doi:10.14311/ppt.2017.3.225Plasma Physics and Technology 4(3):225–233, 2017 © Department of Physics, FEE CTU in Prague, 2017

NON-EQUILIBRIUM STUDIES IN SWITCHING ARC PLASMAS IN JAPAN

Y. Tanakaa,∗, K. Tomitab, Y. Inadac, A.Kumadad, K. Hidakad,T. Fujinoe, K. Suzukif, T. Shinkaig

a Kanazawa University, Kakuma, Kanazawa, Ishikawa 920-1192, Japanb Kushu University, Kasuga, Fukuoka 816-8580, Japanc Saitama University, 542 Shimo-Okubo, Sakura, Saitama 338-8570 Japand The University of Tokyo,7-3-1 Hongo, Bunkyo, Tokyo 113-8654, Japane University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japanf Tokyo Denki University, 5 Senju Aasahi, Adachi, Tokyo 120-8551, Japang Tokyo University of Technology, 1404-1 Katakura, Hachioji, Tokyo 192-0982, Japan∗ tanaka@ec.t.kanazawa-u.ac.jp

Abstract. This paper briefly introduce research work examples of non-equilibrium studies in switchingarcs. In understanding arc behavior, one often assumes local thermodynamic equilibrium (LTE)condition in the arc plasma. However, actual arc plasmas are not completely and not always in LTEstate because of strong temperature change temporally and spatially, and high electric field applicationetc. Recently, we have a collaboration work in numerical simulations and experimental approachesfor decaying arcs without LTE assumption. First, our numerical model is presented for decaying arcswithout chemical equilibrium assumption. Secondly, two experimental methods are introduced formeasuring electron density in decaying arcs without LTE assumption: Laser Thomson Scatteringmethod and the Schack-Hartmann method. Finally, comparison results is shown between the LTEsimulation, the chemically non-equilibrium simulation, and the above experimental measurements.

Keywords: Local thermodynamic equilibrium, chemically non-equilibrium, thermally non-equilibrium,electron density measurement.

1. IntroductionThermal plasmas/arc plasmas are widely used for var-ious applications such as plasma spray coating, rapidsurface modification, fabrication of functional films,plasma arc cutting, nanopowder synthesis, and car-bon nanotube synthesis etc. Switching arcs are alsoimportant applications of arc plasmas in an electricpower transmission system. In understanding the be-havior of thermal plasmas/arc plasmas, local thermo-dynamic equilibrium (LTE) models have been widelyadopted. This LTE model assumes the same tem-peratures for kinetic energies of electrons and heavyparticles. The LTE model also assumes chemicallyequilibrium condition, which corresponds to extremelyhigh reaction rates for all reactions including ioniza-tion, electronic, vibrational and rotational excitations.Therefore, the LTE assumption is equivalent to one-temperature chemically equilibrium (1T-CE) model.Such the LTE model is greatly useful to predict themass and energy transport in thermal plasmas or arcsfor a conventional use, and it successfully interpretsbehaivor of the thermal/arc plasmas. However, moredetailed understanding of the distributions of chemicalspecies in arcs and thermal plasmas has been requiredfor advanced thermal plasma materials processes, aswell as switching arcs.

One phenomenon which causes chemically non-equilibrium effects is high spatial gradient in number

density at medium-temperature or low-temperatureregion of arcs and thermal plasmas. In medium orlow temperature regions, which are always presentsurrounding the high-temperature region of the arcs,the LTE assumption cannot always be established. Itis necessary to account for chemically non-equilibriumeffects in this case [1, 2]. Another important phe-nomenon for deviation from chemical equilibrium con-dition is a rapid change in time, i.e., a transient phe-nomenon in arcs and thermal plasmas. For exam-ple, switching arcs or modulated induction thermalplasmas [3, 4] are fundamentally under transient con-ditions. To study the transient state in arcs andthermal plasmas, attention should be paid to chem-ically non-equilibrium effects. On the other hand, adeviation from thermal equilibrium condition may bedue to high electric field application. In switchingarcs, the transient recovery voltage (TRV) is appliedto a residual arc between the electrodes after currentzero. Such a high voltage application may increasethe electron temperature, leading to two-temperaturestate in residual arcs. To elucidate the aforementionedphenomena in detail, non-equilibrium effects must beconsidered.This paper briefly introduces an example of non-

equilibrium modeling in arc plasmas [5, 6]. In addition,some recent experiments will be introduced for decay-ing arcs with a detailed control of applied voltage

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and injected current using some power semiconduc-tors [7]. In the experiments, two measurement meth-ods were adopted to determine the electron densitywithout LTE assumption: the laser Thomson scatter-ing method [8] and the Shack-Hartmann method [9].Finally, we compare results between the LTE simula-tion, the chemically non-equilibrium simulation, andthe above experimental measurements [6].

2. Non-equilibrium effects forswitching arcs

For simulation of switching arcs, the LTE or one-temperature chemical equilibrium (1T-CE) models hasbeen adopted. However, the following non-equilibriumeffects may be taken into account for its further un-derstanding:(a) Chemically non-equilibrium effects: In

arc plasmas, there are lots of reactions includingmolecular dissociation, association, ionization, recom-bination, attachment and detachment. Any reactionrequires a certain finite time to reach its chemicalequilibrium because the rate coefficients of reactionsare also finite. On the other hand, switching arcs areessentially under transient state, and they have steepgradients in densities of chemical species. Chemicallyequilibrium (CE) in the switching arcs is thereforeachieved only if the relaxation time for any reaction ismuch shorter than the characteristic time of diffusionon the particle composition as well as the transienttime of the states. In other words, a rapid time changeand steep gradient in switching arcs may involve chem-ically non-equilibrium (non-CE) state.(b) Thermally non-equilibrium effects: In

high pressure arcs, the electron temperature Te be-comes close to the heavy particle temperature Th ifthe electron sufficiently transfers its kinetic energy tothe heavy particle through elastic collisions comparedto the energy gained from the external electric field.Establishement of thermal equilibrium state needsmuch less electron energy gain by the electric fieldthan the thermal energy of electrons. Otherwise athermal non-equilibrium condition Te >> Th can beobtained. In switching arcs, the off-axis region hasrelatively lower temperature and lower electron den-sity, which results in lower collision frequency betweenelectrons and heavy particles. At the same time, theelectric field is applied to the off-axis region as wellas on-axis region in the arc. This situation may of-fer thermally non-equilibrium state. Furthermore, tothe switching arcs, a high transient recovery voltage(TRV) is applied after current zero. This high voltageapplication may lead residual arcs to ones in thermallynon-equilibrium state.(c) Non-Boltzmann distribution for a popu-

lation of excited particles: The population of ex-cited particles does not follow the Boltzmann distribu-tion if the population is more influenced by processessuch as the radiative de-excitation than by thermal

excitation and de-excitation. This concept is impor-tant particularly for investigating a physical statein thermal plasmas from spectroscopic observationresults.(d) Non-Maxwellian energy distribution

function: The electron energy distribution function(EEDF) cannot be Maxwellian if the electron–electronenergy relaxation time is much longer than the elec-tron acceleration time by an external electric field,or if the vibrational and rotational excitation crosssection is comparable with the momentum transfercross section by the electron impact. In such cases,the Boltzmann equation should be solved consider-ing such cross sections with an applied electric field.This situation appears in prediction of arc re-ignitionphenomena in a circuit breaker.

The present paper only focuses (a) chemically non-equilibrium (non-CE) effects.

3. Numerical approaches: Modeling onchemically non-equilibrium effects

3.1. Mass conservation equationAmong various non-equilibrium effects, this sectiontreats chemically non-equilibrium (non-CE) effectsbecause the non-CE effects affect the behavior of arcplasmas. In non-CE state, it is difficult to adopt anLTE assumption with the mass action law such as theGuldberg–Waage and Saha equations to obtain theparticle composition distribution and its transient evo-lution. In these cases, the following mass conservationequation for each of species j should be solved con-sidering convection and diffusion effects and reactionrates to determine the time evolution in the particlecomposition distribution:

∂(ρYj)∂t

+∇ · (ρuYj − ρDj∇Yj) = Sj (1)

Sj = mj

L∑`=1

(βrj` − βf

j`)(αf`

N∏i=1

nβf

i`i − α

r`

N∏i=1

nβr

i`i

)(2)

where Yj signifies the mass fraction of species j, ρstands for the mass density of the bulk plasma, Dj

denotes the effective diffusion coefficient of j, αf` and

αr` respectively stand for the rate coefficients of for-

ward and backward reaction `; also, ni is the densityof species i, βf

i` and βri` are the stoichiometric coeffi-

cient in reaction ` for forward and backward directionsfor species i, and N and L respectively denote thenumber of species and reactions considered. Thermo-dynamic and transport properties of plasmas shouldbe calculated at each position at each time using thecalculated temperature, pressure and particle compo-sition combined with the collision integrals betweenthe species.

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3.2. Examples of chemically non-equilibriummodeling for SF6 and N2 arcs

Some research efforts have been undertaken to treatsuch chemically non-equilibrium effects in high-P andhigh-T plasmas for a long time [10]−[14]. Some non-equilibrium effects of SF6 arc plasmas were studiedtheoretically or numerically from the 1990s [15]–[31].Among these studies, chemically non-equilibrium mod-elling on SF6 arcs had been conducted by Gleizes etal. [16]–[20] and the present authors [5],[23]–[31] .

Here, two examples of our recent non-CE modelingis introduced for SF6 and N2 arcs [5, 6].

3.2.1. AssumptionsThe developed model assumes the following things inthe decaying arc plasma for simplicity: (i) The arcplasma has the axisymmetric structure. (ii) The gasflow is laminar flow, thus the turbulent effect is ne-glected. (iii) The optically thin condition is assumedfor radiation. (iv) All the temperatures includingelectron temperature, heavy particle temperature andexcitation temperatures are identical. (v) Electrons,ions and neutral species have the same flow velocity.(vi) Electrode surface phenomena such as electronemission from the electrodes and surface recombina-tion of ions were not considered for simplicity. (vii)Evaporation of the electrode and the nozzle was ne-glected. (viii) For SF6 arcs, 19 species SF6, SF5, SF4,SF3, SF2, SF, S2, F2, S, F, SF+, S+

2 , F+2 , SF−, S+,

F+, S−, F− and e− were taken into account as con-stituents in SF6 arc plasmas. On the other hand, N2arcs were assumed consisting of 5 species N2, N+

2 , N,N+ and e−. (ix) Quasi-neutrality for electronic chargeis established.

3.2.2. Governing equationsThe following equations were solved to simulatean SF6 decaying arc plasmas on the basis of theassumptions in the previous section as follows:

Mass:Dρ

Dt= −ρ(∇ · u), (3)

Momentum:

ρDu

Dt= −∇p+∇ · τ , (4)

τ = τij = 2η[eij −

13δij(∇ · u)

](5)

Energy:

ρCvDT

Dt= −p(∇ · u) +∇ · (λtr∇T ) +Qheat (6)

Qheat =N∑j=1

∇ · (ρDjhj∇Yj) +L∑`

∆Q` − Prad (7)

hj = 1mj

(52kT + kT 2 ∂ lnZj

∂T

)(8)

Cv =N∑j=1

Yjmj

[32k + ∂

∂T

(kT 2 ∂ lnZj

∂T

)](9)

Mass of species j:

ρDYjDt

= ∇ · (ρDj∇Yj) + Sj , (10)

Sj = mj

L∑`

(βrj` − βf

j`)

(kf`

N∏i=1

nβf

i`i − kr

`

N∏i=1

nβr

i`i

)(11)

The equation of state:

ρ = p

κ∑N

j

Yj

mjT

(12)

where ρ: mass density, t: time, u: gas flow vector, p:pressure, τ : stress tensor, η: viscosity, eij : unit tensor,δij : Kronecker delta, T : temperature, Cv: effectivespecific heat at constant volume, λtr: translationalthermal conductivity, Dj : effective diffusion coeffi-cient, hj : enthalpy of species j, Yj : mass fraction ofspecies j, Prad: radiation power, ∆Q`: heating powerfrom reaction heat of reaction `, mj : mass of speciesj, βj`: stoichiometric coefficient of species j for re-action `, kf,r

` : reaction rate coefficient for reaction`, nj : density of species j, κ: Boltzmann constant,DDt = ∂

∂t + u · ∇ is the Lagrangian derivative. Solv-ing (10) calculates the particle composition in thearc plasma considering reaction rate, convection anddiffusion effects.

For N2 arc plasmas, a similar set of governing equa-tions was solved but in forms of Fluent [6].

3.2.3. Properties and rate coefficients forreactions

The thermofluid calculation for arc plasmas needsthe thermodynamic and transport properties such asmass density ρ, specific heat Cv, enthalpy hj , trans-lational thermal conductivity λtr, viscosity η, Prad.These properties were calculated using the particlecomposition and the temperature computed and thecollision integrals at each position at each calcula-tion step. The calculation of the transport propertieswere carried out by the first order approximation ofChapman-Enskog method.For SF6 arcs, 64 forward reactions including the

electron impact ionization, the electron attachment,the electron impact dissociation, and other chemicalreactions were taken into account as well as theirbackward reactions [5]. These temperature-dependentcoefficients were obtained in literatures [16]−[20]. Inthe present work, ion-ion recombination reactions suchas SF+ + F− + F → SF + F + F, SF+ + F− + F→ F2 + S + F, and SF+ + F− + F → F2 + SFwere also taken into account to study the effects ofthese reactions on the composition in residual arcs,especially ion remaining between the electrodes. ForN2 arcs, totally 22 reactions were taken into accountincluding 11 forward reactions and their backwardreactions. The rate coefficients for these reactionswere obtained in literatures [6].

Figure 1 depicts the calculation space. This spacewas divided into 153×170 grids for the r-z two dimen-sional space. This configuration is the same to that in

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Y. Tanaka, K. Tomita, Y. Inada et al. Plasma Physics and Technology

0

10

20

30

0 25 50 75 100 125 15030

20

10

Rad

ial

posi

tion [

mm

]

Axial position [mm]

Cu electrode

PTFE nozzleUin

0 25 50 75 100 125 150

SF6 at 300 K30

20

10

0

30

20

10

Arc plasma

Cu electrode

300 K

Ra

dia

l p

ositio

n [m

m]

Axial position [mm]

Figure 1. Calculation domain.

our experimental device. First, the 100A dc currentwas applied to the arc in the steady state. Then, thetransient state calculation was performed for a currentstepped down from 100A to 0A, i.e. for free recoverycondition for a fundamental study.

3.3. Examples of calculation results3.3.1. SF6 arcs: Transient distribution of F- with

and without ion-ion recombination reactionsFigure 2 indicates time evolutions in F− density dis-tribution under free recovery condition. We here treattransient behavior of F− because F− production isrelated to the electron density and may influence elec-trical conduction just around current zero [5]. Inaddition, we study non-CE effects on ion remainingbetween the electrodes. The upper panels in this fig-ure thus show the results with consideration of ion-ionrecombination reactions such as SF+ + F− + F →SF + F + F, SF+ + F− + F→ F2 + S + F, and SF+

+ F− + F → F2 + SF, whereas the lowers are theresults without consideration of ion-ion recombinationreactions. By comparing the upper panel and thelower panel, we can investigate influence of ion-ionrecombination reactions. At t = 0 µs, F− has higherdensity about 1020 m−3 around the boundary betweenthe arc and cold SF6 gas flow. At t = 5 µs, F− densityincreases rapidly with time around the fringe of thearc plasma. In particular, the arc fringe has higherF− density more than 1021 m−3 around the nozzlethroat inlet, i.e. positions 55 <mm z < 75mm. Thisrapid increase in F− density arises mainly from two-body dissociative attachment reactions with diatomicmolecules F2 + e → F− + F and SF + e → F− + Sjust after the current down. After that, F− density isstill high around 1021 m−3 around the nozzle throatinlet until t = 10 µs. Even at t = 50 µs, F− becomesdistributed with 1021 m−3 in whole arc region.Consideration of the ion-ion recombination reac-

tions influences transient behavior of F− density dis-tribution. At t = 5 µs, F− remains around nozzlethroat inlet but in inner region. The density of F−

becomes lower at the fringe of the arc plasma. Thisis attributed to the contribution of the ion-ion re-combination reactions considered. At t = 10–50 µsF− density is predicted to be lower with the ion-ionrecombination. However, it is noteworthy that F−

still remains with densities of 1020 m−3. This implies

Non-CE

w/ i-i

reactions

Non-CE

w/o i-i

reactions0

1

2

1E+18 1E+211E+20 1E+221E+191.000E18 1.202E18 1.445E18 1.738E18 2.089E18 2.512E18 3.020E18 3.631E18 4.365E18 5.248E18 6.310E18 7.586E18 9.120E18 1.096E19 1.318E19 1.585E19 1.905E19 2.291E19 2.754E19 3.311E19 3.981E19 4.786E19 5.754E19 6.918E19 8.318E19 1.000E20 1.202E20 1.445E20 1.738E20 2.089E20 2.512E20 3.020E20 3.631E20 4.365E20 5.248E20 6.310E20 7.586E20 9.120E20 1.096E21 1.318E21 1.585E21 1.905E21 2.291E21 2.754E21 3.311E21 3.981E21 4.786E21 5.754E21 6.918E21 8.318E21 1.000E22

50 60 70 80 90 1002

1

0

Axial position [mm]

Rad

ial

po

siti

on

[m

m]

0

1

2

50 60 70 80 90 1002

1

0

Axial position [mm]

Ra

dia

l p

ositio

n [

mm

]

[m-3]

(a) t = 0 µs

0

1

2

1E+18 1E+211E+20 1E+221E+191.000E18 1.202E18 1.445E18 1.738E18 2.089E18 2.512E18 3.020E18 3.631E18 4.365E18 5.248E18 6.310E18 7.586E18 9.120E18 1.096E19 1.318E19 1.585E19 1.905E19 2.291E19 2.754E19 3.311E19 3.981E19 4.786E19 5.754E19 6.918E19 8.318E19 1.000E20 1.202E20 1.445E20 1.738E20 2.089E20 2.512E20 3.020E20 3.631E20 4.365E20 5.248E20 6.310E20 7.586E20 9.120E20 1.096E21 1.318E21 1.585E21 1.905E21 2.291E21 2.754E21 3.311E21 3.981E21 4.786E21 5.754E21 6.918E21 8.318E21 1.000E22

50 60 70 80 90 1002

1

0

Axial position [mm]

Rad

ial

po

siti

on

[m

m]

0

1

2

50 60 70 80 90 1002

1

0

Axial position [mm]

Ra

dia

l p

ositio

n [

mm

]

Non-CE

w/ i-i

reactions

Non-CE

w/o i-i

reactions

[m-3]

(b) t = 10 µs

0

1

2

1E+18 1E+211E+20 1E+221E+191.000E18 1.202E18 1.445E18 1.738E18 2.089E18 2.512E18 3.020E18 3.631E18 4.365E18 5.248E18 6.310E18 7.586E18 9.120E18 1.096E19 1.318E19 1.585E19 1.905E19 2.291E19 2.754E19 3.311E19 3.981E19 4.786E19 5.754E19 6.918E19 8.318E19 1.000E20 1.202E20 1.445E20 1.738E20 2.089E20 2.512E20 3.020E20 3.631E20 4.365E20 5.248E20 6.310E20 7.586E20 9.120E20 1.096E21 1.318E21 1.585E21 1.905E21 2.291E21 2.754E21 3.311E21 3.981E21 4.786E21 5.754E21 6.918E21 8.318E21 1.000E22

50 60 70 80 90 1002

1

0

Axial position [mm]

Rad

ial

po

siti

on

[m

m]

0

1

2

50 60 70 80 90 1002

1

0

Axial position [mm]

Ra

dia

l p

ositio

n [

mm

]

Non-CE

w/ i-i

reactions

Non-CE

w/o i-i

reactions

[m-3]

(c) t = 50 µs

Figure 2. F− density distribution in an SF6 arc at10µs after free recovery condition initiation. The up-per panel: with ion-ion recombination; the lower panel:without ion-ion recombination.[5]

that F− is one of the key charged species for electricalconduction in an SF6 residual arc.

3.3.2. N2 arcs: Temperature and compositionchange by chemically non-equilibrium model

We calculated N2 arc behavior in the same arc deviceusing a similar non-CE model [6]. Figure 3 presentsthe time variations in the temperature at axial po-sition of nozzle throat at the center axis under freerecovery condition. This figure includes two resultsby the LTE model and the non-CE model. Duringt = 0–15 µs, the temperature decay calculated by thenon-CE model is similar to that by the LTE model.

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Figure 3. Time evolution in the temperature at nozzlethroat in N2 arcs [6].

The reason is that at the high temperature regionmore than 11000K, the reaction rates are enoughhigh and all the reactions tend to reach their equi-librium. At t = 15–25µs, the LTE model predicts amore rapid temperature decay than the non-CE model.After t = 50 µs, the temperature in the non-CE modeldecreases with a higher decrease rate. After t = 55 µs,the temperature in the non-CE model is lower thanthat by the LTE model. The above difference in thetemperature decreases by the LTE model and thenon-CE model is attributed to reaction rates [6].

Figure 4 shows the time evolution in particle compo-sition at nozzle throat in N2 arcs under free recoverycondition. Solid curves are the results by the non-CEmodel, whereas the dashed curves are the results bythe LTE model. From t = 0 to 10µs, two kinds ofresults hardly have deviation from each other. This isbecause the temperature is still higher than 10000K,and thus the reaction rates for dominant reactions arehigh. However, at t = 10–25µs, the electron numberdensity, as well as the N+ number density, decreasesmore slowly in the non-CE model than those in theLTE model. This higher electron density is due tothe larger amount of exothermic recombination re-actions. At t > 25 µs, N2 density predicted by thenon-CE model recovers more slowly than that by theLTE model. This arises from the delay in associationreaction N + N + M→N2 + M.

4. Experimental approaches: Electrondensity measurement without LTEassumption

We have performed the electron density measurementin an arc under free recovery condition in a arc testdevice without LTE assumption. This measurementresult can be compared with the numerical simulationresult to study arc behavior including non-equilibriumeffects.

4.1. Gas-blast arc deviceFigure 5 shows a photo and the cross section diagramof the nozzle used in our experiments [7]. The nozzle

Figure 4. Time evolution of particle composition atnozzle throat in N2 arcs [6].

0 10 20 300

25

50

75

100

125

150

30 20 10

Radial position [mm]

Axial position [mm]

PMMA nozzle

150

125

100

75

50

25

0-10 10-20 200

50

Radial position [mm]

Ax

ial

po

siti

on

[m

m]

10

10

10

No

zzle

Electrode

(Cu-W)

Electrode

(Cu-W)

No

zzle

[mm]

10 mm x 6 mm hole for

Thomson scattering

Figure 5. Configuration of the electrodes and the nozzle.

and the electrodes have a cylindrical axis-symmetricstructure. The tip of the electrodes were made ofcopper-tungsten alloy. The lower electrode is fixed,while the upper electrode can move. The distancebetween the electrodes is 50mm in open position. Be-tween these electrodes, the arc plasma is formed. Thenozzle is made of polymethyl methacrylate (PMMA),and then the visible light from the arc plasma can beobserved through the nozzle. The nozzle throat widthand length are 10mm and 10mm respectively. At thenozzle throat outlet, there is a observation hole with10mm × 6mm for measuring the electron density inarc plasmas by laser Thomson scattering method. Gasflow is supplied from the downer side along the lowernozzle to the arc plasma axially.Figure 6 depicts the experimental setup including

the arc device and the electrical circuit. The nozzleand the electrodes in Fig. 5 are located inside a cham-ber made of stainless steel. Gas flow is supplied from ahigh-pressure gas tank to the lower side of the arc de-vice. The upper electrode can open for a 50mm strokein about 80ms by high-pressure air. The arc devicewas connected with a dc inverter current source. This

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Y. Tanaka, K. Tomita, Y. Inada et al. Plasma Physics and Technology

gas

gas

Nozzle

Arc plasma Electrode

Chamber

va

vCT2vCT1

vCT3 iIGBT

iarcisource

Current source

IGBT

CT

CT

Voltage

divider

Cylinder

Gas flow

Figure 6. Experimental setup for decaying arc dis-charges.

inverter current source is originally used for plasmacutting arcs, and it is rated at 450V/ 300A. In parallelto the arc device, an insulated gate bipolar transistor(IGBT) semiconductor was connected. Switching onthe IGBT commutates the source current from thearc device to the IGBT element to make the arc un-der free recovery condition. In the experiment, wemeasured the source current isource, the arc currentiarc, the IGBT current iIGBT using the current trans-ducers (CT). The arc voltage was measured with aCR potential divider. At different specified timingafter current commutation, the electron density at thenozzle throat was measured using a laser Thomsonscattering method [8].

4.1.1. Laser Thomson scattering methodLaser Thomson scattering (LTS) is well used for pre-cise measurements of electron density in arc plasmas.When a laser light is injected to an arc plasma, freeelectrons in the arc plasma are excited by electro-magnetic field of the laser light, resulting in the lightscattering. This is called Thomson scattering. TheLTS method yields local electron density and electrontemperature in plasmas with high spatial and tem-poral resolutions without LTE assumption. In caseof the arc plasma which has a short Debye length, aincident laser light with a wavelength larger than theDebye length is often used from the electron term todetermine the electron density and electron temper-ature. We have measured the electron density in anarc under free recovery condition for our arc devicedepicted in Fig. 5 without LTE assumption by LTSmethod [8]. In this study, the second harmonic lightof an Nd:YAG laser at a wavelength of 532 nm wasused for LTS. The 90° scattered light from the laserpath was detected.

Figure 7 indicates an example of LTS spectrum fromthe arc in Ar/20%SF6 at a flow rate of 100 L/min [8].We used an 2D-ICCD camera as a detector, the LTSspectra along the laser path, corresponding the radialdirection of the arc, were simultaneously obtained as

Figure 7. Laser Thomson scattering spectrummeasured for Ar/SF6 arcs and theoretical fittingcurves [8].

indicated in Fig. 7 (a). Figure 7 (b) shows the mea-sured LTS spectrum at the center of the arc, and thetheoretical curves of LTS for different electron densi-ties. In this case, the electron density and the electrontemperature were estimated to be 4.5×1022 m−3 and1.6 eV, respectively, by fitting the theoretical curve tothe measured spectrum.Figure 8 presents the time evolutions in the mea-

sured electron density at the center position in nozzlethroat region in Ar/SF6 arcs under free recovery con-dition. The electric current was changed from 50Ato 0A at t = 0 µs. The gas flow rate of Ar/SF6 is100L/min. As seen, the electron density reaches to8×1022 m−3 at 50A at t = 0 µs. After current downto 0A at t > 0 µs, the electron density decays almostexponentially. In particular, the 100%SF6 arc has amost rapid decay in the electron density with a timeconstant of 10µs. In this way, the electron densitycould be determined for decaying arcs at differentgas mixture and different gas kinds without LTE as-sumption. The comparison of the results by such LTSmethod with the theoretically calculated result in timeevolution in the electron density will be introduced inlater section.

4.1.2. Shack-Hartman methodRecently, two-dimensional distribution of electron den-sity in a plasma is measured by Shack-Hartmann typelaser wavefront sensor [9]. Figure 9 shows the ba-sic concept of a Shack-Hartmann sensor for measur-ing electron density distribution in an arc plasma.A Shack-Hartmann sensor is composed of an imagesensor, e.g. an ICCD camera, and a sheet of micro-lens arrays. Micro-lens arrays convert the localizedwavefront gradients of a laser beam into the shifts

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Figure 8. Temporal evolution in measured electron density in Ar/SF6 (40, 60, and 80% SF6) arcs current commutationunder free recovery condition [8].

of the focal spot positions. A laser beam with theflat wavefront is irradiated to the arc plasmas. Thelaser wavefront profile through the plasma is locallydistorted by different refractive indexes from the lo-cal electron density in the plasma. This distortedwavefront makes the shifted focal spot positions bythe micro-lens array. This shifted spot positions weremeasured by the imaging sensor. This shifted dis-placement depends on the gradient in electron density.Thus, the electron density profile can be obtainedwithout LTE assumption.

Figure 10 indicates the two-dimensional electrondensity distribution at t = −10, 10, 30 and 50 µs aftercurrent commutation from 50A to 0A to producefree recovery condition. The two-dimensional regionof 4.5mm × 4.5mm in the nozzle throat was takenas a region for electron density measurement. TheCO2 gas is supplied from the lower region at a flowrate of 100L/min. At t = −10 µs, the dc arc withan electric current of 50A is established between theelectrodes. As seen in this figure, at t = −10 µs, atwo-dimensional high electron density area can beobtained with magnitudes above 1023 m−3 from up-stream (lower) to downstream (upper). After a cur-rent down to 0A at t > 0 µs, the electron densitydecreases with time under free recovery condition,and the high electron density region becomes nar-rower. At t = 30 µs, the electron density decreasesto 3×1022 m−3. At t = 50 µs, the upstream portionhas the decreased electron density less than 1021 m−3

Such a two-dimensional electron density distributioncan be obtained by Shack-Hartmann method.

x

zy

wavefront

after plasma

microlens

arrayimage sensor

plasma

laser

spot after plasma generation

spot before plasma generation

L0

kth

(k+1)th

(k+2)th

(k-1)th

(k-2)th

(k-3)th

Tk(λ)

Tk+1

(λ)

Tk+2

(λ)

Tk-2

(λ)

Tk-1

(λ)

Tk-3

(λ)

Figure 9. A schematic of a Shack-Hartmann type laserwavefront sensor for measuring electron densities in aplasma [9].

4.2. Comparison of measurement results byLaser Thomson scattering with resultscalculated by chemically non-equilibriummodel

The electron density measured by laser Thomson scat-tering (LTS) method was compared with those calcu-lated by the non-CE model and the LTE model [6].Figure 11 shows the comparison for a N2 decaying arcunder free recovery condition from 50A to 0A. Asseen in this figure, at t = 0–10µs, the measurementresults fairly agree with both those by the non-CEmodel and the LTE model. At t > 10 µs, the LTEmodel predicted a rapid decay in the electron density.However, at t > 10 µs, the electron density measuredby the LTS method is higher than that by the LTEmodel. On the other hand, the non-CE model pre-dicted the electron density fairly agreeing with that

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Y. Tanaka, K. Tomita, Y. Inada et al. Plasma Physics and Technology

µ µ

( / )µ τ ( )tτ

µ µ

µ µ

3 1 

,

ρ3

v

6000 c− −3 1 

T

c T

C

O

 2 1

/( )

Figure 10. Two-dimensional electron density distribution in a CO2 decaying arc plasma at t = (a) 0.1, (b) 10, (c) 30and (d) 50 µs [9].

Figure 11. Comparison of electron density measure-ment results by laser Thomson scattering with calcula-tion results of electron density predicted by chemicallynon-equilibrium model [6].

by the LTS method. The difference in electron densityby the non-CE model from that by the LTE modelis due to consideration of reaction rate of N+

2 + e →N + N. This implies a validity of the non-CE model,and an importance of considering non-CE effect indecaying arcs.

5. ConclusionsThis paper briefly summarizes one recent approachfor switching arcs in Japan: a modeling work of arcplasmas considering non-equilibrium effects in high-pressure high-temperature plasmas, and experimental

works for electron density measurement without LTEassumption. Results indicates an importance of chem-ically non-equilibrium effects in a switching arc.

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