Average Magnetic Field Magnitude Profiles of Wind Magnetic Clouds as a Function of Closest Approach to the Clouds’ Axes and Comparison to Model

Abstract

We examine the average magnetic field magnitude ($| \boldsymbol{B} | \equiv B$) within magnetic clouds (MCs) observed by the Wind spacecraft from 1995 to July 2015 to understand the difference between this $B$ and the ideal $B$-profiles expected from using the static, constant-$\alpha$, force-free, cylindrically symmetric model for MCs of Lepping, Jones, and Burlaga (J. Geophys. Res. 95, 11957, 1990, denoted here as the LJB model). We classify all MCs according to an assigned quality, $Q_{0}$ ($= 1, 2, 3$, for excellent, good, and poor). There are a total of 209 MCs and 124 when only $Q_{0} = 1$, 2 cases are considered. The average normalized field with respect to the closest approach ($\mathit{CA}$) is stressed, where we separate cases into four $\mathit{CA}$ sets centered at 12.5 %, 37.5 %, 62.5 %, and 87.5 % of the average radius; the averaging is done on a percentage-duration basis to treat all cases the same. Normalized $B$ means that before averaging, the $B$ for each MC at each point is divided by the LJB model-estimated $B$ for the MC axis, $B_{0}$. The actual averages for the 209 and 124 MC sets are compared to the LJB model, after an adjustment for MC expansion (e.g. Lepping et al. in Ann. Geophys. 26, 1919, 2008). This provides four separate difference-relationships, each fitted with a quadratic (Quad) curve of very small $\sigma$. Interpreting these Quad formulae should provide a comprehensive view of the variation in normalized $B$ throughout the average MC, where we expect external front and rear compression to be part of its explanation. These formulae are also being considered for modifying the LJB model. This modification will be used in a scheme for forecasting the timing and magnitude of magnetic storms caused by MCs. Extensive testing of the Quad formulae shows that the formulae are quite useful in correcting individual MC $B$-profiles, especially for the first ${\approx\,}1/3$ of these MCs. However, the use of this type of $B$ correction constitutes a (slight) violation of the force-free assumption used in the original LJB MC model.