Dynamic Contraction of the Positive Column of a SelfSustained Glow Discharge in Nitrogen/Air Flow M.N. Shneider1 In collaboration with M.S. Mokrov2 and G.M. Milikh3 (1)Princeton University of Problem in Mechanics, Moscow, Russia (3)University of Maryland, College Park (2)Institute The work was supported by NSF grant ATM 0833921 and AFOSR under the MURI “Plasma Assisted Combustion” LTP: May 3, 2013 Outline 2 • Introduction: Examples of current contraction in large volume weakly-ionized plasma not confined by walls Thermal-ionization instability •Self-consistent time-dependent 2D model for contraction in molecular gas, stabilized by the external circuit and convective heat loss Full set of equations •Axisymmetrical 2D computations for Nitrogen flow •Air flow Regimes of contraction: “soft” and hysteresis Dependence of crytical current density on gas density and temperature Coexistence of constricted and diffused forms along the density gradients •Conclusions Current Contraction 3 anode u cathode Current contraction in Air: h=10 cm, p=35 Torr; u=100 m/s; ne,0~109 cm-3 From: Velikhov et al, 1982 Contraction velocity: 1 – 100 m/s Much slower than typical streamer velocity (106 m/s) !!! Gas discharge in a large volume laser with close-cycle convective cooling; p=50 Torr; u=230 m/s; CO2:N2:He=1:6:12 N.A.Generalov et al, 1977 Streamer-leader transition Gallimberti [1979, 2002] and later Bazelyan et al.  suggested that the formation of a leader is governed by the contraction of a streamer flash current into a small radius channel Motivation and Objectives The objectives of this work is to develop a self-consistent theoretical model which will allow us to: Predict the critical conditions for contraction caused by the ionizationthermal instability Conduct qualitative and quantitative study of the spatial and temporal evolution of current contraction in a molecular gas flows Carry out parametric study of contraction Study of possibility of generation of multiple hot channels in fast nonequilibrium weakly-ionized gas flows 4 Thermal-ionization Instability Plasma perturbations produce Joule heating, increases T and P in the gas Increase in pressure initiates gas dynamics that reduce N Increases E/N on the channel axes, thus increases ION n jE T N i ( E / N ) n 5 Schematic of the discharge Gas flow along z-axis V0=Vsh+VPC+IR We assume Vsh=const during the process of contraction I ( I R) (VPC V0 Vsh I R) ( E / N ) PC i ( E / N ) Current concentrates intocontractedchannel,where (E/N) 6 Model of Current Contraction Plasma Description •continuity equation for electrons and ions •Poisson equation, finds E Loading Circuit V0 = VPC + IR = const Gas Dynamics •gas dynamics equations for N,T,TV •Finds E/N N2 Instead: continuity equations for ne, ni Poisson equation for E Air Instead: continuity equations for ne, ni, n- Poisson equation for E Instead: Gas dynamics quasineutral plasma: neni div j =0 quasineutral plasma: ne + n- ni div j =0 p=NkT=const N~1/T 7 ne ni n Basic Equations N2 n 0 i n 2 Dambn E( E) ionn n t e E j 0 j E EV EV EV ( EV EV0 ) ( N 0 / N )[EV EV0 (T0 )] D V jeE D t x x y y ; VT T T T ( EV EV0 ) T T0 Ncp1 (T ) (T ) (1 v ) jeE ji E N0cp1 t x x y y VT Lz / u EV N /exp( / kTV ) 1 p NkT const EV0 N /exp( / kT ) 1 Te Te(E/N) dQ V0 V I dt R Q 0 EdS 8 Stability analysis for N2 weakly ionized flow in rectangular duct 9 Simplified system of equations for positive column The equation for plasma density, with n/t = 0 and Damb= 0: vion n 1 / T T0 T 2T jE Nc p1 2 The equation for the gas temperature: Nc p1 yt y max I eE n( y ) e ( y )dy zmax const The discharge current: 0 I governs ns, Ts, Es of homogeneous discharge state The linear stability analysis with respect to small perturbations. Fourier series: n ns n0 exp( 0t ) nm exp( mt ) exp(ikm y ), m 1, 2, , km 2 m /ymax , m T Ts T0 exp(0t ) Tm exp( mt ) exp(ikm y ) , with E Es E0 exp(0t ) m Results: 2 k 0, 0 Ts /T0 (1/ – ene Es /( N0cp1T )) 0 Stable, if assumed, I=const where T0=300 K; N0 corresponds to the chosen pressure and T0 k 0, where k Ts /T0[ ee Es2 (ns vˆionvion/ )/(N0cp1Ts ) 1/ km2 ] 0 vˆion d ln vion / d ln E, χ /Ncp1, km 2 m/ymax k peaks when k1=2π/ymax , which corresponds to development of contracted channel Assumed Conditions (N2) Studied in: Shneider, Mokrov, Milikh Present work Phys. Plasmas 19, 033512 (2012) N2; p=100 Torr; L=2 cm; R=2 cm; V0=28.6 kV; R=500 kΩ; τ=1 ms The initial conditions correspond to the homogeneous stationary solution at a current I = 50 mA plasma density, n0 = 2.81∙109 cm−3 vibrational temperature, TV = 1069.5 K translational temperature, T0 = 302.6 K V=V0-IR=3.5 kV Initial temperature perturbation: T(x,r) = 293∙(1 + 3.5∙exp(−r2/0.152)∙exp(−(x−L)2/0.22)) К Tv(x,r) = 1069.5(1 + 3.5∙exp(−r2/0.152)∙exp(−(x−L)2/0.22)) К 10 Contraction in molecular nitrogen at 100 Torr (2D axysimmetrical) 11 Plasma density (1012 cm-3 ) Translational temperature Vibrational temperature Qualitatively similar to 2D plain: Shneider, Mokrov, Milikh Phys. Plasmas (2012) Contraction in molecular nitrogen at 100 Torr (2D axysimmetrical) longitudinal distributions along the propagating channel Plasma density (a), translational (b) and vibrational (c) temperatures Each curve corresponds to a specific time moment from 1 ms to 1.14 ms with the increment of 0.02 ms. Contraction longitudinal velocity from the model V = 10-100 m/s is close to measured by Akishev et al  N2; p=85 Torr; u=50 m/s 12 Hysteresis (two stable states exist) Frame 001 04 Jan 2012 constricted homogeneous 2000 1750 E, V/cm 1500 1250 1000 750 500 250 0 100 200 I, mA Hysteresis regime of contraction: a uniform “cold” glow discharge can be forced to contraction in a designated time and place. Measured I–V characteristic of glow discharge. Open circles correspond to steady-state partially constricted discharge. N2 at P=100 Torr [Dyatko, Ionikh et al., IEEE TRANS. PLASMA SCI., 39, NOVEMBER 2011]. 13 Contraction in weakly-ionized Air flow in plain 2D geometry14 ne divΓe Qe t n divΓ Q t n divΓ Q t Basic Equations Γe ne eE Dene Γ n E Γ n E E j 0 Qe ( ion a )ne d n e ne n Q a ne d n ii n n ne n Q Qe Q j eΓe Γ Γ EV EV EV ( EV EV0 ) ( N 0 / N )[EV EV0 (T0 )] D V jeE D t x x y y ; VT T T T ( EV EV0 ) T T0 Ncp1 (T ) (T ) (1 v ) jeE ji E N0cp1 t x x y y VT Lz / u EV N /exp( / kTV ) 1 p NkT const EV0 N /exp( / kT ) 1 Te Te(E/N) dQ V0 V I dt R Q 0 EdS In air model: 3 types of charged particles: positive and negative ions and electrons Electron-ion recombination, electron attachment & detachment to oxygen; respective V-T relaxation. Assumed Conditions (Air): plain 2D geometry u Air; p=100 Torr; Lx=2 cm; ymax=2 cm; 103 s I = 10 mA was chosen. Under such current the discharge will certainly contract, i.e. the stratification along the coordinate у transverse to the current occurs. ne=1.5x109 cm-3; n-=1.7x1010 cm-3; n+=ne+nT(x,y) = 298∙(1 + 2exp(−y2/1.52)exp(−(x−d)2/0.32)), Tv(x,y) = 956.3∙ (1 + 4 exp(−y2/1.52)exp(−(x−d)2/0.32), The voltage applied to the discharge gap is 4.36 kV, while the source voltage V0 = 9.36 kV, and the load resistance R = 500 kOhm. 15 Air: plain 2D geometry Temporal evolution of the plasma column voltage and discharge current 16 17 Contraction in the air at different pressure: 2D plain geometry Frame 001 27 Oct 2012 Frame 001 27 Oct 2012 001 27 Oct 2012 p=10 Torr critical current I=50 mA 220 p=100 Torr critical current I=0.75 mA 1500 E, V/cm E, V/cm 2000 p=50 Torr critical current I=3 mA 1500 200 E, V/cm 2500 1000 180 160 1000 140 500 500 120 0 0 5 10 15 I, mA 20 0 0 5 10 15 20 25 30 35 0 10 20 30 I, mA 40 50 60 70 I, mA The "current-voltage characteristic" of the glow discharge in air flow at the different pressures. If I< Icr the discharge is uniform, if I> Icr the contracted channel is formed Contraction in the air occurs at much lover currents than in nitrogen (in accordance with experiment: Akishev et al, 1990) At high pressures – only “soft” regime of contraction No contraction occurs at low pressure, p<2-3 Torr N↓ → Icr↑, coexistence of constricted and diffuse regimes along the density gradient Experiments by Ionikh et al. : glow discharge in tube 18 In a steady state partially constricted discharge one part of the column was constricted while the other part remained diffuse in Ar:N2 mixture Glow Discharge with free boundaries (Yatsenko, 1995) The discharge occurred in Ar at 185 Torr. The gap between electrodes is 6 cm. Left panel U=450 V, I=130 mA. Right panel U=500 V, I=115 A In all these examples: coexistence along the current at N=const Red Sprites, Blue Jets and Elves: Transient Luminosity Events (TLE) 19 Gigantic BLUE JET (Adapted from Lyons et al. 2000) http://www.albany.edu/faculty/rgk/atm101/sprite.htm Leader-Streamer Model of Blue Jets 20 Raizer, Milikh and Shneider Geophys. Res. Letters, December 2006 J. Atmosph. Solar and Terrestrial Physics, 2007 What leader provides: •transfers the high potential U~30-50 MV outside cloud up to h ~ 30 km •attachment losses time τа ~ 10-2 s >> τа(18 km) •plasma conductivity is kept much longer •streamers require field ES << ЕS(18 km) N (h) exp( Mgh / kT ) exp(h / ) 7.2 km contraction Leader channel always stops at h~30 km: coexistence of diffuse (streamer corona) and constricted discharges along the current at N(h) Images of Blue Jet (current along the gradient density) 21 2 timescales were detected: slow (leader like) ~ 100 ms; fast (streamer like) ~ 1-10 ms Kuo et al. J. Phys. D: Appl. Phys. 41 (2008) 234014 Leader channel always stops at h~30 km: coexistence of diffuse (streamer corona) and constricted discharges along the current at N(h) N (h) exp( Mgh / kT ) exp(h / ) 7.2 km Silva, Pasko, GRL 39(2012) Conclusions 22 • For the first time self-consistent 2D model of the current contraction in molecular gas, stabilized by the external circuit and convective heat loss, has been developed • The contraction propagation velocity in N2 was estimated and checked against the existing observations • The contraction in N2 happens in the “hard-mode” regime. A hysteresis “CVC” was obtained • The contraction in Air at high pressures happens in the “soft” regime. A hysteresis “CVC” appears at reduced gas densities • Critical current increases with the gas density decreasing: coexistence of constricted and diffuse states along the current and the density gradient • The model can be applied to analyze the critical conditions and simulate transient processes in medium pressure flow-stabilized gas discharges in lasers, plasmachemical reactors and plasma assisted combustors, and in atmospheric electricity phenomena such as blue jets and gigantic blue jets 23 Thank You!