EUTERPE

The EUTERPE gyrokinetic code was created at the EPFL in Lausanne as a global linear particle in cell code for studying electrostatic plasma instabilities . It allows three-dimensional turbulence simulations using a plasma equilibrium calculated with the VMEC code as a starting point. EUTERPE was further developed at the Max Planck IPP and several linear calculations of ion temperature gradient (ITG) driven turbulence in tokamak and stellarator geometry have been carried out using it . Afterwards, the code has been heavily optimized and improved and non-linear dynamics have been included.

The EUTERPE code solves the gyroaveraged Vlasov equation for the distribution function of ions

${\frac {\partial f}{\partial t}}+{\frac {\rm {{d}v_{||}}}{\rm {{d}t}}}{\frac {\partial f}{\partial v_{||}}}+{\frac {\rm {{d}{\vec {R}}}}{\rm {{d}t}}}{\frac {\partial f}{\partial {\vec {R}}}}=0$

The code is based on the particle-in-cell (PIC) scheme, where the distribution function is discretized using markers. The δf approximation is used, so that the distribution function is decomposed in an equilibrium part (Maxwellian) and a time-dependent perturbation.

$\delta f=\sum _{p=1}^{N}w_{p}\delta ^{3}({\vec {R}}-{\vec {R}}_{p})\delta (v_{||}-v_{||p})\delta (\mu -\mu _{p})/(2\pi B),$