Gyrokinetic field theory

The Lagrangian formulation of the gyrokinetic theory is generalized in order to describe the particles\u27 dynamics, as well as the self-consistent behavior of the electromagnetic fields. The gyrokinetic equation for the particle distribution function and the gyrokinetic Maxwell\u27s equations, for the electromagnetic fields, are both derived from the variational principle for the Lagrangian consisting of the parts of particles, fields, and their interaction. In this generalized Lagrangian formulation, the energy conservation property for the total nonlinear gyrokinetic system of equations is directly shown from Noether\u27s theorem. This formulation can be utilized in order to derive the nonlinear gyrokinetic system of equations and the rigorously conserved total energy for fluctuations with arbitrary frequencies. Simplified gyrokinetic systems of equations with the conserved energy are obtained from the Lagrangian with the small electron gyroradii, quasineutrality, and linear polarization?magnetization approximations

Damping of toroidal ion temperature gradient modes

The temporal evolution of linear toroidal ion temperature gradient (ITG) modes is studied based on a kinetic integral equation including an initial condition. It is shown how to evaluate the analytic continuation of the integral kernel as a function of a complex-valued frequency, which is useful for investigating the asymptotic damping behavior of the ITG mode. In the presence of the toroidal magnetic drift, the potential perturbation consists of normal modes and a continuum mode, which correspond to contributions from poles and from an integral along a branch cut, respectively, of the Laplace-transformed potential function of the frequency. The normal modes have exponential time dependence while the continuum mode, which has a ballooning structure, shows a power law decay [proportional] t^?2, where t is the time variable. Therefore, the continuum mode dominantly describes the long-time asymptotic behavior of the perturbation for the stable system. By performing proper analytic continuation for the dispersion relation, the normal modes\u27 growth rate, real frequency, and eigenfunction are numerically obtained for both stable and unstable cases

Dynamics of Zonal Flows in Helical Systems

A theory for describing collisionless long-time behavior of zonal flows in helical systems is presented and its validity is verified by gyrokinetic-Vlasov simulation. It is shown that, under the influence of particles trapped in helical ripples, the response of zonal flows to a given source becomes weaker for lower radial wave numbers and deeper helical ripples while a high-level zonal-flow response, which is not affected by helical-ripple-trapped particles, can be maintained for a longer time by reducing their bounce-averaged radial drift velocity. This implies a possibility that helical configurations optimized for reducing neoclassical ripple transport can simultaneously enhance zonal flows which lower anomalous transport

How to calculate the neoclassical viscosity, diffusion, and current coefficients in general toroidal plasmas

A novel method to obtain the full neoclassical transport matrix for general toroidal plasmas by using the solution of the linearized drift kinetic equation with the pitch-angle-scattering collision operator is shown. In this method, the neoclassical coefficients for both poloidal and toroidal viscosities in toroidal helical systems can be obtained, and the neoclassical transport coefficients for the radial particle and heat fluxes and the bootstrap current with the nondiagonal coupling between unlike-species particles are derived from combining the viscosity-flow relations, the friction-flow relations, and the parallel momentum balance equations. Since the collisional momentum conservation is properly retained, the well-known intrinsic ambipolar condition of the neoclassical particle fluxes in symmetric systems is recovered. Thus, these resultant neoclassical diffusion and viscosity coefficients are applicable to evaluating accurately how the neoclassical transport in quasi-symmetric toroidal systems deviates from that in exactly symmetric systems

Collisionless damping of geodesic acoustic modes

Collisionless time evolutions of geodesic acoustic modes (GAMs) in tokamaks are investigated by the gyrokinetic theory and simulation. It is shown that the collisionless damping of the GAM oscillations is enhanced when the ratio of the typical drift orbit width of passing ions to the radial wavelength of the zonal flow increases