Expansion of a spherical wave front through the magnetosphere. The front thickness (wave duration) is much smaller than r/c. Its shock-free part (﹩\sin \theta \lt \sin {\theta }_{\times }﹩) is plotted in green and the part carrying the shock is in red. The region swept by the shock is shaded in pink; its boundary θ(r) is defined by Equation (110). The wave front is shown at two moments: (1) when it crosses radius R _× (the shock has formed in the equatorial plane, θ = π/2); and (2) when it expands to a larger radius (the shock now occupies a range of θ). The shock radiates gamma rays (red arrows) beamed along β _D (Equation (111)); most of them convert to e ^± pairs.