ECE507 - Plasma Physics and Applications Lctur 7 Prof. Jorg Rocca and Dr. Frnando Tomasl Dpartmnt of Elctrical and Computr Enginring
Collisional and radiativ procsss All particls in a plasma intract with ach othr through lastic and inlastic collisions intrchanging nrgy and giving origin to nw particls and diffrnt xcitation stats Elctrons N Ions N(z) ρ() Photons Two or mor particls can intract simultanously Collisions btwn lctron and atoms can crat ions and fr lctrons Collisions btwn ions and lctrons can rsult in nutral atoms Collisions btwn photons and atoms can crat ions and fr lctrons, tc For ach collisional procsss thr is also an invrs procsss which can occur A+B C+D Invrs procss ECE 507 Lctur 7 2
Collisional and radiativ procsss Th collisions btwn fr lctrons and atoms (ions) can b classifid into: Bound-bound transitions Bound-fr transitions Fr-bound transitions Fr-fr transitions E i Continuum (fr lctrons) Enrgy Fr-Bound Bound-Bound n = 4 n = 3 n = 2 - Bound-Bound Bound-Fr If th kintic nrgy is consrvd th collision is lastic All th collisions in th diagram ar inlastic n = 1 ECE 507 Lctur 7 3
Exampls of collisional and radiativ procsss 1. Elctron impact xcitation A fr lctron with kintic nrgy K gratr than th nrgy E sparating two stats of an atom (ion) can promot th atom to th xcitd stat. Notic that n can b th ground stat or any xcitd stat of th atom. E n+1 E A A K n n1 KΔE A n+1 Th invrs procss is: E n A n Whr n = any quantum stat of th atom A 2. Elctron impact d-xcitation A n1 A K-E K n In this suprlastic procss th fr lctron gains kintic nrgy. E n+1 E E n A n+1 A n ECE 507 Lctur 7 4
Exampls of collisional and radiativ procsss 3. Elctron impact ionization A fr lctron with kintic nrgy K gratr than th atom (ion) ionization nrgy E z can ioniz th atom or ion, incrasing its charg z and crating an additional fr lctron E z+1 A z+1 - E z A z For an lctron with K > E z (K) A z (K-(E (z) E)) A z1 ( E) E = kintic nrgy of th jctd lctron Notic th atom (ion) can b in any xcitd stat. Ionization incrass th charg stat of th atom or ion z z+1 Th invrs procss is collisional rcombination. ECE 507 Lctur 7 5
Exampls of collisional and radiativ procsss 4. Collisional (3 body) rcombination A z1 ( E) (K-(E (z) E)) A z (K) Notic 3 bodis intract E z+1 A z+1 - E z A z On of th lctrons rcombins and th othr gains kintic nrgy. Collisional Rcombination E i Continuum (fr lctrons) Sinc th procss is most probabl whn th fr lctron gains littl kintic nrgy th atom (ion) most probably will b cratd in a highly xcitd stat. Enrgy - Bound-Bound Bound-Bound Bound-Fr n = 4 n = 3 n = 2 n = 1 ECE 507 Lctur 7 6
Exampls of collisional and radiativ procsss 5. Photo-xcitation If th nrgy of a photon h E E n+1 A n+1 E h E n A n h An An 1 Th invrs procss is radiativ dcay or spontanous mission A n1 A n h Spontanous mission is rsponsibl for most of th light producd by th glow dischargs and othr cold low dnsity plasmas. ECE 507 Lctur 7 7
Exampls of collisional and radiativ procsss 6. Photo-ionization If th nrgy of a photon (E i = ionization nrgy) h > E i Continuum (fr lctrons) K h A z A z1 (K) Photoionization h As usual th kintic nrgy of th lctron will allow for consrvation of nrgy. Th invrs procss is photo-rcombination or radiativ rcombination. 7. Radiativ rcombination (2 body rcombination) A z1 (K) A z h Continuum (fr lctrons) Radiativ rcombination tnds to favor th population of low laying stats Th photons producd contribut to a continuum spctra ECE 507 Lctur 7 8
Intnsity Exampls of collisional and radiativ procsss 8. Brmsstrahlung (from th Grman braking radiation ) (K) A z A z K-h h - b V + h Brmsstrahlung radiation occurs prdominantly whn an incidnt lctron is acclratd as it passs a nuclus, causing it to radiat. Collisions corrsponding to diffrnt impact paramtrs b caus diffrnt acclrations rsulting in photons with diffrnt nrgis, givn origin to a broad spctrum of raction. Th invrs procss acclrats lctrons and is calld invrs brmsstrahlung h (K) Az Az K h Photon nrgy Light mission from Bound-Bound transitions Brmsstrahlung continuum ECE 507 Lctur 7 9
Collisional and radiativ procsss Collision cross sction and man-fr path Whn an lctron collids with a nutral atom no forc is flt until th lctron is clos to th atom on th scal of atomic dimnsions (th collisions ar lik billiard balls collisions). Thrfor, w can considr th atom as ssntially a billiard ball of cross-sctional ara No collision Collision No collision If th lctron trajctory falls within th shadow of th cross sction a collision will occur. ECE 507 Lctur 7 10
Collisional and radiativ procsss This can b xtndd to a uniform bam of mononrgtic lctrons ntring a gas with dnsity of atoms N (cm -3 ). X = 0 Vacuum Gas Bam ara A V Th bam flux is = cross sction = N V dx What fraction of th bam rmains as it progrsss a distanc dx into th gas? d # scattrrs A in dx Fraction of obscurd ara d N A dx A N dx ECE 507 Lctur 7 11
Collisional and radiativ procsss dγ Γ Γ (x) N σ dx This rprsnts th statistical avrag for a larg numbr of lctrons and scattrrs. (x)/ 0 can b intrprtd as th probability that an lctron will pntrat th gas a distanc dx without colliding. Th avrag distanc btwn collisions is dfind as th man fr path,. Γ 0 -Nσ x λ x x -N σ x dx 0 -N σ x 0 dx 1 N σ λ 1 N σ Collision man fr path ECE 507 Lctur 7 12
Collisional and radiativ procsss Collision frquncy and collision rat Th numbr of collision pr scond is th collision frquncy. If th lctrons transfr a gas of dnsity N with vlocity V, th collision frquncy is ν V λ V σ V 1 s Collision frquncy is th numbr of collisions ach lctron undrgos pr scond Th total numbr of collisions pr unit volum and pr unit tim is th collision rat, R (cm -3 s -1 ) R N N σn 1 3 cm s Collision rat ECE 507 Lctur 7 13
Collisional and radiativ procsss Collision rat for non-mononrgtic nrgy distributions Inlastic collisions charg mononrgtic bam into distribution with multipl nrgis. Vacuum Gas - Mononrgtic distribution Non-Mononrgtic distribution # lctrons # lctrons Elctrons that collidd Enrgy Enrgy In this cas th collision rat bcoms an intgral R N N 0 F (V) σv) V dv N N σ(v) V or convrting to nrgy with V 1 2 E m 0 F ( E) de 1 2 R N N 0 F (E) σe) 2 E m 1 2 de ECE 507 Lctur 7 14
Collisional and radiativ procsss Unlik th cas of collisions btwn hard balls, th cross sctions for atomic collisions ar nrgy (vlocity) dpndnt Exampl: lctron impact ionization cross sction for Aluminum ECE 507 Lctur 7 15
Collisional and radiativ procsss Elctron impact ionization rat cofficints for diffrnt spcis of aluminum on a loglog scal (lft) and a linar scal (right) ECE 507 Lctur 7 16
Collisional and radiativ procsss Elctron impact ionization cross sction and rat cofficint for th ground stat of Ni-lik silvr to th ground stat of Co-lik silvr ECE 507 Lctur 7 17
Dipol forbiddn transition Dipol allowd transition Uppr lft: lctron impact xcitation cross sction from th ground stat 3d 10 1 S 0 of Ni-lik silvr to th 3d 9 4d 1 S 0 stat (monopol xcitation) Bottom lft: lctron impact xcitation rat cofficint for th sam transition Uppr right: lctron impact xcitation cross sction from th ground stat 3d 10 1 S 0 of Ni-lik silvr to th 3d 9 4p 1 P 1 stat (dipol allowd transition)
Collisional and radiativ procsss Collision rats for non-mononrgtic nrgy distribution Atomic cods Th most accurat possibl collisions rats (or cross sctions) nd to b computd for ach spcific cas. Svral atomic physics cods hav bn dvlopd for this purpos, and som of thm ar accssibl on th wb: 1. Th Flxibl Atomic Cod (FAC) is an intgratd softwar packag to calculat various atomic radiativ and collisional procsss. Dvlopd by M.F. Gu, currntly availabl at http: //kipac-tr.stanford.du/fac/. 2. Los Alamos Atomic Physics Cods, S http://aphysics2.lanl.gov/tmpwb/ for mor information and intractiv onlin vrsion. 3. Robrt D. Cowan, Th Thory of Atomic Structur and Spctra, Univrsity of California Prss, Brkly and Los Angls, California, 1981. Gnral xprssions Howvr, it is usful to hav simpl approximat xprssions of rats that can b usd for ordr of magnitud computations. Usful sourcs of ths includ: 1. Wolfgang Lotz, Elctron-Impact Ionization Cross-Sctions and Ionization Rat Cofficints for Atoms and Ions for Scandium to Zinc, Z. Physik, Vol. 220, pp 466-472, Dcmbr 19, 1968. ECE 507 Lctur 7 19
Collisional and radiativ procsss 2. Rfrncs in: R.W.P. Mc Whirtr, Spctral intnsitis, in Plasma Diagnostics Tchniqus, ditd by R.H. Itddlston and S.L. Lonard. Acadmic Prss, Nw York, 1965. Ths xprssions includ: Elctron impact xcitation of ions (Saton). V Excitation 2 Whr: F E T (n,m) -4 6.5 10 - E(m,n) 3-1 1 F(n,m) xp cm s E T K T (m,n) is th absorption oscillator strngth (m,n) is xcitation potntial in is lctron tmpratur in V K Ionization rat Evaluatd by comparison with Coulomb-Born approximation calibration by Burgss: I E q (T, z, g) (z,g) 2.34 10-7 ionization numbr of q T E 1 4 1 4 (z,g) xp nrgy in V E K T outr lctrons ECE 507 Lctur 7 (z,g) 3 cm s -1 (Hydrogn 1) 20
Collisional and radiativ procsss Radiativ rcombination (Saton) -12 2.05 10 E(z- 1, g) 3-1 cm, 1/2 T (T, z, g) s Notic that th invrs rats can b obtaind by th principl of dtaild balanc spcifically for 3-body rcombination. (E in V) ECE 507 Lctur 7 21
Collisional and radiativ procsss Collisional (3-body) rcombination Th rlation btwn two lvls in thrmal quilibrium is givn by th Saha quation: n Z (q,n) Z (q,n) Z n Z1 q Z dn n dt Solving Z (n,q) Z (n,q) Z1 q Z (n,q) Z n Nxt, th rat quation can b writtn N N - n Z q Z n Z1 q Z1 n Z n 2 B Z (q,n) B Z1 q assuming for th rcombinat ion rat cofficin t I I g 2 g I n g 2 g N N N 2 m k 2 h n 2 m k 2 h T T N 3 2 3 2 -E Z (n, q) k BT 0 -E Z (n, q) k BT stady stat Not that whil th invrs rat cofficint is calculatd assuming stady stat, its valu is basd on th intrinsic proprtis of th ion. As a rsult, it holds outsid of quilibrium. cm 3 s -1 ECE 507 Lctur 7 22
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