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PLASMA IN CONTACT WITH METAL:RF ANTENNA NEAR FIELD BEHAVIORSIN TOKAMAKS(AND INDUSTRIAL PLASMAS)Presenter: David N. SmitheCo-author: Tom JenkinsTech-X CorporationPlasma Physics ColloquiumApplied Math and Physics Dept.Columbia University, NYSeptember 5, 201401

More Acknowledgments Lodestar Research Corporation– Dan D’Ippolito, Jim Myra RF SciDAC (CSWPI) including––––MIT (Paul Bonoli, John Wright)PPPL (Cynthia Phillips, Nicola Bertelli)ORNL (David Green)CompX (Bob Harvey) TechX’ers (Scott Kruger, Jake King) Oak Ridge Leadership Computing Facility– Titan

Funding Acknowledgements DOE (SciDAC, Theory, Phase II SBIR)– DE-FC02-08ER54953– DE-FG02-09ER55006,– DE-FC02-05ER54823 Tech X IR&D

If You Don’t Already Know Me ’87 – Ph.D. (Univ. Mich.) PostDoc (PPPL)– ICRF Core Absorption, 1D Parallel “All Orders” (METS)– Early FEM 2.5D Core Solvers (SHOOT, SPRUCE) ‘89 Hired by Mission Research Corp.– Defense contractor, FDTD PIC codes and radar (MAGIC)– ‘95, PPPL (Phillips) 1D perp “All Orders” for HHFW (METS95) ’05 – MRC bought by ATK, I went to Tech X– Back to Fusion (and some accelerator work) (Vorpal)– Trying to see what 3D FDTD can do in Fusion Antenna Unusual Talent– Good with 3D geometry

The Original Problem We want to model this ( 1 meter) antenna: Which has this ( 10 microns) sheathpotential:

Because RF antennas create impurities– which reduce the Zeffective of the plasma– Which reduces the fusion yield– Which is bad, especially in ITER Impurities are thought to arise from sputtering, whenions fall through the rectified RF sheath, hitting wallwith– 100 volts, a bit higher than Te,edge. Work by D’Ippolito and Myra at Lodestar– Local electric fields 104 to 105 V/m– RF Rectified Sheaths get you 100 Volts

What is an RF Rectified Sheath? Additional plasma DC bias in the sheath, due toRF, so plasma potential never goes wrong way.––––(Show Movie 1)1D Parallel PlateStart with Debye sheath (blue)Oscillating potential (black) Still very small (10 microns – 100 microns)– Antenna is a meter, grid size is 1 mm

How to Defeat the Scale Problem Analogy: in EM-FDTD, we don’t resolve themetallic skin depth, d (msw)-½ , we just set E 0,as a boundary condition. If we need ohmic losses in the skin depth, weuse the local H field to compute current andpower, as in Rs H 2.– E.g., the metallic skin depth is a “sub-grid model”– We model its effect, E 0, not its full physics We “want” to do the same with the sheath.– Can we!? Not as simple as E 0.– But lots of sheath work to draw from

Best Answer So Far D’Ippolito and Myra Boundary Condition– D. A. D’Ippolito and J. R. Myra, Phys. Plasmas 13,102508 (2006) Model sheath as capacitive gap. Simple parameter, D, characterizes capacitor. Follow the action:– Capacitor has oscillating fsheath (RF sheath Voltage)– Nonlinear Capacitor spacing, D( fsheath ), Child-Langmuir– Rectified potential, fDC,rectified fsheath is computed afterthe fact, usable for ion sputtering analysis

Any EE’s in the Audience ? Looks like this.

Do We Believe This? We’ve done 1D PIC (particle-in-cell)benchmarking. From first principles. For industrial plasmas (and maybe fusion), weadd a thin layer of dielectric to the metal wall. The Dielectric layer DOES behave like acapacitor, with well known C/Area (de)-1. (Show Movie 2) Dielectric (blue)

Yes, We Believe Voltage is split, from capacitances inseries, we know one, we suspect weknow the other. Sheath capacitancebased on D( fsheath ) gives correct split.

Also Need a Plasma Sheath potentials will depend on local electric field. That is only correct if the plasma in front of theantenna is correct– eplasma 1000 ! Time domain cold plasma:“Finite-difference time-domain simulation of fusion plasmas at radiofrequencytime scales”, Smithe, Physics of Plasmas 14, 1 2007 (This is actually where the story begins.)

2007 PoP Paper Critical Realization: Cold Plasma Dielectric iszero-D – can make it point-wise implicit in timedomain, to get all cold-plasma waves, stable,regardless of cutoff / resonances. Benchmarking: E.g., ICW mode conversionHigh FieldLow FieldDispersion Relationkx real0kx imag0kx real1kx imag1kx real2kx imag2kx real3kx 50.6350.655x080.6750.6950.715

Time DomainCold Plasma Equations Convert frequency-domain linear plasmadielectric tensor to “auxiliary differential equation”(ADE) time domain method. “Auxiliary Fields” are the linear plasma currents,one per species.09

“Super-Boris” Time DomainCold Plasma Implicit Algorithm 3x(Nspecies 1) matrix is analytically invertible. But messy!10

In the Boundary Cells Key Realization is that Plasma Currents fromTime Domain Plasma is Capacitor Current.– E.g., the sheath IS the boundary condition for Jplasma One More Equation, for sheath potential.– Ugh, redo all that math, make sure energy conserving

The Advantages of Time Domain Explicit FDTD EM code is very well establishedand fast. (e.g., we already had the code!) And handles complex metallic boundaryconditions. Of course, multiple simultaneous frequencies. Which allows for inclusion of nonlinearity, withouta priori guess at modes and frequencies11

An Aside: Example of Nonlinearity:Parametric Decay Instability Use linear plasma electrons, and kinetic ions,(needed for IBW wave in PDI)– Sometimes as expected (comparison to J. Rost Thesis, MIT)– Sometimes not“Time-domain simulation of nonlinear radiofrequency phenomena,” Thomas G. Jenkins, Travis M.Austin, David N. Smithe, John Loverich, and Ammar H. Hakim, Phys. Plasmas 20, 012116 (2013)12

The Disadvantageof Time Domain Yee Cell ! (Bx is at different location of By, Bz) Complicates the JxB in plasma force equation.Also, no warm plasmaeffects, since no longerpoint physics, operations.So no IBW.13

ITER Antenna Simulations (Show Movie 3 and 4) Simulations of ¼ ITER antenna, withsurrounding box shows– slow-wave enhanced sheaths on the surroundingantenna box,– an interesting circulation pattern around the box thatvanishes when field aligned

New Work on ITER Antenna Simulations pre-date energy conserving form– So sheath voltages are not necessarily correct Simulations pre-date Titan usage– Can do all 24 straps now (Hopefully) more material for APS ITER sessiontalk later this fall. And then there is the question of the slow wave

The Slow Wave I was given a 103 range in edge densities to lookat for ITER. (!) Some of those densities show a shortwavelength mode in front of the antenna (Show Movie 5).

“Layer” moves with Density

Does This Have Anything to dowith NSTX Anomalous Losses? This question is presently under study. Concern is that it might be there for ITER as well. I’ve been trying to get a better instinctive idea ofwhat is going on with these slow waves. Cold Plasma, they have to essentially be lowerhybrid resonances. Resonance in the edge is w wLH wp,ion So there is a critical density, but wpi, not wpe.

We are looking at the CModField Aligned Antenna as well

We can see slow waves there too,sometimes at high magnitude

Slow Wave Dispersion The slow waves are NOT a thin layertrapped between two cutoffs, they are athin layer trapped between a cutoff and aresonance. The resonance is what allows for energyto be in the layer, otherwise would be toothin to excite, since need a k .

wLH in the Edge From Stix: wLH-2 (wpi2 Wci2)-1 (WciWce)-1 At edge density, last term neglects away. At edge, (wRF/Wci)2 (nHarmRouter/R0)2 1 So: wLH2/wRF2 wpi2/wRF2 SmallNumber(0.2 - 0.02)

Critical Density Since wLH wpi, insensitive to B field, onlydensity– Assume D plasma. For 30 MHz: 1.7x1017 / m3 For 80 MHz: 2.7x1017 / m3

What are the Reported Densities? NSTX: Expect 5-10x1017m3, at least 3x overcritical density.– Is there some other explanation why densitymight be lower than reported, in front of antenna.Ponderamotive pressure?– The game is on ITER: Density is unknown. Hopefully highenough! The frequency is higher sohappens at higher density.

An Aside: Industrial Applications Many industrial plasmas are maintained bysimilar DC RF fields, with energetic particlesgenerated in the sheath as the ionization source. (Show Movie 6.)

Phase II SBIR Work Still have the scale problem, so still want to usesub-grid sheath. Want EED, use “test” particles. Have created special particle boundaries thatsee the sheath “kick” before impact, or aftersecondary emission, in an attempt to reproducethe “beam” electrons without resolving thesheath. Much interest in estimating steady-state of suchplasmas a priori.

Summary Ultimate goal is estimation of impurity generatingsputtering in ITER, and other tokamaks. Resolved scale problem with RF sheath sub-gridmodel, e.g., single fsheath value represents sheath. Coupled with pre-existing time-domain coldplasma algorithm, and pre-existing 3D CADimporting EM software. Slow wave is a very interesting tangent. SBIR work will also include particles and industrialconcerns.

THANK YOU! Questions, Comments?

Also Need a Plasma Sheath potentials will depend on local electric field. That is only correct if the plasma in front of the antenna is correct – e plasma 1000 ! Time domain cold plasma: “Finite-difference time-domain simulation of fusion plasmas at radiofrequency time scales

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