  We study the equilibrium instability of chiral quarkonia in a plasma in the
presence of constant magnetic and electric field and at finite axial chemical
potential using AdS/CFT duality. The model in use is a supersymmetric QCD at
large 't$\,$Hooft coupling and number of colors. We show that the presence of
the magnetic field and the axial chemical potential even in the absence of the
electric field make the system unstable. In a gapped system, a stable/unstable
equilibrium state phase transition is observed and the initial transition
amplitude of the equilibrium state to the non-equilibrium state is
investigated. We demonstrate that at zero temperature and large magnetic field
the instability grows linearly by increasing the quarkonium binding energy. In
the constant electric and magnetic field, the system is in a equilibrium state
if the Ohm's law and the chiral magnetic effect cancel their effects. This
happens in a sub-space of $(E,B,T,\mu_5)$ space with constraint equation
$\sigma_B B =- \sigma E$, where $\sigma$ and $\sigma_B$ are called electric and
chiral magnetic conductivity, respectively. We analyze the decay rate of a
gapless system when this constraint is slightly violated.
