Collision setup

LTP-PIC includes a Monte-Carlo Collision (MCC) module which utilizes the null collision method to collide charged species against a fixed neutral background. The following collision types are included:

• Electron neutral elastic: Energy conserving collision between a designated electron species and a cold neutral with specified mass.
• Electron neutral excitation: Collision between a designated electron species and a cold neutral with specified mass resulting in neutral excitation. This collision only removed energy from the impacting electron and does not change the properties of the neutral gas.
• Electron neutral ionization: Collision between a designated electron species and thermal neutral resulting in production of a new electron and new ion. The new electron is of the same species as the impacting electron, the user can specify the ion species.
• Ion neutral elastic: Energy conserving collision between a designated ion species and thermal neutral species. The neutral mass is fixed to the value of the impacting ion and sampled based on the user provided temperature.
• Ion neutral charge exchange: Charge exchange collision between a designated ion species and thermal neutral species. The neutral mass is fixed to the value of the impacting ion and sampled based on the user provided temperature.

Note: Collision parameters must be defined after the elastic, excitation, ionization or cxchange parameter is set and before the next collision is listed. For example, in the below input chunk the properties of an elastic collision must appear in the lines after elastic 1 is written and before ionization 1 is written.

Cross-Section Tables

All collision types require input of a table which specifies the cross-section data as a function of kinetic energy (in units of eV). The tables must be specified in a two column format:

• Column 1: Monotonically increasing energy values in electron-volts.
• Column 2: Cross section values in m^2.

There are some additional properties of the collision tables which are important to be aware of:

• Information can be appended before or after the table but MUST be commented out using the # symbol.
• Cross section values are linearly interpolated between the energy values below and above the specified particle energy.
• If the particle has energy below the lowest energy value in the table it is allocated the cross-section of this minimum energy value.
• If the particle has energy above the highest energy value in the table it is allocated the cross-section of this maximum energy value.

Electron-neutral collision tables must be provided in the laboratory frame. That is, we assume that electrons collide with a stationary neutral such that the relative velocity is equal to the electron velocity. More explicitly, the kinetic energy is computed as:

KEe = 1/2*me*|ve|^2

Ion-neutral collision tables must be provided in the center-of-mass (COM) frame, i.e. the kinetic energy in Column 1 should correspond to the sum of kinetic energies of both particles where their velocities are computed in the COM frame. More specifically, consider an impacting ion with velocity v1 and target neutral with velocity v2. The COM velocity is given as:

vcom = (v1 + v1)/2

Therefore the respective velocities of each particle in the COM frame is given as:

v1com = v1 - vcom = (v1 - v2)/2
v2com = v2 - vcom = (v2 - v1)/2

Finally, the combined kinetic energy is given as:

KEcom = 1/2*m*|v1com|^2 + 1/2*m*|v2com|^2
KEcom = 1/4*m*|v1 - v2|^2

This is the kinetic energy listed in Column 1 of the ion-neutral collision cross-section tables.

If the has tables provided with respect to the relative kinetic energy of the impacting ion this can be related to the COM kinetic energy via:

KErel = 1/2*m*|v1 - v2|^2 = 2*KEcom

Therefore to convert such tables into the COM frame you must multiply Column 1 by a factor of 1/2.

Electron/Ion Neutral Elastic Collision

Elastic collision between electrons and neutrals or ions and neutrals are handled via the same framework. If the input species is detected as having a mass of 1.0 (mass 1.0 under the species definition) then it is treated as an electron, otherwise it is treated as an ion. For electrons collisions the user must specify the neutral_mass parameter, otherwise for ions this is taken as being identical to the ion species mass and any input will be ignored.

elastic 1                               #Collision reference number, required
species_in 1                            #Reference number of the species which undergoes the collision, required
neutral_density 9.64e20                 #Number density (1/m^3) of the neutral species which is being impacted, required
neutral_temperature 0.025               #Temperature (eV) of the neutral species which is being impacted, required
neutral_mass 7352.9                     #Mass (units of electron mass) of the neutral species which is being impacted, required for electrons
xsection_file e_he_elastic.dat          #Cross section file name/location, required

Electron Neutral Excitation Collision

Very similar input to the elastic collision case, however the user must also specify the energy to be removed from the impacting electron during excitation of the neutral in parameter neutral_excitation_energy. As a reminder, this model does not change the properties of the neutral gas.

excitation 1                            #Collision reference number, required
species_in 1                            #Reference number of the species which undergoes the collision, required
neutral_density 9.64e20                 #Number density (1/m^3) of the neutral species which is being impacted, required
neutral_temperature 0.025               #Temperature (eV) of the neutral species which is being impacted, required
neutral_mass 7352.9                     #Mass (units of electron mass) of the neutral species which is being impacted, required for electrons
neutral_excitation_energy 19.82         #Excitation energy for the neutral species (eV)
xsection_file e_he_excite1.dat          #Cross section file name/location, required

Electron Neutral Ionization Collision

The ionization algorithm will perform three things:

• Scatter the electron of species electron_in
• Produce and then scatter one new electron of species electron_in
• Produce one new ion of species ion_out sampled from a thermal neutral.

The neutral mass is taken to be equal to that of the ion_out species.

The user may also specify the ionization_b_value which is a model parameter for the partition of energy between the impacting and produced electron. See Equation 20 in Vahedi & Surendra 1995.

ionization 1                            #Collision reference number, required
electron_in 1                           #Reference number of the impacting electron species, required
ion_out 2                               #Reference number of the produced ion species, required
neutral_density 9.64e20                 #Number density (1/m^3) of the neutral species which is being impacted, required
neutral_temperature 0.025               #Temperature (eV) of the neutral species which is being impacted, required
neutral_ionization_energy 24.587        #Ionization energy for the neutral species (eV)
ionization_b_value 10.0                 #Value for electron energy partition model, optional, default value is 10.0
xsection_file e_he_ionize.dat           #Cross section file name/location, required

Ion Neutral Charge Exchange Collision

Neutral mass is taken to be identical to that of the impacting ion. This algorithm simply replaces the velocity of the impacting ion with a sampled thermal neutral.

cxchange 1                              #Collision reference number, required
ion_in 2                                #Reference number of the impacting ion species, required
neutral_density 9.64e20                 #Number density (1/m^3) of the neutral species which is being impacted, required
neutral_temperature 0.025               #Temperature (eV) of the neutral species which is being impacted, required
xsection_file he+_he_cxchange.dat       #Cross section file name/location, required