[en] We find that vertical instability of tokamak plasmas can be controlled by nonaxisymmetric magnetic fields localized near the plasma edge at the bottom and top of the torus. The required magnetic fields can be produced by a relatively simple set of parallelogram-shaped coils. By providing stable equilibria with more highly elongated cross-sections, the addition of these nonaxisymmetric fields can potentially lead to devices with improved β limits (as predicted by Troyon scaling) and improved confinement (as predicted by empirically derived global confinement scaling laws). The nonlinear effect of the coils, with the stabilizing field increasing exponentially in the vacuum regions just above and below the plasma, can potentially reduce the susceptibility to vertical displacement events (VDEs). Although the coils are not stellarator coils, in the sense that they do not produce vacuum flux surfaces or vacuum rotational transform, they do modify the rotational transform of the tokamak near the edge, reducing or eliminating the need for RF current drive in that region for steady-state operation. An analytical calculation with a number of simplifying assumptions is performed for the purpose of demonstrating the physics of the stabilization, and to obtain an estimate of the required magnitude of the nonaxisymmetric field for stabilization. The analytical calculation assumes a large aspect ratio plasma that is well approximated by a cylinder, zero beta, and a uniform equilibrium current density. Stability is determined by a δW calculation, using the stellarator approximation for both the equilibrium and stability calculations. It is estimated that a nonaxisymmetric field with a maximum magnitude at the plasma edge of about 10% that of the toroidal field is needed to see a substantial stabilization effect. A set of nonaxisymmetric coils proposed by Furth and Hartman are calculated to have essentially the same vertical stabilization effect as the simpler parallelogram-shaped coils, so that the vertical stabilization demonstrated experimentally by Furth-Hartman coils supports the feasibility of stabilizing vertical modes by the simpler coil set. The physical mechanism of the stabilization suggests that the stability properties do not depend on the precise shape of the coils, so that curvature can be introduced to optimize relative to other considerations. (author)