Negative-energy perturbations in cylindrical equilibria with a radial electric eld

The impact of an equilibrium radial electric eld E on negative-energy perturbations (NEPs) in cylindrical equilibria of magnetically con ned 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 eld the conditions for the existence of NEPs in equilibria with E = 0 [G. N. Throumoulopoulos and D. P rsch, 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 modi ed. For jei j Ti, a scaling which is satis ed in the edge region of magnetic con nement systems ( is the electrostatic potential), the impact of E on perpendicular NEPs depends on the value of Ti=Te, i.e., a) for Ti=Te < c P=(B =8 ) (P is the total plasma pressure) the electric eld does not have any e ect and b) for Ti=Te > c, a case which is of operational interest in magnetic con nement systems, the existence of perpendicular NEPs depends on e E, where e is the charge of the particle species . In the latter case, for tokamaklike equilibria and H mode parameters pertaining to the plasma edge two regimes of NEPs exist. In the one of them the critical value 2=3 of i @ lnTi=@ lnNi plays a role in the existence of ion NEPs, as in equilibria with E = 0, while a critical value of e does not occur for the existence of electron NEPs. However, E has a \stabilizing" e ect on both particle species in that (a) the portion of particles associated with NEPs (active particles) is nearly independent of the plasma magnetic properties, i.e., it is nearly the same in a diamagnetic plasma and in a paramagnetic plasma, while in equilibria with E = 0 this portion is much larger in a paramagnetic plasma than in a diamagnetic plasma, and (b) the fraction of active particles can decrease from the plasma interior to the edge, e.g., for the case of electron NEPs in an equilibrium of a diamagnetic plasma, contrary to equilibria with E = 0. In particular, the fraction of active electrons decreases with increasing e and for e > 0 4=3 the electric eld stabilizes the electrons, in that the fraction of active electrons becomes smaller than the one corresponding to equilibria with E = 0. In addition, E has similar stabilizing e ects on electron NEPs in stellaratorlike equilibria with pressure pro les identical to those of tokamaklike-equilibria, while it results in an increase of the fraction of active ions in reversedeld-pinchlike equilibria. The present results indicate that the radial electric eld reduces the NEPs activity