Loading in 5 sec....

Lecture Series in Energetic Particle Physics of Fusion PlasmasPowerPoint Presentation

Lecture Series in Energetic Particle Physics of Fusion Plasmas

Download Presentation

Lecture Series in Energetic Particle Physics of Fusion Plasmas

Loading in 2 Seconds...

- 109 Views
- Uploaded on
- Presentation posted in: General

Download Presentation
## PowerPoint Slideshow about 'Lecture Series in Energetic Particle Physics of Fusion Plasmas ' - fritz-calhoun

**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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### Lecture Series in Energetic Particle Physics of Fusion Plasmas

Guoyong Fu

Princeton Plasma Physics Laboratory

Princeton University

Princeton, NJ 08543, USA

IFTS, Zhejiang University, Hangzhou, China, Jan. 3-8, 2007

A series of 5 lectures Plasmas

- (1) Overview of Energetic Particle Physics in Tokamaks (Jan.3)
- (2) Tokamak equilibrium, shear Alfven wave equation, Alfven eigenmodes (Jan. 4)
- (3) Linear stability of energetic particle-driven modes (Jan. 5)
- (4) Nonlinear dynamics of energetic particle-driven modes (Jan. 6)
- (5) Summary and future direction for research in energetic particle physics (Jan. 8)

Tokamak equilibrium, shear Alfven wave equation, Alfven eigenmodes

- Tokamak equilibrium
- Shear Alfven wave equation
- Alfven eignemodes
- Summary

Shear Alfven spectrum, continuum damping, and discrete modes eigenmodes

- Shear Alfven wave dispersion relation
- Continuum spectrum
- Initial perturbation decays due to phase mixing at time scale of
- Driven perturbation at w is resonantly absorbed at continuum damping
- Phase mixing and resonant absorption has exact analogy with Landau damping for Vlasov plasma.

Discrete Alfven Eigenmodes can exist near continuum accumulation point due to small effects such as toroidicity, shaping, magnetic shear, and energetic particle effects.

Coupling of m and m+k modes breaks degeneracy of Alfven continuum :

K=1 coupling is induced by toroidicity

K=2 coupling is induced by elongation

K=3 coupling is induced by triangularity.

Shear Alfven Eigenmodes accumulation point due to small effects such as toroidicity, shaping, magnetic shear, and energetic particle effects.

- Cylindrical limit Global Alfven Eigenmodes
- Toroidal coupling TAE and Reversed shear Alfven eigenmodes
- Elongation EAE and Reversed shear Alfven eigenmodes
- Triangularity NAE
- FLR effectsKTAE

Shear Alfven Equation accumulation point due to small effects such as toroidicity, shaping, magnetic shear, and energetic particle effects.

- Assume low-beta, large aspect ratio, shear Alfven wave equation can be written as

G.Y. Fu and H.L. Berk, Phys. Plasmas 13,052502 (2006)

Shear Alfven Equation: cylindrical limit (straight tokamak) accumulation point due to small effects such as toroidicity, shaping, magnetic shear, and energetic particle effects.

When Alfven continuum has a minimum, a discrete mode can exist

Below this minimum when This mode is called global

Alfven Eigenmode (GAE)

K. Appert, R. Gruber, F. Troyuon and J. Vaclavik 1982, Plasma Phys.24, 1147

Mode coupling between m and m+1 induces a continuum gap shear

Continuum spectrum is modified by toroidicity.

at

Toroidal Alfven Eigenmode (TAE) can exist inside continuum gap

TAE mode frequencies are located inside the toroidcity-induced Alfven gaps;

TAE modes peak at the gaps with two dominating poloidal harmonics.

C.Z. Cheng, L. Chen and M.S. Chance 1985, Ann. Phys. (N.Y.)161, 21

Reversed shear Alfven eigenmode (RSAE) can exist above maximum of Alfven continuum at q=qmin

U

wA

q

wRSAE

rmin

r

rmin

r

rmin

r

w = (n-m/qmin)/R

RSAE (Alfven cascades) were observed in JET plasmas maximum of Alfven continuum at q=q

RSAE exists due to toroidicity, pressure gradient or energetic particle effects

H.L. Berk, D.N. Borba, B.N. Breizman, S.D. Pinches and S.E. Sharapov 2001,

Phys. Rev. Lett.87 185002

S.E. Sharapov, et al. 2001, Phys. Lett. A289, 127

B.N. Breizman et al, Phys. Plasmas 10, 3649 (2003)

G.Y. Fu and H.L. Berk, Phys. Plasmas 13,052502 (2006)

Summary energetic particle effects

- Mode coupling induces gaps in shear Alfven continuum spectrum.
- Discrete Alfven eigenmodes can usually exist near Alfven continuum accumulation point (inside gaps, near continuum minimum or maximum).
- Existence of Alfven eigenmodes are due to “small” effects such as magnetic shear, toroidicity, elongation, and non-resonant energetic particle effects.