The two-dimensional eigenvalue equation for the trapped electron instability in tokamaks is solved analytically by both a perturbation technique and a more exact method of matched asymptotic expansions. The important physical effect is shown to be the spatial localization of the trapped electron term caused by the difference between the pitch of the magnetic field and that of the mode. This localization results in a com-pletely new form for the dispersion relation and does not impede magnetic shear stabilization. Coupling of neighboring rational surfaces is shown to result in an increase of only Π/2 (at most) in the growth rate.
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