Poloidal tilting symmetry of high order tokamak flux surface shaping in gyrokinetics

Justin Ball, Felix I. Parra, Michael Barnes

Research output: Contribution to journalArticlepeer-review


A poloidal tilting symmetry of the local nonlinear -f gyrokinetic model is demonstrated analytically and verified numerically. This symmetry shows that poloidally rotating all the flux surface shaping effects with large poloidal mode number by a single tilt angle has an exponentially small effect on the transport properties of a tokamak. This is shown using a generalization of the Miller local equilibrium model to specify an arbitrary flux surface geometry. With this geometry specification we find that, when performing an expansion in large flux surface shaping mode number, the governing equations of gyrokinetics are symmetric in the poloidal tilt of the high order shaping effects. This allows us to take the fluxes from a single configuration and calculate the fluxes in any configuration that can be produced by tilting the large mode number shaping effects. This creates a distinction between tokamaks with mirror symmetric flux surfaces and tokamaks without mirror symmetry, which is expected to have important consequences for generating toroidal rotation using updown asymmetry.

Original languageAmerican English
Article number045023
JournalPlasma Physics and Controlled Fusion
Issue number4
StatePublished - Feb 22 2016
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear Energy and Engineering
  • Condensed Matter Physics


  • gyrokinetics
  • nonlinear simulations
  • plasma turbulence
  • tokamaks
  • transport properties

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