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Proposed Heuristic Model for Fuzz Growth on Metal SurfacesR. Ochoukov* 1), D.G. Whyte 1), and G.M. Wright 1)1) Plasma Science and Fusion Center, MIT, 190 Albany Street, Cambridge, MA, 02139

* email contact: ochoukov@psfc.mit.educopy of poster available at: http://www.psfc.mit.edu/research/alcator/pubs/APS/index.html

What we know about fuzz so far:- First observed in 2006 on W surfaces under He exposure in NAGDIS-II divertor simulator [Takamura 2006].

- Fuzz consists of nano-scale tendrils 20-100 nm in diameter.

- Fuzz tendrils grown on W surface are made primarily of W [Takamura 2006].

- Spherical voids, ~10 nm in diameter, present inside fuzz, presumably filled with helium [Kajita 2007].

- He concentration in fuzz nano-tendrils is ~1 % and is independent of incident He flux, profile depth, or surface temperature [Woller 2010].

- Growth of fuzz thickness Xo follows diffusion-like equation as function of exposure time t: Xo ~ t1/2 [Baldwin 2008 and Baldwin 2009].

- Fuzz growth occurs at surface temperatures between 1000 and 2000 K and incident He ion energies >10 eV [Kajita 2009].

- Fuzz growth occurs on tungsten and molybdenum surfaces[Kajita 2009].

- Low Z impurities (carbon or beryllium, fraction ~ 0.1 %) impede formation of fuzz [Baldwin 2009].

- Fuzz forms efficient deuterium retention barrier [Baldwin 2011].

- Fuzz modifies surface properties such as floating potential [Takamura 2010] and sputtering yield [Doerner 2011].

Motivation:- Any tritium burning fusion reactor, including D-T operating phase of ITER, will produce large quantities of He ash.- Plasma facing components (PFCs) in ITER and other tritiumburning devices are expected to be made of W: - High melting temperature and hence high resistance tothermal fluxes. - Low sputtering yield by deuterium ions.- W PFCs are expected to operate at high (> 1000 K) temperatures to be above ductile-to-brittle transition.- Fuzz formation is observed in laboratory and tokamak (divertor) environments.Key motivating questions:- Can we predict fuzz growth under different plasma conditions?- What mechanism(s) determine observed fuzz growth dynamics?- What might we expect for limits to fuzz growth?

References:G.M. Wright et al., Growth of tungsten nano-tendrils in the Alcator C-Mod divertor, APS-DPP (2011), Salt Lake City.M.J. Baldwin, R.P. Doerner, D. Nishijima et al., JNM, 390-391 (2009) 886-890.S. Takamura, N. Ohno, D. Nishijima, and S. Kajita, Plasma Fusion Res., 1 (2006) 051.S. Kajita, S. Takamura, N. Ohno et al., Nucl. Fusion, 47 (2007) 1358.K. Woller, D.G. Whyte, and G. Wright, Depth profiles of helium and deuterium in tungsten “fuzz” using elastic recoil detection, APS-DPP (2010), Chicago.M.J. Baldwin and R.P. Doerner, Nucl. Fusion 48 (2008) 035001.S. Kajita, W. Sakaguchi, N. Ohno et al., Nucl. Fusion 49 (2009) 095005.M.J. Baldwin, R.P. Doerner, W.R. Wampler et al., Effects of He on D retention in W exposed to low-energy, high-fluence (D, He, Ar) mixture plasmas, PFC 2011 meeting, Oak Ridge.S. Takamura, T. Miyamoto, and N. Ohno, Plasma Fusion Res., 5 (2010) 039.R.P. Doerner, M.J. Baldwin, and P.C. Stangeby, Nucl. Fusion, 51 (2011) 043001.

Acknowledgments:Supported by USDoE award DE-FC02-99ER54512.

Mathematical model:Key assumption: - Product Γ(Xo, t)∗t = const = Φcritical during fuzz growth.Key hypothesis: dΓ/dXo = -αΓ3/2 (1),Integrating across the thickness of the fuzz layer and using the boundary condition Γ(Xo = 0) = Γo we obtain: -2Γ-1/2 = -αXo - 2Γo

-1/2 (2).Rearranging Equation (2) we obtain: Γ = (αXo/2 + Γo

-1/2)-2 (3).Applying the condition Γt = Φcritical we obtain: t(αXo/2 + Γo

-1/2)-2 = Φcritical (4)or, equivalently:

Discussion of physical insights from model:

Conclusions:- Fuzz growth proceeds after metal surface is exposed to criticalHe fluence Φcritical = 2.4x1024 m-2.- Fuzz growth follows diffusion-like equation:

- Key assumption is: Γt = constant = Φcritical during fuzz growth.- Fuzz growth can be mitigated in pulsed devices through reduction/control of incident He flux.- Continuously running D-T burning fusion reactors with hot(>1000 K) tungsten walls will develop fuzz growth on W PFCs.

What is fuzz:- Fuzz is growth of nano-scale tendrils on metal surfaces inpresence of helium (He) under set of unique conditions.

(a)(b)

Figure 1: Fuzz growth on tungsten (W) surface in Alcator C-Mod tokamak in helium plasma [Wright 2011].

Physical model:

Figure 2: Diagram showing geometry used in mathematical model. Symbol definitions:- Xo − fuzz thickness.- Γo − incident He flux at Xo = 0.- t − exposure time.- tmin − exposure time at Xo = 0.- D − effective diffusion coefficient for fuzz growth.- Φcritical − critical He fluence for fuzz growth.- α − proportionality constant.

Experimental observations:- Fuzz growth follows diffusion-like relation Xo ~ (2Dt)1/2.- Fuzz growth proceeds after “bulk” surface exposed to criticalfluence Φcritical = 2.4x1024 m-2.

21

122= /

ooo Γα

Dt)t,Γ(X

Fuzz

Thi

ckne

ss (µ

m)

~40 stmin = 40 s t varies, Γo constant

MODEL

Fuzz

Thic

knes

s (µ

m) 2.2 µm

6.7x1020 m-2s-1

Figure 3: Dynamics of fuzz growth on W surface at 1120 K at (a) constant Γo and (b) constant t. Data from [Baldwin 2009].

Γo (m-2s-1)

Test of model:Varying ΓoConstant t

Γo(Xo = 0) = 6.7x1020 m-2s-1

2.2 µm

MODEL

EXPERIMENT

EXPERIMENT

(5)

21

122= /

ooo Γα

Dt)t,Γ(X

2

2≡

αΦD

critical

(6)

EXPERIMENT:Γo = 6x1022 m-2s-1

D = 6.8x10-16 m2s-1

tmin = 40 s−> α = 3.5x10-5 s1/2

- Is fuzz growth atomistic process? - nW = 6.8x1028 m-3 and fHe/W = 1% −> nHe = 6.8x1026 m-3

- Effective diffusion length = Φcritical/nHe ~ 1x10-2 m >> fuzzscale-length. - Therefore, fuzz growth is NOT atomistic process!

- Fuzz growth in Alcator C-Mod observed after ~10 s exposureto He plasma (ne = 5x1020 m-3, Te = 20 eV, θgrazing = 10o): - Γo ~ ne*cs*sinθgrazing = 5x1020 x 104x(20/2)1/2sin10o = = 2.7x1024 m-2s-1

- tmin = 2.4x1024 / 2.7x1024 = 1 s < 10 s, consistent with model!

- What about ITER D-T phase? - ne ~ 1x1020 m-3, Te ~ 10 eV, fractionHe ~ 1%, θgrazing = 10o

- Γo ~ 3.9x1021 m-2s-1 −> tmin ~ 600 s, - Fuzz will grow in ITER divertor after ~ 1 D-T shot!

- What about temperature effects? - D follows arrhenius dependence on T. - α ~ D-1/2. - Threshold is not influenced by T, but fuzz thickness increases with T as D1/2.

o

criticalmin Γ

Φt = (7)