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Transport in a field aligned magnetized plasma and neutral gas boundary: The end of the plasma… C.M. Cooper, W. Gekelman, P. Pribyl, J. Maggs, Z. Lucky University of California, Los Angeles February 15, 2013 Overview • Motivation – Relation to Auroral Physics, Divertor Physics • Summary of Enormous Toroidal Plasma Device – Model of ETPD plasma regions • Neutral Boundary Layer model: Plasma Termination 1. 2. Occurs at plasma/neutral gas pressure equilibrium Plasma terminates on current-free ambipolar sheath determined by a generalized Ohm’s law 3. Heating, ionization occur in NBL Measured scaling laws in ETPD Motivation: Aurora The auroral-arc current loop associated with a perpendicular electric field imposed in the magnetosphere [Borovsky 1993] Aurora over Jokulsarlon Lake, Iceland Stephane Vetter, “Nuits sacrees” Feb. 2011 Schematic view of parallel currents j||, plasma motions, vperp, electric fields, and potential contours above auroral arc, sketched in green [Haerendel 1996] J. Borovsky, J. Geo Res 98, A4 6101-6138 (1993) G. Haerendel, J. Atmos. Terr. Phys. 58, 1-4 71-83 (1996) Motivation: Gaseous Divertors Gaseous divertor design for DIII-D Gaseous divertor design for JET Gaseous divertors designed to dissipate plasma particles, momentum, and energy on neutral gas before touching wall R. W. Conn, Fusion and Eng. Design 14 81-97 (1991) Diagram of the ETPD Toroidal Magnets (red) provide a 250 G confining field Vertical Magnets (blue) provide a 6 G vertical field to space out rings LaB6 source injects primaries to form then heat the plasma C.M. Cooper et al, Rev of Sci Inst. 81 083503 (2010) R.J. Taylor et al, Nuclear Fusion 42 46-51 (2002) ETPD Plasma (pink) follows the helical magnetic field up to 120 m Picture of a LaB6 Cathode Frame and Shielding Heater Anode Cathode Experimental Setup • Primary electrons boiled off LaB6 are accelerated along the field by anode. • Primaries ionize neutral gas to create and heat plasma. • Data taken where plasma ends, 90% around machine. Neutral Boundary Layer Probe 400 V discharge 2 mTorr 300 V discharge 2.5 mTorr 2.2 kA 220 V discharge 3.6 mTorr Energy Balance in ETPD 220 V e e e e e e ee e ee e e e e e eHEAT e e Helium Gas B Ionosphere e e ee e i <100 kV ii i ee e e e i e e e e HEAT e e Atmosphere Energy Balance in Aurora 3 Zones in ETPD Plasma + Thermalization Heat of primaries + ionization > Density losses - Conduction/ - Ohmic Heating ionization and cooling - Radial diffusion - Ionization and Radial diffusion Take Data Energy input length mfp, prim ~ 15m Energy loss length p / r r ~ 15m Efield Term. in / v p ~ 1.5m Ambipolar Termination Sheath in NBL! 1 0 -1 -2 -3 -4 Relative y coord (cm) Plasma potential in neutral gas boundary indicative of large fieldaligned electric field 40 20 0 -20 -40 -60 -40 -20 0 20 40 60 Fp (eV) Relative x coord (cm) -40 -20 0 20 40 60 Relative x coord (cm) -40 -20 0 20 40 -40 -20 0 20 40 60 Relative x coord (cm) Relative x coord (cm) Neutral fill of 3.6 mTorr He, a plasma discharge of 194 A 220 V, Btor=250 G, Bver=6 G, Generate Radial Profiles 1 0 -1 -2 -3 -4 Relative y coord (cm) Used to study rate at which particles, momentum, and heat move across the field and out of the plasma 40 20 0 -20 -40 -60 -40 -20 0 20 40 60 Fp (eV) Relative x coord (cm) -40 -20 0 20 40 60 Relative x coord (cm) -40 -20 0 20 40 -40 -20 0 20 40 60 Relative x coord (cm) Relative x coord (cm) Neutral fill of 3.6 mTorr He, a plasma discharge of 194 A 220 V, Btor=250 G, Bver=6 G, Generate Axial Profiles in NBL 1 0 -1 -2 -3 -4 Relative y coord (cm) A Plot data along the center of plasma coordinate “s” Three zones! A B C B C 40 20 0 -20 -40 -60 -40 -20 0 20 40 60 Fp (eV) Relative x coord (cm) -40 -20 0 20 40 60 Relative x coord (cm) -40 -20 0 20 40 -40 -20 0 20 40 60 Relative x coord (cm) Relative x coord (cm) Neutral fill of 3.6 mTorr He, a plasma discharge of 194 A 220 V, Btor=250 G, Bver=6 G, Neutral Boundary Layer Model • Three-fluid, current-free • Continuity equation: ionization and losses n p v p,s S p p, s nnvn,s S p n, s • Momentum equation: pressure equilibration A • Momentum equation: generalized Ohms Law pe Te eEs 0.71 t n n p k B me n p v p , s vn , s en B p p pn mi v p,s p, vn,s n, 0 s s s • Heat equation: ionization and Ohmic heating Te 3 n p v p,s k B en p v p , s Es EionzS p 2 s C Zone A: Pressure Equilibration For 𝑝𝑝 ≥ 𝑝𝑛 • Diffusivity argument: Neutral density convected out along field by plasma, diffuses across field 𝐷𝑎,|| 𝑘𝐵 𝑇𝑛 ≫ 𝐷𝑛 = > 𝐷𝑎,⊥ 𝜈𝑛 • Drag force limited to cross-field neutral diffusion rate 𝝂𝒅𝒓𝒂𝒈 = 𝜵⊥ 𝜞𝒏,⊥ /𝒏𝒏 ≤ 𝑫𝒏 / 𝑹𝒑 𝟐 • Axial neutral flow develops from force balance 𝟎.𝟓𝝂𝒊𝒏 −𝝂𝒄𝒙 /𝒏𝒏 𝑣𝑛,𝑠 =𝑣𝑝,𝑠 𝟎.𝟓𝝂𝒊𝒏 −𝝂𝒄𝒙 /𝒏𝒏 +𝜵⊥ 𝜞𝒏,⊥ /𝒏𝒏 Momentum gained from plasma Momentum lost to stationary neutrals Electron Temperature in Zone A -1 Fp • Constant Te -2 • Ionization ~ 0 (eV) -3 Te (eV) 3 Te Te 2.2 eV 2 2400 2600 2800 3000 3200 Distance from anode (cm) mi en ~ 100 m me Plasma Velocity in Zone A -1 Fp • Plasma velocity is flat • Momentum balance -2 (eV) -3 vp 2 vcr , s 2 105 cm/s 0.5 p , ~ Da , 0.4 n, ~ Dn,a 0.3 (105cm/s) Plasma mach at 2.2 eV 4 0.2 0.1 0 2400 2600 2800 3000 Distance from anode (cm) 0 3200 pe mi v p , s r p ,r s mi ne v p , s vn , s 0.5 in cx • Sets a critical velocity veq , s cs p , p , n , Plasma Density in Zone A -1 Fp • Plasma density is dropping from radial losses -2 (eV) -3 v p,s 1.2 n p s r p ,r Dr Da , ne 0.8 (1012/cm3) 0.4 2400 Dr DBohm 2600 2800 3000 3200 Distance from anode (cm) 1 Dr ~ 4 Da , ~ DBohm 2 ~ 10 cm np 2 Zone B: Ambipolar Electric Field Current-free plasma sees neutral gas at end Electrons stop, ion current penetrates Electric field develops, drives electron current Electric field maintains Current free term. Potential Structure in NBL • Plasma isopotentials form “nested V’s” • White arrows show electric field, parallel field 10x ei • Quasineutral Colormap of plasma potential from 1,300 points interpolated onto toroidal coordinates en D Electron Temperature in Zone B -1 Fp -2 (eV) -3 Te (eV) 3 Fp • Electron temperature rises with potential • For me en LF en mi Te ~F p ~1 eV 2 2400 2600 2800 3000 3200 Distance from anode (cm) Plasma Velocity in Zone B -1 Fp • Plasma velocity drops due to drag on neutrals -2 (eV) -3 4 Plasma mach at 2.2 eV vp 0.5 0.4 0.3 2 (105cm/s) 0.2 0.1 0 2400 2600 2800 3000 Distance from anode (cm) 0 3200 The difference between momentum and temperature loss Electrons • Momentum loss: en – faster • Energy loss: me en – slower Ions • Momentum loss: .5 in cx – slower • Energy loss: .5 in cx– faster In electric field, In electric field, ions mi electrons Plasma Density in Zone B -1 Fp • Plasma density is dropping from radial losses -2 (eV) -3 • Balance between Flux conservation 1.2 ne v p,s n p 0.8 Adiabatic heating (1012/cm3) Te n p 0.4 2400 2600 2800 3000 3200 Distance from anode (cm) Plasma Termination Use generalized Ohms law to solve for electric field eE 0 pe Te 0 en p E (0.71 t n )n p me n p v p , s en s s E E me v p ,s en Je 0.19e en ~ 2V / m Ji en for tn 0.1 , J tot 0 Zone C: Additional Ionization Te 2.2eV R. K. Janev, Elementary Processes in Hydrogen and Helium Plasmas (1987) Electron Temperature in Zone C -1 Fp • Prediction: Electron temperature continues to rise rapidly with potential -2 (eV) -3 Te (eV) 3 2 2400 2600 2800 3000 3200 Distance from anode (cm) Electron Temperature in Zone C -1 Fp -2 F p ~ 2.5eV (eV) -3 Te (eV) 3 v|4.7 eV ~1000 v|2.2 eV 2 2400 2600 2800 3000 3200 Distance from anode (cm) Plasma Density in Zone C -1 Fp • Prediction: Plasma density continues to drop -2 (eV) -3 1.2 ne 0.8 (1012/cm3) 0.4 2400 2600 2800 3000 3200 Distance from anode (cm) Plasma Density in Zone C -1 Fp -2 (eV) -3 1.2 ne 0.8 10% (1012/cm3) 0.4 2400 2600 2800 3000 3200 Distance from anode (cm) Plasma Production in Boundary If all energy gained went into plasma production how much could you make? For Tb Ta , vb va QF Qionz ne F 2.5eV ~ 10% ne ionz Te 24.6eV 2.2eV What’s the mean free path of ionization? v pz nn v|4.7 eV ~ 10 cm Any energy gained by electric field is quickly absorbed by ionization Plasma Velocity in Zone C -1 Fp • Prediction: Plasma velocity will drop to 0 -2 (eV) -3 4 Plasma mach at 2.2 eV vp 0.5 0.4 0.3 2 (105cm/s) 0.2 0.1 0 2400 2600 2800 3000 Distance from anode (cm) 0 3200 Plasma Velocity in Zone C -1 Fp -2 (eV) -3 4 Plasma mach at 2.2 eV vp 0.5 0.4 0.3 2 (105cm/s) 0.2 0.1 0 2400 2600 2800 3000 Distance from anode (cm) 0 3200 • Additional flux is generated by the ionization at the end of the plasma • Still slowing down after ionization ends NBL Conserved Quatities Axial Plasma Flux: 4 1.4 p,s=npvp,s Pp=(np(Ti+Te)/(nnTn)) Normalized Plasma Pressure: 1.0 0.6 2400 2600 2800 3000 3200 Distance from anode (cm) Normalized Plasma Pressure: • End of the plasma occurs where pp=pn • Dropping pressure “interrupted” by termination E field 2 0 2400 2600 2800 3000 3200 Distance from anode (cm) Plasma flux: • Measure of axial particle flux • Only loss of axial flux is radial flux • Filling in of profile • Kinetic effects (trapped particles) Scaling of Ambipolar Electric Field The potential marks a “footprint” for the boundary of the plasma 49 kW 43 kW 39 kW The location and magnitude of Electric field terminating the plasma change as a function of input power Measure plasma parameters Scaled Plasma Parameters pre-NBL (a) • Te is flat at 2.2 eV (b) • Extra power raises density • Axial flow drops (c) Scaling Study pp=pn seq,m=seq,t Es,m=Es,t Measured electric field, Es,m, scales like the theoretical ambipolar value E s ,t me v p , s en 0.19e Measured termination point, seq,m, coincides with location of pressure equilibration seq ,t v p ,s R p2 Dr (Te Ti )n p (s0 ) ln Tn nn Modified Ambipolar Flow in ETPD Electron current Ion current Electron current Ion current Electron current Ion current Ambipolar Flow in NBL • Magnetic field data from probe indicates axial current • Negative current carried by electrons moving in positive direction Data taken at s = 2870 cm, halfway through NBL Non-Zero Current in NBL •NBL not current free •Current trends to zero J T ,meas Bmeas •Drift speed associated with current << bulk flow 0.9 𝑣𝑒,𝑠 < 𝑣𝑖,𝑠 < 𝑣𝑒,𝑠 Types of Current Note: Steady state so Jpolz = 0 Some currents diverge and need to be closed to maintain J=0 Non Transport Causing Some currents are associated with particle drifts and transport Transport Causing Divergence-Free • Poloidal Hall (i-n) Current (+) • Poloidal Diamagnetic Current (-) Non Divergence-Free • Parallel (e-n) Current • Radial Pederson (i-n) Current • Vertical/B Currents Estimation of Jr Jr • Axial current tied to Radial current JS Ar JSo+DS = JSo + Jr AS Kirchoff’s Junction Rule r pr E Er mi vir in ne * r J ir in, Er* Future Work on NBL • Observational – Measure plasma potential and flows in Aurora • Experimental – Study NBL for different pressures and/or gases • Simulation – Model in DEGAS (neutral gas collisional code)* – Model in UEDGE (transport code)* – Runge Kutta solver for fluid model** Future work: 1.5-D Simulation Measured 5 things: ne , Te , vi , p , J p Model neutral gas Solve 5 equations + neutral gas transport: vez ne ne vez S en z z vez ne Te ne vez Te ne ev z z z z viz ne ne viz S in z z viz ne ne viz Ti ne iv z z z Te qe vez 3 ne vez neTe S eT 2 z z z Generalized Source/Sink calibrated by data Conclusions – Plasma terminates on ambipolar electric field – Electric field occurs where diminishing plasma pressure and neutral pressure equilibrate – NBL dominated by termination field through Ohmic heating and ionization – NBL has a small modified ambipolar diffusion due to differences in directional particle motilities Thanks!