Magnetic Fluctuation Power Near Proton Temperature Anisotropy Instability Thresholds in the Solar Wind

The proton temperature anisotropy in the solar wind is known to be constrained by the theoretical thresholds for pressure-anisotropy-driven instabilities. Here, we use approximately $1\times {10}^6$ independent measurements of gyroscale magnetic fluctuations in the solar wind to show for the first time that these fluctuations are enhanced along the temperature anisotropy thresholds of the mirror, proton oblique firehose, and ion cyclotron instabilities. In addition, the measured magnetic compressibility is enhanced at high plasma beta (${\beta }_{\parallel }\gtrsim 1$) along the mirror instability threshold but small elsewhere, consistent with expectations of the mirror mode. We also show that the short wavelength magnetic fluctuation power is a strong function of collisionality, which relaxes the temperature anisotropy away from the instability conditions and reduces correspondingly the fluctuation power.

Figure 1

The distribution of proton temperature anisotropy ($T_{\perp }/T_{\parallel }$) measurements with respect to the parallel plasma beta ${\beta }_{\parallel }$ (upper panel) is constrained by the oblique proton firehose instability threshold (lower dotted line) and the mirror instability threshold (upper dotted line). In the second panel, the magnetic fluctuation amplitude $|\delta B|/|B|$ is shown to be enhanced along the instability thresholds and overall at high ${\beta }_{\parallel }$ where the thresholds converge. The third panel shows magnetic compressibility $\delta B_{\parallel }^2/(\delta B_{\parallel }^2+\delta B_{\perp }^2)$, which is enhanced at high ${\beta }_{\parallel }$ ($>1$) along the mirror threshold, as expected for the mirror instability. The lower panel shows the “collisional age,” which is largest around $T_{\perp }/T_{\parallel }\approx 1$ suggesting that isotropy results largely from Coulomb collisions. Anisotropic plasma is relatively collisionless.

Figure 2

The magnitude of magnetic fluctuations $|\delta B|$ averaged into bins of $T_{\perp }/T_{\parallel }$ vs ${\beta }_{\parallel }$. Enhanced power exists well away from the thresholds, as expected. The regions of enhanced δB corresponds to the enhanced proton heating in Liu et al. (2006).

Figure 3

Magnetic fluctuation amplitude $|\delta B{|}^2$ as a function of the collisional age; the white dots are the most likely value of $|\delta B{|}^2$ in each age bin. Magnetic fluctuations near the proton gyroradius ($k\rho \approx 1/2$) are suppressed in more collisional plasma. Coulomb collisions maintain the isotropy of the protons, which then remain far from the instability thresholds. Note that this corresponds to a factor of 100 suppression of magnetic power $\delta B^2$ over the full range of collisionality.

Figure 4

Wavelet power spectra of magnetic fluctuations at three different time intervals corresponding to perpendicular anisotropy $T_{\perp }/T_{\parallel }=2.2$, ${\beta }_{\parallel }=0.2$ (red trace), parallel anisotropy $T_{\perp }/T_{\parallel }=0.5$, ${\beta }_{\parallel }=1.9$ (blue trace), and isotropic protons $T_{\perp }/T_{\parallel }=1$, ${\beta }_{\parallel }=0.7$ (black trace). The spectra are plotted against $k\rho$ and have been scaled to the same average value over the interval $k\rho \in (0.2,1.0)$, as described in the text. A solid black line with scaling $k^{-5/3}$ is shown. The interval above $k\rho \approx 1/2$ corresponds to the statistical data shown in Figs. 1, 2.