Tearing-mode Stability Properties of a Field-reversed Ion Layer at Marginal Stability

Tearing-mode stability properties are investigated at marginal stability (u=0) for a rotating, nonrelativistic cylindrically symmetric ion layer immersed in an axial magnetic field B0 (r)^ = [B +Bs(r)]^ z Lz 0 Z Jz The analysis is carried out within the framework of a Vlasov-fluid model in which the electrons are described as a macroscopic, cold fluid, and the layer ions are described by the Vlasov equation. Tearing-mode stability properties are calculated numerically for azimuthally symmetric perturbations about an ion layer equilbrium described by fi=const x exp[-(Hk ePe)/T]. Here, H is the energy, Pe is the canonical angular momentum, T-const is the temperature,-w=const is the angular velocity of mean rotation, and the density profile is n(r)=nsech2 2 /22-r /262) 4 2 2s2 2 2 where 6 =2c T/(m i W) and w .=47n 0 e 2 /m. The marginal stability eigenvalue equation for the perturbation amplitude Ae(r) has the form of a Schroedinger equation, with "energy" eigenvalue k 262 and effective potential z V(r)=6 2/r-2(r 26 2)sech2 (r 2/262-r /262). This equation is solved numerically for A6(r) and the normalized axial wave number at marginal stability (denoted by k 2 6) as a function of normalized layer radius r 0 /6 and magnetic field depression a-1/2 [B-B 0 (r=O)]/BO, where a =87n T/B 2 For r /6 > 1, the numerical analysis shows that k 6 can be approximated 0 0 by k 0 5 =r2 0 16 to a high degree of accuracy.