To help reveal the complete picture of linear kinetic drift modes, four independent numerical approaches, based on integral equation, Euler initial value simulation, Euler matrix eigenvalue solution and Lagrangian particle simulation, respectively, are used to solve the linear gyrokinetic electrostatic drift modes equation in Z-pinch with slab simplification and in tokamak with ballooning space coordinate. We identify that these approaches can yield the same solution with the difference smaller than 1%, and the discrepancies mainly come from the numerical convergence, which is the first detailed benchmark of four independent numerical approaches for gyrokinetic linear drift modes. Using these approaches, we find that the entropy mode and interchange mode are on the same branch in Z-pinch, and the entropy mode can have both electron and ion branches. And, at strong gradient, more than one eigenstate of the ion temperature gradient mode (ITG) can be unstable and the most unstable one can be on non-ground eigenstates. The propagation of ITGs from ion to electron diamagnetic direction at strong gradient is also observed, which implies that the propagation direction is not a decisive criterion for the experimental diagnosis of turbulent mode at the edge plasmas.

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A linear gyrokinetic particle-in-cell scheme, which is valid for arbitrary perpendicular wavelength k ⊥ ρi and includes the parallel dynamic along the field line, is developed to study the local electrostatic drift modes in point and ring dipole plasmas. We find the most unstable mode in this system can be either electron mode or ion mode. The properties and relations of these modes are studied in detail as a function of k ⊥ ρi, the density gradient κn, the temperature gradient κT , electron to ion temperature ratio τ = Te/Ti, and mass ratio mi/me. For conventional weak gradient parameters, the mode is on ground state (with eigenstate number l = 0) and especially k ∼ 0 for small k ⊥ ρi. Thus, bounce averaged dispersion relation is also derived for comparison. For strong gradient and large k ⊥ ρi, most interestingly, higher order eigenstate modes with even (e.g., l = 2, 4) or odd (e.g., l = 1) parity can be most unstable, which is not expected by previous studies. High order eigenstate can also easily be most unstable at weak gradient when τ > 10. This work can be particularly important to understand the turbulent transport in laboratory and space magnetosphere.

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The magnetic curvature effects on plasma interchange turbulence and transport in the Z-pinch and dipole-like systems are explored with two-fluid global simulations. By comparing the transport levels in the systems with a different magnetic curvature, we show that the interchange-mode driven transport strongly depends on the magnetic geometry. For the system with large magnetic curvature, the pressure and density profiles are strongly peaked in a marginally stable state and the nonlinear evolution of interchange modes produces the global convective cells in the azimuthal direction, which lead to the low level of turbulent convective transport.