Theory of Universal Eigenmodes in a Sheared Magnetic Field

Collisionless drift-wave eigenmodes in a sheared magnetic field are analyzed using the WKBJ method. It is found that, for $\frac{L_s}{L_n}>{\left(\frac{L_s}{L_n}\right)}_c$, ion-sound dynamics determines the eigenvalues at small ${k_y}^2$ and the eigenmodes are damped. However, at large ${k_y}^2$, electron dynamics dominates and the eigenmodes become marginally stable. For $\frac{L_s}{L_n}<{\left(\frac{L_s}{L_n}\right)}_c$, the eigenmodes are damped for all values of ${k_y}^2$. The critical value ${\left(\frac{L_s}{L_n}\right)}_c$ scales as ${\left(\frac{m_i}{m_e}\right)}^{\frac{1}{4}}$.