Document Type : Research Paper
Authors
Abstract
Ideal magnetohydrodynamic (MHD) equilibrium is vulnerable to numerous unstabilizing mechanisms. Instabilities introduce distortions to the plasma magnetic surfaces and their boundaries, their driving force being the radial gradient of plasma toroidal current density. For certain modal numbers, internal kink modes may develop, and their study is feasible according to the energy principle, in which the change in total potential energy is evaluated due to the disturbance. In this paper, we present a new analysis of MHD equilibrium and stability, and apply it to Damavand Tokamak which has a large aspect ratio. For this purpose, we combine the perturbation and Green's function methods to solve the equilibrium configuration problem. At this stage, plasma profiles are found explicitly in terms of Bessel functions, and we present a simple expression for estimation of total toroidal plasma current. Then the rest of plasma profiles, including poloidal magnetic flux, safety factor, and toroidal current density, are obtained and plotted. In the next step, we turn to the stability calculations and characterize the stable and unstable ideal MHD modes of Damavand plasma.
Highlights
- 3. J. Wesson, “Tokamaks,” Clarendon Press, Oxford (2004).
- 4. T.J. Dolan, “Fusion Research,” rev. ed, Pergamon Press (2001).
- 5. W.M. Stacey, “Fusion Plasma Physics,” Wiley-VCH Press (2005).
- 6. G. Bateman, “MHD Instabilities,” MIT Press, Cambridge (1978).
- 7. R.O. Dendy, “Plasma Physics: An Intro-ductory Course,” Cambridge University Press (1993).
- 8. K. Miyamoto, “Plasma Physics for Nuclear Fusion,” MIT, Cambridge (1980).
- 9. K. Miyamoto, “Controlled Fusion and Plasma Physics,” Taylor & Francis, New York (2007).
- 10. W.D. D'haeseleer, W.N.G. Hitchon, J.D. Callen, J.L. Shohet, “Flux coordinates and magnetic field structure-A guide to a fundamental tool of the plasma theory,” Edited by R. Glowinski, M. Holt, P. Hut, H.B. Keller, J. Killeen, S.A. Orszag and V.V. Rusanov, Springer-Verlag, Berlin (1991).
- 11. ف. دینی، ”پایان‌نامه کارشناسی ارشد، دانشکده فیزیک، دانشگاه صنعتی امیرکبیر،“ تهران، (بهمن 1375).
- 12. J.P. Freidberg, “Ideal magnetohydro-dynamics,” Plenum Press, New York (1987).
- 13. J.P. Freidberg, “Plasma physics and fusion energy,” Cambridge University Press, Cambridge (2007).
- 14. L.S. Solov’ev, “The theory of hydromagnetic stability of toroidal plasma configurations,” Sov. Phys. JETP 26, 400-407 (1968).
- 15. F. Dini, S. Khorasani, R. Amrollahi, “On the green function of axisymmetric magnetostatics,” Iranian J. Sci. Technol, Transaction A 28, 197-204 (2004).
- 16. G. Arfken, “Mathematical methods for physicists,” Academic Press, 3rd ed (1985).
- 17. F. Dini, M. Molaei Emamzadeh, S. Khorasani, J.L. Bobin, R. Amrollahi, M. Sodagar, M. Khoshnegar, “Analytical study of dissipative solitary waves,” Phys. Scr. 77, 025504 (2008).
- 18. ف. دینی و س. خراسانی، ”محاسبه ضریب هدایت نئوکلاسیک با استفاده از کسر ذرات به دام افتاده برای پلاسمای توکامک کشیده دماوند،“ مجله علوم و فنون هسته‌ای 40، 33-25 (1386).
- 19. ف. دینی و س. خراسانی، ”مشاهده آرایش جداساز در شبیه‌سازی ترابرد توکامک کشیده دماوند،“ مجله علوم و فنون هسته‌ای، پذیرفته شده (1387).
- 20. P.J. Mc Carthy, “Analytical solutions to the Grad–Shafranov equation for tokamak equilibrium with dissimilar source functions,” Phys. Plasmas 6, 3554-3560 (1999).
- 21. C.V. Atanasiu, S. Gunter, K. Lackner, I.G. Miron, “Analytical solutions to the Grad–Shafranov equation,” Phys. Plasmas 11, 3510 (2004).
- 22. S. Wang and J. Yu, “An exact solution of the Grad–Shafranov–Helmhotz equation with central current density reversal,” Phys. Plasmas 12, 062501 (2005).
Keywords
- 3. J. Wesson, “Tokamaks,” Clarendon Press, Oxford (2004).
- 4. T.J. Dolan, “Fusion Research,” rev. ed, Pergamon Press (2001).
- 5. W.M. Stacey, “Fusion Plasma Physics,” Wiley-VCH Press (2005).
- 6. G. Bateman, “MHD Instabilities,” MIT Press, Cambridge (1978).
- 7. R.O. Dendy, “Plasma Physics: An Intro-ductory Course,” Cambridge University Press (1993).
- 8. K. Miyamoto, “Plasma Physics for Nuclear Fusion,” MIT, Cambridge (1980).
- 9. K. Miyamoto, “Controlled Fusion and Plasma Physics,” Taylor & Francis, New York (2007).
- 10. W.D. D'haeseleer, W.N.G. Hitchon, J.D. Callen, J.L. Shohet, “Flux coordinates and magnetic field structure-A guide to a fundamental tool of the plasma theory,” Edited by R. Glowinski, M. Holt, P. Hut, H.B. Keller, J. Killeen, S.A. Orszag and V.V. Rusanov, Springer-Verlag, Berlin (1991).
- 11. ف. دینی، ”پایان‌نامه کارشناسی ارشد، دانشکده فیزیک، دانشگاه صنعتی امیرکبیر،“ تهران، (بهمن 1375).
- 12. J.P. Freidberg, “Ideal magnetohydro-dynamics,” Plenum Press, New York (1987).
- 13. J.P. Freidberg, “Plasma physics and fusion energy,” Cambridge University Press, Cambridge (2007).
- 14. L.S. Solov’ev, “The theory of hydromagnetic stability of toroidal plasma configurations,” Sov. Phys. JETP 26, 400-407 (1968).
- 15. F. Dini, S. Khorasani, R. Amrollahi, “On the green function of axisymmetric magnetostatics,” Iranian J. Sci. Technol, Transaction A 28, 197-204 (2004).
- 16. G. Arfken, “Mathematical methods for physicists,” Academic Press, 3rd ed (1985).
- 17. F. Dini, M. Molaei Emamzadeh, S. Khorasani, J.L. Bobin, R. Amrollahi, M. Sodagar, M. Khoshnegar, “Analytical study of dissipative solitary waves,” Phys. Scr. 77, 025504 (2008).
- 18. ف. دینی و س. خراسانی، ”محاسبه ضریب هدایت نئوکلاسیک با استفاده از کسر ذرات به دام افتاده برای پلاسمای توکامک کشیده دماوند،“ مجله علوم و فنون هسته‌ای 40، 33-25 (1386).
- 19. ف. دینی و س. خراسانی، ”مشاهده آرایش جداساز در شبیه‌سازی ترابرد توکامک کشیده دماوند،“ مجله علوم و فنون هسته‌ای، پذیرفته شده (1387).
- 20. P.J. Mc Carthy, “Analytical solutions to the Grad–Shafranov equation for tokamak equilibrium with dissimilar source functions,” Phys. Plasmas 6, 3554-3560 (1999).
- 21. C.V. Atanasiu, S. Gunter, K. Lackner, I.G. Miron, “Analytical solutions to the Grad–Shafranov equation,” Phys. Plasmas 11, 3510 (2004).
- 22. S. Wang and J. Yu, “An exact solution of the Grad–Shafranov–Helmhotz equation with central current density reversal,” Phys. Plasmas 12, 062501 (2005).
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