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As discussed in Section 3.3, we consider three hot sur- face spot models for active ICS: a “cool” T$_{6}$ = 0 . 3, θ$_{spot}$ = π/ 2 spot; a “warm” T$_{6}$ = 1, θ$_{spot}$ = 0 . 3 spot; and “hot” T$_{6}$ = 3, θ$_{spot}$ = 0 . 1 spot. At low fields we find that the only effect the various hot spot models have is to lower E tot relative to the total cascade energy ϵ$_{0}$ (see above). At high fields, the cascades due to warm and hot spots are similar in multiplicities n$_{ϵ}$ and n$_{E}$ for energies ϵ$_{0}$ < ∼ 10 4 MeV; but for energies ϵ$_{0}$ > ∼ 10 5 MeV, the hot spots give multiplicities ∼ 3 

times larger than warm spots; see Fig. 8 [from Eq. (55), at B$_{p,}$$_{12}$ = 1000 a strong cascade requires T$_{6}$ ≥ 3]. Cool spots give much smaller multiplicities (factors of > 10 smaller) than warm or hot spots regardless of the primary photon energy. 

At low fields, the multiplicities of photons and e $^{+}$e − particles produced per primary photon, n$_{ϵ}$ and n$_{E}$ , depend on R c to the ( − 1) power [Eqs. (49) and (50)], such that cascades in non-dipole magnetospheres can be much larger 

