Gyro-average method for global gyrokinetic particle simulation in realistic tokamak geometry

Gyro-average is a crucial operation to capture the essential finite Larmor radius effect (FLR) in gyrokinetic simulation. In order to simulate strongly shaped plasmas, an innovative multi-point average method based on non-orthogonal coordinates has been developed to improve the accuracy of the original multi-point average method in gyrokinetic particle simulation. This new gyro-average method has been implemented in the gyrokinetic toroidal code (GTC). Benchmarks have been carried out to prove the accuracy of this new method. In the limit of concircular tokamak, ion temperature gradient (ITG) instability is accurately recovered for this new method and consistency is achieved. The new gyro-average method is also used to solve the gyrokinetic Poisson equation, and its correctness has been confirmed in the long wavelength limit for realistic shaped plasmas. The improved GTC code with the new gyro-average method has been used to investigate the ITG instability with EAST magnetic geometry. The simulation results show that the correction induced by this new method in the linear growth rate is more significant for short wavelength modes where the finite Larmor radius (FLR) effect becomes important. Due to its simplicity and accuracy, this new gyro-average method can find broader applications in simulating the shaped plasmas in realistic tokamaks.

Analysis of Stability of a Plasma in Porous Medium

The thermal convection of a plasma in porous medium is investigated in the presence of finite Larmor radius (FLR) and Hall effects. Following linear stability theory and normal mode analysis method, the dispersion relation is obtained. It is found that the presence of a magnetic field (and hence the presence of FLR and Hall effects) introduces oscillatory modes in the system which were, otherwise, non-existent in their absence. When the instability sets in as stationary convection, the FLR may have a stabilizing or destabilizing effect, but a completely stabilizing one for a certain wave-number range. Similarly, the Hall currents may have a stabilizing or destabilizing effect but a completely stabilizing one for the same wave-number range under certain condition, whereas the medium permeability always has a destabilizing effect for stationary convection. Also it is found that the system is stable for 𝑔𝛼𝜅 𝜈𝛽 ≤ 27𝜋 4 4 and under the condition 𝑔𝛼𝜅 𝜈𝛽 > 27𝜋 4 4 , the system becomes unstable.

Theoretical study of the Alfven Eigenmode stability in CFETR steady state discharges

The aim of this study is to analyze the stability of Alfven Eigenmodes (AE) in the China Fusion Engineering Test Reactor (CFETR) plasma for steady state operations. The analysis is done using the gyro-fluid code FAR3d including the effect of the acoustic modes, EP Finite Larmor radius damping effects and multiple energetic particle populations. Two high poloidal β scenarios are studied with respect to the location of the internal transport barrier (ITB) at r/a ≈ 0.45 (case A) and r/a ≈ 0.6 (case B). Both operation scenarios show a narrow TAE gap between the inner-middle plasma region and a wide EAE gap all along the plasma radius. The AE stability of CFETR plasmas improves if the ITB is located inwards, case A, showing AEs with lower growth rates with respect to the case B. The AEs growth rate is smaller in the case A because the modes are located in the inner-middle plasma region where the stabilizing effect of the magnetic shear is stronger with respect to the case B. Multiple EP populations effects (NBI driven EP + alpha articles) are negligible for the case A, although the simulations for the case B show a stabilizing effect of the NBI EP on the n=1 BAE caused by alpha particles during the thermalization process. If the FLR damping effects are included in the simulations, the growth rate of the EAE/NAE decreases up to 70 %, particularly for n > 3 toroidal families. Low n AEs (n<6) show the largest growth rates. On the other hand, high n modes (n=6 to 15) are triggered in the frequency range of the NAE, strongly damped by the FLR effects.

Interaction between long-period ULF waves and charged particle in the magnetosphere: theory and observations (overview)

The paper reviews the current state of the problem of interaction between long-period ultra-low-frequency (ULF) waves and high-energy particles. We consider elements of the theory of energy exchange between waves and particles, particle transport across magnetic shells under the influence of the electromagnetic field of a wave, the acceleration of radiation belt particles by both resonant and non-resonant mechanisms. We examine the mechanisms of generation of azimuthally-small-scale ULF waves due to instabilities arising from the wave–particle resonance. The cases of Alfvén, drift-compressional, and drift-mirror waves are analyzed. It is noted that due to the lack of a detailed theory of drift-mirror modes, the possibility of their existence in the magnetosphere cannot be taken as a proven fact. We summarize experimental data on the poloidal and compression ULF waves generated by unstable populations of high-energy particles. We investigate the mechanisms of modulation of energetic particle fluxes by ULF waves and possible observational manifestations of such modulation. Methods of studying the structure of waves across magnetic shells by recording fluxes of resonant particles with a finite Larmor radius are discussed.

Interaction between long-period ULF waves and charged particle in the magnetosphere: theory and observations (overview)

The paper reviews the current state of the problem of interaction between long-period ultra-low-frequency (ULF) waves and high-energy particles. We consider elements of the theory of energy exchange between waves and particles, particle transport across magnetic shells under the influence of the electromagnetic field of a wave, the acceleration of radiation belt particles by both resonant and non-resonant mechanisms. We examine the mechanisms of generation of azimuthally-small-scale ULF waves due to instabilities arising from the wave–particle resonance. The cases of Alfvén, drift-compressional, and drift-mirror waves are analyzed. It is noted that due to the lack of a detailed theory of drift-mirror modes, the possibility of their existence in the magnetosphere cannot be taken as a proven fact. We summarize experimental data on the poloidal and compression ULF waves generated by unstable populations of high-energy particles. We investigate the mechanisms of modulation of energetic particle fluxes by ULF waves and possible observational manifestations of such modulation. Methods of studying the structure of waves across magnetic shells by recording fluxes of resonant particles with a finite Larmor radius are discussed.

Transverse Thermal Instability of Radiative Plasma with FLR Corrections for Star Formation in ISM

Impact of porosity, rotation and finite ion Larmor radius (FLR) corrections on thermal instability of immeasurable homogeneous plasma has been discovered incorporating the effects of radiative heat-loss function and thermal conductivity. The general dispersion relation is carried out with the help of the normal mode analysis scheme taking the suitable linearized perturbation equations of the difficulty. This general dispersion relations is further reduces for rotation axis parallel and perpendicular to the magnetic field. Thermal instability criterion establishes the stability of the medium. Mathematical calculations have been performed to represent the impact of different limitations on the growth rate of thermal instability. It is found that rotation, FLR corrections and medium porosity stabilize the growth rate of the medium in the transverse mode of propagation. Our outcome of the problem explains that the rotation, porosity and FLR corrections affect the dens molecular clouds arrangement and star configuration in interstellar medium.

On Thermal Convection of a Plasma in Porous Medium

The effect of finite Larmor radius of the ions on thermal convection of a plasma is investigated. The case with vertical magnetic field is discussed. Following linear stability theory and normal mode analysis method, the dispersion relation is obtained. It is found that the presence of finite Larmor radius and magnetic field introduces oscillatory modes in the system which were, otherwise, non-existent in their absence. When the instability sets in as stationary convection, finite Larmor radius is found to have a stabilizing effect. Medium permeability has a destabilizing (or stabilizing) effect and the magnetic field has a stabilizing (or destabilizing) effect under certain conditions in the presence of finite Larmor radius effect whereas in the absence of finite Larmor radius effect, the medium permeability and the magnetic field have destabilizing and stabilizing effects, respectively. The sufficient conditions for the non-existence of overstability are also obtained.

Convection of a Rotatory Plasma in Porous Medium

The thermal convection of a plasma in porous medium is investigated to include simultaneously the effect of rotation and the finiteness of the ion Larmor radius (FLR) in the presence of a vertical magnetic field. Following linear stability theory and normal mode analysis method, the dispersion relation is obtained. It is found that the presence of a uniform rotation, finite Larmor radius and magnetic field introduces oscillatory modes in the system which were, otherwise, non-existent in their absence. When the instability sets in as stationary convection, finite Larmor radius, rotation, medium permeability and magnetic field are found to have stabilizing (or destabilizing) effects under certain conditions. In the absence of rotation, finite Larmor radius has stabilizing effect on the thermal instability of the system whereas the medium permeability and the magnetic field may have stabilizing or destabilizing effect under certain conditions. The conditions κ<[ε+(1-ε) (ρ_S C_S)/(ρ_0 C)]η and κ<(ε^2 [ε+(1-ε) (ρ_S C_S)/(ρ_0 C)]ν)/(P^2 [εP{√U (x-2)+√(T_(A_1 ) )}^2-2Q_1 ] ) are the sufficient conditions for non-existence of overstability, the violation of which does not necessary involve an occurrence of overstability.