The application of Gas-phase Kinetics to non-equilibrium plasma systems requires that the kinetics coefficients can be specified independently of the problem or application. For example, some assumption must be made a priori about the electron-energy distribution function (EEDF) when specifying electron-impact kinetics. In reality the EEDF will depend on the reactor conditions, such as the local electric field magnitude or the degree of dissociation of a molecular gas. These conditions are problem-dependent, such that including these effects requires coupling between the kinetics-rate determination and the EEDF determination. While we foresee a need in future Gas-phase Kinetics development for treatment of fundamental reaction cross-section data, there are many systems where application of problem-independent kinetics in plasma modeling is reasonable. Such applications include plasma conditions where the EEDF is nearly Maxwellian, such as near-thermal atmospheric-pressure plasma jets, or very low-pressure, high-electron-density systems for microelectronics processing.

The input file to the Gas-phase Kinetics Pre-processor for a chlorine-plasma excitation process is shown in Example 1.3: Sample Plasma Reaction Mechanism as Read by the Gas-phase Kinetics Pre-processor . As with the previous hydrogen-oxidation example, the file first specifies the elements and species that appear in the mechanism and then describes the reaction mechanism. Here, electrons must be specified both as an element and as a species. The elemental composition of a unipositive ion is that of the corresponding neutral minus one electron. This information is given in the species thermodynamic data and will be described further in the next section. As in the thermal system, three Arrhenius coefficients are used by default to describe reaction rates for electron-impact kinetics. The auxiliary keyword ‘TDEP ’ on a line following the reaction statement indicates that the reaction rate is a function of the temperature of the species specified in the slashes following the TDEP keyword.

As shown in Example 1.3: Sample Plasma Reaction Mechanism as Read by the Gas-phase Kinetics Pre-processor , most of the plasma reactions require some auxiliary information beyond the Arrhenius coefficients to distinguish the reaction description from the default thermal reactions. TDEP is one example of an auxiliary keyword that specifies the temperature dependence of the reaction. EXCI is used typically to indicate an excitation reaction. Such "reactions" are often included to allow calculation of inelastic energy loss rates for electrons, without requiring the user to include all excited states as new species in the reaction mechanism. The auxiliary information following the keyword EXCI represents the energy-loss per collision in electron volts. The keyword DUP is included to allow multiple occurrences of reaction statements that have different rate coefficients or different auxiliary information, but otherwise appear identical. This is frequently necessary in the specification of multiple excitation reactions from the same ground-state species. The use of auxiliary keywords is described in greater detail in the Chemkin Input Manual Input Manual.

Another important aspect of the plasma reactions shown in Example 1.3: Sample Plasma Reaction Mechanism as Read by the Gas-phase Kinetics Pre-processor is that they are all specified as irreversible reactions. This is in contrast to thermal reactions, which are usually reversible and reverse rates can be calculated directly from species thermodynamic properties. In the case of electron kinetics, the interactions between electrons and neutral species can be intrinsically irreversible. While detailed balancing may be appropriate for near-thermal plasmas, the use of Ansys Chemkin thermodynamics is not appropriate for determining reverse rates. In such cases, the user should explicitly supply reverse kinetic parameters, or specify a reverse path as an additional irreversible reaction.

ELEMENTS E CL END
SPECIES  E CL+ CL2+ CL- CL* CL CL2 END
REACTIONS  KELVIN  MOLECULES
! reaction rates from Maxwellian EEDF
  E + CL2  => E + CL2       2.5141E-02  -1.4443E+00   1.6650E+04
    TDEP/E/      !vibrational excitation
    EXCI/ 0.07/
    DUP
  E + CL2  => CL- + CL      5.8901E-09  -2.5619E-01   1.5834E+04
    TDEP/E/      !dissociative attachment
  E + CL2  => 2CL + E       1.5356E-06  -3.4642E-01   7.0850E+04
    TDEP/E/      !dissociation
  E + CL2  => E + CL2       6.3477E-06  -5.3987E-01   1.3920E+05
    TDEP/E/      !electronic excitation
    EXCI/ 9.25/
    DUP
  E + CL2  => CL2+ + 2E     1.1227E-04  -6.0067E-01   1.8070E+05
    TDEP/E/      !ionization
  E + CL-  => CL + 2E       3.1197E-06  -2.8757E-01   7.2058E+04
    TDEP/E/      !detachment
  E + CL  =>  E + CL*       1.2363E-05  -6.1356E-01   1.3297E+05
    TDEP/E/      !4s excitation
  E + CL  =>  E + CL        1.2363E-05  -6.1356E-01   1.3297E+05
    TDEP/E/      !4s excitation energy loss
    EXCI/ 9.55/
    DUP
  E + CL  =>  E + CL        9.4444E-05  -7.3093E-01   1.5413E+05
    TDEP/E/      !3d excitation
    EXCI/11.65/
    DUP
  E + CL  =>  CL+ + 2E      2.3736E-04  -7.0894E-01   1.8374E+05
    TDEP/E/      !ionization
  E + CL*  => CL+ + 2E      2.6471E-05  -4.3906E-01   6.3670E+04
    TDEP/E/      !Cl* ionization
  CL- + CL2+    => CL + CL2        5.00E-08  0.0         0
  CL- + CL+     => 2CL             5.00E-08  0.0         0
END

Consider a simple form of the electron conservation equation for a closed system:

(1–2)

where is the electron molar concentration and the electron molar production rate. The representation of this equation begins with Gas-phase Kinetics subroutine calls:

CALL CKINIT(LENIWK, LENRWK, LENCWK, LINKCK, LOUT, ICKWRK, RCKWRK, CCKWRK, IFLAG)
CALL CKINDX(ICKWRK, RCKWRK, MM, KK, II, NFIT)
CALL PKINDX(ICKWRK, KEL, KKION)
CALL CKKTFL(ICKWRK, KTFL)
CALL CKWC(T, C, ICKWRK, RCKWRK, WDOT)

As in the hydrogen-oxidation example, the first call is to the initialization subroutine CKINIT. CKINDX provides general chemistry indices, while PKINDX provides plasma-specific index information. In this case, we call PKINDX to get KEL, the location in the species array of the electron. In other words, there is no requirement for the species ‘E ’ to be in any particular order in the mechanism species list. KKION is the number of positive and negative ions in the chemistry mechanism. The call to CKKTFL initializes the species temperature flag array in the Gas-phase Kinetics workspace. Without this call, it is assumed that all species share a common temperature, which is always the first entry in the temperature array passed to Gas-phase Kinetics in all subsequent calls. KTFL is a user-defined vector that defines the locations in the temperature array that correspond to each species temperature. This allows the application to define a different number of temperatures in the system than the total number of species. For example, in a two-temperature plasma, where T(1) is the gas temperature and T(2) is the electron temperature, the user sets KTFL(KEL) = 2, and all other entries are set to ‘1 ’. Finally, in the call to CKWC, T is the temperature array, and C is the vector of species molar concentrations. The output variable, WDOT, is the vector, where is the KELth entry.