 0.9 AU. For the three radial distances, the raw spectrum is shown by red diamonds; the corrected spectrum, after the subtraction of the noise, is shown by blue dots. The black solid line gives the fit with the model function (1), the dashed line gives $f^{-2.8}$ power-law for comparison and the dotted line indicates the noise level of the Helios-SCM $B_y$. Vertical red lines give the Doppler shifted kinetic scales: in (a), ${\rho }_p$ and ${\rho }_e$ appear at $f_{\rho p}=2.9$ Hz and $f_{\rho e}=325$ Hz, respectively; in (b) they appear at $f_{\rho p}\simeq 1$ Hz and $f_{{\rho }_e}=130$ Hz, respectively; and in (c) they appear at $f_{\rho p}\simeq 1$ Hz and $f_{{\rho }_e}=110$ Hz, respectively.

Figure 2

Results of the fitting procedure of the most intense spectra at 0.3 AU with Eq. (1): dissipation scale ${\ell }_d=V/2\pi f_d$ as a function of the electron Larmor radius ${\rho }_e$; the linear dependence ${\ell }_d=1.8{\rho }_e$ is indicated by the dashed line, with the correlation coefficient $C=0.68$.

Figure 3

Probability distribution functions of the mean plasma parameters at 0.3 AU for the 3344 spectra shown in Fig. 4 (black lines) and for the 39 most intense spectra [green (gray) lines]: (a) proton density $n_p$, (b) solar wind speed $V$, (c) proton temperature $T_p$, (d) electron temperature $T_e$, (e) magnetic field magnitude $B_0$, (f) proton thermal pressure $n_p{k}_B{T}_p$, (g) proton plasma beta ${\beta }_p$, (h) electron beta ${\beta }_e$.

Figure 4

(a) The 3344 individual Helios 1–SCM spectra of $B_y$ as a function of the spacecraft-frame frequency $f$ at 0.3 AU in the fast wind; the 39 most intense spectra are marked by green (gray) crosses; the SCM noise for $B_y$ component is indicated by a dotted line. (b) The 3344 spectra corrected for the noise contribution as a function of $f$ normalized to the Doppler shifted electron Larmor radius frequency $f_{\rho e}=V/\left(2\pi {\rho }_e\right)$. (c) The same spectra, rescaled by their amplitude at $f_0=0.051f/f_{\rho e}$ (see the text); the result is shown as a 2D histogram with the number of data points proportional to the darkness of the red color. The dashed line displays the model function, Eq. (3).

Figure 5

The complete turbulent spectrum from energy injection scales up to the sub-electron scales at 0.3 and 0.9 AU as measured by Helios. The energy containing scales (which correspond to $\sim f^{-1}$ spectrum) and the MHD inertial range ($\sim f^{-5/3}$) are covered by the Helios–MAG instrument (gray lines). The Helios–SCM instrument covers the kinetic scales (blue dots), studied in the present paper. The black solid lines indicate model functions $f^{-1}, f^{-5/3}$ and $f^{-8/3}exp(-1.8f/f_{{\rho }_e})$ at different frequency ranges. The two most energetic spectra at high frequencies are the extrapolations of the kinetic spectrum in the fast wind that we expect to measure with PSP at 0.05 and 0.1 AU. The dashed line gives Helios–SCM noise, the dashed-dotted and dotted lines indicate noise levels of the different magnetic sensors on PSP. The Doppler shifted ion inertial length ${\lambda }_p$ (green stars) marks the transition from the inertial to the kinetic range; the electron Larmor radius ${\rho }_e$ (red diamonds) marks the dissipation cutoff.