  Charged rotating Kerr-Newman black holes are known to be superradiantly
unstable to perturbations of charged massive bosonic fields whose proper
frequencies lie in the bounded regime $0 < \omega < \text{min}
\{\omega_{\text{c}} \equiv m \Omega_{\text{H}} + q\Phi_{\text{H}},\mu\}$ [here
$\{\Omega_{\text{H}}, \Phi_{\text{H}}\}$ are respectively the angular velocity
and electric potential of the Kerr-Newman black hole, and $\{m,q,\mu\}$ are
respectively the azimuthal harmonic index, the charge coupling constant, and
the proper mass of the field]. In this paper we study analytically the complex
resonance spectrum which characterizes the dynamics of linearized charged
massive scalar fields in a near-extremal Kerr-Newman black-hole spacetime.
Interestingly, it is shown that near the critical frequency $\omega_{\text{c}}$
for superradiant amplification and in the eikonal large-mass regime, the
superradiant instability growth rates of the explosive scalar fields are
characterized by a non-trivial (non-monotonic) dependence on the dimensionless
charge-to-mass ratio $q/\mu$. In particular, for given parameters $\{M,Q, J\}$
of the central Kerr-Newman black hole, we determine analytically the optimal
charge-to-mass ratio $q/\mu$ of the explosive scalar field which {\it
maximizes} the growth rate of the superradiant instabilities in the composed
Kerr-Newman-black-hole-charged-massive-scalar-field system.
