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## Section: New Results

### Collisions in gyrokinetic equation

Participants : Afeintou Sangam, Vladimir T. Tikhonchuk.

Charged particles in plasma in strong magnetic fields undergo a complicated motion, which is a combination of a fast cyclotron gyration around the magnetic field lines and a relatively slow dynamics along and across the magnetic field lines. Gyrokinetic equations, devised to describe plasma under such conditions, eliminate the fast cyclotron gyration from the equation of motion, thus reducing the space-velocity phase space dimension from six to five.

Originally, the gyrokinetic formulation was devised for a collisionless plasmas. The quest for retaining collisions in gyrokinetic equations is ongoing. Collisions are important if one wants to describe the transport properties of a magnetized plasma on a macroscopic level. A description of the transport of energy and momentum was proposed in Refs.  [18], [20], [19], [22], [21]. However, mathematical description of collisions in these works is too complicated for numerical implementation. We develop a simplified description of collision operators in the gyrokinetic formulation that preserve the pertinent conservation features and suitable for numerical modeling. A comparison of these operators with several test cases is under investigation.