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Appendix A: Time correction method validation

	Fig. A.1 Simulated beam speeds vs. deviation angle Δφ. Colors denote beam speeds (red: 0.2c, green: 0.14c, and blue: 0.07c). The fundamental and harmonic components are represented by solid and dashed lines, respectively. Horizontal lines indicate initial speeds. Dash-dotted lines show maximal and mean separation angles between the two STEREO in our data set.
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We validated our time correction method via simulations of electron beams propagating away from the Sun (Fig. A.1). Simulated beams travel with a given constant speed along the X axis while emitting radio emissions at frequencies between 40 kHz and 1 MHz (i.e. at a frequency range of STEREO/Waves used in this study). We have considered the F- and H-components using the electron density model by Sittler & Guhathakurta (1999). A modeled spacecraft lies on a circle around the Sun with a radius of 1 au in the ecliptic (Z = 0), so its position can be parametrized by angle . We applied the time correction method (Eq. (1)) to observed times by the modeled spacecraft. Our results show that differences between initial and derived beam speeds are negligible for small angles. For a mean separation angle between the two STEREO spacecraft

in our data set (φ = 50°), this difference ranges from 1% to 7%. The difference at φ = 100° varies between 7% and 20%. Moreover, variations between the F- and H-components are minor.

	Fig. A.2 Analysis of measurements recorded by STEREO-A from 14:15 to 16:00 UT on September 27, 2013 assuming the F-component: panel a): radial distances from the Sun vs. uncorrected (in black) and corrected times assuming Parker-spiral propagation (in blue, red, purple, and orange); panel b): parker-spiral paths and the spacecraft location (in green).
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We also investigated the role of Parker-spiral propagation on estimates of speed and acceleration (Fig. A.2). We analyzed the data from STEREO-A from September 27, 2013 assuming the F-component (Sect. 2.3). The emitting energetic electrons were assumed to travel along four Parker-spiral lines with respect to spacecraft position. The parameters obtained for various time corrections are not significantly different. For a comparison, results with no time correction are shown in black. We thus conclude that the time correction method is applicable to our data set and that it provides us with reasonable results for electron beam dynamics with typical speeds in the solar wind.

© ESO, 2015