Including chemical reactions

Chemical reactions can be defined in the input_data%file, as in the following example:

reaction_list
-----------------------
# Ionization
e + N2 -> e + e + N2+,field_table,C25 N2 Ionization 15.60 eV
e + N2 -> e + e + N2+,field_table,C26 N2 Ionization 18.80 eV
e + O2 -> e + e + O2+,field_table,C43 O2 Ionization 12.06 eV
# Attachment
e + O2 + O2 -> O2- + O2,field_table,C27 O2 Attachment
e + O2 -> O- + O,field_table,C28 O2 Attachment
# Detachment (Panchesnyi 2013)
O2- + M -> e + O2 + M,c1*exp(-(c2/(c3+Td))**2),1.24e-17 179.0 8.8
O- + N2 -> e + N2O,c1*exp(-(c2/(c3+Td))**2),1.16e-18 48.9 11.0
# Negative ion conversion (Panchesnyi 2013)
O- + O2 -> O2- + O,c1*exp(-(c2/(c3+Td))**2),6.96e-17 198.0 5.6
O- + O2 + M -> O3- + M,c1*exp(-(Td/c2)**2),1.1e-42 65.0
# Positive ion conversion (Kossyi et. al. 1992, Aleksandrov and Bazelyan 1999)
N2+ + O2 -> O2+ + N2,c1*(300/Tg)**c2,6e-17 0.5
N2+ + N2 + M -> N4+ + M,c1*(300/Tg)**c2,5e-41 2.0
N4+ + O2 -> O2+ + 2N2,c1,2.5e-16
O2+ + O2 + M -> O4+ + M,c1*(300/Tg)**c2,2.4e-42 3.0
# Electron recombination (Kossyi et. al. 1992)
e + N4+ -> 2N2,c1*(300/Te)**c2,2e-12 0.5
e + O4+ -> 2O2,c1*(300/Te)**c2,1.4e-12 0.5
-----------------------

The format of these reactions is

reaction,rate_type,value(s) [, length unit]

where:

reaction is the reaction formula, as in the example above
rate_type denotes the method used to obtain the reaction rate. Several options are described below.
value(s) are one or more values needed to obtain the reaction rate, for example the name of a table or the coefficients of a function
length unit optionally denotes the length unit used in the reaction rate. It can be m (the default) or cm. This setting can be used to convert reaction rates given in units of cm^3/s or cm^6/s to m^3/s or m^6/s respectively. The time unit is always a second.

All the species that are present in the chemistry file will automatically be present in the simulation, so it is not necessary to provide a list of species.

Chemistry syntax

Reaction syntax

M denotes 'any' gas molecule
X+ means a positively charged species X
X- means a negatively charged species X
2X means X + X (same for 3X etc.)

Note that in the output, special characters such as + and - are converted, because only alphanumeric symbols and _ can be include in Silo variable names.

Supported reaction rate formats

Field-dependent reactions

If the reaction depends on the reduced electric field, rate_type should be set to field_table, and value should be set to the name of the table in input_datafile. For example

e + N2 -> e + e + N2+,field_table,C25 N2 Ionization 15.60 eV

means that the rate for this reaction will be obtained by interpolating the tabulated data following the string "C25 N2 Ionization 15.60 eV". An example of such tabulated data is given below, where the first column is the field in Townsend:

C25 N2 Ionization 15.60 eV
-----------------------
1.000000000000000000e+00 0.000000000000000000e+00
1.151000000000000023e+00 0.000000000000000000e+00
1.326000000000000068e+00 0.000000000000000000e+00
1.526000000000000023e+00 0.000000000000000000e+00
1.758000000000000007e+00 0.000000000000000000e+00
2.024000000000000021e+00 0.000000000000000000e+00
2.330000000000000071e+00 0.000000000000000000e+00
...
-----------------------

Functional expressions

Reactions with analytic formulas can be included by giving the form of the analytic expression. This expression should not contain spaces, and it should be one of the following:

c1
c1*(Td-c2)
c1*exp(-(c2/(c3+Td))**2)
c1*exp(-(Td/c2)**2)
c1*(300/Te)**c2
(c1*(kB_eV*Te+c2)**2-c3)*c4
c1*(Tg/300)**c2*exp(-c3/Tg)
c1*exp(-c2/Tg)
c1*Tg**c2
c1*(Tg/c2)**c3
c1*(300/Tg)**c2
c1*exp(-c2*Tg)
10**(c1+c2*(Tg-300))
c1*(300/Tg)**c2*exp(-c3/Tg)
c1*Tg**c2*exp(-c3/Tg)
c1*exp(-(c2/(c3+Td))**c4)
c1*exp(-(Td/c2)**c3)
c1*exp(-(c2/(kb*(Tg+Td/c3)))**c4)

For these expressions, the values specified should be c1, c2, etc. So for example

O- + O2 + M -> O3- + M,c1*exp(-(Td/c2)**2),1.1e-42 65.0

means that the reaction rate is given by 1.1e-42 * exp(-(Td/65.0)**2). The above symbols have the following meanings:

symbol	meaning	unit
Td	The reduced electric field E/N	Townsend
Te	Electron 'temperature' (given by 2energy/(3kB))	K
Ti	Ion temperature	K
Tg	Gas temperature	K
kB	Boltzmann constant	J/K
kB_eV	Boltzmann constant	eV/K

Ignoring the production of certain species

To simplify a reaction set, it is possible to ignore the production of certain species. This can be done by adding a table of the following form:

ignored_species
-----------------------
NO2
NO
O
N
-----------------------

When ignored species occur on the left-hand side of a reaction, and if they do not correspond to the background gas that is initially present, the reaction will be ignored. When ignored species occur on the right-hand side of a reaction, their production will be ignored, but the reaction will still be included.

Reaction groups

Sometimes, there are many similar reactions. To write these more compactly, the following syntax is available, somewhat similar to ZDPlaskin:

e + @x -> e + e + @x+,field_table,@source
@x = N2,N2,O2
@source = C25 N2,C26 N2,C43 O2

The symbols with an @ will be replaced by the respective values specified in the lines below. So for this example, the reaction set would become:

e + N2 -> e + e + N2+,field_table,C25 N2
e + N2 -> e + e + N2+,field_table,C26 N2
e + O2 -> e + e + O2+,field_table,C43 O2

The number of such replacement groups is flexible.

Adding new types of reactions

First check if the new format can be computed according to one of the existing expressions, for example with different parameters (e.g., you could one parameter less, or allow for a minus sign). If this is the case, you only have to make modifications in m_chemistry::read_reactions().

Add a new case statement with the new reaction format
Determine which of the existing rate functions you can re-use
Modify the coefficients according to the new format

If instead you have to add a completely new rate function, this can be done as follows:

Define a new parameter, e.g. integer, parameter :: rate_analytic_kN = ... in m_chemistry
Add a new case statement with the new reaction format in m_chemistry::read_reactions()
Implement the new reaction with a new case in m_chemistry::get_rates()

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