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

Bao, Jian; Zhang, Lin; Kuley, Animesh; Wang, Z. X.

doi:10.1063/1.4952773

Cited by 12 publications

(9 citation statements)

References 54 publications

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“…A more general theory and computing technique for RF waves was proposed in 2000 by Hong Qin's G-gauge theory [31], which was used to develop a particle simulation code [32] to study high frequency waves in magnetized plasmas [33]. As a pioneering work in kinetic simulations of RF waves in toroidal geometry, GTC [34,35] has been applied to investigate lower hybrid wave (LHW) physics using a simple and efficient scheme with fluid ion plus drift-kinetic electron in cylindrical and toroidal geometry [36] recently. Linear dispersion relations and nonlinear effects in ion Bernstein waves [37] were then verified using fully kinetic ions.…”

Section: Nuclear Fusionmentioning

confidence: 99%

“…This is a challenge for low frequency Alfvén waves. However, for LHW and ICRF waves, the perpendicular wave length has the same order of magnitude as the electron skin depth, and the parallel wavelength is on the order of the ion skin depth c/ω pi [35] from experimental parameters. Therefore, the canceling problem can be overcome.…”

Section: Gyrokinetic Maxwell's Equationsmentioning

confidence: 99%

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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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Section: Nuclear Fusionmentioning

confidence: 99%

Section: Gyrokinetic Maxwell's Equationsmentioning

confidence: 99%

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

et al. 2017

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“…Another widely used and successful tool, the gyrokinetic toroidal code (GTC) has undergone continuous development for the past two decades and has been applied to the study of plasma transport in the core region 17 . GTC is a well-benchmarked, first-principles code which has been extensively applied to the investigation of neoclassical transport 18,19 , microturbulence [20][21][22][23][24][25] , mesoscale Alfvén eigenmodes [25][26][27] excited by energetic particles, macroscopic MHD modes [28][29][30] (kink and tearing modes) and radio frequency (RF) waves [31][32][33][34][35][36][37] in the core region. However, the assumptions used in studying turbulence in the core region may not be valid in the SOL region.…”

Section: Introductionmentioning

confidence: 99%

Kinetic particle simulations in a global toroidal geometry

Singh

Kuley

et al. 2019

Physics of Plasmas

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The gyrokinetic toroidal code (GTC) has been upgraded for global simulations by coupling the core and scrapeoff layer (SOL) regions across the separatrix with field-aligned particle-grid interpolations. A fully kinetic particle pusher for high frequency waves (ion cyclotron frequency and beyond) and a guiding center pusher for low frequency waves have been implemented using cylindrical coordinates in a global toroidal geometry. The two integrators correctly capture the particle orbits and agree well with each other, conserving energy and canonical angular momentum. As a verification and application of this new capability, ion guiding center simulations have been carried out to study ion orbit losses at the edge of the DIII-D tokamak for single null magnetic separatrix discharges. The ion loss conditions are examined as a function of the pitch angle for cases without and with an electric field. The simulations show good agreement with past theoretical results and with experimentally observed feature in which high energy ions flow out along the ion drift orbits and then hit the divertor plates. A measure of the ion direct orbit loss fraction shows that the loss fraction increases with the ion energy for DIII-D in the initial velocity space. Finally, as a further verification of the capability of the new code, self-consistent simulations of zonal flows in the core region of the DIII-D tokamak were carried out.

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“…This new conservative scheme has no restriction of the perpendicular grid size to resolve the electron skin depth for the long wavelength MHD wave simulation, and only requires a very small number of kinetic markers (20 markers per cell) to achieve sufficient accuracy in linear simulation. In addition to the simulations of the low frequency drift-Alfvé nic modes described in the paper, the new conservative scheme has also been successfully applied to the simulations of radio frequency (RF) waves such as lower hybrid wave in tokamak plasmas [16,17].…”

Section: Introductionmentioning

confidence: 99%

A conservative scheme for electromagnetic simulation of magnetized plasmas with kinetic electrons

Bao

Zhang

2018

Physics of Plasmas

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A conservative scheme has been formulated and verified for gyrokinetic particle simulations of electromagnetic waves and instabilities in magnetized plasmas. An electron continuity equation derived from drift kinetic equation is used to time advance electron density perturbation by using the perturbed mechanical flow calculated from the parallel vector potential, and the parallel vector potential is solved by using the perturbed canonical flow from the perturbed distribution function. In gyrokinetic particle simulations using this new scheme, shear Alfvé n wave dispersion relation in shearless slab and continuum damping in sheared cylinder have been recovered. The new scheme overcomes the stringent requirement in conventional perturbative simulation method that perpendicular grid size needs to be as small as electron collisionless skin depth even for the long wavelength Alfvé n waves. The new scheme also avoids the problem in conventional method that an unphysically large parallel electric field arises due to the inconsistency between electrostatic potential calculated from the perturbed density and vector potential calculated from the perturbed canonical flow. Finally, the gyrokinetic particle simulations of the Alfvé n waves in sheared cylinder have superior numerical properties compared with the fluid simulations, which suffer from numerical difficulties associated with singular mode structures.

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

Cited by 12 publications

References 54 publications

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

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

Kinetic particle simulations in a global toroidal geometry

A conservative scheme for electromagnetic simulation of magnetized plasmas with kinetic electrons

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