Nonlinear ballooning modes in tokamaks: Stability and saturation

C. J. Ham, S. C. Cowley, G. Brochard, H. R. Wilson

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

The nonlinear dynamics of magneto-hydrodynamic ballooning mode perturbations is conjectured to be characterised by the motion of isolated elliptical flux tubes. The theory of stability, dynamics and saturation of such tubes in tokamaks is developed using a generalised Archimedes' principle. The equation of motion for a tube moving against a drag force in a general axisymmetric equilibrium is derived and then applied to a simplified 's-' equilibrium. The perturbed nonlinear tube equilibrium (saturated) states are investigated in an 's-α' equilibrium with specific pressure and magnetic shear profiles. The energy of these nonlinear (ballooning) saturated states is calculated. In some cases, particularly at low magnetic shear, these finitely displaced states can have a lower energy than the equilibrium state even if the profile is linearly stable to ballooning modes (infinitesimal tube displacements) at all radii. Thus nonlinear ballooning modes can be metastable. The amplitude of the saturated tube displacement in such cases can be as large as the pressure gradient scale length. We conjecture that triggering a transition into these filamentary states can lead to hard instability limits. A short survey of different pressure profiles is presented to illustrate the variety of behaviour of perturbed elliptical flux tubes.

Original languageEnglish (US)
Article number075017
JournalPlasma Physics and Controlled Fusion
Volume60
Issue number7
DOIs
StatePublished - Jun 8 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear Energy and Engineering
  • Condensed Matter Physics

Keywords

  • ballooning modes
  • filaments
  • nonlinear

Fingerprint Dive into the research topics of 'Nonlinear ballooning modes in tokamaks: Stability and saturation'. Together they form a unique fingerprint.

  • Cite this