Benchmark Simulations of Gyro-Kinetic Electron and Fully-Kinetic Ion Model for Lower Hybrid Waves in Linear Region

Li, Dehui; Xiang, Nong; Lin, Y.; Wang, Xueyi; Cheng, Yang; Ma, Jin

doi:10.1088/1009-0630/16/9/03

Cited by 7 publications

(6 citation statements)

References 24 publications

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“…(1), (3)(4), (7)(8)(9) and (26-29) form a closed system for electron model with canonical momentum, while Eqs. (1), (3), (10), (13)(14), (18) and (26-29) form a closed system for electron model with kinetic momentum. In linear and nonlinear regimes, both electron models with kinetic and canonical momentum can be used in LH wave studies with similar complexity and numerical performance.…”

Section: Field Equationsmentioning

confidence: 99%

“…The black part represents the linear terms and the red part represents the nonlinear terms in Eq. (14).…”

Section: Defining the Particle Weight Asmentioning

confidence: 99%

“…We start from the electron model with kinetic momentum, and its corresponding Eqs. ( 1), ( 3), (10), (13)(14), ( 18) and (26)(27)(28)(29) are used.…”

Section: The Analytic Dispersion Relation From Electromagnetic Partic...mentioning

confidence: 99%

“…[9][10][11] Particle-in-cell simulation approach is a powerful tool for studying nonlinear physics. Several algorithms and models of particle simulation of radio frequency (RF) waves in simple geometry (slab or cylinder) have been developed, e.g., GeFi [12][13][14] , Vorpal 15,16 and G-gauge 17,18 codes. However, nonlinear RF simulation capability is unavailable for the toroidal geometry before our earlier work, in which we developed the electrostatic particle simulation of LH wave propagation in tokamaks.…”

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confidence: 99%

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Nonlinear electromagnetic formulation for particle-in-cell simulation of lower hybrid waves in toroidal geometry

et al. 2016

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Electromagnetic particle simulation model has been formulated and verified for nonlinear processes of lower hybrid (LH) waves in fusion plasmas. Electron dynamics is described by the drift kinetic equation using either kinetic momentum or canonical momentum. Ion dynamics is treated as the fluid system or by the Vlasov equation. Compressible magnetic perturbation is retained to simulate both the fast and slow LH waves. Numerical properties are greatly improved by using electron continuity equation to enforce consistency between electrostatic potential and vector potential, and by using the importance sampling technique. The simulation model has been implemented in the gyrokinetic toroidal code (GTC), and verified for the dispersion relation and nonlinear particle trapping of the electromagnetic LH waves.

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Section: Field Equationsmentioning

confidence: 99%

“…The black part represents the linear terms and the red part represents the nonlinear terms in Eq. (14).…”

Section: Defining the Particle Weight Asmentioning

confidence: 99%

“…We start from the electron model with kinetic momentum, and its corresponding Eqs. ( 1), ( 3), (10), (13)(14), ( 18) and (26)(27)(28)(29) are used.…”

Section: The Analytic Dispersion Relation From Electromagnetic Partic...mentioning

confidence: 99%

mentioning

confidence: 99%

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Nonlinear electromagnetic formulation for particle-in-cell simulation of lower hybrid waves in toroidal geometry

et al. 2016

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“…Instead of directly solving the perpendicular Ampère's law, GeFi applies the force balance equation to calculate the perturbed parallel magnetic field δB , which is then used to compute the perturbed vector potential δA through Ampère's law. A two dimensional kinetic code based on this model was then developed in slab geometry to study the physics of Harris sheet [40] and tearing instability [41], which was followed by the simulations of propagation property [42] and Landau damping [43] of LHW in uniform plasmas.…”

Section: Nuclear Fusionmentioning

confidence: 99%

A closed high-frequency Vlasov–Maxwell simulation model in toroidal geometry

et al. 2017

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A fully-kinetic ion and gyrokinetic electron Vlasov-Maxwell particle simulation model is derived through Lie transform perturbation theory for Hamiltonian systems in terms of four ordering parameters B , ω , and δ. This model is closed by the field equations of Poisson's equation and Ampere' law. This scheme preserves the phase-space volume, and retains the ion cyclotron motion, while fine scale electron motion is ignored, so that the frequency falls in the range Ω i ω < Ω e. Using a perturbative method (δf), and ignoring the high order terms, this model is then formulated in a magnetic flux coordinate system with equilibrium Maxwellian distribution of particles. Thus, this model is especially suitable for the global particle simulation of high-frequency physical processes such as lower hybrid waves and waves in the ion cyclotron range of frequencies.

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Particle simulations of mode conversion between slow mode and fast mode in lower hybrid range of frequencies

et al. 2016

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The propagation and mode conversion of lower hybrid waves in an inhomogeneous plasma are investigated by using the nonlinear δf algorithm in a two-dimensional particle-in-cell simulation code based on the gyrokinetic electron and fully kinetic ion (GeFi) scheme [Lin et al., Plasma Phys. Controlled Fusion 47, 657 (2005)]. The characteristics of the simulated waves, such as wavelength, frequency, phase, and group velocities, agree well with the linear theoretical analysis. It is shown that a significant reflection component emerges in the conversion process between the slow mode and the fast mode when the scale length of the density variation is comparable to the local wavelength. The dependences of the reflection coefficient on the scale length of the density variation are compared with the results based on the linear full wave model for cold plasmas. It is indicated that the mode conversion for the waves with a frequency of 2.45 GHz (ω ∼ 3ωLH, where ωLH represents the lower hybrid resonance) and within Tokamak relevant amplitudes can be well described in the linear scheme. As the frequency decreases, the modification due to the nonlinear term becomes important. For the low-frequency waves (ω ∼ 1.3ωLH), the generations of the high harmonic modes and sidebands through nonlinear mode-mode coupling provide new power channels and thus could reduce the reflection significantly.

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Benchmark Simulations of Gyro-Kinetic Electron and Fully-Kinetic Ion Model for Lower Hybrid Waves in Linear Region

Cited by 7 publications

References 24 publications

Nonlinear electromagnetic formulation for particle-in-cell simulation of lower hybrid waves in toroidal geometry

Nonlinear electromagnetic formulation for particle-in-cell simulation of lower hybrid waves in toroidal geometry

A closed high-frequency Vlasov–Maxwell simulation model in toroidal geometry

Particle simulations of mode conversion between slow mode and fast mode in lower hybrid range of frequencies

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