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details of chemical and thermal modelling {#sec:chem_detail}
=========================================

Reaction rates {#sec:reaction_rates}
--------------

  No.       Reaction                                                                        Rate coeff. ${\mathrm{[cm^3\,s^{-1}]}}$                                                                                          Ref.
  --------- ------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------- ------
  1         ${\mathrm{H}}+{\mathrm{e}} \rightarrow {\mathrm{H^+}} + 2{\mathrm{e}}$          $k_1=$                                                                                                                            1
  2         ${\mathrm{He}}+{\mathrm{e}} \rightarrow {\mathrm{He^+}} + 2{\mathrm{e}}$        $k_2=$                                                                                                                            1
  3         ${\mathrm{He^+}}+{\