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with ( jk ) = (00), such that the cascades are even weaker: n$_{E}$ ≤ 4 and n$_{ϵ}$ = 0. When ICS is active, both n$_{ϵ}$ and n$_{E}$ can be larger, though not as large as would be predicted by an extrapolation of Eqs. (49) and (50) to high fields. In order for ICS to affect the cascade, however, the primary photon must have an energy 

the energy of the electron/positron produced by this photon, E$_{max}$ ∼ (0 . 1–0 . 5) ϵ$_{0}$ [Eq. (C9)], must be larger than the min- imum energy at which ICS is effective, ∼ 0 . 3 γ$_{crit}$m$_{e}$c 2 (see Appendix C1). Note that this energy is approximately equal 

<img src='content_image/381166.jpg'>

to ϵ$_{RICS}$ , the energy of a typical ICS photon upscattered by the primary electron at high fields [Eq. (8)]; therefore, at high fields a typical ICS photon is able to initiate a weak cascade. We find that for B$_{p}$ < ∼ 0 . 5 B$_{Q}$ a significant fraction ( ∼ 20%–60%) of the total cascade energy ϵ$_{0}$ resides in the photons; as in the low field case [Eq. (52)], this fraction de- creases as either ϵ$_{0}$ or B$_{p,}$$_{12}$ increases. For B$_{p}$ > ∼ 0 . 5 B$_{Q}$ , even ignoring photon splitting, the total photon energy fraction is very low, < 10%; but with photon splitting included, it is almost negligible, < 1%. The photon and pair cascade spec- tra for B$_{p,}$$_{12}$ = 10 and 100 when ICS is active from a “warm spot” ( T$_{6}$ = 1, θ$_{spot}$ = 0 . 3) are shown in Fig. 7. 

