Abstract
This paper reports selfconsistent global linear gyrokineticparticleincell simulations of shear Alfvén waves destabilized by fast particles in tokamak geometry. Resonant excitation of toroidal Alfvén eigenmodes by fast particles and their transition to energetic particle modes (when the fastparticle drive is large enough) has been observed in the simulations.
We thank P. Helander and S. Günter for carefully reading the manuscript. We appreciate discussions with Ph. Lauber and comments by A. Bottino. The computations have been done on the HGW Linux cluster (technical support from H. Leyh and M. Borchardt is acknowledged) and on the IBM Blue Gene/P supercomputer at the Rechenzentrum der MaxPlanckGesellschaft und des MaxPlanckInstituts für Plasmaphysik.
I. INTRODUCTION
II. BASIC EQUATIONS AND NUMERICAL APPROACH
III. SIMULATIONS
IV. CONCLUSIONS
Key Topics
 Fast particle effects
 101.0
 Particleincell method
 21.0
 Plasma gyrokinetics
 18.0
 Magnetohydrodynamics
 11.0
 Particle distribution functions
 10.0
Figures
The shear Alfvén spectrum for the case considered (for parameters see main text). The SAW continuum is plotted. The dominant frequency resulting from the PIC simulation (the stable TAE mode) is compared with the TAE mode computed with the ideal MHD eigenvalue code.
The shear Alfvén spectrum for the case considered (for parameters see main text). The SAW continuum is plotted. The dominant frequency resulting from the PIC simulation (the stable TAE mode) is compared with the TAE mode computed with the ideal MHD eigenvalue code.
Time dependency of the electrostatic (left) and magnetic (right) potentials measured with the PIC code. One sees that the poloidal modes are coupled with each other.
Time dependency of the electrostatic (left) and magnetic (right) potentials measured with the PIC code. One sees that the poloidal modes are coupled with each other.
Radial structures of the electrostatic (left) and magnetic (right) potentials measured with the PIC code. One sees that the mode is centered on the gap position and has a TAEtype poloidal spectrum.
Radial structures of the electrostatic (left) and magnetic (right) potentials measured with the PIC code. One sees that the mode is centered on the gap position and has a TAEtype poloidal spectrum.
The frequency (left) and the growth rate (right) of the TAE mode destabilized by the fast particles (sweep over the fast particle density, the fast particle temperature is kept constant). The TAE mode transforms continuously into the EPM instability as increases. On the right, the PIC growth rate (solid line) is compared with the growth rates resulting from the hybridMHD approach (Refs. 34 and 35) (dashed line). For parameters see the main text.
The frequency (left) and the growth rate (right) of the TAE mode destabilized by the fast particles (sweep over the fast particle density, the fast particle temperature is kept constant). The TAE mode transforms continuously into the EPM instability as increases. On the right, the PIC growth rate (solid line) is compared with the growth rates resulting from the hybridMHD approach (Refs. 34 and 35) (dashed line). For parameters see the main text.
Radial structures of the electrostatic (left) and magnetic (right) potentials measured with the PIC code for the EPM mode corresponding to (this mode can be dubbed a TAEtype EPM similar to Ref. 19). This EPM mode has a poloidal spectrum similar to the TAE mode but the radial width is much larger than that of a typical TAE mode such as shown in Fig. 3.
Radial structures of the electrostatic (left) and magnetic (right) potentials measured with the PIC code for the EPM mode corresponding to (this mode can be dubbed a TAEtype EPM similar to Ref. 19). This EPM mode has a poloidal spectrum similar to the TAE mode but the radial width is much larger than that of a typical TAE mode such as shown in Fig. 3.
The frequency (left) and the growth rate (right) of the TAE mode destabilized by the fast particles (sweep over the temperature of the fast particles, is kept constant). On the right, the PIC growth rate, which includes all FLR and FOW effects (solid line, circles), is compared with the PIC growth rate resulting from the simulations without the fastparticle FLR effects (dotted line, squares). The hybridMHD (Refs. 34 and 35) growth rate (dashed line, no symbols) is shown, too. For other parameters see main text.
The frequency (left) and the growth rate (right) of the TAE mode destabilized by the fast particles (sweep over the temperature of the fast particles, is kept constant). On the right, the PIC growth rate, which includes all FLR and FOW effects (solid line, circles), is compared with the PIC growth rate resulting from the simulations without the fastparticle FLR effects (dotted line, squares). The hybridMHD (Refs. 34 and 35) growth rate (dashed line, no symbols) is shown, too. For other parameters see main text.
The frequency (left) and the growth rate (right) of the TAE mode destabilized by the fast particles (sweep over the temperature of the fast particles, is kept constant). EPM instability appears at the lower temperatures, where the fast particles resonantly interact with the bottom part of the continuum. For parameters see main text.
The frequency (left) and the growth rate (right) of the TAE mode destabilized by the fast particles (sweep over the temperature of the fast particles, is kept constant). EPM instability appears at the lower temperatures, where the fast particles resonantly interact with the bottom part of the continuum. For parameters see main text.
Radial structures of the electrostatic (left) and magnetic (right) potentials measured with the PIC code (for , see Fig. 7). The mode is centered in the position of the gap and has a TAEtype poloidal spectrum (with the dominant poloidal modes and ).
Radial structures of the electrostatic (left) and magnetic (right) potentials measured with the PIC code (for , see Fig. 7). The mode is centered in the position of the gap and has a TAEtype poloidal spectrum (with the dominant poloidal modes and ).
Radial structures of the electrostatic (left) and magnetic (right) potentials measured with the PIC code (for , see Fig. 7). The mode is shifted radially from the gap position. A single poloidal mode dominates. This is a nonperturbative EPM mode.
Radial structures of the electrostatic (left) and magnetic (right) potentials measured with the PIC code (for , see Fig. 7). The mode is shifted radially from the gap position. A single poloidal mode dominates. This is a nonperturbative EPM mode.
The frequency (left) and the growth rate (right) of the TAE mode (sweep over the fastparticle density gradient). The fastparticle temperature , the fast particle density . For other parameters see main text.
The frequency (left) and the growth rate (right) of the TAE mode (sweep over the fastparticle density gradient). The fastparticle temperature , the fast particle density . For other parameters see main text.
The radial structure of the electrostatic potential obtained with the PIC code. The figure on the left corresponds to . The figure on the right results from the simulations with . Other parameters in these two simulations coincide.
The radial structure of the electrostatic potential obtained with the PIC code. The figure on the left corresponds to . The figure on the right results from the simulations with . Other parameters in these two simulations coincide.
The frequency (left) and the growth rate (right) of the TAE mode destabilized by the fast particles (convergence study with respect to the marker resolution). The fastparticle temperature , the fast particle density . For other parameters see main text.
The frequency (left) and the growth rate (right) of the TAE mode destabilized by the fast particles (convergence study with respect to the marker resolution). The fastparticle temperature , the fast particle density . For other parameters see main text.
The frequency (left) and the growth rate (right) of the TAE mode destabilized by the fast particles (convergence study with respect to the radial grid resolution). The fastparticle temperature , the fast particle density . For other parameters see main text.
The frequency (left) and the growth rate (right) of the TAE mode destabilized by the fast particles (convergence study with respect to the radial grid resolution). The fastparticle temperature , the fast particle density . For other parameters see main text.
The frequency (left) and the growth rate (right) of the TAE mode destabilized by the fast particles (convergence study with respect to the number of iterations in Ampére’s law). In this simulation, ion markers, electron markers, and fastparticle markers have been taken. The radial resolution is . The fastparticle temperature , the fast particle density .
The frequency (left) and the growth rate (right) of the TAE mode destabilized by the fast particles (convergence study with respect to the number of iterations in Ampére’s law). In this simulation, ion markers, electron markers, and fastparticle markers have been taken. The radial resolution is . The fastparticle temperature , the fast particle density .
Article metrics loading...
Full text loading...
Most read this month
Most cited this month










Electron, photon, and ion beams from the relativistic interaction of Petawatt laser pulses with solid targets
Stephen P. Hatchett, Curtis G. Brown, Thomas E. Cowan, Eugene A. Henry, Joy S. Johnson, Michael H. Key, Jeffrey A. Koch, A. Bruce Langdon, Barbara F. Lasinski, Richard W. Lee, Andrew J. Mackinnon, Deanna M. Pennington, Michael D. Perry, Thomas W. Phillips, Markus Roth, T. Craig Sangster, Mike S. Singh, Richard A. Snavely, Mark A. Stoyer, Scott C. Wilks and Kazuhito Yasuike

Commenting has been disabled for this content