Two-dimensional gyrokinetic integral eigenmode equation for drift instabilities in tokamak

Based on the Vlasov equation, a set of two-dimensional gyrokinetic integral eigenmode equations for drift instabilities in tokamak plasmas is derived. All kinetic effects of ions, including transience parallel to the magnetic field, drifts induced by the curvature and gradient of the magnetic field, and drifts induced by the equilibrium electric potential, and the effects of finite Larmor radius are taken into account. Not only the radial structure but also the poloidal structure of the modes as well as coupling of neighboring poloidal modes induced by toroidicity of the magnetic field can be obtained from these equations. This is an alternative to ballooning mode representation treatment, which can give mode structures along magnetic field lines only. The equations provide a theoretical base for relevant numerical simulation investigations.