1 / 24

Selected Issues in Energetic Particle Theory

This presentation discusses predictive capabilities, nonlinear regimes, and mysteries in energetic particle theory in magnetic confinement systems. It also explores the interplay of kinetic and fluid resonances and transport barriers for energetic particles.

shelleyh
Download Presentation

Selected Issues in Energetic Particle Theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 8th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems 6-8 October 2003, San Diego, California, USA Selected Issues in Energetic Particle TheoryPresented by Boris Breizman In collaboration with H. Berk, J. Candy, A. Ödblom, V. Pastukhov, M. Pekker, N. Petviashvili, S. Pinches, S. Sharapov, Y. Todo, and JET-EFDA contributors

  2. Outline • Predictive capabilities of linear theory and simulations • Near-threshold nonlinear regimes • Remaining mysteries in Alfvén Cascade observations • Nonlinear modification of Alfvén wave damping • Interplay of kinetic and fluid resonances • Convectiveand diffusive scenarios for global transport • Transport barriers for energetic particles • Remarks about next steps 2

  3. Products of linear theory • Mode frequencies • Frequencies are robust (for perturbative modes) and easy to measure in experimens • Mode structure • Robust, measurable and usable in nonlinear theory (for perturbative modes) • Growth rates • Energetic particle drive can be calculated reliably but it changes quickly due to nonlinear effects • Damping rates • Except for collisional damping, the damping rates from the background plasma are exponentially sensitive to plasma parameters (ion Landau damping, radiative damping, continuum damping) 3

  4. Things to do in linear analysis • Fast particle phase space study in presence of linearly unstable • modes to find robust conditions for global diffusion • Issue: possible partial depletion of phase space • Comprehensive sensitivity study of instability boundaries to plasma • parameters • Mode suppression over a sufficiently broad radial interval • to create a transport barrier for energetic particles • Careful assessment of edge effects (boundary conditions for the • modes, particle orbits, etc.) 4

  5. Near-threshold nonlinear regimes • Macroscopic plasma parameters typically evolve slowly on • instability time-scale. • Perturbation technique is adequate near instability threshold. • Identification of soft and hard nonlinear regimes is crucial • (does the unstable system move towards marginal stability?). • Bifurcations in single-mode saturation can be analyzed. • Formation of long-lived nonlinear structures is likely. • Multi-mode scenarios with marginal stability and possibly transport • barriers are of interest. 5

  6. Alfvén Cascades (initial step) IFS-JET collaboration: PRL 87, 185002-1 (2001) Frequency initially below TAE gap, while safety factor decreases in time Frequency sweeps predominantly upward, usually not downward Frequency signals are repetitive for a large number of n-values Sometimes frequency merges into the TAE gap 6

  7. Transition from Alfvén Cascades to TAEs (2002 advance) Mode tail near continuum resonance (zoomed) Mode structure 200 200 q0=2.915 200 200 q0=2.875 40 40 q0=2.86 40 40 q0=2.84 7

  8. Continuum damping for Alfvén Cascades (new results) • Damping rate grows exponentially as q0 approaches rational surface: • Low frequency limit: 8

  9. Frequency and damping rate  - single poloidal harmonic (m=12)  - two coupled poloidal harmonics (m=12, m=11) W G/W Analytic estimate Safety factor q0 Safety factor q0 9

  10. Mysteries in Alfvén Cascades(partially resolved) • Transition from Alfvén Cascades to TAE • Suppression of Alfvén Cascades at low frequencies 10

  11. Mysteries in Alfvén Cascades(unresolved) • Frequency rolling • Mode enhancement at low frequency 11

  12. Fishbone onset Linear responses from kinetic and fluid resonances are in balance at the instability threshold but the nonlinear responses can differ significantly. • QUESTIONS TO ANSWER: • Which resonance produces the dominant nonlinear response? • Is this response stabilizing or destabilizing? APPROACH: • Analyze nonlinear regime near the instability threshold. • Perform hybrid kinetic-MHD simulations to study strong • nonlinearity. 12

  13. Double resonance layer at Linear near-threshold mode 13

  14. Early nonlinear dynamics Normalized evolution equations for on-axis displacement with cubic MHD nonlinearity: Explosive nonlinear solution : Weak MHD nonlinearity of the q=1 layer destabilizes fishbone perturbations 14

  15. Remaining challenges • Transition from explosive growth to slowly growing MHD structure • (island near q=1 surface) • Modification of fast particle distribution • Explanation of mode saturation and decay • Quantitative simulation of frequency sweeping • Burst repetition rate in presence of injection 15

  16. Convective transport in phase space . 16

  17. Intermittent losses of fast ions . Experiments show both benign and malignant effects. • Rapid losses in early experiments • (K. L. Wong, et. al. TFTR; Heidbrink, et. al. DIII-D) Study of rapid loss: IFS- NIFS collaboration, Physics of Plasmas 10, 2888 (2003) 17

  18. stored beam energy with TAE turbulence Simulation of intermittent losses in TFTR (Y. Todo et al.) TAE excitations reduce stored energy, especially that of counter-injected beam 18

  19. Temporal relaxation of radial profile Counter-injected beams are confined only near plasma axis. Co-injected beams are confined efficiently. Pressure gradient periodically collapses at criticality. Large pressure gradient sustained at plasma edge. 19

  20. Resonances in phase spacefor low amplitude modes . N=1: Red N=2: Green N=3: Blue 20

  21. Resonances in phase spaceat mode saturation . N=1: Red N=2: Green N=3: Blue 21

  22. Issues in diffusive transport modeling • Reconciliation of mode saturation levels with experimental data. • Edge effects in fast particle transport. • Transport barriers for marginally stable profiles. • Resonance overlap in 3D. 22

  23. Theoretical problems to study(please feel free to do more) • Diagnostic applications of benign modes. • Quantitative interpretation of experimental data for nonlinearly • saturated isolated modes (TAE’s, Cascades, high-frequency modes, • etc.) • Transport barriers for energetic particles in presence of many • unstable modes. • Parameter window for fast particle confinement in fusion devices. • Intermittent strong bursts versus stochastic diffusive transport. • Lifecycle of fishbones and EPMs starting from instability threshold. • Fast nonlinear frequency sweeping. • Interplay of kinetic and fluid resonances. 23

  24. Elements of style • Look for puzzles/discrepancies of basic importance. • Identify key physics ingredients qualitatively/analytically. • Develop internally consistent reduced models and “bare bones” codes • to capture and simulate essential physics and to perform broad • parameter scan. • Develop advanced techniques for large-scale simulations. • Use reduced models to validate large codes. • Use large codes to model present experiments (quantitatively!) • and to extrapolate them (conclusively!) to reactor conditions. 24

More Related