local power into the curvature radiation from a single electron/positron. The spectrum of primary photons from a unit volume is $${d^2\dot{N}\over dVdE_{\gamma}}\sim {l_{cur}n_{GJ}\over E_{cur}}{1\over
E_{\gamma}}$$ where $E_{\gamma}\leq E_{cur}$. These primary curvature photons collide with the soft photons produced by synchrotron radiation of the secondary $e^{\pm}$ pairs, and produce the secondary $e^{\pm}$ pairs by photon-photon pair production. Although pair production inside an outer gap is limited to a small region ($r_{in}\leq r \leq r_{lim}$), pair production outside the outer gap can cover a much wider range because the synchrotron photons produced by the secondary pairs are more abundant than the thermal photons from the stellar surface. The former cannot get into the outer gap because of the field line curvature (cf. CHR I) but they can convert most curvature photons from the outer gap into the secondary pairs. In a steady state the distribution of secondary electrons/positrons in a unit volume $${d^2N\over dVdE_e}\approx {1\over \dot{E}_e}\int 
{d^2\dot{N}(E'_{\gamma}=2E'_e)\over dVdE_{\gamma}}dE'_e
\sim {1\over \dot{E}_e}{l_{cur}n_{GJ}\over E_{cur}}\ln\left({E_{cur}\over
E_e}\right),$$ with $\dot{E}_e$ the electron energy loss into synchrotron radiation, $$\dot{E}_e=-{2\over 3}{e^4B^2(r)\sin^2\beta(r)\over m^2c^3}
\left({E_e\over mc^2}\right)^2,$$ $B(r)$ is the local magnetic field and $\beta (r)$ the local pitch angle, $$\sin\beta(r)\sim \sin\beta(R_L)\left({r\over R_L}\right)^{1/2}.$$ $\sin\beta(R_L)$ is the pitch angle at the light cylinder. 