Nonlinear stability and instability in collisionless trapped electron mode turbulence

2002 ◽  
Vol 9 (8) ◽  
pp. 3318-3332 ◽  
Author(s):  
D. A. Baver ◽  
P. W. Terry ◽  
R. Gatto ◽  
Eduardo Fernandez
Keyword(s):  
Nonlinear Stability ◽  
Stability And Instability ◽  
Electron Mode ◽  
Trapped Electron

Gyrokinetic simulation of collisionless trapped-electron mode turbulence

2005 ◽  
Vol 12 (7) ◽  
pp. 072309 ◽  
Author(s):  
Tilman Dannert ◽  
Frank Jenko
Keyword(s):  
Electron Mode ◽  
Trapped Electron

Study of turbulence in the high betap discharge using only RF heating on EAST

2022 ◽  
Author(s):  
shuyu Zheng ◽  
Debing Zhang ◽  
Erbing Xue ◽  
Limin Yu ◽  
Xianmei Zhang ◽  
...  
Keyword(s):  
Electron Collision ◽  
Rf Heating ◽  
Plasma Parameters ◽  
Equilibrium Data ◽  
Electron Mode ◽  
Radio Frequency Waves ◽  
Thermal Diffusivities ◽  
Gyrokinetic Simulations ◽  
Trapped Electron ◽  
Scale Length

Abstract High poloidal beta scenarios with favorable energy confinement (β_p~1.9, H_98y2~1.4) have been achieved on Experimental Advanced Superconducting Tokamak (EAST) using only radio frequency waves heating. Gyrokinetic simulations are carried out with experimental plasma parameters and tokamak equilibrium data of a typical high β_p discharge by the GTC code. Linear simulations show that electron temperature scale length and electron density scale length destabilize the turbulence, collision effects stabilize the turbulence, and the instability propagates in the electron diamagnetic direction. These indicate that the dominant instability in the core of high β_p plasma is collisionless trapped electron mode. Ion thermal diffusivities calculated by nonlinear gyrokinetic simulations are consistent with the experimental value, in which the electron collision effects play an important role. Further analyses show that instabilities with k_θ ρ_s>0.38 are suppressed by collision effects and collision effects reduce the radial correlation length of turbulence, resulting in the suppression of the turbulence.

Analysis of Geometric Invariants for Three Types of Bifurcations in 2D Differential Systems

2021 ◽  
Vol 31 (07) ◽  
pp. 2150105
Author(s):  
Yongjian Liu ◽  
Chunbiao Li ◽  
Aimin Liu
Keyword(s):  
Fixed Points ◽  
Nonlinear Stability ◽  
Pitchfork Bifurcation ◽  
Transcritical Bifurcation ◽  
Two Dimensional ◽  
Saddle Node Bifurcation ◽  
Differential Systems ◽  
Nonlinear Connection ◽  
Geometric Invariants ◽  
Stability And Instability

Little is known about bifurcations in two-dimensional (2D) differential systems from the viewpoint of Kosambi–Cartan–Chern (KCC) theory. Based on the KCC geometric invariants, three types of static bifurcations in 2D differential systems, i.e. saddle-node bifurcation, transcritical bifurcation, and pitchfork bifurcation, are discussed in this paper. The dynamics far from fixed points of the systems generating bifurcations are characterized by the deviation curvature and nonlinear connection. In the nonequilibrium region, the nonlinear stability of systems is not simple but involves alternation between stability and instability, even though systems are invariably Jacobi-unstable. The results also indicate that the dynamics in the nonequilibrium region are node-like for three typical static bifurcations.

scholarly journals Intrinsic rotation drive by collisionless trapped electron mode turbulence

2016 ◽  
Vol 23 (4) ◽  
pp. 042309 ◽  
Author(s):  
Lu Wang ◽  
Shuitao Peng ◽  
P. H. Diamond
Keyword(s):  
Electron Mode ◽  
Trapped Electron

scholarly journals On the Nonlinear Stability and Instability of the Boussinesq System for Magnetohydrodynamics Convection

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1049
Author(s):  
Dongfen Bian
Keyword(s):  
Equilibrium State ◽  
Nonlinear Stability ◽  
Lower Boundary ◽  
Equilibrium Temperature ◽  
Mhd Equations ◽  
Boussinesq System ◽  
Fluid Viscosity ◽  
Asymptotically Stable ◽  
Temperature Dependent ◽  
Stability And Instability

This paper is concerned with the nonlinear stability and instability of the two-dimensional (2D) Boussinesq-MHD equations around the equilibrium state ( u ¯ = 0 , B ¯ = 0 , θ ¯ = θ 0 ( y ) ) with the temperature-dependent fluid viscosity, thermal diffusivity and electrical conductivity in a channel. We prove that if a + ≥ a − , and d 2 d y 2 κ ( θ 0 ( y ) ) ≤ 0 or 0 < d 2 d y 2 κ ( θ 0 ( y ) ) ≤ β 0 , with β 0 > 0 small enough constant, and then this equilibrium state is nonlinearly asymptotically stable, and if a + < a − , this equilibrium state is nonlinearly unstable. Here, a + and a − are the values of the equilibrium temperature θ 0 ( y ) on the upper and lower boundary.

Trapped electron effects onηi-mode and trapped electron mode in RFP plasmas

2014 ◽  
Vol 54 (4) ◽  
pp. 043006 ◽  
Author(s):  
S.F. Liu ◽  
S.C. Guo ◽  
W. Kong ◽  
J.Q. Dong
Keyword(s):  
Electron Mode ◽  
Trapped Electron ◽  
Electron Effects

scholarly journals Destabilization of the trapped-electron mode by magnetic curvature drift resonances

1976 ◽  
Vol 19 (4) ◽  
pp. 561 ◽  
Author(s):  
J. C. Adam ◽  
W. M. Tang ◽  
P. H. Rutherford
Keyword(s):  
Electron Mode ◽  
Trapped Electron
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