This block contains information about particle collisions. See EPOCH input deck for more information on the input deck.

EPOCH has a particle collision routine with scattering algorithms based on the model presented by Sentoku and Kemp¹ or the model presented by Pérez et al ², which in turn was based on the work of Nanbu and Yonemura³. This adds a new output block named “collisions”, and since version 4.19, there are two possible collision modes: binary and background. Binary collisions pair particles together, and apply scatter to both particles. In the background mode, particle species are split into fast-background pairs, where only particles in the fast species are scattered. Originally, EPOCH could only run in the full binary-collisions mode, which accepts the following keys:

• use_nanbu - This logical flag determines whether the scattering angle of Pérez/Nanbu will be used. The default is “T”. If “F”, the Sentoku-Kemp algorithm will be used.

• coulomb_log - This may either be set to a real value, specifying the Coulomb logarithm to use when scattering the particles or to the special value “auto”. If “auto” is used then the routine will calculate a value based on the local temperature and density of the particle species being scattered, along with the two particle charges. If omitted, the default value is “auto”.

• collide - This sets up a symmetric square matrix of size $nspecies \times nspecies$ containing the collision frequency factors to use between particle species. The element (s1,s2) gives the frequency factor used when colliding species s1 with species s2. If the factor is less than zero, no collisions are performed. If it is equal to one, collisions are performed normally. For any value between zero and one, the collisions are performed using a frequency multiplied by the given factor. If “collide” has a value of “all” then all elements of the matrix are set to one. If it has a value of “none” then all elements are set to minus one. If the syntax “species1 species2 value” is used, then the (species1,species2) element of the matrix is set to the factor “value”. This may either be a real number, or the special value “on” or “off”. value may also be set to “background” to specify a fast-background pair (see below). The “collide” parameter may be used multiple times. The default value is “all” (ie. all elements of the matrix are set to one, modelling physical collisions).

• collisional_ionisation - If this logical flag is set to “T” then the collisional ionisation model is enabled. This process is independent of field_ionisation (see here). However, in order to set up collisional_ionisation you must also specify ionisation energies and electrons in a species block (see here). The default value is “F”.

• coll_n_step - Number of time-steps, $n$, between collision calculations. This key speeds up the collisions routine by reducing the number of collision calculations performed. On steps which apply collisions, the calculation is performed using a time-step of $n$*dt, where dt is the simulation time-step. The default is 1 (calculate collisions every step).

• ci_n_step - Only performs the collisional ionisation calculation once every $n$ steps, where $n$ is set by this parameter. This is done to speed up the code, and the default is 1 (every step). When this is greater than 1, the assumed time-step for the collisional ionisation calculation is $n$*dt. Note that an ion may only be ionised once per calculation, so if $n$ is too high, the number of ions will be underestimated.

An example deck using full binary collisions could be set up as follows.

begin:collisions
   use_collisions = T
   use_nanbu = T
   coulomb_log = auto
   collide = all
   collide = spec1 spec2 off
   collide = spec2 spec3 0.5
   coll_n_step = 10
end:collisions

With this block, collisions are turned on, the Nanbu-Pérez scattering algorithm is used and the Coulomb logarithm is automatically calculated. All values of the frequency array are set to one except (spec1,spec2) is set to minus one (and also (spec2,spec1)) and (spec2,spec3) is set to 0.5. Note: only a frequency value of 1 provides a physical scatter. Collisions are only calculated once every 10 steps, but using an inferred time-step of 10*dt.

Background collisions

The background collisions mode offers a speed-up compared to the binary method when applicable. This mode assumes the particles in one species are considerably faster than the particles in a background species, so the relative velocity between fast and background particles is roughly the fast particle speed. This eliminates the need to pair particles together in a local cell, as in the binary-collision case. However, background particles will not experience scatter in this mode. This mode was originally intended for electron-ion collisions, where both species had temperatures on the order of keV. An example of fast-background collisions is given below:

begin:collisions
   use_collisions = T
   coulomb_log = 5
   collide = none
   collide = Electron Ion1 background
   collide = Electron Ion2 background
   collide = Electron Electron on
   
   use_cold_correction = F
   rel_cutoff = 0.01
   back_update_dt = 5.0e-15 
end:collisions

The above example deactivates all collisions, then sets up two fast-background pairs, with the Electron providing the fast species in both pairs, and Ion1 and Ion2 taking the background roles. Full binary collisions are used for Electron-Electron collisions, as these do not satisfy the fast-background assumptions. Additional speed-up parameters are used which only apply to background collisions. These are:

• use_cold_correction - The Nanbu-Pérez collisions model has a low temperature correction factor, given in equation (20) of Pérez². In some cases, this only affects particles with energy on the order of eV, and may be ignored in hot plasma. If “F”, this calculation is skipped. The default is “T”, to perform the full calculation.

• rel_cutoff - Collisions are calculated in the centre-of-mass frame between colliding fast and background particles. In practice, only the fast particle momentum is transformed. This parameter takes a number between 0 and 1, and if the fractional momentum change between frames is lower than this number, the frame transform is skipped. The default is 0, so frame transforms are always considered.

• back_update_dt - If the background species number density varies slowly, we do not need to re-calculate each step. This parameter specifies the time-step of recalculation for the background number density, and also the Coulomb logarithm if coulomb_log is set to auto. The default is 0, so background variables are re-calculated each step.

References