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## Section: New Results

### Field aligned interpolation for gyrokinetics

Participants : Michel Mehrenberger, Maurizio Ottaviani, Yaman Güclü, Guillaume Latu, Eric Sonnendrücker.

A theoretical justification of the field align method is provided in the simplified context of constant advection on a 2D periodic domain: unconditional stability is proven, and error estimates are given which highlight the advantages of field-aligned interpolation. The same methodology is successfully applied to the solution of the gyrokinetic Vlasov equation, for which we present the ion temperature gradient (ITG) instability as a classical test-case: first we solve this in cylindrical geometry (screw-pinch), and next in toroidal geometry (circular Tokamak). A paper has been submitted [14].