Fig. 4
From: Density response to magnetic field fluctuation in the foreshock plasma
The same panel as Fig. 3 but the slope is evaluated for the second-order nonlinear magnetic field fluctuation by subtracting by variance of the magnetic field fluctuation, \(\delta B_{\mathrm {nl}}^2 = \delta B_{\mathrm {t}}^2 - \langle \delta B_{\mathrm {t}}^2 \rangle\). Curved lines in gray are the prediction from the quasi-static balance with a slope relation to the beta-tilde \((2 (1-\tilde{\beta }))^{-1}\)