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When a magnetically confined plasma is heated strongly and a threshold heating power level is exceeded, it may spontaneously transition from a low confinement (or L-mode) state to a high confinement (or H-mode) state. [1] In the H-mode, the energy confinement time is significantly enhanced, i.e., typically by a factor of 2 or more. [2] [3] [4] H-mode profiles have a characteristic edge pedestal.

Physical mechanism

This transport bifurcation is due to the suppression of turbulence in the edge plasma. There is substantial evidence that the suppression of turbulence is the consequence of the formation of a sheared flow layer and an associated edge radial electric field. The local suppression of turbulence leads to a reduction of transport and a steepening of the edge profiles. [5]

A variety of mechanisms can give rise to sheared flow, or favour its growth:

  • The main process for sheared flow generation is generation by the turbulence itself via the Reynolds stress mechanism. Simply put, transport generated by the fluctuations produces a radial current jr that spins up the plasma via the j × B Lorentz force. [6] [7]
  • This radial current can also actively be produced by electrode biasing. [8]
  • Sheared flow may be favoured by reduced viscous damping, which might explain the dependence on rational surfaces observed in the stellarator W7-AS. [9]
  • Sheared flow can also be generated by external momentum input.

The details of the feedback mechanism between turbulence and sheared flow are the subject of ongoing studies. [10] [11]

In summary, the H-mode is the consequence of a self-organizing process in the plasma. The mechanism is probably closely related to the mechanism for forming an Internal Transport Barrier.

See also


  1. F. Wagner et al, Development of an Edge Transport Barrier at the H-Mode Transition of ASDEX, Phys. Rev. Lett. 53 (1984) 1453 - 1456
  2. M. Keilhacker, H-mode confinement in tokamaks, Plasma Phys. Control. Fusion 29 (1987) 1401-1413
  3. F. Wagner et al., H-mode of W7-AS stellarator, Plasma Phys. Control. Fusion 36 (1994) A61
  4. The International Global H-mode Confinement Database
  5. F. Wagner, A quarter-century of H-mode studies, Plasma Phys. Control. Fusion 49 (2007) B1-B33
  6. P.H. Diamond and Y.-B. Kim, Theory of mean poloidal flow generation by turbulence, Phys. Fluids B 3 (1991) 1626
  7. S.B. Korsholm et al, Reynolds stress and shear flow generation, Plasma Phys. Control. Fusion 43 (2001) 1377-1395
  8. R.J. Taylor et al, H-mode behavior induced by cross-field currents in a tokamak, Phys. Rev. Lett. 63 (1989) 2365-2368
  9. H. Wobig and J. Kisslinger, Viscous damping of rotation in Wendelstein 7-AS, Plasma Phys. Control. Fusion 42 (2000) 823-841
  10. P.H. Diamond et al, Self-Regulating Shear Flow Turbulence: A Paradigm for the L to H Transition, Phys. Rev. Lett. 72 (1994) 2565 - 2568
  11. M.A. Malkov and P.H. Diamond, Weak hysteresis in a simplified model of the L-H transition, Phys. Plasmas 16 (2009) 012504