Field-Line Length and Energetic Particle Transit: The Spiral Path Delay From Sun to Earth

Solar energetic particles do not travel the radial distance from Sun to Earth; they follow the Parker spiral, which is longer, and the difference is a measurable delay. This study integrates the spiral length for wind speeds of 300, 400 and 600 kilometres per second and converts length to scatter-free transit times for particles at 0.3 and 0.1 times the speed of light. The field line reaching 1 AU is 1.276 AU long in a 300 kilometre per second stream, 1.167 AU at 400 and 1.080 AU at 600. For the 400 kilometre per second case a 0.3c particle needs 32.4 minutes along the spiral against the 8.32-minute radial photon time, a spiral-geometry delay of 24.0 minutes before any scattering is added. Onset-timing analyses that use the radial path underestimate the path and therefore over-attribute delay to scattering or release time. The study is simulated and computed, not measured.