6. Gaseous Breakdown 6.1 Generation of ionized particles 6.2 Townsend discharge and breakdown criteria (Paschen’s law) 6.3 Streamer discharge 6. Gaseous Breakdown Pulsed Power Engineering, 2014 6.1 Generation and degeneration of ionized particles 3. Basic Pulsed Power Circuits and Energy Storage Systems Pulsed Power Engineering, 2011 Genera&on of Ionized Par&cles in Gases Collisional ioniza&on + X + e → X + e + e Electron collisional ioniza&on X * + e → X + + e + e * + X + Y → X + Y + e Penning ioniza&on Thermal ioniza&on X + X + KE → X + X + + e Photo-‐ioniza&on X + hν → X + + e 6. Gaseous Breakdown n=∞ n=** n=* X* n=∞ n=1 hc ≥ φj λ X Y Pulsed Power Engineering, 2014 Degenera&on of Ionized Par&cles in Gases Electron a;achment X + e → X − + hν Radia&ve a;achment − XY + e → X + Y Dissocia&ve a;achment X + Y + e → X- + Y X - + hv → X + e Photo-‐detachment XY + + e → (XY)* → X * + Y X + + Y − → X + Y + hν − X + Y → XY + hν X + Y + Z → XY + Z X + + Y − → X* + Y* 6. Gaseous Breakdown 3-‐body recombina&on X +e+Y→X +Y + Radia&ve recombina&on * − Ea 0 X + + e + e → X* + e + 3-‐body a;achment Recombina&on X + + e → X * + hν + φi Electron -‐ Ion dissocia&ve recombina&on Radia&ve recombina&on Ion -‐ Ion 3-‐body recombina&on Charge exchange recombina&on Pulsed Power Engineering, 2014 Electron Emission from Electrode Electron energy at the far distance from the electrode Electron energy Poten8al barrier and electron energy distribu8on func8on at a metal surface in vacuum Poten8al barrier e2 − 4πεx Fermi Level ξ フェルミレベル Poten8al barrier under an e-‐field Electron energy distribu8on func8on Vacuum 金属内 Metal TABLE: Work func8ons eφ [eV] Material Al Ba C Cu Li Mo W BaO SrO K Ca Ni eφ 4.25 2.11 2.5~4.7 4.33 2.1~2.9 4.15 4.54 0.99 1.27 1.8~2.5 2.2~3.2 5.02 Material Zr Cs Hg Ta Th Ai2O3 CaO W-Cs W-Ba W-Th W-Zr eφ 4.2 1.8~1.96 4.52 4.04 3.35 3.9 1.77 1.36 1.56 2.63 3.14 6. Gaseous Breakdown Pulsed Power Engineering, 2014 A;achment ANachment of free molecules onto the electrode surface Chemical bond → Chemical aNachment Intermolecular force → Physical aNachment Thermionic emission Thermal electron emission occurs because the thermal energy given to electrons exceeds the poten8al energy barrier, known as work func8on, of the metal. Electron current density is given by " eϕ % j = AT exp $ − ' # kT & 2 Richardson’s Equa8on T is a temperature，A is an emission coefficient depending upon the electrode material. Thorium TABLE: Emission coefficient A Cathode materials W W-O-Ba Ba oxides Th Th carbide C A ［A/cm2/K2］ 70 3 40 3 550 48 6. Gaseous Breakdown Pulsed Power Engineering, 2014 Scho;ky effect An electric field applied to the thermal cathode E lowers the surface poten8al barrier by an amount ΔW, and increases the emission current. ϕ ! = ϕ − ΔW = ϕ − e eE / 4πε 0 # eϕ " & 2 j = AT exp % − ( Electron emission current with E $ kT ' Field emission (tunnel effect) Field emission in pure metals occurs in high electric fields (108-‐109 V/cm) and strongly dependent upon the work func8on. This is explained by quantum tunneling of electrons. $ −6.83 × 109 ϕ 2 3 ' 6.2 × 10−2 ξ 1 2 E2 )) j≅ exp && − 12 E (ϕ + ξ )ϕ % ( 6. Gaseous Breakdown Fowler-‐Nordheim Eq. Pulsed Power Engineering, 2014 Secondary electron emission Electrons are subsequently emiNed from the surface by the incident of energe8c par8cles, whose energy exceeds the work func8on of the material. → γ effect Einj > ϕ The number of electrons produced by a single par8cle is named the secondary electron emission coefficient or gamma (γ) coefficient. secondary electron energe8c par8cle surface TABLE: Secondary electron emission coefficient γ Material Li K Cu MgO BaO, SrO W Pt Mo NaCl γ 0.5 0.7 1.3 6~7 5~12 1.5 1.6 1.3 6~7 6. Gaseous Breakdown Pulsed Power Engineering, 2014 Photoelectron emission Electrons are subsequently emiNed from the surface by the incident of energe8c photons, whose energy exceeds the work func8on of the material. → Einstein’s photoelectric effect hc >ϕ Photon energy：hc/λ λ The number of electrons produced by a single photon is named the quantum efficiency, ηQ. Materials with large ηQ is likely to be used as photocathodes. photon surface Photocathode： S10：Ag-‐Bi-‐O-‐Cs, S11：Sb-‐Cs, S20：Na-‐K-‐Sb-‐Cs Quantum efficiency as a func8on of the wavelength of light 6. Gaseous Breakdown Pulsed Power Engineering, 2014 6.2 Townsend discharge and Breakdown criteria (Paschen’s Law) 6. Gaseous Breakdown Pulsed Power Engineering, 2014 Townsend Discharge E-field Collisional ioniza&on (α effect) Under an electric field, electrons are accelerated neutral and collide with neutral par8cles to ionize them. ion The number of ions produced per unit length electron along the field is named the collisional ioniza8on Electron collisional ionization coefficient or α coefficient. Increase in electrons for the length dx Electron multiplication owing to electron collisional ionization 6. Gaseous Breakdown Pulsed Power Engineering, 2014 Townsend Discharge due to γ Effect Anode Cathode n0 n0 e αd n0 (eαd − 1) n0 (eαd − 1) = n0 M γMn0 eαd γMn0 (eαd − 1) γn0 M Total current flowing between the electrodes can be αd I e 0 I = 1 − γ (eαd − 1) Since α is exponen8ally increased with increasing the field strength, the current depends on the field strength significantly. γM 2 n 0 (γM )2 n0 (γM )2 n0 eαd (γM )2 n0 (eαd − 1) electron flow posi8ve ion flow nega8ve ion flow 6. Gaseous Breakdown Pulsed Power Engineering, 2014 Electron A;achment (η effect) Electrons are likely to aNach electronega8ve par8cles to produce a nega8ve ions. The number of nega8ve ions produced per unit length along the field is named the aNachment coefficient or η coefficient. Increase in electrons for the length dx dn = −nηdx ∴n = n0 e−ηx In the situa8on that α and η effects present simultaneously, ( α −η )x n = n e （α -‐ η）： Effec8ve ioniza8on coefficient 0 For example, SF６: "E % α = 27 $ − 87 ' p #p & 6. Gaseous Breakdown E > 89p [kV/cm] increase E < 89p 〃 decrease Pulsed Power Engineering, 2014 Breakdown Criteria (Paschen’s Law) Breakdown voltage of a gap VS is derived from the Townsend breakdown criteria and the following experimental rela8on between α, E and p, " B % α p = Aexp #− & $ E p' TABLE: Constants A, B Paschen’s curve (N2) 6. Gaseous Breakdown Pulsed Power Engineering, 2014 Physical Interpreta&on of Paschen’s Curve Important facts: ・Electron are accelerated in the electric field. Vbd Left Right e-‐field, mean free path ・Electrons of which energy is sufficiently large collide with neutral par8cles and ionize them. Vmin pdmin ・Posi8ve ions collide with cathode and generate (secondary) electrons. ・Discharge begins when the space between anode and cathode are filled with charged par8cles. p⋅d Minimum (pd) of Paschen’s curve Right (i) p varied at constant d (ii) d varied at constant p Ler (iii) p varied at constant d (iv) d varied at constant p 6. Gaseous Breakdown Pulsed Power Engineering, 2014 (A) Right-‐hand Side of Paschen’s Curve ( pd>(pd)min) Feature Vbd ・ Presence of plenty of par8cles between electrodes ・Short mean free path Case(1) d: fixed, p: varied 6. Gaseous Breakdown Vmin pdmin p⋅d Pulsed Power Engineering, 2014 Case(2) d: varied, p: fixed Vbd Vmin ⊕ E E Long gap 6. Gaseous Breakdown pdmin p⋅d ⊕ Short gap Pulsed Power Engineering, 2014 (B) LeV-‐hand Side of Paschen’s Curve ( pd <(pd)min) Feature ・Large mean free path ・ Electron energy is sufficiently large to ionize neutral par8cles. Case(3) d: fixed, p: varied 6. Gaseous Breakdown Vbd Vmin pdmin p⋅d Pulsed Power Engineering, 2014 Case(4) d: varied, p: fixed Vbd Vmin pdmin p⋅d ⊕ ⊕ Short gap 6. Gaseous Breakdown Long gap Pulsed Power Engineering, 2014 6.3 Streamer Discharge 6. Gaseous Breakdown Pulsed Power Engineering, 2014 Theory of Streamer Discharge Townsend Discharge (Condi8on: low pressure, short gap, low over-‐voltage） このような条件下では、１個の電子なだれによって生 成される空間電荷数が少なく，空間電荷による電界 歪みは無視できる。一個の電子なだれによって生成さ れた空間電荷数がある臨界値以下である。 exp(αd ) < N cr ＋ E ー Ncr：電荷の臨界値～108個 例） N2ガス，p =760 Torr，d =1 cm を考える． 直流絶縁破壊電圧 約31 kV，換算電界 E/p = 41 V/(cm･Torr)． 印加したパルス電圧の過電圧率 K を10％とすれば，E/p = 45 V/(cm･Torr)． このとき，電子なだれで生成される荷電粒子数 N は， N = exp(αd ) ≈ 4 × 106 6. Gaseous Breakdown Pulsed Power Engineering, 2014 荷電粒子はなだれ内で拡散しながら増殖 していくため，頭部の半径 r は拡散方程 式から次式のようになる。 r= 陰極 陽極 印加電界E0 4 Dt ＋ —― 電子なだれヘッドの正イオン数をN，電 子の拡散係数をDとすれば，空間電荷 による電界Esは次のようになる。 eN Es = 4πε 0 r 2 長ギャップ，圧力大，高過電圧率： このような条件下では、電子なだれによっ て生成される空間電荷量が増加し，それ による電界歪みが無視できず，荷電粒子 の生成が促進される。 ⇒ Streamer Discharge 6. Gaseous Breakdown E(x) E0 d Distor8on of electric field due to the space charge of electron avalanche Pulsed Power Engineering, 2014 Posi&ve Streamer, Nega&ve Streamer 陽 極 陽 極 二次なだれ 放電光 (a) 陰 極 (b) ストリーマ進展機構（ミークの理論） Posi8ve streamer (Cathode heading streamer) 6. Gaseous Breakdown ストリーマ進展機構（レータの理論） 負ストリーマ、陽極向けストリーマ Pulsed Power Engineering, 2014 Townsend Discharge and Streamer Discharge 右図は，タウンゼント放電か らストリーマ放電への移行が 起きるときの pd 積が，過電 圧率 K に対してどのように変 化するかを示したもの。 この境界は，さまざまな要因 ，例えば γ 効果による陰極表 面上での二次電子生成，な だれ内での電子増倍，初期 電子の生成法などに依存する。 Streamer Townsend タウンゼント放電からストリーマ放電への移行 6. Gaseous Breakdown Pulsed Power Engineering, 2014 Time-‐resolved observa&on of streamer in Air Cable Blumlein line 120 ns, 50 kV ICCD camera 1.5ns gate (10ns) Pickup coil Triggered gap switch Voltage divider Pickup coil Trigger module Discharge chamber wire-‐cylinder Wire diam. 0.5 mmf Cylinder diam. 70 mmf 6. Gaseous Breakdown Oscilloscope 500 MHz Discharge chamber (40ns) Computer Pulsed Power Engineering, 2014 Time-‐Evolu&on of Posi&ve Streamers Cylindrical coaxial electrode system 5 ns 35 ns 15 ns 45 ns 25 ns 65 ns 5~105 ns dt = 100 ns Cylinder diam. 70 mm Wire diam. 0.5 mm Voltage 50 kV Time resolu8on 1.5 ns (exposure 8me) 6. Gaseous Breakdown Pulsed Power Engineering, 2014 Temperatures of Discharge Plasma, Pressure dependent Conven8onal Discharge Plasmas 1 atm. Temperature [K] 105 ● Low pressure glow discharges Non-‐thermal plasma (Te ≫ Tg) Te 4 10 Large volume Low intensity light emission 3 10 Large photon energy Tg → UV emission 2 10 10-‐4 10-‐2 1 102 104 106 ● High pressure arc discharges Pressure [Torr] Thermally equilibrium plasma (Te 〜 Tg) Electron temperature and gas temperature in Mercury (Hg) discharges Small volume High intensity light emission Low photon energy → visible emission Novel technologies: Pulsed Discharges, High-‐Frequency Discharges
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