A fully kinetic ion model is useful for the verification of gyrokinetic turbulence simulations in certain regimes, where the gyrokinetic model may break down due to the lack of small ordering parameters. However, for a fully kinetic model to be of value, it must first be able to accurately simulate low frequency drift-type instabilities typically well within the domain of gyrokinetics. Here, a fully kinetic ion model is formulated with weak gradient drive terms and applied to the toroidal ion-temperature-gradient (ITG) instability for the first time. Implementation in toroidal geometry is discussed, where orthogonal coordinates are used for particle dynamics, but field-line-following coordinates are used for the field equation allowing for high resolution of the field-aligned mode structure. Variational methods are formulated for integrating the equation of motion allowing for accuracy at a modest time-step size. Linear results are reported for both the slab and toroidal ITG instabilities. Good agreement with full Vlasov and gyrokinetic theory is demonstrated in slab geometry. Good agreement with global gyrokinetic simulation is also shown in toroidal geometry.
This paper obtains the topological 1-soliton solution of the nonlinear Schrödinger's equation in 1+2 dimensions, with power law nonlinearity and time-dependent coefficients. The solitary wave ansatz is used to obtain the solution. It will also be proved that the power law nonlinearity must reduce to Kerr law nonlinearity for the topological solitons to exist.
Fully kinetic turbulence models are of interest for their potential to validate or replace gyrokinetic models in plasma regimes where the gyrokinetic expansion parameters are marginal. Here, we demonstrate fully kinetic ion capability by simulating the growth and nonlinear saturation of the ion-temperature-gradient instability in shearless slab geometry assuming adiabatic electrons and including zonal flow dynamics. The ion trajectories are integrated using the Lorentz force, and the cyclotron motion is fully resolved. Linear growth and nonlinear saturation characteristics show excellent agreement with analogous gyrokinetic simulations across a wide range of parameters. The fully kinetic simulation accurately reproduces the nonlinearly generated zonal flow. This work demonstrates nonlinear capability, resolution of weak gradient drive, and zonal flow physics, which are critical aspects of modeling plasma turbulence with full ion dynamics.
This paper talks about obtaining an exact 1-soliton solution of the generalized Radhakrishnan, Kundu, Lakshmanan equation with nonlinear dispersion. The solitary wave ansatz will be used to carry out the integration. It will be proved that dark optical solitons can exist only when the power law nonlinearity reduces to Kerr law.
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