Journal of Nuclear Science, Engineering and Technology (JONSAT)
In cooperation with the Iranian Nuclear Society

Modeling and robust control system design for plasma current in damavand tokamak

Document Type : Research Paper

Authors

H. Zandi 1
M. Fatahi 1
B. Moaveni 1
H. Rasouli 2

1 Department of Systems and Control, Faculty of Electrical Engineering, K.N. Toosi University of Technology (KNTU), P.O.Box: 1355-16315, Tehran, Iran

2 Plasma and Nuclear Fusion Research School, Nuclear Science and Technology Research Institute, AEOI, P.O.BOX:14399-51113, Tehran, Iran

https://doi.org/10.24200/nst.2021.1200
Abstract
In the present work, a dynamic model of plasma current and its relation with the currents of active coils is derived using the Hamilton-Lagrange and energy functions. Model parameters of the plasma current are calculated using the analytical approach and the parameter estimation methods. The parameter estimation is performed based on the gray-box model. The experimental data of three shots in the presence of plasma in Damavand Tokamak have been used to estimate the parameters of the model. The results of plasma current modeling show a dynamic model with variable parameters as a function of plasma conditions and plasma position. In the present work, based on the obtained dynamical model, a robust PI controller has been designed to control the plasma current using the currents of the central solenoid and equilibrium coil. The simulation results using real experimental data indicate the acceptable performance of the designed control system.

Highlights

1. R. Kienberger, et al, Atomic transient recorder, Nature. 427, 817 (2004).

 

2. A. McPherson, et al, Studies of multiphoton production of vacuumultraviolet radiation in the rare gases, Journal of the Optical Society of America B, 4, 595 (1987).

 

3.   C. Spielmann, et al, Generation of coherent X-rays in the water window using 5-femtosecond laser pulses, Science (80-. ). 278, 661-664 (1997).

 

4.   M.-C. Chen, Bright, coherent, ultrafast soft x-ray harmonics spanning the water window from a tabletop light source, Phys. Rev. Lett. 105, 173901 (2010).

 

5.   K. Zhao, et al, Tailoring a 67 attosecond pulse through advantageous phase-mismatch, Opt. Lett. 37, 3891-3893 (2012).

 

6.   M. Lewenstein, et al, Theory of high-harmonic generation by low-frequency laser fields, Phys. Rev. A. 49, 2117 (1994).

 

7.   P.B. Corkum,Plasma perspective on strong field multiphoton ionization, Phys. Rev. Lett. 71, 1994 (1993).

 

8.   Y. Chou, et al, Optimal control of high-order harmonics for the generation of an isolated ultrashort attosecond pulse with two-color midinfrared laser fields, Phys. Rev. A. 91, 63408 (2015).

 

9.   D. Peng, Enhancing high-order harmonic generation by sculpting waveforms with chirp, Phys. Rev. A. 97, 53414 (2018).

 

10. D. Peng, et al, Enhancing high-order harmonic generation by sculpting waveforms with chirp, Phys. Rev. A, 97, 53414 (2018).

 

11. Y.S. You, et al, High-harmonic generation in amorphous solids, Nature Communications, 8, 724 (2017).

 

12. Pengfei Wei1, Candong Liu1, Molecular high harmonic generation in a twocolor field, 18, (11)/ Optics Eepress (2010).

 

13. I.J. Kim, et al, Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field, Phys. Rev. Lett. 94, 243901 (2005).

 

14. P. Wei, et al, Selective enhancement of a single harmonic emission in a driving laser field with subcycle waveform control, Phys. Rev. Lett. 110,  233903 (2013).

 

15. Cornelia Hofmann, Alexandra S. Landsman, Ursula Keller, Disentangling Long Trajectory Contributions in Two-Colour High Harmonic Generation, Appl. Sci. 8, 341 (2018).

 

16. M. Mofared, E. Irani, R. Sadighi-Bonabi, Enhancing high harmonic generation by the global optimization of a two-color chirped laser field, Phys. Chem. Chem. Phys. 21, 9302–9309 (2019).

 

Keywords

Damavand tokamak
Plasma current dynamic
Hamilton-lagrange method
Gray-box model
Robust controller
1. R. Kienberger, et al, Atomic transient recorder, Nature. 427, 817 (2004).
 
2. A. McPherson, et al, Studies of multiphoton production of vacuumultraviolet radiation in the rare gases, Journal of the Optical Society of America B, 4, 595 (1987).
 
3.   C. Spielmann, et al, Generation of coherent X-rays in the water window using 5-femtosecond laser pulses, Science (80-. ). 278, 661-664 (1997).
 
4.   M.-C. Chen, Bright, coherent, ultrafast soft x-ray harmonics spanning the water window from a tabletop light source, Phys. Rev. Lett. 105, 173901 (2010).
 
5.   K. Zhao, et al, Tailoring a 67 attosecond pulse through advantageous phase-mismatch, Opt. Lett. 37, 3891-3893 (2012).
 
6.   M. Lewenstein, et al, Theory of high-harmonic generation by low-frequency laser fields, Phys. Rev. A. 49, 2117 (1994).
 
7.   P.B. Corkum,Plasma perspective on strong field multiphoton ionization, Phys. Rev. Lett. 71, 1994 (1993).
 
8.   Y. Chou, et al, Optimal control of high-order harmonics for the generation of an isolated ultrashort attosecond pulse with two-color midinfrared laser fields, Phys. Rev. A. 91, 63408 (2015).
 
9.   D. Peng, Enhancing high-order harmonic generation by sculpting waveforms with chirp, Phys. Rev. A. 97, 53414 (2018).
 
10. D. Peng, et al, Enhancing high-order harmonic generation by sculpting waveforms with chirp, Phys. Rev. A, 97, 53414 (2018).
 
11. Y.S. You, et al, High-harmonic generation in amorphous solids, Nature Communications, 8, 724 (2017).
 
12. Pengfei Wei1, Candong Liu1, Molecular high harmonic generation in a twocolor field, 18, (11)/ Optics Eepress (2010).
 
13. I.J. Kim, et al, Highly efficient high-harmonic generation in an orthogonally polarized two-color laser field, Phys. Rev. Lett. 94, 243901 (2005).
 
14. P. Wei, et al, Selective enhancement of a single harmonic emission in a driving laser field with subcycle waveform control, Phys. Rev. Lett. 110,  233903 (2013).
 
15. Cornelia Hofmann, Alexandra S. Landsman, Ursula Keller, Disentangling Long Trajectory Contributions in Two-Colour High Harmonic Generation, Appl. Sci. 8, 341 (2018).
 
16. M. Mofared, E. Irani, R. Sadighi-Bonabi, Enhancing high harmonic generation by the global optimization of a two-color chirped laser field, Phys. Chem. Chem. Phys. 21, 9302–9309 (2019).
 

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