J. Plasma Fusion Res. SERIES, Vol.3 (2000) 279-Zg3

Hydrogen Recycling and Wall Equilibrationin Long-Pulse Operation
MIODUSZEWSKI Peter*
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37716, U.S.A.
(Received: I February 2000 / Accepted: 12 April 2000)

Abstract
Wall recycling of hydrogen isotopes effects fueling and plasma performance. In most present fusion
devices with pulse lengths in the range of several seconds, recycling evolves during the discharge and,hence, fueling conditions are not stationary. In order to find out what is needed to provide stationary
recycling conditions, this paper studies the particle balance between plasma, wall, and external exhaust.
A crucial factor is the recycling coefficient which, on a given surface, depends on the particle flux andtrapped fluence. For a typical fusion device, the particle flux to the wall surface can vary over four ordersof magnitude and the recycling coefficient will change accordingly. As an example, we have studied thewall surface of the DIII-D tokamak and calculated the incident particle fluxes with the DEGAS code for
85 segments ofthe wall. For each ofthese segments we have calculated the trapped fluence and recycling
coefficients for a typical discharge. The result shows that different parts of the vacuum vessel are
important during different phases of the discharge.

Keywords:
recycling, particle balance, trapping, wall pumping, wall equilibration

1. Introduction

implanted into the walls. If the device is equipped withexternal particle pumping, a certain fraction of the total

Wall recycling of hydrogen isotopes affects wallinventory and plasma performance. Wall recycling
usually evolves as a function of time during thedischarge from low recycling (depleted walls) to highgas can also be exhausted from the system. To obtain abetter understanding of the distributions of the total gas,
we construct a particle balance including the plasma

recycling (saturated walls). Due to the increasing
recycling coefficient, plasma fueling and plasma
performance can potentially change as a function oftime. In order to shed some light on the processes

inventory, wall inventory, and the exhausted gas. In thefollowing equations, Npt, N-, and Np.p are theinventories of the plasma, the wall, and the pumprespectively:

dN_, _ N_,_?=4.<D(t1_f+CII'pinvolved in recycling and wall equilibration, this paper
investigates wall recycling processes by analyzing
space- and time-dependent recycling coefficients.

INlt''n l+(r-€) n l(r -n).or0*?1.

2. Particle Balance Between Plasma, Wall,and External Exhaust+(1-€).0.N,

Of the total amount of gas puffed into a tokamak orstellarator plasma discharge, typically only lO-2OVoends up in the plasma itself, whereas the rest is*Correspondin7 author's e-mail: mioduszewspk@ ornl. gov
279[tt-rt.

o@*+(1)@2000 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchMioduszewski, P. et al., Hydrogen Recycling and Wall Equilibration in Long-Pulse Operation

-d.N,
dNp^p

dt

=,*

@o*Yh9a)Nw (t)\ot ft)[t'(3)

Here 4 is the fueling efficiency, @ is the gas input(TonL/s), t, is the particle confinement time, R is therecycling coefficient, e is the fraction of the gas flow
exhausted by the divertor or pump limiter, and a is theparticle-induced desorption (PID) coefficient. The gas

46time (s)Fig. 1 Particle balance with zr* = 1.3 sec, including PID
and no eldernal pumping.

input { is taken as a step function between t = 0 and / =5 s, and the particle balance as a function of time is obtained by integrating Eqs. (l) to (3) numerically. The re-12.10

sult is depicted in Fig. I for a fixed recycling coefficientof R = 0.85. It can be seen that at a pulse length of r = 5o 9.6

s the density is not stationary. The particle confinement-c.9Etime is taken as Tp = 0.2 s, so that the global confinement time with the given R = 0.85 is rr* = rrl(l - ft) =1.3 s. If, on the otherhand, pumping is turned on, as indicated in Fig. 2, ro* is 0.5 s and the density is stationary,i.e. if the pulse length is large compared to zo*, thebalance between plasma density, wall pumping, and external exhaust is stationary. This can also be achieved
with a lower recycling coefficient, since it reduces ?o*,and the critical parameter is the ratio of the pulse lengthto rD+.
While this example demonstrates the effect of thevarious elements of the balance equations, in reality the8 z.zobE 4.8z=

2.40lime(s)Fig. 2 Particle balance with pumping turned on ond zr* =0.5 sec

recycling coefficient is not constant and will change as afunction of time during the discharge. In the next
paragraph we will develop a simple analytical formulanr, is:that can be used to describe the time-dependence of therecycling coefficient in the above balance equations.

ln'--n.
R(n,,)=a tanh\Lr'-

3. Fluence-Dependent Recycling Coefficient+c.

(4)

The parameters a and c adjust the initial value and thefinal value ofR (unity), n,r^and 6are used to adjust for
the incident particle energy. For particle energies of 50,

During a plasma discharge the local recycling
coefficients evolve as functions of the trapped fluencewhich is usually a function of time. So, for a given
incident flux, the recycling coefficients evolve as afunction of time. We have constructed an analyticalformula for the recycling coefficient which is a good
approximation of measured values [] and also of TRIM
calculations published by W. Eckstein [2]. The recycling
coefficient as a function of the trapped particle density

100, 200 eV, the recycling coefficient according to Eq.
(4) is shown in Fig. 3. The number of trapped particles
resulting from this recycling coefficient as a function ofincident fluence is depicted in Fig. 4.
It is obvious that different parts of the vacuum
vessel will behave differently with respect to recycling.
If we introduce the fluence-dependent recycling into the280

Mioduszewski, P. et al., Hydrogen Recycling and wall Equilibration in Long-pulse
50eV 100eV 2OeV

Ioperation

balance equations , we get the density evolution with a

0.9

variable recycling coefficient. The resulting particle

OTbalance with external pumping is shown in Fig. 5, where

0.7

pumping is switched on at I = 2.5 seconds.

_.
0.6
r(U4. Spatial Variation of Recycling Coefficient
Having a model for the fluence- or time-0.,0.4

dependence of the recycling coefficient is not sufficient

0.3

to describe recycling in a fusion device, because theparticle fluxes incident on different parts of the wallvary widely, leading to different evolutions of the020.1010

rut0l9recycling coefficient on different parts of the wall. To

1020 1021 fincomplete the picture, we investigate the spatial

q1 @arricbd#)

dependence of the recycling coefficient using a concreteFig. 3 The recycling coefficient as a function of trapped
particle fluence.

example, the DIII-D vacuum vessel.
For these calculations the wall was subdivided into
poloidal85
segments for which the incident particle flux
was determined with the DEGAS code [L.W. Owen].
The evolution of the recycling coefficients in each of thesegments was determined with Eq. (4). The division of
the vacuum vessel wall into zones is indicated in Fig. 6

and the recycling coefficients of 6 wall segments are
depicted in Fig. 7.

bI

€rg

In Fig. 7 the recycling coefficient as a function oftime remains low in segment l, approximately at theinner midplane where the flux is low. The three highest€101021
I (partlcles/1#)

20finFig.4 Trapped particle fluence n,, as a function ofincident fluence and particle energy.

8.fi21{?
-10EC)

oE86bo=CLN
100o24E5E.

15o502z0or (s)xwall (cm)Fig. 5 Density evolution with fluence-dependent

recycling coefficient and external pumping.

Fig. 6 The (5) zones of the Dlll-D vacuum vessel.

281

Mioduszewski, P. et al., Hydrogen Recycling and Wall Equilibration in Long-Pulse Operation
150

1.0
E088

if, Ac.E€ o.zoIIo.ooaq,
Eos20.4

eo\?r,rl*lti,l.Jr,,ltt

F-EC'Eo0e/()

r! -10A,qaEsoE

uo'T'It/o850E1o<.{}

50c001234

o-50"50time (s)| (s)Fig. 9 Particle balance in a Dlll-D discharge: input gas

Fig. 7 Recycling coefficients as a function of time on 6
segments of Zone 2.

puff, plasma particle content, divertor exhaust.
and wall inventory.

1023

surpasses the flux pumped in the baffle. Then, after

1022
oco

about I second, the neutral flux on the baffle becomesequal to the flux on the inner wall, and at the same timethe overall pumping becomes dominated by the outerwall. Although the outer wall flux is small, the recycling.DN

coefficient is low and the surface area is large and,6

therefore, the total pumping here dominates the global
recycling.
Using the recycling coefficient in Fig. 3 for 100 eVparticles; a trapped fluence of 102r m-2 would lead torecycling near unity with the surface near equilibration.
In the divertor, incident fluxes in excess of 5 x 1022
m-2s-l have been observed. This means that a trapped.go 1021

o(E(tcc\E20to- 101019

fluence of l02r m-2 could be reached within one second,
whereas other areas, with particle fluxes of e.g. 1020
m-2s-r, would need several hundred seconds to reach the01234
rime (s)saturation fluence. Fortunately, this situation can becontrolled by applying external pumping. As indicatedabove, an additional particle sink, as introduced byexternal pumping, can dominate the overall recycling
and shorten the equilibration time correspondingly.

Fig. 8 Pumped particle fluxes in Tone 1 through 5 (1 =top wall, 2 = innerwall, 3 = divertor. 4 = baffle. 5 =outer wall).

5. Dynamic Retention and External Control
It has been shown that the change of the wall

recycling coefficients correspond to the segments ofhigh fluxes close to the inner strike-point. Combining all
segments into 5 zones and adding up the fluxes for all
segments in each zone, we obtain the pumped particle
flux in each zone. The pumped particle fluxes for agiven time and for each segment are depicted in Fig. 8.
The initial pumping is dominated by the divertor(Zone 3) due to the large surface area and high flux.
After about 0.2 s the total flux pumped by the inner wallinventory during a plasma discharge can be controlled ineither direction, i.e. it can be either increased ordecreased. Without external pumping, the inventory will
eventually have to increase until the walls are saturated.
However, when external pumping is applied, the wallinventory can be depleted and the particles removed
from the walls are eventuallv removed from the svstem.
282

Mioduszewski, P. et al., Hydrogen Recycling and wall Equilibration in Long-pulse operation

This leads to a totally different picture of wall

6. Summary and Gonclusion
Wall equilibration due to recycling can takehundreds or even thousands of seconds if no external

equilibration. In a plasma discharge with external
pumping, the walls respond to externally imposedsources and sinks. The wall inventory becomes

particle exhaust is provided. However, providing andynamic. As a consequence, the recycling coefficientand, therefore, the wall equilibration time can be

external particle sink to the particle balance, can force
the equilibration to shorter times. In addition, it has been

controlled externally.

demonstrated that the wall inventory can be dynamicallyThis depletion of the wall inventory has been
demonstrated in several tokamaks such as Tore Supra,
DIII-D, and TEXTOR. As an example, we show in fig.
9 the evolution of a DIII-D discharge with gas puff,changed with external exhaust such as provided bypumped limiters or divertors, so that the recycling
coefficient becomes one of the controllable parameters
in a magnetic fusion device.

plasma inventory, particle exhaust, and wall inventory[3]. The wall inventory is usually obtained from theReferences

particle balance.

[1] Haasz, A. et al., J. Nucl. Mater.232,2l9 (1996).
[2] Eckstein. W., Garching Report IPP 9133, October

The left-hand-side of the plots depicts the particle
rates in Torrl/s and the right-hand side shows theparticle inventories in Torrl. The figure shows that,with sufficient pumping, the external gas source can bebalanced and the exhausted gas can surpass the input.
For constant plasma density, the extra particles can only
originate from the walls. Similar results have beenreported from other machines [4].

1980.

[3] Mioduszewski, P.K., Hogan, J.T., Owen, L.W.,
Maingi, R. et al., J. Nucl. Mater. 220-222,91-103(l995).

[4] Banno,T., Noda, N., Finken, K.H. et a/. J. Nucl.
Mater. 220-222, 478-482 (1995).

283