# Gyrokinetic simulations

The gyrokinetic formalism [1] [2] [3] is based on first principles and provides a valuable tool for investigating low frequency turbulence in fusion plasmas.

Kinetic theory describes the evolution of the distribution function $f(\vec r, \vec v)$ on the basis of the Vlasov equation:

$\frac{\rm d f}{\rm d t} = \frac{\partial f}{\partial t} + \vec v \cdot \nabla_r f + \frac{q}{M}(\vec E + \vec v \times \vec B)\cdot \nabla_v f = 0$

The gyro-kinetic approach introduces a simplification by decomposing the full particle orbits into a rapid gyration about the magnetic field lines and a slow drift of the gyro centre $\vec R$:

$\vec r = \vec R + \vec \rho(\alpha)$

where $\alpha$ is the gyro-angle. By averaging over this gyro-angle one arrives at the gyro-kinetic equation, which describes the evolution of the gyro centre in a phase space with one less dimension than the full Vlasov equation due to the averaging over the gyro-phase angle:

$f(\vec R, v_{||},v_\perp)$

The gyro-kinetic equation is only valid for studying phenomena on timescales longer than the inverse of the gyro-frequency, and spatial scales larger than the gyro-radius. This is appropriate for, e.g., ITG (ion temperature gradient) turbulence.

## Research activities

The Theory Group at the Laboratorio Nacional de Fusión collaborates with the Barcelona Supercomputing Center and the Max Planck IPP at Greifswald for the development and exploitation of the EUTERPE global gyrokinetic code.

The code EUTERPE has recently been benchmarked against the TORB code [4][5] in both linear and non-linear simulations.[6]