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Fusion Engineering and Design 88 (2013) 46– 50

Contents lists available at SciVerse ScienceDirect

Fusion Engineering and Design

jo ur nal homep age : www.elsev ier .com/ locate / fusengdes

odeling the gas flow in the neutralizer of ITER neutral beam injector usingirect Simulation Monte Carlo approach

iang-Long Wei, Chun-Dong Hu ∗, Li-Zhen Liang, Zhi-Wei Liunstitute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, PR China

r t i c l e i n f o

rticle history:eceived 21 December 2011eceived in revised form 22 June 2012ccepted 16 October 2012vailable online 17 November 2012

a b s t r a c t

The neutralizer is a key element in the neutral beam injector, where the energetic ion beam converts tothe needed neutral beam. Within the gas neutralizer, the gas flow pattern has a great influence on theneutralization efficiency of the ion beam and the gas load on the vacuum vessel. In most of the neutral-izers currently used, the gas flow falls within the transitional and molecular flow regimes. Considered

eywords:BIeutralizeras flow simulationSMC

the Direct Simulation Monte Carlo (DSMC) method is a benchmarking in the simulation of transitionalregime flow, it was firstly introduced to the gas neutralizers in this study. The simulation procedure hasbeen described in detail and applied to the ITER neutralizer case for demonstration. The predictions arecompared with existing results using Test Particle Monte Carlo (TPMC) method, and indicate the impor-tance of molecular collisions. The results show that the distribution of gas flow is nearly linear in mostregion of the neutralizer, but there are some stagnation zones around the gas inlet.

. Introduction

High power neutral beam injector (NBI) has been considered toe one of the major core plasma heating and non-inductive cur-ent driver systems for magnetic confinement fusion devices. Thengineering structure and operating principle of NBI are similar forifferent fusion devices [1]. A sketch of the NBI for Internationalhermonuclear Experimental Reactor (ITER) is shown in Fig. 1, itlso indicates the possible gas flow in the injector [2]. Ions arextracted and accelerated to the required energy from the beamource. In order to cross the intense magnetic field of the fusionevice, the neutral beam is necessary and a neutralizer is followedo the beam source for neutralizing the energetic ions. The residualons should be deflected and dumped into a target (i.e., residual ionump) to avoid the damage on the walls of the injection port.

The performance of neutralizer will determine the neutral-zation efficiency in the NBI and influence the energy utilizationfficiency of the heating and current drive systems. Generally, therere three kinds of neutralizer for NBI: gas [3], plasma [4] and pho-odetachment [5] neutralizer. In the gas neutralizer, the energeticons undergo kinds of collisions with the gas molecules, including

harge transfer which leads to the neutralization. Thus, the neutral-zation efficiency has a strong relationship with target thickness �i.e., target gas line density) in the gas neutralizer. The problem

∗ Corresponding author at: P.O. Box 1126, Shushanhu Road 350, Hefei, Anhui30031, PR China. Tel.: +86 551 5595661.

E-mail addresses: jlwei@ipp.ac.cn (J.-L. Wei), cdhu@ipp.ac.cn (C.-D. Hu).

920-3796/$ – see front matter © 2012 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.fusengdes.2012.10.004

© 2012 Elsevier B.V. All rights reserved.

is that abundant gas will effuse from each end of the neutralizer,imposing the re-ionization losses of neutral beam in the down-stream of neutralizer and the collision losses of ion beam duringthe acceleration. There is an optimum neutralizer thickness �opt

for different energy and different species ion beam [3]. However, itis more important to determine inlet gas quantity to reach �opt inthe accurate operation, and which depends on the gas flow patternin the neutralizer. During several decades of progress of NBI, thereare just a few of such researches reported in the publication. Pirkleand Conrad carried out gas flow measurements for a novel neutralbeam neutralizer [6]. A series of pressure profiles within the noveland normal neutralizer were measured for various inverse Knud-sen number. For the determination of the needed pumping speedin the vacuum vessel, Luo and Day calculated the gas density profilein the whole beamline of ITER heating neutral beam injector using a3D Test Particle Monte Carlo (TPMC) method [7]. Porton et al. werethe first to introduce augmented Burnett equations to develop a gasmodeling of the neutralizer for Joint European Tour (JET) [8]. Theresults have good accuracy when compared against experimentaldata in the transitional regime.

Direct Simulation Monte Carlo (DSMC) is a probabilistic simu-lation method [9], which is particularly suited to the research onrarified gas dynamics. DSMC has been fully proved against plentyof experiments and become a benchmarking for other new meth-ods used in the simulation of transitional regime flow [10]. The

degree of rarefaction of a gas is generally expressed through theKnudsen number (Kn = �/L), which is the ratio of the mean freepath to the characteristic length. Considered the gas flow in mostneutralizers falls within the transitional (Kn ∼ 0.1) and molecular

J.-L. Wei et al. / Fusion Engineering and Design 88 (2013) 46– 50 47

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3. Example

The structures and operation modes of gas neutralizers weresimilar in different injectors. The ITER neutralizer case was taken as

Construct cell network &set ini�al values

Star t

puff par�cl es into the neut raliz er

Move par�c les & comput eintera c�on with sur face

Delete the out sid e par�cles

Ind ex par�cles into cells

Compute colli sion sbetwee n mol ecul es

Sampl e flow proper�es

Steady flow

Output the resul ts

No

Yes

Fig. 1. The gas flow in the ITER neutral beam injector. Th

ow (Kn > 1) regimes, the present work was undertaken to adopthe DSMC approach to model the gas flow in neutralizer for the firstime. The procedure of modeling was described and applied to ITEReutralizer case for demonstration.

. DSMC modeling

The basic statistical mechanics equation for rarified gas is Boltz-ann equation. It has been proved that the DSMC method is

onsistent with the Boltzmann equation [11], and both of themre based on the hypothesis of molecular chaos and dilute gas. Dueo the above hypothesis, it can be supposed in the DSMC methodhat: (1) the binary collisions are dominant molecular collisions inhe chaos and dilute gas, and (2) the molecular motions and thentermolecular collisions can be uncoupled when the time step ishorter than the mean collision time. In order to reduce the cal-ulated amount addition, each simulation molecule is assumed toepresents a cloud of real molecules which have the same prop-rties. According to the actual gas properties, there are kinds ofolecular collision model and gas–surface interaction model to be

elected. In these models, the post-collision velocity and energy ofhe simulation molecules are selected randomly according to sometatistical law.

The flow chart [12] of the simulation of gas flow in neutral-zer by the DSMC method is shown in Fig. 2. At first, an adjustableumber of cells and coordinate system are constructed, along withome initial values and constants are set. And then, set the inletoundary on the number, positions and velocities of the puffingolecules. Because the molecules are uncharged, the movement of

he molecules is straight. The point of intersection between linearotion equation of the molecule and surface equation can be easily

ound in the coordinate system. According to the actual condition ineutralizer, different gas–surface interaction model can be used. Toeduce the computation load, the molecules which are out of neu-ralizer must be deleted. Next, index all the molecules in the orderf the cells. Since most of collisions are prone to occur betweenwo molecules closing to each other, a pair of molecules is selectedandomly in the same cell to simulate the impact. However, thesewo molecules are not certain to impact. It has a probability thatepends on the collision cross section and relative velocity. Andhere are some collision models to choose from, which determine

he kinetic and internal energy of molecule after colliding. The num-er of collisions is different from each cell due to different densitynd temperature. Finally, sample the flow properties which are sta-istical quantities from the microscopic amounts of every molecule.

ed narrows indicate the possible gas flow directions [2].

And now, a process of the simulation of gas flow in neutralizer iscompleted in one time step �t. Finally, take plenty of repeated runsuntil the flow properties results are saturated.

Stop

Fig. 2. Flow chart of simulation of gas flow in the neutralizer by DSMC method.

48 J.-L. Wei et al. / Fusion Engineering and Design 88 (2013) 46– 50

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vector length is proportionate to the velocity value. When injectinginto the neutralizer, the inflowing gas has an inlet velocity nor-mally across the boundary. Through the molecular collisions andmolecule–surface interactions, it becomes a regular longitudinal

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4x1019

5x1019

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Fig. 3. 2D physical model

n example, and Ref. [7] provided the density profile results to com-are with. The ITER neutralizer has four parallel channels of 3 m in

ength, 1.7 m in height and 0.11 m in width. The gas D2 is introducedhrough a series of circular holes in a vertical tube, which is placedt a relative position of 0.72 of the full length of the neutralizer. Inhis case, only the gas load from neutralizer is considered. The totalnlet gas quantity is 18 Pa m3/s in the neutralizer, and 4.5 Pa m3/sn each channel. The gas can be pumped out from the either end ofeutralizer, where a vacuum environment is provided by the cry-pumping system. However, the gas molecules may reflect fromhe wall of other elements (e.g., gas baffle, electrostatic screen) inhe beamline and return to the neutralizer. The similar 2D physical

odel of a channel of ITER neutralizer was built, but the gas inletoles were simplified to a gap in one of the channel walls (shown

n Fig. 3).The inlet flow temperature, Tin, the temperature of reflected

olecules, Tre, and the wall temperature, Tw, were all set equalo 300 K. The amount of reflected molecules was supposed tore1 = 0.1Qin and Qre2 = 0.2Qin respectively, in order to attain the gasensity at the outlets in agreement with the results of case 3 inef. [7]. An implicit boundary condition was applied to determinehe inlet velocity [13]. That is, (uin)j = 〈 uj〉. The term on the rightide is the cell-average velocity of the upstream boundary cells. Inddition, as the vacuum degree of gas flow and the smoothness ofall were not very high, the velocity of reflected molecule from

he walls followed the Maxwell–Boltzmann distribution law. Theariable Hard Sphere (VHS) model was adopted to simulate theolecular collisions, which is suitable to the single-component gas

14,15]. In such model, the scattering between two molecules issotropic, but the cross-section decreases as the relative velocityncreases. The practical applications showed that, the influence ofhis dependence of the collision cross-section on the properties ofhe flow field is essential.

. Results and discussion

11 × 150 uniform rectangular cells were applied in this study.he sub-cells were forsaken for the little change to the results. Over

× 105 molecules were simulated and the time step was 5 × 10−6 s.ach 5 time steps, the numbers and velocities of molecules wereampled once in the order of cells. The total number of samplesas 40,000 that is, the simulation time was 1 s. Note that, the num-

er of sample to reach assumed steady flow was 4000 (i.e., 0.1 s).ence, the flow properties of each cell were calculated with aver-ge results of 36,000 samples. At first, the collisionless MC methodas applied to this 2D ITER neutralizer model. It displays a cen-

erline density profile which is similar to the axial density profilef 3D TPMC method in Ref. [7] (Fig. 4). Hence, the 2D model heres reasonable. The density distribution is nearly linear across the

ost part of channel. But the profile given by the DSMC is gen-le around the gas inlet, and its maximum is 29% less than that ofollisionless results. Apparently, the reason is the molecular col-

isions introduced. When consider the molecular collisions, these

olecules quickly stream toward the outlets and become rare,ecause of the isotropic molecular collisions. Besides, the molec-lar collisions are more frequent as the gas density increasing. A

annel of ITER neutralizer.

direct result of this dilution effect is that, the actual gas thick-ness is less than estimation of collisionless method at the sameinlet gas quantity. The thickness obtained by DSMC with molecularcollisions and without molecular collisions is 9.14 × 1019 m−2 and8.52 × 1019 m−2 in this model, respectively.

The other properties of the gas flow in the ITER neutralizer chan-nel by DSMC are shown in Fig. 5. The value of the Knudsen numberKn ranges from 0.5 at the inlet and larger than 2 at the outlets, whichmeans that the channel falls within the transitional and molecu-lar flow regimes. Not only will the collisionless assumption induceerror in the transitional regime, but also application of CFD tech-nology in Ref. [8] may cause the deviation in the molecular regime.As the decreasing of molecular collisions in the downstream, themotions of the molecules reach uniformly, resulting in the veloc-ity across the channel is increasing in the both directions. Thecenterline pressure profile is given here for the comparison withexperimental data in future. Perhaps the most interesting resultin Fig. 5 is significant change in the inlet and outlet temperatures.Compared with the velocity profile, the temperature drop to eitheroutlet is in accordance with the rise of the absolute value of axialvelocity. Due to the acceleration of velocity, part of the internalenergy is converted to kinetic energy, so the temperature decreasesat both edges of the neutralizer. In addition, the internal energy isrelevant to the temperature and volume in real gas, so the infinityvacuum volume also result in the falling temperature near the neu-tralizer outlet. Meanwhile the injecting molecules impact intenselywith the reflecting ones around the inlet, heating the gas and mak-ing the temperature explosion.

As indicated in the distributions of various centerline prop-erties, the gas flow is more complex near the entrance, whichneeds further investigation. The gas flow with the channel is bestdescribed via the velocity vector plot as provided in Fig. 6(a). The

0.0 0.5 1.0 1.5 2.0 2.5 3.0

x (m )

Fig. 4. DSMC and collisionless MC prediction of centerline density profile in the ITERneutralizer channel.

J.-L. Wei et al. / Fusion Engineering and Design 88 (2013) 46– 50 49

0 50 100 150 200 250 300280

290

300

310

320

330

340

350

T (

K)

x (c m)

0 50 100 150 200 250 3000.00

0.05

0.10

0.15

0.20

P (

Pa)

x (cm)

0 50 100 150 200 250 300

-400

-200

0

200

400

u (

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)

x (c m)

0 50 100 150 200 250 3000

1

2

3

4

5

Kn

x (c m)

(a) (b)

(c) (d)

Fig. 5. Various centerline profiles in the ITER neutralizer channel by DSMC: (a) Knudsen number, (b) axial velocity, (c) pressure and (d) temperature.

Fig. 6. 2D maps around gas inlet of (a) the velocity vector plot, the contours of (b) temperature, (c) density and (d) pressure.

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0 J.-L. Wei et al. / Fusion Engine

ow quickly. Besides, it’s clearly illustrated that the velocity at theositive side of inlet is larger than that of the negative side. The rea-on is the longer wall provides a greater persistence of the viscousorce. Note that, there is a small vortex at negative side of the inlet

arked with dash line.Deviated from the nearly symmetric distribution of tempera-

ure (Fig. 6(b)), the density and pressure distribution are obviouslysymmetric about the centerline of inlet (Fig. 6(c) and (d)). Due tohe high speed of injecting flow, the pressure close to the entrance isery low, and the large pressure gradient will push some moleculesoving to this area. Furthermore, the viscous action of wall slows

own the movement of molecules to the outlets. Under commonnfluence of the two effects, the stagnation zone forms at the nega-ive side of the inlet. Because the gas is only supplied at one wall, allhe distributions, especially the gas density, are asymmetric abouthe centerline of the channel. A larger stagnation zone arises on thepposite wall of inlet.

For 1 MeV D− ion beam of the ITER injector, the estimated �opt

f D2 is about 1.4 × 1020 m−2 from the cross section data [2]. Andhe pressure between the beam source and neutralizer is calcu-ated to be 0.015 Pa to reduce the stripping losses. The gas targethickness in the calculated result here is 60% of the optimum value,ut the outlet pressure is high to 0.05 Pa. Definitely speaking, theeutralization region is from the grounded grid to the exit of RID.he complex structure of the other parts of neutralization regionill take the DSMC modeling into trouble. However, as the Kn result

ndicated, it is molecular flow regime outside the neutralizer, whichs easier to simulate via TPMC approach without molecular colli-ions. With such hybrid simulation, the whole neutralization regionan be well researched.

. Conclusion

The DSMC method is a benchmarking in the simulation of rar-fied gas flow. In this study, it has been applied to the gas neutralizerf neutral beam injector for the first time. A 2D computationalodel of one channel of ITER neutralizer was built, and gas flow

nside the model was simulated via DSMC approach for demon-tration. The centerline density profile of the channel was givennd compared with existing results via TPMC method, which indi-

ates the importance of molecular collisions. The gas flow in theas channel was characterized when combined with the other cen-erline profiles. A closer research revealed the complication of gasow around the inlet.

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and Design 88 (2013) 46– 50

The DSMC approach can be expanded to the other gas neu-tralizer for NBI or neutral beam accelerator, and assist to find theoptimum operation mode. Considered the collisions between theenergetic charged particles or molecules, it will be used to studythe gas flow in the presence of beam and neutralization process.

Acknowledgements

This work was supported by the National Natural ScienceFoundation of China under Grant No. 10875146, the ChineseAcademy of Sciences Knowledge Innovation Project: the studyof neutral beam steady-state operation of the key technical andphysical problems, and the Chinese Academy of Sciences Knowl-edge Innovation Project: the study and simulation on beaminteraction with background particles in neutralization area forNBI.

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