Presented at the 16th International Conferenceon Plasma Surface Interactions

in Controlled Fusion DevicesMay 24, 2004

Portland, Maine

Experimental diagnosis and kinetic computation ofneutral penetration in the Alcator C-Mod edge plasma

J.W. Hughes, D. Mossessian, J. Terry, B. LaBombard, MIT PSFC, D. Stotler, PPPL

Neutral-plasma interactions are expected to have a significant influence on edge plasma conditions inthe edge region of a tokamak plasma, and thus on global plasma confinement. In particular, the particlesource from ionization should be considered in the study of plasma transport within the H-modepedestal. On Alcator C-Mod, a tokamak that often exhibits edge gradient scale lengths on the order ofmillimeters, we measure profiles of electron density (ne) and temperature (Te) with high spatialresolution edge Thomson scattering and scanning Langmuir probes, giving the background profiles thatdetermine neutral-plasma interaction rates. From these profiles and radial profiles of Dα emissivity,obtained from measured images of edge emission, we infer atomic density (n0) profiles and theassociated radial distribution of the ionization source rate (Sion). Using experimental variations inplasma density, we examine the changes in plasma neutral profiles under varied regimes of operation,and look for relationships between atomic mean free path and ne pedestal width. Modeling of edgeneutral transport is also performed. Because neutral mean free paths can be of the same order ascharacteristic density gradient scale lengths in the C-Mod edge plasma, we require a fully kineticcalcuation of neutral particle transport. We employ KN1D, a kinetic solver for atomic and moleculardistribution functions in slab geometry. The computation produces profiles of n0 and Sion for givenbackground plasma profiles, while accounting for all relevant interactions, including electron impactionization and multiple charge exchange events. Benchmarking of the code is performed against the2D Monte Carlo neutral transport code, DEGAS 2. Benchmark runs and comparisons of computationalresults with experimental data are presented and discussed.

Outline

• Importance of edge transport barriers, and their experimentaldiagnosis

• High resolution measurements on Alcator C-Mod and profile analysis• General features of empirically determined neutral density, ionizationprofiles

• Trends in edge particle transport during variation of H-mode regime• Kinetic computation of neutral penetration in the H-mode edge;comparison with experimental values

• Status of computational benchmarking

Overview and Motivation• Tokamak edge conditions strongly influence core energyconfinement1,2

• The high confinement regime (H-mode)3 of operation is associatedwith large particle, temperature gradients near the last closed fluxsurface (LCFS); local elevation of electron temperature (Te) anddensity (ne) results in an edge pedestal, the height of which is tightlycoupled to global stored energy4

• Confinement predictions for large next-step devices require accurateextrapolations of the H-mode pedestal; understanding must be had ofthe physics determining pedestal heights, widths and gradients

• Cross-field particle transport phenomena (plasma physics) andneutral ionization (atomic physics) are both expected to be importantin the edge transport barrier region. How do we assess their relativeimportance experimentally?

• Transport barrier associated withhigh Te, ne gradients, localized tonarrow pedestal region

• Typical pedestals are 2—6 mm inwidth

• On average the Te pedestal is widerand is located slightly inside the nepedestal

• Profiles are fit to a modified tanhfunction6 for ease of analysis:

H-modes and edge transport barrierroutinely obtained on Alcator C-Mod tokamak5

δ

0

2 )+1][tanh( 0

+R(-RH-m

b+f -RRh

L-mode

H-mode

from Ref. 4=

-δ)0-R(R +δ)

from Ref. 4

Empirical scalings of density pedestal width(∆n) on C-Mod exhibit much uncertainty

from Ref. 4

Discharges withfixed target density,

varied field andcurrent

Discharges withfixed target density,

varied current

• Simple theoretical considerations,7balancing plasma and neutral fluxesin the pedestal and accounting forionization, suggest a ∆n characteristicof neutral atomic penetration length

• Result would be a width scaling theinverse of ne,PED

• Previous analysis suggested theopposite trend on C-Mod in EnhancedDα (EDA) H-modes over a range ofplasma currents (0.6-1.2 MA)- ∆n scaled equally well with 1/q95- Raising IP both lowers q and raises ne,PED- Attempts to isolate density effect byscanning ne at fixed current have met withlimited success

Experimental Method

Edge Thomson scattering (ETS)9Te of 30—1000 eV, ne: 0.3—5x1020 m-3

20 points about LCFS along chord through magnetic axis

Scanning Langmuir probe10Scans of Te, ne in scrape-off layer (SOL) over a ~100ms reciprocatingstrokeCapable of brief penetrations past the LCFS

Profiles from diagnostics are mapped to machine midplanealong surfaces of constant flux from EFIT equilibriumreconstruction code12

Balmer-α imaging camera11Tangential view at outboard midplaneAbel-inverted profiles of Balmer-α emissivity

A suite of high resolution edge diagnosticsis used to study the C-Mod plasma edge

Edge TS, scanning probe profilescombined for analysis

• Steady H-mode periods chosen fortime-averaging TS data (2-3 pulsespreferrable for obtaining goodstatistics)• Probe thrust in chosen time window;density is scaled by 0.6 in order tomatch the absolutely calibrated TS• Shifts of few millimeters or less areapplied to the midplane-mappedprofiles, matching them and givingTe,LCFS (~70eV) consistent with powerbalance• Composite profiles suitable forneutral analysis are generated

Chord-integrated brightness fromhorizontal slice through image

Inferred D-alphaemissivity

Image of outboard midplaneambient Dα light

Resolution ∆x~2mm

R

z

• Images of background D-alpha used to determine radial emissivity profiles• With the above profiles of Te, ne, can calculate neutral density andionization rates via Johnson-Hinnov13

• Brightness often finite even at largest radius, meaning inversion must betruncated just beyond limiter radius

Experimental Results

• EDA H-modes were generatedwith auxiliary ICRF heating in5.6T discharges of variedcurrent IP

• Characteristics of edge quasi-coherent (QC) mode14examined over a range ofedge q- Mode is responsible for enhancedparticle transport

- Mode amplitude correlates inverselywith the rate of density rise15

- Lower current, i.e. higher q, givesincreased transport and more "EDA-like" plasmas

• Edge TS, probe scans andbackground D-alpha imagingoccurred during H-modeperiods for comparison ofplasma, neutral transport

Clear steepeningof ne pedestal ascurrent is raised

Relatively little ne,PED variation wasobtained at fixed current, despiteattempts to change target density:three distinct families of ne profiles

- Profiles are mapped to machine midplane and averagedover time windows of steady discharge- The modified tanh fits to these average profiles clearlydemonstrate a wider density pedestal at the lowest IP- This is contrary to the previous 1/q scaling, based ondata at IP>0.6MA

(EFITdeterminationof separatrixworsens as IPis lowered)

z (m) [@ R=0.69m]

Experimental determinationof neutral profile

Ionizationrate

Neutraldensity

D-alphaemissivity

Electrondensity

Electrontemperature

• Time windows chosen containingvalid edge TS profiles, probe scansand Dα profiles

• As IP is lowered:- ne pedestal drops in proportion- Neutral density (n0) penetrates farther intocore plasma

- Ionization rate (Sion) becomes less peaked inpedestal region, and an increase in scrapeoff layer (SOL) ionization, Dα is observed

• Gradient scale lengths of ne, n0 arevery similar in the 0.76, 0.98 MAdischarges; however transportmust differ, as Sion in the 0.98 MA isclearly more peaked.

• Ln=|ne/ ne|; L0=|n0/ n0|• ∆n = the full width of the ne pedestal, from themodified tanh function fitted to the combinedTS and probe profile

• Neutral mean free paths λ are given byv0/ne<σv>, with neutral velocity v0corresponding to energy of 20eV, a typical SOLplasma temperature

• Maximum ∆n are consistent with roughestimates of λCX, λion

• Actual L0 are less than ∆n on average, moreconsistent with an effective MFP:λeff=v0/ne(<σv>ion+2<σv>CX)

Behavior of plasma andneutral gradient scale

lengths

Assume diffusive transport: Γ=Deff n

• 1-D analysis, slab geometry appropriate in pedestalregion

• Integrate inferred Sion profile to generate Γe(R); B.C. onΓe inside pedestal region estimated from dN/dt of plasma

• Perpendicular particle transport increases with increasingq, growing considerably as IP reduced to 0.5MA (q95~8)

Average DeffDeff(R)

• In these discharges TS pedestals show mean ∆n~2-5 mm at "standard"currents of 0.75-1 MA (q95~4-6), but ∆n~4-10 mm at IP=0.5MA (q95~8);characteristic gradient decreases with IP, down to near L-mode levels

• Can say little about density dependence of ∆n, due to the small range ofne,PED obtained at each current- Dependence of ne,PED on target density known to be weak4

- Reduced RF power during experiment placed an upper limit on the target densities at whichL-H transitions could be induced

• Several complete n0, Sion profiles are derived- Neutral density gradient scale lengths consistent with mean free path variation as ne changes- ne gradient scale length in pedestal is typically longer than L0 in a given shot- Deff wells are crudely inferred from these data; ∆n may be tied more to the Deff well width thanthe ionization profile width, which is sometimes ill-defined (i.e., when Sion peaks outside theLCFS)

• Deff trend with IP highlights the increased transport as discharges movedeeper into the EDA regime (higher q)

• Detailed analysis of QC mode data from probes, phase contrastimaging and gas puff imaging should reveal more about mode behaviorin these shots, providing additional information about particle transport

Discussion of experimental results

Computational Results

Geometry

1-D space, 2-D velocity, kinetic transport codefor molecular and atomic hydrogen (written in IDL )

Input

Self-consistent velocity space distributions [fH2(vr,vx,x),fH(vr,vx,x)], molecular dissociation, fluid moments,molecular ion density and temperature profiles.

PH2

SOL Core

Limiter

Limiter

Boundary Conditions

Plasma Backgound (Core, SOL, limiter shadow),’midplane’ neutral pressure, 1D geometry

Options IncludedSelf collisions, cross-collisions: D+, D2, D0, D2

+collisions with ’limiter sides’

Zero mass flux onto ’wall’ and ’limiter’ sides, limiterrecycling, RT molecules from wall, ’Black’ core plasma

Wall

Output

KN1DKinetic Neutral 1-D Transport Code

Since neutral mean free paths are of the same order as gradient scalelengths, a kinetic analysis of the neutral transport is desired

from Ref. 16

Neutral D0 density

Ionization rate

Dα emissivity

Typical comparisonwith experimental

results

EXPERIMENTALKN1D RUN 1KN1D RUN 2

LIMITER

LCFS

• Plasma ne, Te used as inputs;density of neutral source scaled inorder to provide the best match withexperiment

• Orange curves are from full run ofKN1D, with a molecular source atthe wall, and taking into accountrecycling of limiters

• Green curves are from the atomicmodule of KN1D only, assuming aFrank-Condon source of D0 enteringfrom the far right

• Disagreement with experiment intwo regions- 1) Limiter shadow and outermost SOL- 2) Pedestal region

1

2

• In core plasma and mid-SOL, KN1D reproduces experimentalresults fairly well; however . . .

1) Discrepancy near limiter: the purely atomic simulation agreeswith experiment better than the full KN1D run- Larger n0 in the full KN1D case is the result of dissociation of D2 evolvingfrom limiter surfaces, with a D0 source rate as high as 1024m-3s-1; possiblycode overestimates the recycling off limiter sides

- Alternatively, at R>91cm, ne from the probe may be much lower than newhere Dα measurement occurs, since probe is in a limiter shadow with ashort connection length; the drop in probe density allows D0 in code topenetrate well into the SOL, creating the bump in Sion and Dα

2) Discrepancy about LCFS: Both computations show a greater n0 inpedestal and a sharper bump in Sion- Experimental uncertainties? Spatial resolution of diagnostics dr < 2mm;TS and camera are absolutely calibrated (though browning of camerafibers may be an issue)

- Is the KN1D solver operating correctly in this region of very shortgradient scale lengths? Benchmarking the code is an important step

- Could a non-1D effect be introducing a real physical effect not modeledwith the code?

~

Efforts underway to benchmarkKN1D against DEGAS 2 17

TH (KN1D)TH (DEGAS 2)

• DEGAS 2 is a Monte Carlo neutralparticle transport code

• DEGAS 2 benchmark18 at right:- neutral H0 launched from x=0 at T=1eVinto a slab of plasma 1m thick

- the x=0 surface reflects neutralsperfectly

- the x=1 surface is an exit- only interaction used is proton-hydrogencharge exchange

• Use atomic module of KN1D:- recompiled with a particle mirror at x=0(normally x=0 is a perfect absorber)

- ionization is made negligible by reducingTe to 0.5eV

• In either case, atomic D isaccelerated and heated as particlesdiffuse through slab

• Results match extremely well

ni is such that plasmapressure is constantacross slab(pi=0.85x1020 eV m-3)

Neutralmirror VH

nH (KN1D)nH (DEGAS 2)

KN1DDEGAS 2

The above case

Ti 10X higher,pi 17% higher

Return flux distribution

• Raise Ti such that Ti(x=0)>>TH(x=0), anddiscrepancies begin

• KN1D reports larger neutral driftvelocity, temperature in the initial 2cmof slab

• Further into plasma, two codes agreefairly well in terms of TH, nH gradient

• Case at left has x=0 as anexit (KN1D default) such thatthe return flux of neutrals Γ-(x=0) can be isolated

• Neutral albedo is defined asthe return flux over the inputflux: Γ-(x=0)/Γ+(x=0)

• KN1D neutrals are reflectedfrom plasma at higherenergies (and at a lowerrate) than DEGAS 2neutrals: longer averagepenetration!

Ti

TH (KN1D)TH (DEGAS 2)

nH (KN1D)nH (DEGAS 2)

• High spatial resolution measurements of ne, Te, and Dα emission enableinferrence of ionization profiles and effective particle transport coefficients

• Inferred levels of particle transport rise as discharges are pushed fartherinto the EDA operational regime by raising edge q

• Definite changes in scale lengths of ne, n0 profiles observed as edge q ispushed to highest levels and ne,PED approaches the low (for C-Mod) valueof 1x1020m-3

• More work can be done toa) correlate width and depth of the Deff well to plasma parametersb) examine the relative contributions of plasma transport and neutral physics to thescaling of the pedestal width

c) do these things in both H-mode and L-mode• Kinetic computation of neutral penetration agrees well with experiment inmost regions, but diverges prominently in the pedestal region, for reasonsthat are not clear

• Benchmarking is proceeding to determine under what conditions KN1Dyields believable results; initial results are promising, but much workremains

Conclusions

References1. M. Greenwald, et al., Nucl. Fusion 37, 793 (1997).2. T.H. Osborne et al., Plasma Phys. Control. Fusion 40, 845 (1998).3. ASDEX Team, Nucl. Fusion 29, 1959 (1989).4. J.W. Hughes et al., Phys. Plasmas 9, 3019 (2002).5. I.H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994).6. R.J. Groebner and T.N. Carlstrom, Plasma Phys. Control. Fusion 40, 673 (1998).7. R.J. Groebner et al., Phys. Plasmas 9, 2134 (2002).8. Y. Takase, et al., Phys. Plasmas 4, 1647 (1997).9. J.W. Hughes et al., Rev. Sci. Instrum. 72, 1107 (2001).10. B. LaBombard et al., Nucl. Fusion 40, 2041 (2000).11. S.J. Zweben et al., Phys. Plasmas 9, 1981 (2002).12. L.L. Lao, Nucl. Fusion 25, 1611 (1985).13. L.C. Johnson and E. Hinnov, J. Quant. Spectrosc. Radiat.Transfer 13, 333 (1973).14. M. Greenwald, et al., Phys. Plasmas 6, 1943 (1999).15. A. E. Hubbard, et al., Phys. Plasmas 8, 2033 (2001).16. B. LaBombard, PSFC Research Report, PSFC/RR-01-3 (2001).17. D.P. Stotler and C.F.F. Kerney, Contrib. Plasma Phys. 34, 392 (1994).18. D.P. Stotler, et al., in Proceedings of the Sixteenth International Conference on

Fusion Energy, IAEA, Vienna, 1997.