Electromagnetic particle simulation of the effect of toroidicity on linear mode conversion and absorption of lower hybrid waves

Abstract

Effects of toroidicity on linear mode conversion and absorption of lower hybrid (LH) waves in fusion plasmas have been studied using electromagnetic particle simulation. The simulation confirms that the toroidicity induces an upshift of parallel refractive index when LH waves propagate from the tokamak edge toward the core, which affects the radial position for the mode conversion between slow and fast LH waves. Furthermore, moving LH antenna launch position from low field side toward high field side leads to a larger upshift of the parallel refractive index, which helps the slow LH wave penetration into the tokamak core. The broadening of the poloidal spectrum of the wavepacket due to wave diffraction is also verified in the simulation. Both the upshift and broadening effects of the parallel spectrum of the wavepacket modify the parallel phase velocity and thus the linear absorption of LH waves by electron Landau resonance.

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

“…where  n and  u represent the particle noise errors induced from the kinetic markers to the perturbed density and the perturbed canonical flow, respectively, Eqs. (17) and (18) Applying the Fourier transform  ik to Eqs. (7) and (11) and considering Eqs.…”

“…(7) and (11) and considering Eqs. (17) and (18), we can derive the dispersion relation of shear Alfvé n wave with particle noise error: (20) From Eq. (20), it is seen that the particle noise error is amplified with increasing  e and the perpendicular wavelength through the second and third terms on the RHS, respectively, which explains the numerical difficulty of the electromagnetic simulation of the long wavelength modes with  In conservative scheme, we use the kinetic markers to calculate the perturbed canonical flow as Eq.…”

“…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].…”

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

“…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.…”

Kinetic particle simulations in a global toroidal geometry

“…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.…”