Fig. 4.

In situ diagnostics and analysis. a In situ observation of the magnetic cloud (MC; shaded region) preceded by a shock (red vertical line). All data except suprathermal electrons (WIND spacecraft) were obtained by the Advanced Composition Explorer (ACE) spacecraft. a Field magnitude B; b field inclination angle θ (with respect to the ecliptic plane); c azimuthal angle ϕ (0 deg pointing to the Sun), d pitch angle distribution of suprathermal electrons; e solar wind speed V; f proton density N _p; g temperature T _p (superimposed by T _p/T _exp); h plasma β; i average charge states of iron $⟨Q⟩$ _Fe = ∑_i Q _i n _i (density is normalized such that ∑_i n _i = 1), and j various composition ratios. The dashed lines in a–c, e show the model fitting results with red (blue) indicating the Gold-Hoyle (Lunquist) solution (Methods section). k, l Grad-Shafranov reconstruction (Methods section) of the MC. k Shows the reconstructed cross section traversed by ACE. The flux function A(x, y) is represented by the black contours. The thick white contour marks the MC boundary A _b = 38.9 T·m. The strength of axial field B _z(A) is indicated by colors, with the maximum marked by a white dot. The measured magnetic field vectors are projected along the spacecraft path y = 0 (white arrows). l shows the twist τ of MC field lines (black line) as a function of $∣A-A_0∣\mathrm{∕}∣A_b-A_0∣$. A ₀ = 160.4 T·m gives the MFR center; also shown are Φ _p/Φ _t, dΦ _p/dΦ _t, and $K_r\mathrm{∕}{\Phi }_{\mathrm{t}}^2$ (ref. ¹⁷)