1. M.N. Shneider 1 In collaboration with M.S. Mokrov 2 and G.M. Milikh 3 ( 1) Princeton University (2) Institute of Problem in Mechanics, Moscow, Russia (3) University of Maryland, College Park The work was supported by NSF grant ATM 0833921 and AFOSR under the MURI “Plasma Assisted Combustion” LTP: May 3, 2013 Dynamic Contraction of the Positive Column of a Self- Sustained Glow Discharge in Nitrogen/Air Flow

2. 2 Outline 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

3. 3 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 u anode cathode Current contraction in Air: h=10 cm, p=35 Torr; u=100 m/s; n e,0 ~10 9 cm -3 From: Velikhov et al, 1982 Current Contraction Gallimberti [1979, 2002] and later Bazelyan et al. [2007] suggested that the formation of a leader is governed by the contraction of a streamer flash current into a small radius channel Contraction velocity: 1 – 100 m/s Much slower than typical streamer velocity (10 6 m/s) !!!

4. 4 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 ionization- thermal 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 non- equilibrium weakly-ionized gas flows

5. 5 Thermal-ionization Instability Increase in pressure initiates gas dynamics that reduce N Increases E/N on the channel axes, thus increases ION Plasma perturbations produce Joule heating, increases T and P in the gas

6. 6 Schematic of the discharge Gas flow along z-axis V 0 =V sh +V PC +IR We assume V sh =const during the process of contraction

7. 7 Model of Current Contraction Plasma Description continuity equation for electrons and ions Poisson equation, finds E Gas Dynamics gas dynamics equations for N,T,T V Finds E/N Loading Circuit V 0 = V PC + IR = const Gas dynamicsInstead: p=NkT=const N~1/T continuity equations for n e, n i Poisson equation for E Instead: quasineutral plasma: n e  n i div j =0 N2N2 continuity equations for n e, n i, n - Poisson equation for E Instead: quasineutral plasma: n e + n -  n i div j =0 Air

8. 8 ; Basic EquationsN2N2

9. 9 Stability analysis for N 2 weakly ionized flow in rectangular duct Simplified system of equations for positive column The equation for plasma density, with  n/  t = 0 and D amb = 0: The linear stability analysis with respect to small perturbations. Fourier series: where T 0 =300 K; N 0 corresponds to the chosen pressure and T 0 The equation for the gas temperature: I governs n s, T s, E s of homogeneous discharge state with The discharge current: Results: where  k peaks when k 1 =2π/y max, which corresponds to development of contracted channel Stable, if assumed, I=const

10. 10 Assumed Conditions (N 2 ) N 2 ; p=100 Torr; L=2 cm; R=2 cm; V 0 =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, n 0 = 2.81∙10 9 cm −3 vibrational temperature, T V = 1069.5 K translational temperature, T 0 = 302.6 K V=V 0 -IR=3.5 kV Initial temperature perturbation: T(x,r) = 293∙(1 + 3.5∙exp(−r 2 /0.152)∙exp(−(x−L) 2 /0.22)) К T v (x,r) = 1069.5(1 + 3.5∙exp(−r 2 /0.152)∙exp(−(x−L) 2 /0.22)) К Studied in: Shneider, Mokrov, Milikh Phys. Plasmas 19, 033512 (2012) Present work

11. 11 Contraction in molecular nitrogen at 100 Torr (2D axysimmetrical) Plasma density (10 12 cm -3 ) Translational temperature Vibrational temperature Qualitatively similar to 2D plain: Shneider, Mokrov, Milikh Phys. Plasmas (2012)

12. 12 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 in molecular nitrogen at 100 Torr (2D axysimmetrical) longitudinal distributions along the propagating channel Contraction longitudinal velocity from the model V = 10-100 m/s is close to measured by Akishev et al [1990] N 2 ; p=85 Torr; u=50 m/s

13. 13 Hysteresis (two stable states exist) Hysteresis regime of contraction: a uniform “cold” glow discharge can be forced to contraction in a designated time and place. N 2 at P=100 Torr Measured I–V characteristic of glow discharge. Open circles correspond to steady-state partially constricted discharge. [Dyatko, Ionikh et al., IEEE TRANS. PLASMA SCI., 39, NOVEMBER 2011].

14. 14 ; 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. Contraction in weakly-ionized Air flow in plain 2D geometry Basic Equations

15. 15 Air; p=100 Torr; L x =2 cm; y max =2 cm; 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. n e =1.5x10 9 cm -3 ; n - =1.7x10 10 cm -3 ; n + =n e +n - T(x,y) = 298∙(1 + 2exp(−y 2 /1.5 2 )exp(−(x−d) 2 /0.3 2 )), Tv(x,y) = 956.3∙ (1 + 4 exp(−y 2 /1.5 2 )exp(−(x−d) 2 /0.3 2 ), The voltage applied to the discharge gap is 4.36 kV, while the source voltage V 0 = 9.36 kV, and the load resistance R = 500 kOhm. Assumed Conditions (Air): plain 2D geometry u

16. 16 Air: plain 2D geometry Temporal evolution of the plasma column voltage and discharge current

17. 17 Contraction in the air at different pressure: 2D plain geometry  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↓ → I cr ↑, coexistence of constricted and diffuse regimes along the density gradient The "current-voltage characteristic" of the glow discharge in air flow at the different pressures. If I I c r the contracted channel is formed

18. 18 In a steady state partially constricted discharge one part of the column was constricted while the other part remained diffuse in Ar:N 2 mixture Experiments by Ionikh et al. [2008]: glow discharge in tube 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

19. 19 http://www.albany.edu/faculty/rgk/atm101/sprite.htm Red Sprites, Blue Jets and Elves: Transient Luminosity Events (TLE) Gigantic BLUE JET (Adapted from Lyons et al. 2000)

20. 20 Leader-Streamer Model of Blue Jets Raizer, Milikh and Shneider Geophys. Res. Letters, December 2006 J. Atmosph. Solar and Terrestrial Physics, 2007 transfers the high potential U~30-50 MV outside cloud up to h ~ 30 km attachment losses time τ а ~ 10 -2 s >> τ а (18 km) plasma conductivity is kept much longer streamers require field E S << Е S (18 km) What leader provides: contraction Leader channel always stops at h~30 km: coexistence of diffuse (streamer corona) and constricted discharges along the current at N(h)

21. 21 Kuo et al. J. Phys. D: Appl. Phys. 41 (2008) 234014 Images of Blue Jet (current along the gradient density) 2 timescales were detected: slow (leader like) ~ 100 ms; fast (streamer like) ~ 1-10 ms Silva, Pasko, GRL 39(2012) Leader channel always stops at h~30 km: coexistence of diffuse (streamer corona) and constricted discharges along the current at N(h)

22. 22 Conclusions 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 N 2 was estimated and checked against the existing observations The contraction in N 2 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, plasma- chemical reactors and plasma assisted combustors, and in atmospheric electricity phenomena such as blue jets and gigantic blue jets

23. 23 Thank You!