  The impact of an equilibrium radial electric field $E $ on negative-energy
perturbations (NEPs) (which are potentially dangerous because they can lead to
either linear or nonlinear explosive instabilities) in cylindrical equilibria
of magnetically confined plasmas is investigated within the framework of
Maxwell-drift kinetic theory. It turns out that for wave vectors with a
non-vanishing component parallel to the magnetic field the conditions for the
existence of NEPs in equilibria with E=0 [G. N. Throumoulopoulos and D.
Pfirsch, Phys. Rev. E 53, 2767 (1996)] remain valid, while the condition for
the existence of perpendicular NEPs, which are found to be the most important
perturbations, is modified. For $|e_i\phi|\approx T_i$ ($\phi$ is the
electrostatic potential) and $T_i/T_e > \beta_c\approx P/(B^2/8\pi)$ ($P$ is
the total plasma pressure), a case which is of operational interest in magnetic
confinement systems, the existence of perpendicular NEPs depends on $e_\nu E$,
where $e_\nu$ is the charge of the particle species $\nu$. In this case the
electric field can reduce the NEPs activity in the edge region of tokamaklike
and stellaratorlike equilibria with identical parabolic pressure profiles, the
reduction of electron NEPs being more pronounced than that of ion NEPs.
