This section configures binary Coulomb collisions settings.

Please note that the OSIRIS collision package is still in the ‘development’ stage (where it possibly will be forever.) First, as described below, most options besides the default ones are currently undertested if not nonfunctional. Anyone wishing to use those functions is advised to work with the development team to finish implementing and benchmarking them.

Furthermore, in a broader sense, the correct and efficient addition of collisions to the PIC algorithm remains an open problem. To a certain extent doing so inherently ‘breaks’ the PIC algorithm, in that it inserts a somewhat arbitrary force into the particle-field push loop. Anyone using this package is advised to familiarize themselves with the basic functioning of the code (an effort has been made to include elucidating inline documentation); a partial bibliography has also been included in the header of the source file. That said, if the user sets the default options, and sufficiently resolves the collision physics (both in terms of collision steps per collision period and colliding particles per collision cell), the package should ‘work’ correctly.

The input deck can include the following data:

  • n_collide, integer, default = 0
  • nx_collision_cells(x_dim), integer, default = 1
  • coulomb_logarithm_automatic, logical, default = .true.
  • coulomb_logarithm_value, real, default = 0.0
  • collision_model, string, default = ‘Sentoku’
  • cross_section_correction, string, default = ‘None’
  • timestep_cross_corr, logical, default = .false.
  • frame_correction, string, default = ‘None’
  • root_finder, string, default = ‘None’

Note it is also necessary to set either the n0 or the omega_p0 parameters in the simulation section to specify the reference density; and the q_real, if_collide, and if_like_collide parameters in species section for any species which are colliding.

n_collide specifies the number of iterations between collisions. If set to 0 collisions will be turned off. This parameter must be a multiple of n_sort (see the species section).

nx_collision_cells specifies the number of simulation cells per collisional cell in each direction. The PIC grid must be a multiple of the collisional grid on each node (i.e. the total grid divided by the number of nodes in a given direction.) Currently the load balancer does not respect the collision cells, so nx_collision_cells should be set to 1 in any balanced direction.

coulomb_logarithm_automatic specifies whether to self-consistently calculate the Coulomb logarithm from the local plasma density and temperature (default) or use a fixed Coulomb logarithm value.

coulomb_logarithm_value specifies the Coulomb logarithm value to be used if coulomb_logarithm_automatic is set to false.

The following options preserve all of the functionality that was present as pre-compiler options in the old code (pre 2015). However the options other than the defaults have not been tested thoroughly and caution is urged in using any of them. Most users will want to ignore these fields. All strings are case-insensitive.

collision_model specifies which collision model to use. Accepted options are ‘Sentoku’, ‘Nanbu’, ‘Nanbu_rel’, and ‘Isotropic’. Note that ‘Nanbu’ and ‘Nanbu_rel’ are only rudimentarily implemented at the moment (see root_finder below) and so if it is desired to use them that section of the code will need to be developed. Also note that ‘Isotropic’ scatters into 4π at every collision step and so is only meant for testing.

cross_section_correction specifies the method to transform the effective cross section in a way which maintains Lorentz invariance (see Peano et al. 2009). Accepted options are ‘None’, ‘Rejection’, and ‘Scattering.’

timestep_cross_corr is to be used when ‘cross_section_correction’ is set to anything other than ‘None;’ it multiplies the effective cross section by 2, to correct for the reduction of cross section in the lab frame caused by the cross section correction algorithm.

frame_correction accepts the strings ‘none’, ‘time’, and ‘time_density’. This option increases the cross section by the relativistic gamma factor of the more massive particle as seen in the lab frame, either by one factor (‘time’), or by two factors (‘time_density’). This is preserved from the earlier version of the code but its use is not well documented. Unless you know you need this, it is recommended to leave this as ‘none’.

root_finder specifies which algorithm to use to invert the Nanbu equation for the cross section. It accepts ‘Newton’ for a Newton solver; ‘Linear’ for a linear-interpolation look-up table; ‘Cubic’ for a cubic interpolation look-up table; and ‘None’. However, if using either Nanbu collision model, all options other than ‘Newton’ will result in a run-time error; ‘Linear’ and ‘Cubic’ are not currently implemented (the look-up tables need to be written) and ‘None’ is meant as an inconsistent default option to make sure the user actively chooses the algorithm. In addition, the Newton solver is very inefficient and is not advised for production runs. Therefore if the user wishes to use a Nanbu collision model, it is highly recommended that a more efficient algorithm be implemented (either writing the look-up tables for the interpolating solvers, or implementing the improved method of Perez et al. 2012)

Here is an example of a collisions section.

collisions
{
 n_collide = 1,  ! collide every time step
 nx_collision_cells(1:2) = 8,8, ! each collision cells has 8x8 PIC cells
   
 coulomb_logarithm_automatic = .false., ! fixed Coulomb logarithm
 coulomb_logarithm_value = 4.0,
}