# Statistical analysis of interplanetary magnetic field path lengths from solar energetic electron events observed by WIND

## TL;DR

This study introduces a new method for calculating interplanetary magnetic field path lengths from solar energetic electron events, reducing uncertainties and revealing a mostly Parker spiral-like magnetic topology.

## Contribution

A novel velocity dispersion analysis approach using flux rise times instead of onset times improves path length accuracy in solar electron event analysis.

## Key findings

- Average path length is around 1.1 AU, close to Parker spiral predictions.
- Path length distribution fits Gaussian well for certain flux fractions.
- Results imply minimal magnetic field line meandering in these events.

## Abstract

We calculate the interplanetary magnetic field path lengths traveled by electrons in solar electron events detected by the WIND 3DP instrument from $1994$ to $2016$. The velocity dispersion analysis method is applied for electrons at energies of $\sim$ $27$ keV to $310$ keV. Previous velocity dispersion analyses employ the onset times, which are often affected by instrumental effects and the pre-existing background flux, leading to large uncertainties. We propose a new method here. Instead of using the peak or onset time, we apply the velocity dispersion analysis to the times that correspond to the rising phase of the fluxes that are a fraction, $\eta$, of the peak flux. We perform statistical analysis on selected events whose calculated path lengths have uncertainties smaller than $0.1$ AU. The mean and standard deviation, ($\mu$, $\sigma$), of the calculated path lengths corresponding to $\eta=$ $3/4$, $1/2$, and $1/3$ of the peak flux is ($1.17$ AU, $0.17$ AU), ($1.11$ AU, $0.14$ AU), and ($1.06$ AU, $0.15$ AU). The distribution of the calculated path lengths is also well fitted by a Gaussian distribution for the $\eta=3/4$ and $1/3$ cases. These results suggest that in these electron events the interplanetary magnetic field topology is close to the nominal Parker spiral with little field line meandering. Our results have important implications for particles' perpendicular diffusion.