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MHD Flow Layer Formation at Boundaries of Magnetic Islands in Toroidal Plasmas

MHD Flow Layer Formation at Boundaries of Magnetic Islands in Toroidal Plasmas. J. Q. Dong 1,2 , Y. X. Long 1 , Z. Z. Mou 1 1, Southwestern Institute of Physics 2, Institute for Fusion Theory and Simulation(ZJU) November 15, 2006, Zhejiang University Hangzhou. Outline. 1, Introduction

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MHD Flow Layer Formation at Boundaries of Magnetic Islands in Toroidal Plasmas

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  1. MHD Flow Layer Formation at Boundaries of Magnetic Islands in Toroidal Plasmas J. Q. Dong1,2, Y. X. Long1, Z. Z. Mou1 1, Southwestern Institute of Physics 2, Institute for Fusion Theory and Simulation(ZJU) November 15, 2006, Zhejiang University Hangzhou

  2. Outline 1, Introduction 2, MHD flow layers due to tearing mode in tokamak plasmas 3, MHD flow layers in helical devices 4, MHD flow layer formation at boundaries of magnetic islands in tokamak plasmas 5, Summary

  3. 1, Introduction • Advanced operation modes withinternal transport barriers (ITBs) aredesirable formagneticfusion ignition in toroidal devices • ITBsare often formed in vicinities of low safety factor q rational surfaces • ITBformation is correlated with E × Bsheared flows • Two kinds of flows have essentially been considered: mean flowandzonal flow of m=n=0

  4. ITBs coincidewithMHDactivities Correlation between edge MHD and ITB emergence (monotonic q-profiles, ITBs linked with q=2 or q=3 radius) E. Joffrin et al., NF 2001 H-mode workshop, San Diego, 26-28 sept 03 A. Bécoulet

  5. A third kind of flow--MHD flow with strong shear may exist in toroidal plasmas • MHD flow: 1) driven by magnetic energy released in MHD activities, 2) with helical structures, 3) large spatial scales and 4) slow temporal scales in comparison with turbulence • MHD flow layers formed at boundaries of magnetic islands induced by nonlinear development of tearing modes (TM) are studied • Possible correlation of the MHD flow with ITB formation dynamics is discussed

  6. 2, MHD flow layers due to tearing mode in tokamak plasmas Linear analysis, Ishii et al., PoP 7 (2000).

  7. Linear analysis, Held et al., PoP 6, 1999.

  8. Non-linear simulation, Ishii, PoP 7, (2000).

  9. Non-linear analysis, Held et al., PoP 6, 1999.

  10. 3, MHD flow layers in helical devices • Flow layers due to interchange mode (Ichiguchi, 31st EPS, 2004)

  11. Sheared flow at magnetic island boundaries on LHD • Island studies on LHD explore it in detail • (Ida & Inagaki, IAEA Lyon & PRL Jan 2002) • Strong poloidal flow shear at island boundary => strong ExB shear • Points to new understanding of physics of how ITB trigger might be associated with rational values of q Vq with different island sizes

  12. 4, MHD flow layers at boundaries of magnetic islands in tokamak plasmas MHD flow layer formation due to tearing modes mediated by electron viscosity as well as resistivity is studied in detail and the results are presented

  13. 1)Equilibrium and MHD equations • We consider the standard sheared slab configuration, , (1) • The plasma sheet is of scale length a in x-direction, has a current in z-direction, • The equilibrium flow velocity ,

  14. Theresistivityandviscosityare both assumed to be constant first • Non-linear reduced MHD equations 1) Ohm’s law+Faraday’s law 2) Plasma vorticity equation • Spectrum method is adopted

  15. 2) Linear analysis of of TMs ξ ξ Plasma displacement profiles for m>1,m=1 and double tearing modes ξ The case of non-monotonic q profile is considered hereafter

  16. Electron viscosity TM (Dong, PoP 2003)

  17. 3)Non-linear simulations • Equilibrium configuration ,

  18. (1) electron viscosity TM • Profile evolutions of magnetic field and plasma displacement

  19. Poloidal velocity and its shear versus distance between the two resonant surfaces

  20. Profiles of poloidal velocity shear and perturbed radial magnetic field; structure of magnetic islands

  21. (2) Resistive TM ( =constant) The poloidal velocity The amplitude of the profiles velocity shear versus magnetic Reynolds number S

  22. Profiles of velocity shear and radial component of perturbed magnetic field

  23. Half e-fold-width of the velocity layer, normalized toradial scale length a

  24. (2) Resistivity TM ( ) Magnetic energy converts to kinetic energy

  25. Evolution of magnetic island width and amplitude of velocity shear

  26. Contour of

  27. Profile of velocity

  28. Profile of velocity shear

  29. 5, Discussion and summary • Assuming we estimated • This is comparable with the turbulence suppression shearing rate • MHDflow layers are demonstrated to form at the boundaries of the magnetic islands induced by double tearing modes

  30. The flow velocity and its shear increase with the distance between the two resonant flux surfaces • The flow velocity and its shear increase with the magnetic Reynolds number • A half e-fold-width of the velocity layer decreases with the magnetic Reynolds number • This may provide triggering for ITB emergence • Further theoretical and experimental studies are expected

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