![Page 1: Continuum Absorption at Frequency Tipw3fusion.ph.utexas.edu/ifs/iaeapi/talks/a2-4-chen-eugene-pi-talk.pdf · Continuum Absorption at Frequency Tip Eugene Chen In collaboration with:](https://reader034.vdocument.in/reader034/viewer/2022042322/5f0c58597e708231d434f0a4/html5/thumbnails/1.jpg)
Continuum Absorption at Frequency Tip
Eugene Chen
In collaboration with:Herb Berk, Boris Breizman and Linjin Zheng
Institute for Fusion Studies, UT Austin
IAEA Technical Meeting on Plasma InstabilitySep 5th, 2011
Austin, TX
![Page 2: Continuum Absorption at Frequency Tipw3fusion.ph.utexas.edu/ifs/iaeapi/talks/a2-4-chen-eugene-pi-talk.pdf · Continuum Absorption at Frequency Tip Eugene Chen In collaboration with:](https://reader034.vdocument.in/reader034/viewer/2022042322/5f0c58597e708231d434f0a4/html5/thumbnails/2.jpg)
Continuum Absorption
● Occurs in inhomogeneous plasma where Alfven velocity is a function of position (x)(x).
● When external driving frequency matches with local shear Alfven frequency, phase mixing occurs around the resonance and wave energy is dissipated to the plasma.
● The energy absorption rate is calculated by introducing an artificial growth rate to mimic the effects of viscous dissipation. (e.g., Chen and Hasegawa 1974)
![Page 3: Continuum Absorption at Frequency Tipw3fusion.ph.utexas.edu/ifs/iaeapi/talks/a2-4-chen-eugene-pi-talk.pdf · Continuum Absorption at Frequency Tip Eugene Chen In collaboration with:](https://reader034.vdocument.in/reader034/viewer/2022042322/5f0c58597e708231d434f0a4/html5/thumbnails/3.jpg)
Estimation of Absorption Rate
Q is independent of , proportional to
![Page 4: Continuum Absorption at Frequency Tipw3fusion.ph.utexas.edu/ifs/iaeapi/talks/a2-4-chen-eugene-pi-talk.pdf · Continuum Absorption at Frequency Tip Eugene Chen In collaboration with:](https://reader034.vdocument.in/reader034/viewer/2022042322/5f0c58597e708231d434f0a4/html5/thumbnails/4.jpg)
Slope of the Continuum is usually not a constant...
What is the absorption rate as the slope approaches zero??
![Page 5: Continuum Absorption at Frequency Tipw3fusion.ph.utexas.edu/ifs/iaeapi/talks/a2-4-chen-eugene-pi-talk.pdf · Continuum Absorption at Frequency Tip Eugene Chen In collaboration with:](https://reader034.vdocument.in/reader034/viewer/2022042322/5f0c58597e708231d434f0a4/html5/thumbnails/5.jpg)
Numerical Investigation (I)
● We use a GradShafranov Solver TOQ to generate the numerical equilibra. The input parameters are poloidal current flux and pressure profile.
● Our ideal MHD code AEGIS is adaptive, thus, high density of grids are placed in the vicinity of continuum.
![Page 6: Continuum Absorption at Frequency Tipw3fusion.ph.utexas.edu/ifs/iaeapi/talks/a2-4-chen-eugene-pi-talk.pdf · Continuum Absorption at Frequency Tip Eugene Chen In collaboration with:](https://reader034.vdocument.in/reader034/viewer/2022042322/5f0c58597e708231d434f0a4/html5/thumbnails/6.jpg)
Numerical Investgiation (II)
● A poloidal current is driven at x=0.2 with a tunable frequency.
● We investigate the absorption as a function of frequency near to the frequency tip.
![Page 7: Continuum Absorption at Frequency Tipw3fusion.ph.utexas.edu/ifs/iaeapi/talks/a2-4-chen-eugene-pi-talk.pdf · Continuum Absorption at Frequency Tip Eugene Chen In collaboration with:](https://reader034.vdocument.in/reader034/viewer/2022042322/5f0c58597e708231d434f0a4/html5/thumbnails/7.jpg)
Estimation of Absorption Rate at Continuum Tip
![Page 8: Continuum Absorption at Frequency Tipw3fusion.ph.utexas.edu/ifs/iaeapi/talks/a2-4-chen-eugene-pi-talk.pdf · Continuum Absorption at Frequency Tip Eugene Chen In collaboration with:](https://reader034.vdocument.in/reader034/viewer/2022042322/5f0c58597e708231d434f0a4/html5/thumbnails/8.jpg)
Reverse Shear Tip (I)
![Page 9: Continuum Absorption at Frequency Tipw3fusion.ph.utexas.edu/ifs/iaeapi/talks/a2-4-chen-eugene-pi-talk.pdf · Continuum Absorption at Frequency Tip Eugene Chen In collaboration with:](https://reader034.vdocument.in/reader034/viewer/2022042322/5f0c58597e708231d434f0a4/html5/thumbnails/9.jpg)
Reverse Shear Tip (II)
![Page 10: Continuum Absorption at Frequency Tipw3fusion.ph.utexas.edu/ifs/iaeapi/talks/a2-4-chen-eugene-pi-talk.pdf · Continuum Absorption at Frequency Tip Eugene Chen In collaboration with:](https://reader034.vdocument.in/reader034/viewer/2022042322/5f0c58597e708231d434f0a4/html5/thumbnails/10.jpg)
TAE Frequency Gap
![Page 11: Continuum Absorption at Frequency Tipw3fusion.ph.utexas.edu/ifs/iaeapi/talks/a2-4-chen-eugene-pi-talk.pdf · Continuum Absorption at Frequency Tip Eugene Chen In collaboration with:](https://reader034.vdocument.in/reader034/viewer/2022042322/5f0c58597e708231d434f0a4/html5/thumbnails/11.jpg)
Estimation of Continuum Absorption at TAE Tip
● The tip is formed due to the toroidal coupling of two adjacent poloidal harmonics. Both harmonics need to be taken into account.
● We applied the TAE tip model (Rosenbluth, Berk et at.; Breizman and Sharapov) to the problem.
● It can be shown that as ,
, where
.
● Absorption shall vanish at the tip!
![Page 12: Continuum Absorption at Frequency Tipw3fusion.ph.utexas.edu/ifs/iaeapi/talks/a2-4-chen-eugene-pi-talk.pdf · Continuum Absorption at Frequency Tip Eugene Chen In collaboration with:](https://reader034.vdocument.in/reader034/viewer/2022042322/5f0c58597e708231d434f0a4/html5/thumbnails/12.jpg)
Lower TAE Tip
![Page 13: Continuum Absorption at Frequency Tipw3fusion.ph.utexas.edu/ifs/iaeapi/talks/a2-4-chen-eugene-pi-talk.pdf · Continuum Absorption at Frequency Tip Eugene Chen In collaboration with:](https://reader034.vdocument.in/reader034/viewer/2022042322/5f0c58597e708231d434f0a4/html5/thumbnails/13.jpg)
Upper TAE Tip
![Page 14: Continuum Absorption at Frequency Tipw3fusion.ph.utexas.edu/ifs/iaeapi/talks/a2-4-chen-eugene-pi-talk.pdf · Continuum Absorption at Frequency Tip Eugene Chen In collaboration with:](https://reader034.vdocument.in/reader034/viewer/2022042322/5f0c58597e708231d434f0a4/html5/thumbnails/14.jpg)
TAE Frequency
● For eigenmodes, ,
independent of position.
Numerical results show good agreement.
![Page 15: Continuum Absorption at Frequency Tipw3fusion.ph.utexas.edu/ifs/iaeapi/talks/a2-4-chen-eugene-pi-talk.pdf · Continuum Absorption at Frequency Tip Eugene Chen In collaboration with:](https://reader034.vdocument.in/reader034/viewer/2022042322/5f0c58597e708231d434f0a4/html5/thumbnails/15.jpg)
Summary and Conclusions
● In the case of reverse shear tip and lower TAE tip, analytic results and numerical results are in adequate agreement with each other.
● The response of upper TAE tip cannot be obtained in the TAE tip model of Rosenbluth and Berk et al. / Breizman and Sharapov.
● The numerical results around TAE frequency are in agreement with analytic model.
● We are modifying the tip model to see why the discontinuous absorption at upper TAE tip is achieved.