Collision

Table of Contents

• structure of the collision operator
  • of moments of the distribution function
  • kicks in velocity space
  • handling of conservation and exchange of momentum and
• to activate collisions

Implementation of collisions.

Author

P.Donnel

Date

07.2020

structure of the collision operator

The collision operators implemented in ORB5 are all using the same structure. This structure can be decomposed in 4 big stages which are independent.

of moments of the distribution function

The collision operators rely on a truncated moment expansion of the distribution function. in practice, these moments are computed inside spatial bins. There is a priori a freedom to choose the way the spatial binning is performed. In ORB5 it has been chosen to have spatials bins depending on the radial and poloidal coordinates but not on the toroidal coordiante. This choice has been done having in mind axisymmetry. Note that other options could be implemented for tests.

kicks in velocity space

Once the moments computed, it is possible to compute the drag and the diffusion acting on each marker. These parameters are functions of moments of the distribution function, of the initial position of the marker considered in the velocity space and of course of the type of collision considered (linear/nonlinear, intra/inter-species).

handling of conservation and exchange of momentum and

energy between species

Due to the truncation of the moment expansion and the finite numerical resolution, the Langevin kicks in velocity space are not ensuring conservations of parallel momentum and energy. A procedure has therefore be developed in order to ensure conservation of density, total parallel momentum and energy inside each spatial bin.

The idea of this procedure is to modify the weights (p and w) after the Langevin kicks using an Ansatz for the form of the correction term. This Ansatz directly derives from the collision operator. Therefore unphysical modification of the distribution function is avoided.

to activate collisions

There are 5 parameters to control the collisions.

• nsel_collisions: which corresponds to the choice of the collision operator (none, linear/nonlinear, intra-species only or with inter-species collisions)
• nu_ref: which is collision frequency of reference: |

  \[ \nu_{ref} = \frac{N_0 e^4 \ln \Lambda}{4 \pi \epsilon_0^2 \sqrt{m_0} \left(T_0 \right)^{3/2}} \]

All collisions frequencies are consistently derived from the value of the collision frequency of reference. Note that in the electrostatic limit, the reference density is not fixed by the model. It means that fixing the reference collision frequency is somehow equivalent to choose the density of reference. For electromagnetic simulations, the reference collision frequency should be consistent with the value of Beta. This is not the case in the current version implemented.

-ns_coll: number of radial bins for spatial binning

-nchi_coll: number of poloidal bins for spatial binning

-N_slide_save: the moments computed in each spatial bins are averaged over N_slide_save time steps to avoid spurious oscillations. This is motivated by the slow evolution of profiles (typically the confinement time) compared to the typical time step.