20 Zach Medin and Dong Lai 10 1 10 2 10 3 10 4 10 5 10 0 10 1 dN/dln r 0 r$_{0}$ (10$^{6}$ cm) e $^{+}$e- pairs Photons Curvature Synchrotron 10 1 r$_{0}$ (10$^{6}$ cm) 10 1 10 2 r$_{0}$ (10$^{6}$ cm) Figure 11. The number of photons and electrons + positrons as a function of the radius where they are created, r$_{0}$$_{,}$$_{ph}$ or r$_{0}$ , for B$_{p,}$$_{12}$ = 1 (left panel), 44 . 14 (middle panel), and 1000 (right panel). The neutron star spin period is assumed to be P$_{0}$ = 1 and a dipole field geometry is used. The ⊥→‖ ‖ photon splitting mode is active, and the primary electron has γ$_{0}$ = 2 × 10 $^{7}$; the effects of ICS are not included. The curve labeled “ e $^{+}$e − pairs” shows where the secondary electrons and positrons are created, “Photons” shows where the photons that escape the magnetosphere (i.e., that do not split or pair produce) are created, “Curvature” shows where the curvature photons are emitted by the primary electron (which continues in a similar manner beyond the graph out to the light cylinder), and “Synchrotron” shows where the synchrotron photons are emitted by the secondary pairs. 10 0 10 1 10 2 10 3 10 4 10 5 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 dN/dln   (MeV) B$_{p,12}$ =1 B$_{p,12}$ =44.14 B$_{p,12}$ =1000 Curvature photons 10 -1 10 0 10 1 10 2 10 3 10 4 10 5  (MeV) B$_{p,12}$ =1 B$_{p,12}$ =44.14 B$_{p,12}$ =1000 Curvature photons 10 0 10 1 10 2 10 3 10 4 10 1 10 2 10 3 10 4 dN/dln E E (MeV) B$_{p,12}$ =1 B$_{p,12}$ =44.14 B$_{p,12}$ =1000 10 2 10 3 10 4 10 5 E (MeV) B$_{p,12}$ =1 B$_{p,12}$ =44.14 1000 Figure 12. The final photon and pair spectra of electron-initiated cascades. The primary electron has Lorentz factor γ$_{0}$ = 2 × 10 7 (the left two panels) and 4 × 10 7 (right two panels), and the surface magnetic field strengths are B$_{p,}$$_{12}$ = 1, 44 . 14, and 1000. The neutron star spin period is P$_{0}$ = 1 and a dipole field geometry is adopted. The secondary photon spectra are shown in the top two panels; the pair spectra are shown in the bottom two panels. The curve labeled “Curvature photons” in each of the top two panels (the dot-dashed line) shows the spectrum of curvature radiation emitted by the primary electron, which is the same for all field strengths.