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Frequency Chirping of Energetic-Particle-Driven Geodesic Acoustic Modes in Tokamaks

R. Wu, A. Biancalani, D. Gossard, R. Ivanov, A. Mishchenko, X. Wang, F. Zonca

Abstract

A suprathermal population of ions is present in tokamak plasmas due to external heating mechanisms and fusion reactions. These energetic particles (EP) can drive wave unstable, via inverse Landau damping. An example is the energetic-particledriven geodesic acoustic mode (EGAMs). In this work, we perform a systematic gyrokinetic investigation of the EGAM linear and nonlinear dynamics, using the global gyrokinetic particle-in-cell code ORB5. The nonlinear saturation given by the EP redistribution in phase space is characterized by a saturation level scaling quadratically with respect to the linear growth rate. The nonlinear EP dynamics in phase space has also effects on the EGAM frequency. To this extent, we investigate the frequency chirping, and we find that the chirping rate scales linearly with the linear growth rate over a wide range of EP concentrations. This scaling is consistent with the theoretical prediction of Chen-Zonca [L. Chen, and F. Zonca, Rev. Mod. Phys. 88, 015008 (2016)].

Frequency Chirping of Energetic-Particle-Driven Geodesic Acoustic Modes in Tokamaks

Abstract

A suprathermal population of ions is present in tokamak plasmas due to external heating mechanisms and fusion reactions. These energetic particles (EP) can drive wave unstable, via inverse Landau damping. An example is the energetic-particledriven geodesic acoustic mode (EGAMs). In this work, we perform a systematic gyrokinetic investigation of the EGAM linear and nonlinear dynamics, using the global gyrokinetic particle-in-cell code ORB5. The nonlinear saturation given by the EP redistribution in phase space is characterized by a saturation level scaling quadratically with respect to the linear growth rate. The nonlinear EP dynamics in phase space has also effects on the EGAM frequency. To this extent, we investigate the frequency chirping, and we find that the chirping rate scales linearly with the linear growth rate over a wide range of EP concentrations. This scaling is consistent with the theoretical prediction of Chen-Zonca [L. Chen, and F. Zonca, Rev. Mod. Phys. 88, 015008 (2016)].
Paper Structure (18 sections, 9 equations, 10 figures)

This paper contains 18 sections, 9 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Theoretical Background
  3. Geodesic Acoustic Modes
  4. Energetic-Particle-Driven GAMs
  5. Model and Equilibrium
  6. Tokamak Equilibrium and Plasma Profiles
  7. The ORB5 Gyrokinetic Code
  8. Signal Processing and Diagnostic Methods
  9. Simulation Results
  10. GAM Benchmark
  11. Rosenbluth--Hinton Test
  12. GAM Frequency and Damping
  13. EGAM
  14. Radial Electric Field and Frequency Evolution: Linear vs Nonlinear Regimes
  15. Dependence of Linear Growth Rate and Saturation Level on EP Concentration
  16. ...and 3 more sections

Figures (10)

  • Figure 1: Initial EP symmetric bump-on-tail distribution function for a simulation with $n_{EP}/n_i = 0.12$, $v_{bump}/v_{ti} = 4$. Reproduced from Biancalani et al. (2017) biancalani2017
  • Figure 2: Tokamak geometry with $R_0 = 1 \ m$, $a = 0.3125 \ m$
  • Figure 3: Temporal evolution of the radial electric field perturbation at s = 0.9, showing damped GAM oscillations.
  • Figure 4: Logarithmic fit of the GAM oscillation envelope at s = 0.9, used to evaluate the damping rate.
  • Figure 5: Time evolution of the radial electric field $E_r(t)$ at $s=0.9$ with an EP concentration of $7\%$. Panel (a) corresponds to the linear simulation, while panel (b) corresponds to the nonlinear simulation.
  • ...and 5 more figures