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 Summary of Enormous Toroidal Plasma Device Relation to Auroral Physics, Divertor Physics Summary of Enormous Toroidal Plasma Device Model of ETPD plasma regions Neutral Boundary Layer model: Plasma Termination Occurs at plasma/neutral gas pressure equilibrium Plasma terminates on current-free ambipolar sheath determined by a generalized Ohm’s law Heating, ionization occur in NBL Measured scaling laws in ETPD

Motivation: Aurora J. Borovsky, J. Geo Res 98, A4 6101-6138 (1993) 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 divertors designed to dissipate plasma particles, momentum, and energy on neutral gas before touching wall Gaseous divertor design for JET 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 ETPD Plasma (pink) follows the helical magnetic field up to 120 m C.M. Cooper et al, Rev of Sci Inst. 81 083503 (2010) R.J. Taylor et al, Nuclear Fusion 42 46-51 (2002)

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 220 V discharge 3.6 mTorr 2.2 kA

Energy Balance in Aurora Energy Balance in ETPD 220 V e HEAT e HEAT Helium Gas B Ionosphere HEAT e e i HEAT Atmo- sphere <100 kV Energy Balance in Aurora

3 Zones in ETPD Plasma Take Data Heat Density + Thermalization of primaries + ionization > losses Conduction/ ionization - Radial diffusion Ohmic Heating and cooling - Ionization and Radial diffusion Heat Density Take Data Energy input length Energy loss length Efield Term.

Ambipolar Termination Sheath in NBL! Plasma potential in neutral gas boundary indicative of large field-aligned electric field 1 -1 -2 -3 -4 40 20 -20 -40 All plots generated from z2011_02_ep_plots, colorbar moveable, vplasma4 is on dif col Relative y coord (cm) -60 -40 -20 0 20 40 60 -40 -20 0 20 40 60 -40 -20 0 20 40 -40 -20 0 20 40 60 Fp (eV) Relative x coord (cm) Relative x coord (cm) 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 Used to study rate at which particles, momentum, and heat move across the field and out of the plasma 1 -1 -2 -3 -4 40 20 -20 -40 All plots generated from z2011_02_ep_plots, colorbar moveable, vplasma4 is on dif col Relative y coord (cm) -60 -40 -20 0 20 40 60 -40 -20 0 20 40 60 -40 -20 0 20 40 -40 -20 0 20 40 60 Fp (eV) Relative x coord (cm) Relative x coord (cm) 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 Plot data along the center of plasma coordinate “s” Three zones! A B C A B C 1 -1 -2 -3 -4 40 20 -20 -40 All plots generated from z2011_02_ep_plots, colorbar moveable, vplasma4 is on dif col Relative y coord (cm) -60 -40 -20 0 20 40 60 -40 -20 0 20 40 60 -40 -20 0 20 40 -40 -20 0 20 40 60 Fp (eV) Relative x coord (cm) Relative x coord (cm) 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 A Momentum equation: pressure equilibration Momentum equation: generalized Ohms Law B Heat equation: ionization and Ohmic heating C

Zone A: Pressure Equilibration For 𝑝 𝑝 ≥ 𝑝 𝑛 Diffusivity argument: Neutral density convected out along field by plasma, diffuses across field 𝐷 𝑎,|| ≫ 𝐷 𝑛 = 𝑘 𝐵 𝑇 𝑛 𝜈 𝑛 > 𝐷 𝑎,⊥ Drag force limited to cross-field neutral diffusion rate 𝝂 𝒅𝒓𝒂𝒈 = 𝜵 ⊥ 𝜞 𝒏,⊥ / 𝒏 𝒏 ≤ 𝑫 𝒏 / 𝑹 𝒑 𝟐 Axial neutral flow develops from force balance Momentum gained from plasma 𝑣 𝑛,𝑠 = 𝑣 𝑝,𝑠 𝟎.𝟓𝝂 𝒊𝒏 − 𝝂 𝒄𝒙 / 𝒏 𝒏 𝟎.𝟓𝝂 𝒊𝒏 − 𝝂 𝒄𝒙 / 𝒏 𝒏 + 𝜵 ⊥ 𝜞 𝒏,⊥ / 𝒏 𝒏 Momentum lost to stationary neutrals

Electron Temperature in Zone A -1 -2 -3 (eV) Fp Constant Ionization ~ 0 3 2 (eV) Te Axial profiles generated from 2011-02-te_plots, 2011-02-ep_plots and 2011-07-bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012 2400 2600 2800 3000 3200 Distance from anode (cm)

Plasma Velocity in Zone A -1 -2 -3 (eV) Fp Plasma velocity is flat Momentum balance Sets a critical velocity 4 2 (105cm/s) vp 0.5 0.4 0.3 0.2 0.1 Plasma mach at 2.2 eV Axial profiles generated from 2011-02-te_plots, 2011-02-ep_plots and 2011-07-bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012 2400 2600 2800 3000 3200 Distance from anode (cm)

Plasma Density in Zone A -1 -2 -3 (eV) Fp Plasma density is dropping from radial losses 1.2 0.8 0.4 (1012/cm3) ne Axial profiles generated from 2011-02-te_plots, 2011-02-ep_plots and 2011-07-bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012 2400 2600 2800 3000 3200 Distance from anode (cm)

Zone B: Ambipolar Electric Field Current-free plasma sees neutral gas at end i e e i i e e Electrons stop, ion current penetrates i i i e e i e i e e i Electric field develops, drives electron current i i e e i i i e e e Electric field maintains Current free term. i e i e i

Potential Structure in NBL Plasma iso-potentials form “nested V’s” White arrows show electric field, parallel field 10x Quasineutral lei Axial profiles generated from 2011-02-te_plots, generated on 11/29/2011, used on all posters Parallel arrows 10x len lD Colormap of plasma potential from 1,300 points interpolated onto toroidal coordinates

Electron Temperature in Zone B -1 -2 -3 (eV) Fp Electron temperature rises with potential For 3 2 (eV) Te Fp Axial profiles generated from 2011-02-te_plots, 2011-02-ep_plots and 2011-07-bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012 2400 2600 2800 3000 3200 Distance from anode (cm)

Plasma Velocity in Zone B -1 -2 -3 (eV) Fp Plasma velocity drops due to drag on neutrals 4 2 (105cm/s) vp 0.5 0.4 0.3 0.2 0.1 Plasma mach at 2.2 eV Axial profiles generated from 2011-02-te_plots, 2011-02-ep_plots and 2011-07-bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012 2400 2600 2800 3000 3200 Distance from anode (cm)

The difference between momentum and temperature loss Electrons Momentum loss: – faster Energy loss: – slower In electric field, electrons HEAT. Ions Momentum loss: – slower Energy loss: – faster In electric field, ions SLOW.

Plasma Density in Zone B -1 -2 -3 (eV) Fp Plasma density is dropping from radial losses Balance between Flux conservation Adiabatic heating 1.2 0.8 0.4 (1012/cm3) ne Axial profiles generated from 2011-02-te_plots, 2011-02-ep_plots and 2011-07-bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012 2400 2600 2800 3000 3200 Distance from anode (cm)

Plasma Termination Use generalized Ohms law to solve for electric field

Zone C: Additional Ionization R. K. Janev, Elementary Processes in Hydrogen and Helium Plasmas (1987)

Electron Temperature in Zone C -1 -2 -3 (eV) Fp Prediction: Electron temperature continues to rise rapidly with potential 3 2 (eV) Te Axial profiles generated from 2011-02-te_plots, 2011-02-ep_plots and 2011-07-bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012 2400 2600 2800 3000 3200 Distance from anode (cm)

Electron Temperature in Zone C -1 -2 -3 (eV) Fp IONIZATION 3 2 (eV) Te Axial profiles generated from 2011-02-te_plots, 2011-02-ep_plots and 2011-07-bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012 2400 2600 2800 3000 3200 Distance from anode (cm)

Plasma Density in Zone C -1 -2 -3 (eV) Fp Prediction: Plasma density continues to drop 1.2 0.8 0.4 (1012/cm3) ne Axial profiles generated from 2011-02-te_plots, 2011-02-ep_plots and 2011-07-bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012 2400 2600 2800 3000 3200 Distance from anode (cm)

Plasma Density in Zone C -1 -2 -3 (eV) Fp IONIZATION 1.2 0.8 0.4 (1012/cm3) ne Axial profiles generated from 2011-02-te_plots, 2011-02-ep_plots and 2011-07-bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012 10% 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 What’s the mean free path of ionization? Any energy gained by electric field is quickly absorbed by ionization

Plasma Velocity in Zone C -1 -2 -3 (eV) Fp Prediction: Plasma velocity will drop to 0 4 2 (105cm/s) vp 0.5 0.4 0.3 0.2 0.1 Plasma mach at 2.2 eV Axial profiles generated from 2011-02-te_plots, 2011-02-ep_plots and 2011-07-bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012 2400 2600 2800 3000 3200 Distance from anode (cm)

Plasma Velocity in Zone C -1 -2 -3 (eV) Fp Additional flux is generated by the ionization at the end of the plasma Still slowing down after ionization ends IONIZATION 4 2 (105cm/s) vp 0.5 0.4 0.3 0.2 0.1 Plasma mach at 2.2 eV Axial profiles generated from 2011-02-te_plots, 2011-02-ep_plots and 2011-07-bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012 2400 2600 2800 3000 3200 Distance from anode (cm)

NBL Conserved Quatities Normalized Plasma Pressure: Axial Plasma Flux: 4 2 1.4 1.0 0.6 Gp,s=npvp,s Pp=(np(Ti+Te)/(nnTn)) 2400 2600 2800 3000 3200 Distance from anode (cm) 2400 2600 2800 3000 3200 Distance from anode (cm) Axial profiles generated from 2011-02-te_plots, 2011-02-ep_plots and 2011-07-bdot_plots Fits from 2011_02_getaxialprofiles, generated on 3/20/2012 Normalized Plasma Pressure: End of the plasma occurs where pp=pn Dropping pressure “interrupted” by termination E field 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 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 Measured termination point, seq,m, coincides with location of pressure equilibration

Modified Ambipolar Flow in ETPD Electron current Ion current Electron current Ion current Ion current Electron 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 Drift speed associated with current << bulk flow Axial profiles generated from 2011-02-te_plots, triangles are current in boundary, redlines is integrated pederson current /8 0.9 𝑣 𝑒,𝑠 < 𝑣 𝑖,𝑠 < 𝑣 𝑒,𝑠

Types of Current Some currents diverge and need to be closed to maintain J=0 Note: Steady state so Jpolz = 0 Divergence-Free Non Divergence-Free Some currents are associated with particle drifts and transport Parallel (e-n) Current Radial Pederson (i-n) Current Vertical/B Currents Poloidal Hall (i-n) Current (+) Transport Causing Poloidal Diamagnetic Current (-) Non Transport Causing

Estimation of Jr Jr JS JSo+DS = JSo + Jr Ar AS Axial current tied to Radial current JS Ar JSo+DS = JSo + Jr AS Kirchoff’s Junction Rule

Future Work on NBL Observational Experimental Simulation 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: Model neutral gas Solve 5 equations + neutral gas transport: 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

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