J. Plasma Fusion Res. SERIES, Vol.7 (2006) 319-322

Collision Database for Low-T Hydrogen Plasmas
JANEV Ratko K., REITER Detlev, SAMM Ulrich and MARCHUK Oleksandr
Institute of Plasma Physics, Forschungszentrum Juelich GmbH,EURATOM Association, Trilateral Euregio Cluster, D-52425 Juelich, Germany（Received: 4 October 2004 / Accepted: 12 April 2005）

Abstract
A comprehensive cross section database for collision processes between constituents of a low-temperature,
low-density hydrogen plasma e, H+ , H, H− , H2 , H+2 , H+3 is established. The processes involving electronically
and/or vibrationally excited reactants or reaction products are also included in the database. The presented
data information is based on critical assessment of the available experimental and theoretical data, and on theuse of well established scaling relationships or relatively simple theoretical models for generation of crosssections when such were not found in the literature. All derived cross sections are represented by analytic fit
functions that have physically correct energy behavior at both low (near threshold) and high collision energies.
The database, however, still contains gaps for certain important state-selective collision processes requiredfor constructing a complete H/H2 collision-radiative model.
Keywords:
collision process, cross section, hydrogen plasma
1．Introduction
The understanding of spectroscopic, transport andother properties of low-temperature hydrogen plasmas
requires detailed knowledge of collision and radiative
processes that take place in such plasmas. The constituents of pure hydrogen plasmas with temperature in
the range 0.01 – 300 eV and densities below ∼ 1015
cm−3 include e, H+ , H, H− , H2 , H+2 , H+3 , where H and H2
may be in electronically excited states, and H 2 (and H∗2 ),H+2 and H+3 may be ro-vibrationally excited. The large
number of states associated with the internal degrees
og freedom of neutral and molecular hydrogen species
makes the collision kinetics of hydrogen plasmas extremely complex. On the other hand, the role of excitedspecies in a hydrogen plasma is obviously of paramountimportance, as evidenced by the spectroscopic observations (frequently also used as plasma diagnostic tools[1,2]), and collision processes of excited species withplasma electrons, protons and ground state atomic andmolecular species must be included in the collision kinetics scheme to determine their populations. Anotherfeature of electronically or (ro-)vibrationally excitedspecies is that the cross sections for many of their collision processes are significantly larger than those forcorresponding processes involving ground state species.
Moreover, the thresholds of inelastic processes and all
related collision characteristics (e.g., energy and angular distributions of reaction products) have a strong

dependence on the excited state energies and consequently, significantly aﬀect the plasma energy and momentum transport [3].
In the present contribution we describe a H/H2 collision database that includes cross section information forcollision processes of both ground state and electronically and vibrationally excited hydrogen plasma constituents. A detailed account of this database is given
elsewhere [4]. We should mention that the earlier attempts to construct a H/H2 collision database either do
not adequately describe the processes with vibrationallyexcited molecular species [5], or do not include all important collision processes and the most accurate crosssection information [6,7].
2．Collision processes in low-T hydrogen plasmas
2.1 Collision processes of H (n  1)

The collision processes of ground state (n = 1) andexcited (n > 1) hydrogen atom with plasma electronsand protons include: excitation, ionization, transitions
between excited states, radiative and three-body recombination, and charge transfer (in the proton impactcase). The proton impact excitation and ionization processes have small cross sections in the energy region
pertinent to low-T plasmas (as defined above), except
for the high-n states. However, due to its resonance
C 2006 by The Japan Society of Plasma

Science and Nuclear Fusion ResearchCorresponding author’s e-mail: r.janev@fz-juelich.de319

Collision Database for Low-T Hydrogen Plasmas

nantly populates the n = 2 and n = 3 states of H (produced on the basis of proton reactant). The resonant
charge transfer and associative detachment in H− +H
collisions are also characterized by a large cross sections at low energies.
The predominant low-energy process of H+2 (v) withelectrons is the dissociative recombination, resulting inproduction of H(n  2) excited atoms. The cross section magnitude, as well as the n-distribution of excitedreaction products are sensitive to the value of initial vibrational state of H+2 . At energies above 10 eV, the dissociative excitation starts to compete with dissociative
recombination, and eventually becomes dominant at energies above 20 eV. The low-energy collisions of H+2(vi ) with H2 (X;v) are dominated by charge transfer andH+3 (v3 ) formation (particle exchange) processes. While
the former is theoretically studied fairly exhaustively,
the information on vi –v3 and v–v3 selectivity of the latteris still rather limited. This information is, however, critical for the cross section magnitude and quantum stateof reaction products of processes of H+3 (v3 ) with otherplasma constituents (notably with e and H− ).
Dominant low-energy collision process of H+3 (v3 )with electrons is the dissociative recombination, producing either three H atoms or H + H2 (v). While thetotal cross section of this process for v3 = 0 is experimentally well established, including the energy dependence of branching ratio 3H/(H + H2 ), large discrepancies in experimental data exist regarding its v 3 dependence. Very little is known also regarding the quantum
states of atomic products, as well as the v-distributionof H2 . The cross sections of collision processes of H+3(v3 ) with H2 (v) in the thermal energy region are also notwell known, neither are the cross sections of the mutual
recombination of H+3 and H+2 with H− .

character, the charge transfer is a powerful process atlow collision energies for all n, and scales like n 4 forn  4.
Of neutral-neutral collision processes the most important for the low-T plasma kinetics are those involving H(n = 1) and H(n  2). Among them, the processes of mixing the angular momentum states, excitation transfer and associative and non-associative ionization show cross sections that in the low energy region
are suﬃciently large to produce rate coeﬃcients comparable to those of electron impact inelastic processes.
2.2 Collision processes of H 2 (N 1,3 Λg,u ; v)

Most of the available cross section data for electronand proton impact processes of H2 are those involving
the ground electronic state X 1 Σ+g , vibrationally unexcited (v = 0). Theoretical cross section calculations forelectron impact excitation (to higher electronic states)
and ionization, however, do exist for v  1. Electron
impact induced transitions between electronically (andvibrationally) excited states, or for ionization from electronically (and vibrationally) states are very sparse andusually performed using rather crude approximations(such as the Gryzinski-Bartky-Bauer classical model,see [4]). Besides excitation and ionization, other electron impact processes included in the database are: vibrational excitation of ground electronic state of H2(via formation of resonant H−2 resonant states, or by radiative decay of exited electronic states), dissociative
attachment and dissociative excitation and ionizationof H2 (X;v) in all v-states. The cross section information for electron impact dissociative processes involving
electronically excited states of H2 , is presently missingin the literature. There is also very little information on
the non-radiative decay processes of excited electronicstates (auto-ionization, pre-dissociation).
Most important low-energy proton impact processesof H2 (X;v) are: vibrational excitation and electrontransfer. The latter becomes exothermic (and evenquasi-resonant) for v  4, characterized by a large crosssection. In the thermal energy region, the particle exchange process becomes also important. The electrontransfer in proton collisions with electronically excited
H2 should have large cross section for certain vibrational levels (due to an energy quasi-resonance), but thisprocess has not been studied so far.

3．Data assessment and presentation
The cross section data information available in theliterature for each considered collision process, either
experimental or theoretical, was critically assessed anda preferred (or “recommended”, when the information
was abundant) cross section was derived with an assigned accuracy in various energy regions. When only
one set of data was found in the literature for a given
process, that set was taken to represent the cross section
with its accuracy assigned by the author(s), or, in caseof theoretical data, derived on the basis of accuracy ofthe method used in the calculations for a particular energy region.
The cross sections for many processes involving excited initial states are known to obey certain scaling relationships (at least in well defined energy regions) that

2.3 Collision processes of H− , H+2 and H+3

The most important low-energy processes of H− negative ion with electrons and protons are the electron detachment and the mutual neutralization (electron capture), respectively. The electron capture process domi320

Collision Database for Low-T Hydrogen Plasmas

where x = E/∆E, ∆E is the threshold energy, and Ai
are the fitting parameters. Similarly, for the electron
impact induced transitions to triplet excited states of H 2
from its ground electronic and vibrational state, the fit
function was chosen in the form:
1 +3σtot
exc X Σg (v = 0) → N Λσ
γ
1A(2)
= 3 · 1 − β (×10−16 cm2 )xx

follow from the general theory or particular theoreticalmodels. Such scaling relationships were used to generate cross section for processes for which no data information was found in the literature. Finally, to fillin certain gaps in the available data, or make appropriate inter-/extrapolations, the predictions of certain relatively simple models, known to provide a reasonable description of corresponding physical process, were used.
All cross sections derived by applying the above prescriptions have been represented by analytic fit functions, the form of which was chosen to preserve theknown (or expected on general theoretical grounds) thenear threshold (when such exists) and high energy crosssection behavior. An example of such analytic fit function is given below for the dipole allowed electron impact excitation cross sections of singlet states of H 2
from its ground electronic and vibrational state:σexc X 1 Σ+g (v = 0) → N 1 Λuα 
1A2 A35.984· 1−+ 2 + A4 ln(x)· A1 +=∆Exxxx(×10−16 cm2 )The excitation cross sections for the lowest singlet andtriplet states of H2 given by the above fit functions areshown in Figs. 1 and 2, respectively. The fits represent
the derived cross sections with an rms deviation of 2–3%.
4．Conclusions
We have presented the content of a cross section
database for collision processes taking place in lowtemperature, low-density hydrogen plasmas. The processes mentioned in this presentation are only those thatplay a major role in the kinetics of ionizing and recombining plasmas. The scope of the database is, however,considerably broader and includes processes important
for the description of hydrogen neutral beams propagating through a hydrogen plasma. The present article addresses also the question of completeness of theH/H2 collision database, emphasizing the existing gaps
in the database and in the present knowledge as well,regarding certain important collision processes in lowT hydrogen plasmas. These gaps are particularly serious for the processes involving electronically (and vibrationally) excited H2 states and for the state-selectiveprocesses involving the formation and destruction of H+3ion.

(1)

1.E-16CB

σexc (cm 2)

1.E-17D

1.E-18B'

1.E-19
1.E+01D'B''

1.E+02

1.E+03

1.E+04E (eV)

Fig. 1 Total electron impact excitation cross sections ofB, C, D, B’, D’, B’’ singlet electronic states of H2from the H2 (X 1 Σ+g ; v = 0) ground state.

[2]

1.E-16a[3]d2tot(cm )σexc

1.E-17[1]b

1.E-18ec1.E-19[4]
1.E-20
1.E+00

1.E+01

1.E+02

1.E+03E (eV)[5]

Fig. 2 Total electron impact excitation cross section of a,b, c, d and e triplet states of H2 from its (X 1 Σ+g ;v = 0) ground state.

[6]
321

References
D. Reiter, P. Bogen and U. Samm, J. Nucl. Mater.
196-198, 1059 (1992).
U. Fantz, D. Reiter, B. Heger et al., J. Nucl.
Mater. 367, 290 (2001).
“Nuclear Fusion Research:
Understanding
Plasma Surface Interaction”, Springer Series in
Chemical Physics, 78, R.E.H. Clark, D. Reiter(Eds), Springer Verlag, ISBN: 3-540-23038-6(2005).
R.K. Janev, D. Reiter and U. Samm, “Collision
processes in low-temperature hydrogen plasmas”,
FZ-Juelich Report, 4105 (2003).
R.K. Janev et al., “Elementary Processes inHydrogen-Helium Plasmas”, Springer-Verlag,
Berlin-Heidelberg, (1987).
K. Sawada and T. Fujimoto, J. Appl. Phys. 78,

Collision Database for Low-T Hydrogen Plasmas[7]2913 (1995).
A. Pigarov, in Topical Issue Phys. Scr. T96(2001).

322