(6.7) of CHR II or Eq. (22) of Zhang and Cheng (1997), but they come out very close to each other.). The local Lorentz factor of the accelerated electrons/positrons in the outer gap is $$\gamma_e(r)=\left({3\over 2}{s^2\over e^2c}eE_{||}(r)c\right)^{1/4}.$$ Because of the high soft photon density, the high-energy emission from the Crab pulsar is described by synchrotron self-Compton process.

In an outer gap, the number of primary charged particles in a volume element $\Delta V$ is roughly given by $dN=n_{GJ}\Delta A\Delta l$, where $n_{GJ}={\bf{\Omega}}\cdot{\bf{B}}/2\pi e c$ is the local Goldreich-Julian number density, $B\Delta A$ is the magnetic flux through the accelerator and $\Delta l$ is the path length along its magnetic field lines. Using the thin gap approximation, the total number of charged particles in the outer gap is $$N\sim {\Omega \Phi\over 4\pi c e}R_L,$$ where $\Phi \sim f(R_L)B(R_L)R^2_L\Delta \phi$ and $\Delta \phi$ is the angular range of the outer gap extending along the azimuthal direction, estimated in previous section. These primary $e^{\pm}$ pairs will lose their energy by radiating curvature photons with a characteristic energy $$E_{cur}(r)={3\over 2}\hbar\gamma^3_e(r){c\over s(r)}.$$ The power into curvature radiation for $dN$ $e^{\pm}$ pairs through in A unit volume is $${dL_{cur}\over dV}\approx l_{cur} n_{GJ}(r),$$ where $l_{cur}=eE_{||}(r)c$, is the 