Threshold of the temperature gradient driven instability

For more info about our services contact : help@bestpfe.com

Table of contents

1 Introduction: turbulence and transport in Tokamaks 
1.1 Nuclear fusion
1.1.1 Nuclear fusion reaction
1.1.2 Lawson criterion
1.2 Kinetic description of plasma turbulence
1.2.1 Vlasov equation
1.2.2 Quasi-neutrality equation
1.2.3 Difficulty of nonlinear simulation
1.3 Reduced model
1.3.1 Trapped particle model
1.3.2 Simplifications in fluid turbulence
2 Bounce averaged gyrokinetics δf equations in Fourier space. 
2.1 Introduction
2.2 Bounce averaged gyrokinetics
2.2.1 Model equations
2.2.2 Scale separation
2.2.3 Normalization
2.3 δf equations in Fourier space
2.4 Description of nonlinear interactions
2.4.1 Description of k+p+q = 0
2.4.2 Description of the nonlinear terms
2.4.3 Different approaches and connections to previous models
2.4.4 Conserved quantities.
2.5 Conclusion
3 Linear Phase 
3.1 Linear dispersion relation
3.1.1 Plasma dielectric function: ǫ(ω)
3.1.2 Singularity and residue
3.2 Threshold of the temperature gradient driven instability
3.2.1 Threshold of κT and the wave number k
3.2.2 Threshold of κT and ion to electron temperature ratio τ
3.2.3 Threshold of κT and the trapped particle ratio ft
3.3 Linear instability
3.3.1 Numerical method: argument principle
3.3.2 Linear instability for isotropy system: γ(k) with k = kα = kψ
3.3.3 Linear instability for anisotropic system: γ ¡ kψ, kα ¢ .
3.4 Conclusion
4 Isotropic model: Sabra and GOY 
4.1 Model equations
4.1.1 Phase approximation
4.1.2 Model equations
4.2 Nonlinear simulation of the Sabra model
4.2.1 Code verification
4.2.2 k spectra of the electrostatic potential energy Eφ
4.2.3 k spectra of the entropy Ef and kinetic effect
4.2.4 The effect of free parameter α
4.3 Influence of phase information: GOY vs Sabra
4.3.1 Oscillatory dynamics of the GOYModel
4.3.2 Comparison of entropy
4.3.3 Oscillation of the k-spectra
4.4 Conclusion
5 Anisotropic model: LDM 
5.1 LDMof bounce averaged gyrokinetics
5.1.1 LDMGrid
5.1.2 Vlasov-Poisson equation
5.1.3 Numerical scheme
5.1.4 Definition of zonal flow and dissipation
5.2 Kinetic ions
5.2.1 Temporal spectrumof Eφ and Efi
5.2.2 Spectrum of electrostatic potential Eφ in wave number plane
5.2.3 k spectra of Eφ and Efi
5.3 Kinetic electrons
5.3.1 Temporal spectrumof Eφ and Efe
5.3.2 Predator-prey dynamics between zonal flow and turbulence modes
5.3.3 Spectrum of Eφ in wave number plane
5.3.4 k spectra of electrostatic potential energy Eφ and entropy Efe
5.4 Fully kinetic system
5.4.1 Temporal spectrumof Eφ, Efi and Efe
5.4.2 Spectrum of Eφ in wave number plane
5.4.3 k spectra of Eφ, Efi and Efe
5.4.4 Comparison of the k-spectra: adiabaticity
5.5 Conclusion
6 Conclusion and perspective 
A Calculating the coefficients of GOY model 
B The linear dispersion relation solver 
B.1 Linear dispersion relation ǫ(ω)
B.2 Eigenvalue solver
C Formulation of gyro correction 
D Comparison ofJ0s and its approximations 
E Electrostatic potential energy Eφ and entropy Efs 
F Method of numerical integration