1. Development of CR Model for OES in Hydrogen Plasma
INTRODUCTION
Jeong-Jeung Tang,
Ji-Hun Kim, and
Yong-Seok Hwang
Department of
Nuclear Engineering,
Seoul National University.
Optical Emission Spectroscopy(OES) is one of the plasma diagnostic methods. This method uses the spectrum emitted from atoms during excited atoms are de-excited with spontaneous radiation. This spectrum has an intensity which is proportional to the number density of excited atoms Therefore, to analyze the spectrum a model is required, which is describing excitation and de-excitation of atoms in the plasma. The present work introduces Collisional-Radiative(CR) model which is capable of dealing broad region of Te and ne. In the previous analysis about the hydrogen plasma, CR model deals with only atom(H) and monatomic ion(H+) to obtain populations of excited levels. But an experimental plasma has molecules(H2) and molecular ions(H2+, H3+) as well as mono atomic particles. Besides, excited atoms are produced by dissociation of molecular particles. Therefore, this work integrates CR model and reaction balance equations of particles to produce modified CR model considering effects of the molecular particles. And the population of the excited levels calculated by the present model is different from the result of the previous CR model, which means that the previous CR model needs to be modified according to Te and ne range. 1 2
CR Model In Monatomic Hydrogen Plasma
What if there are molecular particles ?
Assumption1)
The radiation emitted from the plasma isn’t reabsorbed by plasma.
because of the energy gap between respective angular momentum states in a same principal quantum state is negligible.
Every quantum states are quasi-steady state.
In specific region of ne and Te, relative density looks to have a linearity. From this relation, we can determine the Te at some ne or the ne at some Te. But, an experimental plasma has the various ions and neutrals. Therefore, it needs to be considered a contribution of other particles to excited levels. The present work solves the balance equations of molecular particles with CR model. And this effect is appeared against the pressure.
General Features of CR Model in Cold Plasmas
Effect of Molecular Particles on CR Model in Cold Plasmas
Fig. 1
Fig. 2
Fig. 1 and 2 show the variation of populating and depopulating ratio at state 3 against a change of ne .
Fig. 3 shows the variation of exited level relative density, when Te=10eV, H(1)=1015cm-3, H+=ne.
In the low-density region, every fig. show that the phenomena are similar with the corona phase. But, in the high-density region, the features of the Saha-Boltzmann distribution are appeared. And, in the mid-density region, both the radiative component and the collisional component have to be concerned.
Fig. 4
Fig. 5
Fig. 4 and 5 show the effect of pressure on CR model. The condition of Fig. 4 is Te=10eV, ne=1013cm-3, and Fig. 5. is p=10 mTorr. Detail condition will be explained at the next section.
Comparing Fig. 1 and Fig. 4, they show that H2 and H2+ have a little contribution. Besides, the contribution changes by pressure. And their effect is larger than the effect of H+.
Fig. 5 shows that their effect vary with the respective levels.
Generally, OES in hydrogen plasma uses Hα/Hβ ratio. Therefore, We have to know exact exited level density, particularly level 3 and 4, in order to diagnose the plasma. This is the reason why this effect has to be considered.
Fig. 3. 3 4
Balance Equations for modified cr model
Other conditions for Modified CR model
List of Reaction2)
Charge Conservation
Chamber
H+ e → H+ + e
H2 + e → 2H + e①
H2 + e → H2+ + 2e
H2 + e → H+ + H + 2e②
H2+ + e → 2H+ + 2e
H2+ + e → H + H+ + e
H2+ + e → 2H③
H3+ + e → H2 + H(n=2)
H3+ + e → H+ + 2H + e
H2+ + H2 → H3+ + H
n1 + n2 + n3 = ne R
Charge Conservation
N2 + (1/2) N1 + (1/2)n1 + n2 +(3/2) n3 = p/(kbTg) L
Parameter
ai Reaction rate
τj Containment time for each species (i=1, 2, 3)
T1 Transit time of H atoms across the chamber
(=4(V/A)/v0)
γ Recombination factor for H atoms at the wall
V/A Volume to surface ratio of the source chamber
p Hydrogen gas pressure
Tg Hydrogen gas temperature
v0 Mean velocity of H atoms
Quartz
Fig. 7
R = 1 cm
L = 30 cm
V/A = 0.5
Fig. 6
Reaction Channel
→ H(1) + H(n) [n=1~6] or → H(2) + H(2)
→ H+ + H(1) or → H+ + H(2)
→ H(1) + H(n) [n≥2]
Wall Loss of H and Ions
Particle Balance Equation
Condition 3)
H(1) (N1) 2a2N2ne + a4N2ne + (a6+a7)n2ne + 2a9n3ne - a1N1ne - γ(N1/T1) = 0
H1+ (n1) a1N1ne + a4N2ne + (2a5+a6)n2ne + a9n3ne - (n1/τ1) = 0
H2+ (n2) a3N2ne - (a5+a6+a7)n2ne - (n2/τ2) = 0
H3+ (n3) a10N2n2 - (a8+a9)n3ne - (n3/τ3) = 0
Unknown N1 , N2 , n1 , n2 , n3 , τ1
Given V/A , v0 , Tg , τ2 , τ3 , γ
Variable ne , Te , p 4) 5) 5 6
algorithm of Modified CR model
results of Modified CR model
Most particles in cold plasma are neutral. And there is three or more orders of magnitude difference between population of ground and excited levels. So, this mathematical scaling problem makes matter worse. In the present work, to solve this problem, once program solves the balance equations. And the population of H and H+ obtained proceeding step are applied to the CR model as initial conditions. And the CR model gives the population of excited levels. Then, the results calculated from first and second step become initial conditions for the Modified CR model. Finally, Modified CR performs integrative calculation for the population of every particles without the scaling problem.
CR model
Modified
CR model
Modified
ne=1010 (cm-3)
ne=1011 (cm-3)
ne=1010 (cm-3)
ne=1011 (cm-3)
Fig. 8
Fig. 9
Fig. 8. and Fig. 9. show the Hα/Hβ ratio. The value by modified model is larger than original CR model.
Fig. 10 shows the reaction rate. of dissociation.
The Hα/Hβ ratio increases because the effect on states 3 is larger than 4. And an amount of molecular particles increase with pressure. Therefore, the Hα/Hβ ratio increases with a same ne.
Balance
Equations H H+
CR Model
H H2 H+ H2+ H3+
H(n)
Modified
CR Model
H(n) H2
H+ H2+ H3+
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Department of Nuclear Engineering
Seoul National University