Modeling interaction of thermal plasmas with electrodes

Transcription

1 Univrsidad da Madira Dpartamnto d Física Modling intraction of thrmal plasmas with lctrods Mikhail Bnilov Dpartamnto d Física, Univrsidad da Madira, Portugal ICAMDATA 2008, Bijing, China, Oct. 30, 2008

2 Fundamntal and/or applid rsarch for industrial nds Novmbr 2008: 80 yars sinc th word plasma was introducd for dsignation of an ionizd gas. From 1909 to 1957, Langmuir conductd fundamntal rsarch whil working at GE. Papr by Irving Langmuir in Proc. Nat. Acad. Sci

3 Fundamntal and/or applid rsarch for industrial nds It is amazing how littl nd nginrs to know about undrlying physics in ordr to dvlop an xcllnt product! Ultra High Prformanc/Prssur Lamps - Pur mrcury vapor, 200 bar, th arc gap typically 0.7 to 1.3 mm. - Compactnss, outstanding arc luminanc (brightr than th sun), a wll suitd spctrum, long lif, - Th UHP lamp is th idal light sourc for projction applications. - What is a dominating mchanism of production of light? - For mrcury prssurs abov 200 bar mor light is mittd in th continuum radiation than in spctral lins! - 3 -

4 Fundamntal and/or applid rsarch for industrial nds In principl, givn all our diagnostic possibilitis, w thought that w could pin down th ssntial paramtrs just by varying all kinds of paramtrs and obsrving if that rmovd th problm or not. Howvr, th lamp is so complicatd that it has too many status variabls th approach did not work out, so far. From a lttr from an industrial physicist Modlrs can hlp th industry by dvloping dtaild computational modls capabl of dscribing complx phnomna on th basis of first principls without invoking mpirical and/or fit paramtrs => application-orintd fundamntal rsarch. Transport, kintic, and radiation cofficints ar rquird => th nd for atomic and molcular data. This talk is concrnd with an xampl: modling of intraction of thrmal plasmas (high-prssur arc dischargs) with lctrods

5 Intraction of thrmal plasmas with lctrods: an xampl plasma cathod Th currnt is distributd ovr th front surfac of th cathod in a mor or lss uniform way; th diffus mod. Th currnt is localizd in a rgion occupying a small fraction of th surfac (cathod spot); a spot mod. Sid-on obsrvation of a cathod of an arc discharg in argon. W, R = 0.75 mm, p = 4.5 bar, I = 2.5 A. From S. Lichtnbrg t al

6 Motivation An adquat organization of currnt transfr to lctrods of highprssur arc dvics is of xtrm importanc. Exampl of HID lamps: dgradation of th lctrods, blackning of th walls, Elctrods of high-prssur arc dischargs hav bn undr intnsiv invstigation for many dcads. (Th rviw Elctrod componnts of th arc discharg by G. Eckr, 1961: 600+ rfrncs!) Plasma-lctrod intraction is govrnd by thin layrs nar-lctrod plasma layrs which ar difficult to rsolv xprimntally: vry small dimnsions, xtrm conditions typical for arc dischargs. Diffrnt mods of currnt transfr to lctrods of arc dischargs rprsnt slf-organization phnomna and must b dscribd as such. That was ralizd only rcntly Rliabl xprimntal data and slf-consistnt thortical modls startd to mrg in th 1990s and mostly for cathods

7 Contnts of th talk Introduction Basic physics of nar-lctrod plasmas: why ar th cathod and th anod so diffrnt? Unifid modling of nar-cathod and nar-anod plasma layrs Cathods of high-prssur arc dischargs - Th modl of nonlinar surfac hating - Simulation of diffrnt stady-stat mods - Stability of diffrnt stady-stat mods - Can w control apparanc of spots? - Simulation of nar-cathod phnomna in plasmas of mtal halids What do w know about anods of high-prssur arc dischargs? Conclusions - 7 -

8 Why ar th cathod and th anod so diffrnt? Dominating physical procsss in th narlctrod plasma log n log n i log n Saha T T h log x j 2 /σ = w rad T = T h n = n Saha n = n i Lngh scal Bulk plasma Ys Ys Ys Ys Elctrod radius Layr of thrmal prturbation Layr of thrmal non-quilibrium Ionization layr Spac-charg shath Spac-charg shath ELECT- RODE Ionization layr L = κt / w No Ys Ys Ys tp rad κ m / kn mν No No Ys Ys tn h h h No No No Ys d = D kt k p L Radiationdominatd LTE plasma Layr of thrmal prturbation Layr of thrmal non-quilibrium = a h / No No No No h = U n ε 0 D / i - 8 -

9 Why ar th cathod and th anod so diffrnt? Ion and lctron currnts to th lctrod surfac ar gnratd in th ionization layr. If th shath voltag is zro, ( ) ji = j 0 i = ( ) j = j 0 = D D ia a n d Saha n d Saha n,n i + - n Saha SH IONIZATION LAYER OF THERMAL LAYER NON-EQUILIBRIUM d L tn x If th lctrod is ngativ, If th lctrod is positiv, j j i ( 0) ( sat ) << j, ji = ji = 1+ ( 0) ( sat ) << ji, j = j = 1+ T T h T T h D D ia a n d Saha n d Saha - 9 -

10 Why ar th cathod and th anod so diffrnt? Exampl: Hg lamp p = 30 bar, j = 10 7 A/m n i,n (m -3 ) T,T h (K) E (V/m) x At th dg of th layr of thrmal prturbartion: T h = T = 8,800 K, L tp = 130 µm At th dg of th ionization layr: T h 3,000 K, T 6,000 K, d 0.4 µm Elctron and ion currnts: j (0) = A/m 2 > j j i (sat) = A/m 2 << j n n i n Saha E 10-7 T SH IL TN TP Bulk 3000 T h x (m) x10 5-4x10 5-6x10 5-8x10 5-1x10 6 Paramtrs in th nar-anod layr. T w = 3,000 K, U = V. From N. A. Almida, M. S. Bnilov, and G. V. Naidis

11 Why ar th cathod and th anod so diffrnt? j i (sat) << j < j (0) This is th root caus of th diffrnc btwn opration of th anod and th cathod. On th anod, th rol of th spac-charg shath consists in rplling 3/4 of th lctrons coming to th shath dg from th ionization layr. On th cathod, lctron thrmal conduction from th bulk is insufficint to provid n ndd to transport currnt. An additional hating of th lctrons may com only from acclration in th shath of th lctrons mittd by th cathod surfac. Whil th shath on an anod plays a passiv rol, th shath on a cathod is activ

12 Why ar th cathod and th anod so diffrnt? Exampl: Hg lamp p = 30 bar, j = 10 7 A/m 2 Vry high T ; Vry high lctric filds (300 tims highr than in th nar-anod rgion); Th nrgy flux gnratd in th spaccharg shath and th ionization layr is much gratr than th hat conduction flux from outsid. n i, n (m -3 ) n i n 10-7 n Saha T Paramtrs in th nar-cathod layr. T w = 3,000 K, U = 38 V. From N. A. Almida, M. S. Bnilov, and G. V. Naidis E TN SH IL TP Bulk T h 0 T, T h E (10 3 K) (V/m) x (m) -5x10 7-1x10 8-2x10 8-2x10 8-3x10 8-3x

13 Unifid modling of nar-lctrod layrs Th systm of quations Equations of consrvation of spcis: J α = ω α, α = i,, Nt rats of production of particls in volum ractions: a ω = ω = ω i a = k n n i a k r n i n 2 Transport quations for a wakly to strongly ionizd collision-dominatd plasma (Stfan-Maxwll quations): p β n α α n + β n kt nd α Z αβ αβ C α E + αβ ρα ρ [ p ( n n ) E] ( ) T v v R = 0 α β α i

14 Unifid modling of nar-lctrod layrs Th systm of quations T αβ = m α T m β α + + m m β β T α, D αβ = 3π 16 2kT πm αβ αβ 1/ 2 1 nq ( 1,1) αβ Elctron nrgy quation: nk T m n i ( p v ) a i ( ) ( T T ) + w = h h n D a n Losss of lctron nrgy du to inlastic collisions: n D v i E ( ) w = E ω + i w rad

15 Unifid modling of nar-lctrod layrs Havy-particl nrgy quation: h hp + n Th systm of quations i v E + 2 3nk T m n Poisson quation: ε 0 E = ( ) i i a i ( T T ) + = 0 n i n h n D a n D i Boundary conditions at th surfac of th lctrod n i = 0 T h = T w j jm T w : Tmpratur of th lctrod surfac m n C 4 2kT w = J nc 4 2kT = 5 2 p v + h

16 Unifid modling of nar-lctrod layrs Boundary conditions on th plasma sid ionization n = n = n i S quilibrium T = T = h T q balanc btwn Joul hating and radiation losss Input paramtrs for modling gas, lctrod matrial, p, j, T w Dnsity of th nrgy flux from th plasma to th cathod surfac q c 5 = kt + A J + i i hp 2 A: work function of th cathod matrial ( E A) J + h + h

17 Unifid modling: transport cofficints of th plasma Th binary diffusion cofficints: D αβ 3π 8kT = 32 πm Enrgy-avragd cross sctions for momntum transfr: αβ αβ 1/ 2 1 nq ( 1,1) αβ 1 Enrgy-dpndnt cross sctions ion-atom Q ia ε in monoatomic gass: rsonanc charg xchang. Corrction factor ion-atom: Cross sctions lctron-atom: availabl for inrt gass and Hg. Not nough data for som othr systms of intrst! Corrction factor lctron-atom: Lorntzian formula with th Maxwllian lctron nrgy distribution. Cross sctions lctron-ion: Coulomb intraction. Corrction factor lctron-ion: by Spitzr and Härm formula. Q 1,1 1 2 xp 2 kt 3 0 kt C ia = ( ) ( ) Q 1 d.

18 Unifid modling: transport cofficints of th plasma Thrmal-diffusion cofficints for ions and atoms: Thrmal-diffusion cofficint for th lctrons: intrpolation btwn th Lorntzian formula with th Maxwllian lctron nrgy distribution and th Spitzr and Härm formula. Th thrmal conductivity of lctrons: κ a : th Lorntzian formula with th Maxwllian lctron nrgy distribution. κ i : th Spitzr and Härm formula. Th thrmal conductivity of havy particls: 2,2 2,2 2,2 Th avrag cross sctions Q Q, Q ar rquird. 2,2 : th Spitzr and Härm formula. Q ii ( ) ( ) ( ) = κ a + κ i C i h Ca h 0 2,2 2,2 Q ia Q : not nough data, xtrapolation has to b usd., aa κ ( ) ( ) ( ) aa, ia ii κ = κ + κ hp a i

19 Unifid modling: kintic and radiation cofficints Th ionization rat constant: k i = k dir + k stp Th rat constant of dirct ionization, k dir : G. S. Voronov 1997 A practical fit formula for ionization rat cofficints of atoms and ions by lctron impact: Z = 1 28 Th rat constant of stpwis ionization, k stp : calculatd in a simplifid way, without account of non-quilibrium populations of xcitd stats. Th rcombination rat constant: calculatd in trms of k i with th us of dtaild balancing. Radiation nrgy losss: calculatd in a simplifid way, in trms of th nt mission cofficint, with th us of an intrpolation btwn th valu corrsponding to th LTE plasma (for high n ) and th rat of xcitation of ths stats by lctron impact (for low n )

20 Cathods of high-prssur arc dischargs LAYER OF THERMAL NON-EQUILIBRIUM Th plasma-cathod intraction is govrnd by a thin nar-cathod plasma layr comprising th spac-charg shath and th ionization layr. powr input mittd lctrons ions, plasma lctrons CATHODE BODY NEAR-CATHODE LAYER Sinc this layr is thin, it may b calculatd locally in 1D. A complt solution can b found in two stps: - Solution on th plasma sid: th 1D problm dscribing th currnt transfr across th nar-cathod plasma layr is solvd and all paramtrs of th layr ar dtrmind as functions of T w and U. In particular, functions q = q(t w,u) and j = j(t w,u) ar found. - Solution insid th cathod: th quation of hat conduction is solvd with th boundary condition q = q(t w,u)

21 Cathods of high-prssur arc dischargs This modl may b calld th modl of non-linar surfac hating. Th modl producs multipl solutions, dscribing diffrnt mods of currnt transfr => no ncssity to switch mchanisms by hand in ordr to obtain diffrnt mods! Th modl was proposd by W. L. Bad and J. M. Yos, Tchnical Rport of Avco Corporation, For many dcads, it was virtually forgottn and has bn r-invntd mor than onc. W. Numann, Th Mchanism of th Thrmomitting Arc Cathod (1987): a dtaild prsntation of th modl of Bad and Yos. Ironically, th possibility of xistnc of multipl solutions was not mntiond. Th fact that th modl indd producs multipl solutions dscribing diffrnt mods of currnt transfr was provd in th lat 1990s. Aftr this, th modl has bcom univrsally accptd

22 Solution on th plasma sid: a simplifid modl Equations Th ionization layr: a hydrodynamics dscription Equation of motion of th ion fluid accounting for ion inrtia, ion prssur gradint, lctric fild forc, friction forc du to lastic collisions of ions with nutral particls, friction forc du to ionization of nutral particls. Equation of balanc of th lctron nrgy in th ionization layr. Boundary conditions On th plasma sid of th ionization layr: ionization quilibrium. On th dg of th spac-charg shath: th Bohm critrion. Th spac-charg shath: a kintic dscription Equations A kintic quation dscribing th motion of ions, Th Poisson quation. Boundary condition at th shath dg: th Bohm critrion

23 Enrgy flux from th plasma to th cathod Main mchanisms: hating of th cathod surfac by incidnt ions and cooling du to thrmionic mission. Th dpndnc of q on T w is non-monotonic. In th convntional hat xchang, q(t w ) is falling! Th rising sction of th dpndnc q(t w ) is a sourc of thrmal instability q (10 8 W/m 2 ) Plasma approachs full ionization and th ion hating gts saturatd U=14 V Ion hating incrass fastr than thrmionic cooling T w (10 3 K) W, Ar, 1 bar. From M. S. Bnilov and M. D. Cunha

24 Gnral pattrn of diffrnt mods 18 U (V) cntral spot and two dg spots four dg spots thr dg spots 12 cntral spot 10 I (A) two dg spots diffus mod on dg spot Currnt-voltag charactristics of diffrnt mods. W, R = 2 mm, h = 10 mm, Ar, 1 bar.,,,: bifurcation points. From M. S. Bnilov, M. D. Cunha, and M. Carpaij

25 Pattrn of stability of diffrnt mods Mods with a spot at th cntr or with multipl spots ar always unstabl. Th only mods that that can b stabl ar th diffus mod and th high-voltag branch of th 1 st 3D spot mod. Th transition btwn ths two mods is nonstationary and accompanid by hystrsis. U (V) diffus mod, unstabl sction 1 st spot mod, stabl sction 1 st spot mod, unstabl sction diffus mod, stabl sction I (A) 600 W, R = 2 mm, h = 10 mm, Ar, 1 bar. From M. S. Bnilov and M. J. Faria

26 Charactristics of th diffus mod 50 U (V) 40 1, : h = 24 mm, R = 0.75 mm. 2, : h = 25 mm, R = 0.5 mm. 3, +: h = 15 mm, R = 0.3 mm T w (10 3 K) h = 24 mm h = 29 mm h = 19 mm I (A) I (A) 8 Currnt-voltag charactristics of th diffus mod. Tmpratur at th cntr of a cathod oprating in th diffus mod. R = 0.75 mm. W, Ar, 2.6 bar. From M. S. Bnilov and M. D. Cunha Exprimnt: Bochum

27 Comparison with th xprimnt, diffus mod 40 P (W) 30 R = 0.5 mm 25 Q c, Q r (W) 20 Q r, h = 30 mm Q r, 20 mm R = 0.3 mm 10 Q c, 20 mm 10 5 Q c, 30 mm I (A) Total powr losss of a cathod oprating in th diffus mod. W, h = 20 mm, Ar, 2.6 bar. From D. Nandlsätdt t al Modlling: Madira I (A) 6 Powr rmovd by hat conduction and irradiatd powr. W, R = 0.5 mm. Ar, 2.6 bar, diffus mod. From M. S. Bnilov and M. D. Cunha Exprimnt: Bochum

28 Charactristics of th diffus and 1 st 3D spot mods diffus mod U (V) [1] [1] [1] diffus mod [2] 50 pyromtry, spot mod Dabringhausn t al 2005 probs, spot mod Dabringhausn t al 2005 U (V) st 3D spot mod, high-voltag branch, Bnilov 2007 spot mod high Scharf t al I (A) I (A) 8 R = 0.3 mm R = 0.75 mm, rounding 100 µm Currnt-voltag charactristics. W, h = 20 mm, Ar, 2.6 bar. [1]: L. Dabringhausn t al [2]: M. S. Bnilov, M. Carpaij, and M. D. Cunha Which branch of th 1 st 3D spot mod is obsrvd in th xprimnt? 20 spot mod low Scharf t al st 3D spot mod, low-voltag branch, Bnilov 2007 diffus mod

29 Stability of diffrnt mods in xprimntal conditions s In this xprimnt, both th diffus mod and th high-voltag branch of th mod with a spot at th dg ar stabl in th whol currnt rang invstigatd (1A 6A). => No rproducibl diffus-spot transition! U (V) s 0.14 ms -1.7 s s -1.4 s 3.7 ms λ -1 = 29 ms -1.6 s s -0.9 s I (A) 8 W, R = 0.75 mm, h = 20 mm, rounding 100 µm, Ar, 2.6 bar. From M. S. Bnilov and M. J. Faria

30 Ar availabl xprimntal data rprsntativ for arc cathods? Hg, p = 30 bar, j = 10 7 A/m 2 Ar, p = 1 bar, j = 10 7 A/m n i,n (m -3 ) ϕ T,T h (K) ϕ (V) n i,n (m -3 ) ϕ T,T h (K) ϕ (V) n Saha n Saha n i n 10-7 T w = 3,000 K, planar cathod T T h x (m) n i n 10-6 T w = 3,300 K, 1 mm radius cathod From N. A. Almida, M. S. Bnilov, and G. V. Naidis T T h x (m) Th physics of th nar-cathod layr is similar!

31 Can w control apparanc of spots? Stady-stat spots U (V) Diffus mod flat front surfac rounding 50 µm rounding 100 µm 70 U (V) st 3D spot mod Solid: stabl branch Dottd: unstabl branch rounding 100 µm rounding 50 µm flat front surfac I (A) I (A) 2 W, R = 0.5 mm, h = 12 mm, Ar, 2 bar. From M. S. Bnilov and M. D. Cunha Rounding of th cathod dg dos not affct th diffus mod but may rndr it th only possibl on, i.., absolutly stabl

32 Can w control apparanc of spots? Transint spots I t R. Böttichr, W. Grasr, and A. Kloss 2004 R. Böttichr and M. Kttlitz 2006 P. G. C. Almida, M. S. Bnilov, and M. D. Cunha 2008 Initial and final stady stats ar diffus. If th variation of currnt is blow a crtain thrshold, th diffus mod is prsrvd during th transition. Othrwis, a transint spot appars

33 Can w control apparanc of spots? COST-529 standard lamp, currnt jumps from 0.3 A to 1.3 A. W, R = 0.35 mm, h = 11 mm, rounding 25 µm, Hg, 4 bar. P. G. C. Almida, M. S. Bnilov, and M. D. Cunha Possibility of prvntion of spots: I t P. G. C. Almida, M. S. Bnilov, and M. D. Cunha

34 A fr on-lin modlling tool A 2D simulation tchniqu has rachd a point at which it can b automatd. A fr on-lin tool for 2D simulation of currnt transfr to thrmionic cathods: Thr is no nd to study thortical paprs in ordr to b abl to us th tool!

35 Cathod of arcs in plasmas of mtal halids Th plasma-producing gas in mtal halid (MH) lamps rprsnts a mixtur of molcular and atomic spcis composd of Hg and (som of) th following lmnts: Na, Tl, Dy, Sc, Cs, I, and Ar. Th nutral spcis takn into account in this modl ar th following: Hg, Na, Tl, Cs, Dy, Sc, I, NaI, TlI, CsI, DyI, DyI 2, DyI 3, ScI, ScI 2, ScI 3. Ion spcis producd in ionization of atoms ar Hg +, Na +, Tl +, Dy +, Sc +, Cs +, I +, I -. Th prsnc of molcular ions is nglctd. Partial composition of a plasma at th dg of th ionization layr is dtrmind by quations of local balanc of production and loss of vry plasma spcis in volum ractions for givn lmntary composition of th mixtur and givn valus of th havy-particl tmpratur T h, lctron tmpratur T, and gas prssur p. Thr is no dtaild balancing btwn dirct and rvrs ractions at th dg of th ionization layr, thrfor th calculation rquirs, in addition to thrmodynamic data, also kintic data (in contrast to th cas of an LTE plasma, T h = T ). Availabl kintic data ar scarc!

36 MH plasma composition at th dg of th ionization layr Undr quilibrium conditions, at T = T h, th dnsitis of fr mtal atoms ar smallr than th dnsitis of mtal iodids. As T incrass, iodids dissociat in collisions with lctrons n i (m -3 ) TlI NaI Hg Na 4 8 T (10 3 K) 12 Dnsitis of nutral spcis. p = 5 bar, T h = 2500 K, Hg:Na:Tl:I=0.89:0.005:0.05: From M. S. Bnilov, M. D. Cunha, and G. V. Naidis Tl I

37 Variation of th work function of th cathod surfac Calculation with th us of data from J. Almanstöttr, B. Ebrhard, K. Günthr, and T. Hartmann 2002 (for Na-Hg) and R. F. Wlton 2002 (Cs-Hg). Data for othr systms ar ndd! Evn smalls amounts of th alkali vapor in th plasma, of th ordr of 1% and lss, can produc a significant ffct on th work function. Th dcras of th work function producd by Cs is strongr than that producd by Na and coms into play in a widr rang of T w A f (V) Z Cs =10-2 Z Na =10-2 Na-Hg Cs-Hg T w (10 3 K) Work function of tungstn covrd by a monolayr of Na or Cs in Na-Hg or Cs-Hg plasmas. p = 5 bar. From M. S. Bnilov, M. D. Cunha, and G. V. Naidis 2005.

38 Diffus mod and its stability, Na-Hg plasma Formation of th sodium monolayr affcts th diffus mod of currnt transfr in th sam dirction that th prsnc of mtal atoms in th gas phas dos: T w and U dcras, rang of stability of th diffus mod xpands. Formation of th sodium monolayr producs only a modrat ffct. 50 U (V) T w : Hg T w : Na-Hg, Z Na =1% U: Hg U: Na-Hg, Z Na =1% 4 T w (10 3 K) Lins: maximal tmpratur of 0 0 th cathod surfac and CVC s. Diffus mod on a tungstn I (A) 50 cathod, p = 5bar, R =1mm, h = 14.5mm. Points: stability limit of th diffus mod with Z Na = 0.08% on a covrd cathod (th full circl); in th Na-Hg plasma with Z Na = 0.08% on a clan cathod (th opn circl); in th Hg plasma (th squar). From M. S. Bnilov, M. D. Cunha, and G. V. Naidis

39 Diffus mod and its stability, Cs-Hg plasma Formation of th csium monolayr changs th plasma-cathod intraction dramatically: th tmpratur of th cathod surfac dcrass vry strongly, th diffus-mod currntvoltag charactristic bcoms N-S-shapd. Th qustion of stability of th diffus mod in th Cs-Hg plasma rquirs an additional mathmatical tratmnt. 50 U (V) U: Hg T w : Hg T w : Cs-Hg, Z Cs =0.01% U: Cs-Hg, Z Cs =0.01% I (A) 50 4 T w (10 3 K) Maximal tmpratur of th cathod surfac and CVC s. Diffus mod on a tungstn cathod, p = 5bar, R = 1mm, h = 14.5mm. From M. S. Bnilov, M. D. Cunha, and G. V. Naidis

40 Thr is a lot mor to say about arc cathods Modlling of cathods of a complx shap consisting of svral pics mad of diffrnt matrials; Thory of spots on larg cathods; Th maximum tmpratur of th cathod surfac (tmpratur insid th spots, tmpratur of small cathods at vry high currnts);

41 What do w know about anods of high-prssur arcs? F. G. Baksht, G. A. Dyuzhv, N. K. Mitrofanov, and S. M. Shkol'nik, Tch. Phys. 42, 35 (1997). Exprimntal, also data at low currnts. Multipl anod constriction on anods is shown to b a rsult of an instability in th nar-anod rgion (rathr than in th bulk plasma) T. Amakawa, J. Jnista, J. Hbrlin, and E. Pfndr, J. Phys. D: Appl. Phys. 31, 2826 (1998). Dtaild numrical simulations, no shath S. M. Shkolnik, in Encyclopadia of Low-Tmpratur Plasmas, ditd by V. F. Fortov (Nauka, Moscow, 2000), pp A usful rviw papr V. A. Nmchinsky, J. Phys. D: Appl. Phys. 38, 4082 (2005). Thortical, physics of nar-anod layr in atmosphric prssur nitrogn M. Rdwitz, L. Dabringhausn, S. Lichtnbrg, O. Langnschidt, J. Hbrlin, and J. Mntl, J. Phys. D: Appl. Phys. 39, 2160 (2006). Dtaild xprimntal invstigation at currnts A, Ar, X, Kr, 1-10 bars

42 What do w know about anods of high-prssur arcs? Enrgy flux to th anod surfac is formd in th layrs of thrmal prturbation and of thrmal nonquilibrium. Is physics of ths layrs in th xprimnt with inrt gass and in industrial dvics th sam? SHEATH ELECT- RODE IONIZATION LAYER log n log n i log n Saha T T h BULK PLASMA LAYER OF THERMAL PERTURBATION LAYER OF THERMAL NON- EQUILIBRIUM log x Hg, p = 30 bar, j = 10 7 A/m 2 Ar, p = 1-10 bar, j = 10 7 A/m 2 L tp = 0.13 mm << lctrod diamtr => j 2 /σ = w rad in th bulk plasma L tp = mm lctrod diamtr => j 2 /σ w rad in th bulk plasma => Th physics of th layr of thrmal prturbation may b diffrnt

43 What do w know about anods of high-prssur arcs? Simulation of th arc plasma-anod intraction rquirs modlling not only of th nar-anod layr, but also of th adjacnt bulk plasma. Nar-anod layrs ar dscribd by th sam quations that nar-cathod layrs and may b simulatd by mans of th sam cod; an xampl has alrady bn shown. Mthods of simulation of bulk of arc dischargs ar wll dvlopd. => Thr ar no major problms in th modlling

44 Conclusions Th plasma-cathod intraction in high-prssur arc dischargs is govrnd by a thin nar-cathod plasma layr. A slf-consistnt and univrsally accptd thory and simulation mthods hav bn dvlopd and validatd xprimntally. Thr is a possibility of simulation of complx 3D gomtris, nonstationary ffcts, complx mixturs,... Th plasma-anod intraction in high-prssur arc dischargs dpnds not only on a thin nar-anod layr, but also on th adjacnt part of th bulk plasma, and is thrfor mor difficult for xprimntal invstigation. Du to advancs achivd in numrical modlling of nar-cathod layrs and of th bulk plasma, numrical simulation of anod phnomna is, at last in principl, straightforward. Quit a bit of atomic and molcular data is still lacking!