prediction of material erosion and lifetime during major ... · fusion engineering and design 60...

Fusion Engineering and Design 60 (2002) 527–546

Prediction of material erosion and lifetime during majorplasma instabilities in tokamak devices

Ahmed Hassanein *Argonne National Laboratory, 9700 South Cass A�enue, Argonne, IL 60439, USA

Abstract

Surface and structural damage to plasma-facing components due to the frequent loss of plasma confinementremains a serious problem for the tokamak reactor concept. The deposited plasma energy during major disruptions,edge-localized modes (ELMs), and vertical displacement events (VDEs) causes significant surface erosion, possiblestructural failure, and frequent plasma contamination. Surface damage consists of vaporization, spallation, and liquidsplatter of metallic materials. Structural damage includes large temperature increases and high thermal stresses instructural materials and at the interfaces between surface coatings and structural members. To evaluate the lifetimesof plasma-facing materials and nearby components and to predict the various forms of damage that they experience,comprehensive models (contained in the HEIGHTS computer simulation package) are developed, integrated self-consis-tently, and enhanced. Splashing mechanisms such as bubble boiling and various liquid magnetohydrodynamic (MHD)instabilities and brittle destruction mechanisms of nonmelting materials can be serious erosion mechanisms and arebeing studied in detail. The ejected macroscopic particles (MPs) will interact with incoming plasma particles and withthe vapor cloud above the surface. Therefore, the dynamic behavior of MPs in the vapor cloud and their influenceon total erosion rate is important. Results of self-consistent MHD calculations are presented in which the dynamicsof both the vapor cloud and MP interaction are coupled with incoming plasma ions and electrons from the scrape-offlayer during a disruption. The design requirements and implications of plasma facing and nearby components arediscussed, along with recommendations to mitigate and reduce the effects of plasma instabilities on reactorcomponents. Published by Elsevier Science B.V.

Keywords: Erosion; Disruptions; Melting; Splashing; Vapor shielding; HEIGHTS package

www.elsevier.com/locate/fusengdes

1. Introduction

Interaction of powerful plasma and particlebeams (power densities up to hundreds of GWm−2 and time duration up to tens of ms) withvarious materials significantly damages exposed

target surfaces and nearby components. Investiga-tion of material erosion and damage due to in-tense energy deposition on target surfaces isessential for many applications, space studies;study of the earth surface interaction with collid-ing asteroids and comets, creation of new sourcesof radiation; high-energy physics applications;thermonuclear and inertial fusion studies, etc. Ex-perimental and theoretical activities in this field

* Tel.: +1-630-252-5889; fax: +1-630-252-3250.E-mail address: [email protected] (A. Hassanein).

0920-3796/02/$ - see front matter Published by Elsevier Science B.V.

PII: S0920-3796(02)00008-X

mailto:[email protected]

A. Hassanein / Fusion Engineering and Design 60 (2002) 527–546528

move toward the common goal of achieving abetter understanding of the physics phenomenaand material properties of various plasma–sur-face interactions under extreme conditions of hightemperature and pressure. An important applica-tion of this understanding is in future tokamakfusion devices during plasma interaction withplasma-facing materials (PFMs).

Damage to plasma-facing and nearby compo-nents as a result of various plasma instabilitiesthat cause loss of plasma confinement remains amajor obstacle to a successful tokamak reactorconcept. Plasma instabilities can take variousforms, such as major disruptions, which includeboth thermal and current quench (sometimes pro-ducing runaway electrons); edge-localized modes(ELMs), and vertical displacement events (VDEs).The extent of the damage depends on the detailedphysics of the disrupting plasma, the physics ofplasma–material interactions, and the designconfiguration of plasma-facing components(PFCs) [1]. Plasma instabilities such as hard dis-ruptions, ELMs, and VDEs will cause both sur-face and bulk damage to plasma-facing andstructural materials. Surface damage includes high

erosion losses attributable to surface vaporization,spallation, and melt-layer erosion. Bulk damageincludes large temperature increases in structuralmaterials and at the interfaces between surfacecoatings and structural materials. These largetemperature increases can cause high thermalstresses, possible melting and detachment of sur-face material, and material fatigue and failure.Other bulk effects of plasma instabilities, particu-larly those of longer duration, such as VDEs, andthose with deeper deposited energy, such as run-away electrons, can deliver high heat flux valuesat the coolant channels, possibly causing burnoutof these tubes [2]. In addition to these effects, thetransport and redeposition of the eroded surfacematerials to various locations on plasma-facingand nearby components are a major concern forplasma contamination, safety (dust inventory haz-ard), and successful and prolonged plasma opera-tion after instability events [3], Fig. 1 is aschematic illustration of the various interactionzones and physics currently included in the HighEnergy Interaction with General HeterogeneousTarget Systems (HEIGHTS) simulation package ina self-consistent and integrated way duringplasma instability events.

Fig. 1. Schematic illustration of various interaction zones and physics involved during plasma instabilities.

A. Hassanein / Fusion Engineering and Design 60 (2002) 527–546 529

Several key factors can significantly influencethe overall response and erosion lifetime of a PFCas a result of the intense energy that is depositedduring these plasma instabilities. These factorsare, (a) characteristics of particle-energy flow (i.e.particle type, kinetic energy, energy content, de-position time, and location) from the scrape-off-layer (SOL) to the divertor plate; (b)characteristics of the vapor cloud that developsfrom the initial phase of energy deposition ontarget materials and its turbulent hydrodynamics;(c) photon-generated continuum and atomic lineradiation and transport in the vapor cloud andnearby regions; and (d) characteristics of plasma–solid-melt-layer–debris interactions.

The HEIGHTS simulation package has been de-veloped to study in detail the various effects ofsudden high-energy deposition of various sourceson target materials [4]. The package consists ofmany integrated models that follow the beginningof a plasma disruption at the SOL up to thetransport of the eroded debris and splashed targetmaterials as a result of the deposited energy. Onemodel in the package, the SOLAS code, describesthe plasma behavior in the SOL during a disrup-tion and predicts the plasma parameters and con-ditions at the divertor plate [5].

To evaluate the various damage mechanisms toplasma-facing and nearby components caused byplasma instabilities, we have developed full multi-dimensional comprehensive radiation magnetohy-drodynamic (MHD) models that use advancednumerical techniques such as particle-in-cell(PIC), forward-reverse, and Ray Tracing methods[4]. These models, which use such advanced nu-merical methods, are needed for a realistic analy-sis of disruption conditions and overallconsequences. Detailed physical models ofplasma–solid– liquid–vapor interaction in astrong oblique magnetic field have also been de-veloped in a fully self-consistent multidimensionalmodel that is coupled with radiation MHDmodels.

Factors that influence the lifetime of PFCs suchas loss of vapor-cloud confinement and vaporremoval due to MHD instabilities, damage tonearby components from intense vapor radiation,melt splashing, and brittle destruction–explosive

erosion of target materials, can also be modeled indetail [6,7]. The HEIGHTS package being used forreactor design estimates is validated against well-diagnosed experiments in disruption simulationfacilities [8]. A major part of the current workfocuses on modeling the behavior and erosion of ametallic surface with a liquid layer, subject tovarious internal and external forces during theenergy deposition phase, as on the explosive ero-sion, and on the characteristics of brittle-destruc-tion erosion associated with carbon-basedmaterials (CBMs). Although in general, goodagreement is found for many of the cases studied,discrepancies still exist and must to be resolved.

Accurate prediction of mass losses requires fulldescriptions of evolving media above the targetsurface that consist of a mixture of vapor andmacroscopic particles (MPs) moving toward thedisrupting plasma as schematically illustrated inFig. 1. Photon radiation from the upper hot re-gion of the vapor will then be absorbed by bothdivertor surface and the surface of the ejectedMPs. This leads to further surface vaporization ofdivertor and MP surfaces. In such a mixture,additional screening of the target surface by theMP cloud can occur. This could lead to a signifi-cantly reduced power flux to the surface due to‘droplet shielding’, which is analogous to the va-por shielding effect [3]. In a well-confined vaporcloud, the flight lifetime of MPs in the vapor isshort, and complete burning of the emitted MPsoccurs. This droplet shielding effect can lead tofurther reduction of the total erosion loss.

To correctly predict macroscopic erosion, afour-moving-boundaries problem is solved inHEIGHTS [4]. The front of the vapor cloud is onemoving boundary, determined by solving vaporhydrodynamic equations. The second movingboundary, due to surface vaporization of thetarget, is calculated from target thermodynamics.A third moving boundary, behind the surfacevaporization front, is due to the melt-splashingfront. Finally, the fourth moving boundary is atthe liquid–solid interface; it further determinesthe new thickness of the melt layer. The SPLASH

code (part of the HEIGHTS package) calculates themacroscopic mass losses by using the splashing-wave concept as a result of each macroscopic


erosion-causing mechanism [4]. Thus, total ero-sion is calculated from the sum of all possibleerosion mechanisms. An overall assessment oferosion lifetime of PFCs should then includeatomic surface vaporization, macroscopic erosionfrom liquid–metal splashing and brittle destruc-tion of CBMs, and erosion damage to nearbycomponents from intense vapor radiation anddeposition.

2. Plasma–material interaction leading to meltingand vaporization

Plasma-facing surfaces are rapidly heated dur-ing plasma instabilities by direct impact of en-ergetic plasma particles and radiation. The energydeposition in the bulk material is calculated byusing models that include the physics of energyloss by plasma ions and electrons in target mate-rials. HEIGHTS package calculates in detail thespatial and time dependence of beam energy de-position in various target materials. Energy depo-sition methods include analytical, semi-empirical,and Monte Carlo techniques for accurate predic-tion of the deposited energy. The deposited en-ergy flux can be high enough to rapidly melt andvaporize the surface material. The thermal re-sponse of the material is calculated by solving amultidimensional (up to 3-D) time-dependentheat-conduction equation, with movingboundaries, i.e. the receding eroded surface andthe solid– liquid interface, with boundary condi-tions that include heats of melting and vaporiza-tion [2], Most of the calculations presented in thisstudy is, however, is 2-D time-dependent analysis.

It is known that during the early stage of anintense power deposition on a target material, avapor cloud from the target debris will formabove the bombarded surface. This shielding va-por layer, if well confined, will significantly re-duce the net energy flux to the originally exposedtarget surface to only a few percent of its initialincident value; thereby substantially reducing thenet vaporization rate [2,9]. Depending on the typeof application, this shielding layer can be eitherbeneficial (i.e. the protection is desirable) orharmful (protection is not desirable). For exam-

ple, the shielding by the earth’s atmosphere at thesurface of colliding asteroids and comets duringentrance can prolong the object lifetime and bemore dangerous to earth. Also in laser or elec-tron beam welding or cutting of materials thedeveloped vapor cloud is harmful since it reducesthe beam power flux to target surface and, there-fore, reducing welding or cutting efficiency. Theshielding efficiency of this vapor-plasma cloudwill, however, depend on several factors. The netpower flux that reaches the target surface deter-mines the net erosion and thus the lifetime ofPFCs. Net erosion damage to PFCs due toplasma instabilities should include surface vapor-ization loss, erosion damage to nearby compo-nents from intense vapor radiation, andmacroscopic erosion from liquid–metal splashingand brittle destruction of CBMs.

Initially, the neutral vapor emitted from thesolid or liquid target surface expands freelyacross magnetic field lines in the direction normalto the surface. As the cold vapor is heated byincident plasma particles, it becomes ionized andexpands, following the direction of the obliquemagnetic field lines. The parameters and the dy-namics of the target plasma depend on the energyflux and the type of target material. Low-Z targetplasma (e.g. carbon, beryllium, lithium, etc.) ex-pands to larger distances from the surface,whereas vapor shields formed from higher-Z ma-terials (e.g. tungsten, molybdenum, etc.) staycloser to the surface. The incoming plasma parti-cles are completely stopped in the vapor plasmaand the plasma energy flux is converted to pho-ton radiation. Although reduced from its originalvalue, the net energy flux to the target surface(dominated by photon radiation) is large enoughto cause melting and further erosion of metalliccomponents.

The expansion of vapor plasma into the vac-uum (surrounding gas or plasma) above the ex-posed target surface under the influence of astrong magnetic field is determined by solving theMHD equations for conversation of mass, mo-mentum, and energy:

��

�t+�(�Vb )=0, (1)


��Vb�t

+�P=F,b (2)

and

�E�t

+�(EVb )+P�Vb =�(K�T)�Qr+�Qb+Jb 2

�,

(3)

where V is vapor plasma velocity, � is density, Eis energy, P is pressure, F is external force, K isvapor plasma thermal conductivity, T is vaportemperature, Qr is radiation flux, Qb is the inci-dent particle flux from the disrupting plasma, J isplasma current density, and � plasma electricalconductivity. All variables of these equations areboth time- and space-dependent. The plasmabeam particle flux deposited in the vapor is calcu-lated by similar methods for the slowing down incold target i.e. by inelastic and elastic collisions,however, an additional stopping mechanism isused which arises from the free electron due toionization. This free electron stopping term cansubstantially shorten the range of both plasmaions and electrons in the ionized vapor leading tohigh-energy deposition rate at the front vaporzone.

The vapor plasma once ionized and with largeelectrical conductivity, is assumed to move freelyalong magnetic field lines. The vapor plasmaequation-of-motion is solved in two directions,along and perpendicular to divertor surface. Theequation of motion in a strong magnetic field canthen be written as:

�dVbdt

= −�P+Fb m, (4)

Fb m=1c

[Jb ×Bb ], (5)

where Fm is magnetic force, J is plasma currentdensity, c is speed of light, and B is magnetic fluxdensity. The induced magnetic force will act as aretarding force to vapor expansion. The electric, �,and magnetic field B are defined from Maxwellequations:

1c

��t

=�×Bb +4�

cJb (6)

1c

�Bb�t

= −�×�� (7)

The time variation of the induced electric fieldin the vapor plasma is usually very small.Therefore:

�×Bb = −4�

cJb , (8)

and

�� =1c

[Vb ×Bb ]+Jb�

(9)

The time-varying magnetic field in the vaporplasma can then be given by:

�Bb�t

= −�× [Vb ×Bb ]+�×� c2

4��×Bb n (10)

The magnetic force Fm, is composed of a mag-netic pressure force, Fp, and a tension, Ft, due tothe curvature of the magnetic field lines, where:

Fp= −��Bb 2

8�

�(11)

Ft= −1

4�(Bb �)Bb (12)

The melt layer, developed during a disruption,is exposed to various forces, such as electromag-netism, gravitation, mechanical vibration, plasmamomentum, surface tension, and ablation recoil[10], For metallic components such as berylliumand tungsten, erosion lifetime due to these abnor-mal events will be controlled and dominated bythe evolution and hydrodynamics of the meltlayer during disruption, and the resultant loss ofliquid material from the surface. In contrast,CBMs do not melt and, therefore, do not erodeby these processes; this was a major reason for thechoice of graphite and carbon-fibre-compositesfor some PFCs in current fusion machines and inthe international thermonuclear experimental re-actor (ITER) design. However, CBMs may sufferfrom another splashing erosion mechanism; anexplosive-type erosion, as described later.

In future tokamak devices, �10–200 MJ m−2

will be deposited on the divertor plates during thedisruption thermal quench, a time of the order of0.1–10 ms. These corresponds to a heat fluxes


Fig. 2. Time evolution of tungsten surface temperature, melt-ing thickness, and vaporization losses during a disruption.

The subsequent decrease in the surface temper-ature was caused by the reduction in absorbedheat flux due to vapor shielding and conductionof heat into the material. The subsequent behav-ior is mainly determined by the energy flux fromthe emitted photon radiation in the vapor cloud,as discussed above, and by vapor-electron heatconduction.

Fig. 3 shows tungsten solid– liquid–vapor tem-peratures as a function of distance for 10 MJ m−2

energy density deposited at two disruption times,i.e. 0.1 and 1 ms. At the shorter disruption time,both the liquid–solid and the vapor temperaturesare higher than in the case of longer disruptiontimes. A longer disruption time causes the vaporto expand to larger distances above the divertorsurface and also causes the energy flux thatreaches the divertor surface to diffuse deeper intothe bulk and produce a thicker melt layer. Anorder-of-magnitude increase in the energy density,i.e. from 10 to 100 MJ m−2 would only result inabout 30% increase in the erosion rate and lessthan that in melting thickness. This is mainlybecause most of the incident plasma energy isused to heat up the front regions of plasma vapor[6]. This means that most of the radiation-flux isemitted in the direction away from the PFCs.Depending on the divertor design and configura-

�10 G m−2. Fig. 2 shows a typical time evolu-tion of a tungsten surface temperature�melt-layer thickness, and vaporization losses during adisruption for an incident plasma energy of 100MJ m−2 deposited in 1 ms, as predicted by theHEIGHTS package [4]. An initial magnetic fieldstrength of 5 T with an incident angle of 2–6° isused in these calculations. The sharp initial rise insurface temperature is due to the direct energydeposition of incident plasma particles at the ma-terial’s surface.

Fig. 3. Spatial evolution of tungsten solid– liquid–vapor cloud temperatures at two disruption times.


tion, the expanding hot vapor and its radiationcan damage nearby components, particularly forclosed-divertor configurations. It is, therefore, de-sirable to keep the normal expansion of vapor toa minimum.

Based on the above results, for a disruptionenergy density of �10 MJ m−2 and a disruptiontime of 1 ms, the calculated vaporization andmelting thickness for a tungsten plate are about 2and 180 �m, respectively. The vaporized 2 �mthick layer expands 30–60 cm in vapor cloudabove the target surface. The melt layer thicknessis much more than the vaporized thickness, there-fore, the lifetime of a metallic target wouldstrongly depend on the fraction of melt layer lostper event. A sacrificial 20-mm-thick carbon layerwould then lead to a lifetime of �500 disruptionsdue to vaporization alone (i.e. without includingerosion from other mechanisms, as will be dis-cussed later) or a lifetime of 130 disruptions fortungsten if 50% of the melt layer is lost for theabove disruption energy density and duration. Ithas also been found that, depending on the diver-tor configuration and design, the transport anddeposition of the radiation generated from theprimary vapor cloud can be high enough to causesevere melting and erosion of nearby components.The vapor cloud that develops on the front of thesurface of the nearby components may not be aseffective as the primary cloud in protecting adja-cent components because of strong vapor diffu-sion losses, vapor-cloud optical properties, andgeometrical effects [11].

The detailed vapor motion above the exposedsurface and its stability–confinement is calculatedby solving the vapor MHD equations in twodimensions for conservation of mass, momentum,and energy under the influence of a magnetic field[12,13]. The vapor cloud, if well confined, greatlyreduces the net energy flux to the surface, leadingto one to two orders of magnitude less erosion byvaporization [9], The magnetic field lines are ini-tially frozen into the surface of the liquid metallayer because of the liquid’s high conductivity.However, as more vapor is emitted from thesurface, the expanding dense ionized vapor willsweep and distort the oblique magnetic field lines.Near the upper vapor boundary, the magnetic

field lines become almost parallel to the vaporsurface. Such a situation of distorted magneticfield distribution leads to a flute-type MHD insta-bility in the vapor plasma [13], As a consequenceof the loss of vapor confinement, the turbulentdiffusing hot vapor may then deposit its energyon nearby components, causing more erosion.The overall net erosion rate and resultant damagewill depend on the parameters of the disruptingplasma, the size of the disruption spot, designconfiguration, and the type of PFM. In addition,the incidence of the hot disrupting plasma ontothe cold plasma of the vapor shield may give riseto electric fields [14]. The electric field may causelateral Eb ×Bb drifts that can lead to deflection ofeither the vapor shield plasma [15] or the incidentplasma [16], or both. Experimental evidence forthe influence of Eb ×Bb drifts on plasma shieldefficiency and erosion is not yet proved.

Photon radiation and transport in the vaporplasma are very important in predicting disrup-tion erosion of PFCs. Opacity and emissivity datafor the developed vapor plasma varies signifi-cantly because the vapor contains very cold anddense plasma regions near the target surface andvery hot and less-dense plasma regions where thedisrupting plasma ions and electrons deposit theirenergy. The models in the HEIGHTS package [2]allow for the treatment of nonlocal thermody-namic equilibrium (non-LTE) of the vapor-cloud-generated plasma, multigroup and multidimen-sional analysis of the produced photon spectra,and self-consistent kinetic models for both thecontinuum and line radiation generated in thevapor cloud. Calculated photon spectra emittedfrom the outermost regions of tungsten vapor fortwo deposited plasma energy densities (10, 100MJ m−2) and for beryllium at 100 MJ m−2 areshown in Fig. 4. Most of the incident plasmaenergy flux (�80%) during the disruption isquickly converted into radiation energy in thevaporized material. Most of the radiation energywill be deposited at locations other than the orig-inal disruption location. In some cases, the dam-age from the plasma-energy-converted radiationcan exceed the damage at the original location,particularly in a closed divertor configuration.


Fig. 4. HEIGHTS—calculated photon spectra emitted from outermost vapor regions for different deposited plasma energies.

The emitted radiation spectrum depends on va-por–plasma parameters such as vapor tempera-ture and vapor density, which is determined fromthe detailed physics of vapor–plasma interactions.For the case of higher energy disruption, morepower is deposited in the vapor that heats thevapor front to higher temperatures and causes itto emit harder photon spectra, which in turn,deposit more energy at the material surface. Dueto its lower atomic number, beryllium vapor ismuch less radiant than the higher-atomic-numbertungsten vapor; therefore, its temperature is muchhigher than that of tungsten vapor and conse-quently, its photon spectrum is harder and theyield is much higher.

Line radiation in the vapor is particularly im-portant for materials with lower atomic numbersand high-temperature vapor clouds. In manycases of disruption on beryllium targets, �90%of the emitted radiation energy is in the form of afew strong lines of radiation. Careful treatment ofline transport in vapor clouds is important andrequired to correctly calculate the net energy fluxto the material surface [2].

3. Material erosion mechanisms

3.1. Erosion in metals including macroscopicparticle formation

Surface vaporization losses of metallic PFMsare generally small (only a few �m) over a widerange of plasma conditions during short plasmainstabilities [2]. In most disruption cases, the melt-layer thickness of metallic components can be oneto two orders of magnitude higher than surfacevaporization losses [3], as shown in Fig. 2. Theloss of melt layer during the course of a disrup-tion will seriously decrease the erosion lifetime ofPFCs. During a reactor disruption, the melt layeris subject to various forces such as electromag-netism, gravitation, mechanical vibration, plasmamomentum, surface tension, and ablation recoil.Several mechanisms can cause melt-layer loss dur-ing plasma instabilities [10]. Experimental obser-vations in laboratory disruption simulationdevices are, however, consistent with two impor-tant mechanisms of melt-layer removal [1]. Thesemechanisms are melt splashing due to the forma-tion, growth, and explosion of vapor bubbles


inside the liquid layer, and growth of hydrody-namic instabilities due to plasma impact momen-tum (‘plasma wind’) at the liquid surface andforces generated by current decay in the liquidmetal layer.

Therefore, hydrodynamic instabilities, such asthe Kelvin–Helmholtz (K–H) instability, willarise and form liquid droplets that will be carriedaway by the plasma wind. The amount and rateof melt-layer loss is difficult to predict and isexpected to depend on many parameters, such asheat flux, impurity and gas content, materialproperties, and disrupting plasma parameters.More work is needed to study the details ofmacroscopic erosion of metallic materials duringan intense deposition of energy.

3.2. Erosion in carbon-based materials

Due to the self-shielding layer effect discussedabove, erosion by vaporization of carbon materi-als is also limited to �10 �m for a wide range ofdisrupting plasma conditions. This is about onlyone to two orders of magnitude lower than itwould be if no vapor shielding exist [9]. However,in many cases, graphite and CBMs have alsoshown large erosion losses that significantly ex-ceed losses from surface vaporization. A phe-nomenon, called ‘brittle destruction’, has beenobserved in various disruption simulation facili-ties [4], Physical mechanisms that cause brittledestruction of CBMs are not yet clear. One mech-anism could be cracking caused by thermome-chanical stresses that develop during the intensedeposition of energy [17–19], Another proposedmechanism is that material is ejected by the sharprise in the pressure of gas trapped in the networkof pores between intergranular and intercrystalliteboundaries that can cause explosive ejection ofmaterial [20]. These processes are likely to dependon the material microstructure.

The macroscopic erosion of CBMs will dependon three main parameters, net power flux to thesurface; exposure time; and the threshold energyrequired for brittle destruction [20]. The requiredenergy is critical in determining the net erosionrate of CBMs and is currently estimated fromdisruption simulation experiments. More experi-

mental data and additional detailed modeling areneeded to evaluate the erosion of CBMs, e.g. therole of brittle destruction.

Surface ablation, i.e. formation and ejection ofMPs, is characterized by splashing or destructionwaves, assuming that a layer of material heatedabove certain threshold energy is removed in theform of MPs [7]. Ablation of both melting andcarbon-based materials is occurs in splashing–de-struction waves when a layer of material is heatedabove a certain threshold energy, Qth, and isremoved in the form of MPs, This energythreshold for splashing is roughly equal to thesum of a thermal energy Qheat (required to heatthe liquid above a certain threshold temperatureTth including heat of fusion, Qf, for melting mate-rials), a separation energy to remove the MPsfrom the surface, and a kinetic energy for themoving droplets. The separation energy of thesplashed droplets is determined from the surfacetension of the liquid metal. The value of Qth is,therefore, calculated from:

Qth=Qheat+Qs+Qk, (13)

where:

Qheat=� Tth

T o

c�dT+Qf (for melting materials)

(14)

Qs=Ndrop4�Rdo2 �s, Ndrop=

dm/dtVdo(4/3)�Rdo

3 , (15)

and,

Qk=12

�Vdo2 (16)

where To is initial material temperature, c� isspecific heat, Qs is energy required for dropletsseparation, Qk is kinetic energy of ejected MP,Vdo is ejected velocity, Rdo is radius (size), Ndrop isdensity of the ejected MP, dm/dt is ablation rate,and as is surface tension. For hydrodynamic in-stabilities, Tth is near the melting temperatureTmelt, while for bubble boiling, Tth is near thevaporization temperature Tvap. Therefore, thethreshold energy for macroscopic erosion is deter-mined from material properties, mechanism ofmacroscopic destruction, and dynamics of vapor-cloud expansion above the target surface.


Macroscopic brittle erosion of CBMs from ther-mal stresses and macroscopic pore explosion canbe described in a way similar to that used formetallic materials, by using the concept of a de-struction wave, with the separation energy Qs,defined in this case from the binding energy of thegrains–crystallites. Since the MPs are ejected as aresult of the vapor pressure P, similar to theexternal pressure Pout, the velocity of MPs can beestimated from Vdo��Pout/�. For a Pout of �50atm (pressure of vapor cloud), Vdo�50 m s−1 [7].

4. Interaction between macroscopic particles andvapor plasma

The ejected waves of MPs will form a ‘dropletcloud’ above the target surface and expand insidethe initial vapor cloud. MPs are treated as separatemedia that interact with the surrounding inhomo-geneous vapor-cloud plasma through exchange ofmass, momentum, and energy. To calculate ofmass and energy exchange, MP vaporization iscalculated by equations similar to those for vapor-cloud dynamics [7]. Mass losses and the corre-sponding decrease in MP radius (size) arecalculated by solving the mass, momentum, andenergy conservation equations given by [21]:

dRd

dt= −

�out

Ndrop

, (17)

dEd

dt=Wrad+Wcond−4�Rd

2�out(c�Td+Qf+Qv)

(18)

where Ed is net energy of MP, Wrad and Wcond areradiation and conduction energy fluxes, �out is netvapor flux from MPs surface, Td is surface temper-ature of MP, and Qv is heat of vaporization. Thenet vapor flux from the MPs surface is defined asthe difference between the vapor flux leaving thesurface (corresponding to the surface temperature)and the vapor flux from the surrounding vaporcloud that condenses at the MPs surface. Due tothe decreasing MP radius, the interaction of MPswith vapor can be either collisional or collisionless.The collisionality condition is determined by theparameter, �, where:

�=16�Vo

Vd

��Rd

�o

�, (19)

where the subscript o refers to the vapor mediaand �o is vapor mean free path. For ��1, theStokes formula with viscosity �d is used while for��1, the friction force is calculated assuming theinteraction of freely moving vapor with sphericalparticles. Absorption of photon radiation powerby each MP is calculated by using the absorptioncross section that takes into effect geometricalscreening by other MPs. The total absorption andreflection of photon radiation are summed over allemitted MPs. Influence of a magnetic field on MPsmotion and dynamics is negligible, therefore the[J×B ] force is not taken into account. Fig. 5 is aschematic illustration of MP evolution and inter-action with the vapor cloud during a plasmainstability event.

Once MPs are emitted into the vapor plasma,they will alter the hydrodynamic evolution of thevapor plasma. The corresponding coupled mass-,momentum-, and energy-conservation equationsbecome complicated and are given simply in con-ventional terms by [21]:

Fig. 5. Schematic illustration of droplet shielding conceptduring plasma instabilities.


��

�t+�(�Vb )=�Sb net, (20)

�dVbdt

= −�a P+1c

[(�×Bb )×Bb ]+Fb plas+Fb MP,

(21)

dEdt

−E�

d�

dt+P�Vb = −�q� k+Qplas+QMP+Qrad+�Wb net,

(22)

where Snet is net vapor flux from droplets surface,Fplas is deposited plasma momentum, FMP is de-posited droplet momentum in the vapor-cloud, qk

is heat conduction flux along and across the mag-netic field, Qplas is SOL plasma energy flow to thevapor cloud, QMP is droplet kinetic energy in thevapor, Qrad is radiation power, and Wnet is energyflux from vaporizing droplets. The vapor energydensity, E, consists of both the thermal and ion-ization energy:

E=32(1+z)nkT+n

� z

o

I(z)dz, (23)

where n is vapor number density and I(z) is theionization potential of the vapor plasma.

One purpose of this work is to study vaporplasma dynamics in a mixture of atomic vaporand MPs in order to find the contribution ofablation losses relative to total mass losses. If thevapor plasma is well confined by the magneticfield, there is no motion of the vapor plasmaalong the divertor surface in the poloidal direc-tion, (�, and MP dynamics are determined bytheir interaction with the vapor plasma moving inboth toroidal, �, and radial, r, directions. There-fore, MPs remain within the vapor cloud up tofull vaporization, i.e. complete burning or untilleaving the vapor cloud in the r direction.

Photon radiation transport inside the vaporplasma will finally determine net energy flux tothe surface and consequently will determine thelifetime of the target plate. For quasi-stationaryconditions, the transport equation for the radia-tion has the form:

�b �Ib =�vIb vp−vIb (24)

where Ib is the radiation intensity, Ib vp is thePlanckian radiation, is the frequency, �v is thevapor plasma emission coefficient, � is the solid

angle, and v is the vapor and MPs absorptioncoefficient The ‘forward–reverse’ method is usedin this analysis to calculate the photon radiationtransport in the vapor–droplet plasma. The corre-sponding equations in two directions are given by[21]

�12

dI ��

dx=�vIvp

� −vI � (25)

W rad� =

��

0

I �d, Wrad=W

rad

+ +Wrad

− (26)

where I + is the photon flux moving upward (for-

ward), I�− is the photon flux moving downward

(reverse), and Wrad is the total emitted radiation.To calculate � and �, as well as thermodynamicproperties, full kinetic equations are solved in theevolving vapor-cloud plasma for all level popula-tions of charged particles. The kinetic equationsare solved at each time step, taking into accountinduced radiation; therefore, radiation transportwere calculated in a self-consistent way. In thesecalculations, the radiation flux is composed of twoseparate components, continuum radiation fluxand line radiation flux. The continuum spectrumis divided into multigroups in logarithmic scalefor a wide range of photon energy. The radiationtransport for each line is calculated separately,also using multigroup approximation for eachline. For most cases, the number of groups for thecontinuum spectra Nc�1000 and for lines 50�NL�500 depending on target vapor material andcondition. Therefore, radiation transport in thevapor plasma was calculated for a total numberof groups that exceed several thousand.

The front hot and less-dense vapor cloud ex-pands in the normal direction with a vapor cloudvelocity of �1 km s−1. However, the front vaporplasma does not influence the denser and coldervapor near the target surface that contains theMPs. The effective size of this front part of thevapor cloud is determined by absorption depth ofthe incoming plasma particles, particularly plasmaelectrons. After a transition time of a few tens of�s, depending on target material, the spatial dis-tribution of plasma parameters (such as density,temperature, and magnetic field) become quasi-stationary, as shown for a beryllium target (at 400


Fig. 6. Spatial evolution of beryllium vapor temperature,density, and toroidal magnetic field during a disruption.

plasma with lower Z�1. For lithium, the size ofthe radiative region is similar to the size of thezone where incoming plasma flux is absorbed. Forhigher-Z materials such as beryllium and carbon,the radiation heat conduction is high enough tokeep part of the vapor plasma outside the absorp-tion zone at a higher temperature. Radiation ab-sorption ceases at temperatures lower than theionization temperature. Near the wall, the secondzone of the cold region contains MPs that canabsorb radiation; thus, a sharp decrease occurs inSin as shown in Fig. 7.

The ejected MPs move across the cold densevapor with a maximum velocity at ejection Vej�100 m s−1, determined from the vapor pressureabove the target surface. Nevertheless, the MPsare slowed down because the vapor velocity nearthe target surface is �Vej. Fig. 8 shows thespatial evolution of a lithium droplet with aninitial radius of 10 �m and velocity of 50 m s−1 asit moves across the lithium vapor cloud at time=400 �s. The lithium droplet is completely vapor-ized at a distance �2 mm above the target with alifetime �life of �40 �s in the vapor cloud. The‘birth time’, i.e. time when the particle–dropletwas ejected, is also shown. The MPs that wereborn earlier were moved a far distance from thetarget surface for a longer time. A berylliumdroplet travels much longer distance than alithium droplet because of its higher vaporizationenergy and less radiation power to the droplet

�s snapshot) in Fig. 6 [21]. At the front of theexpanding vapor cloud, density is lowest (n�2×1017 cm−3) and temperature is highest (T�28eV). The denser and colder vapor region actuallyconsists of two zones. The first zone, very near thetarget surface, is governed by MP vaporization,thus, density is high and temperature is low (T�0.3–0.5 eV), which means that the vapor is mostlyneutral (Z�0.5) in this zone. The second zoneconsists of vapor plasma with Z�1 and is char-acterized by a low or negligible radiation. Thelittle radiation absorbed by some free electrons isenough to keep the vapor at this temperature.Most of this radiation Sin, is absorbed by MPsnear the target surface. Flowing vapor from thetarget surface pushes upward on the magneticfield, therefore, the field in the vapor cloud isdecreased to Bz�3 T in beryllium vapor. Thus,the inclination angle of the magnetic field lines inthe vapor cloud changes from �o=6° to ��20°.

Fig. 7 shows the spatial distribution of de-posited plasma power (Splasma), upward radiationflux (Sout) and downward radiation flux (Sin) to-ward the target [21]. The energy of plasma parti-cles is absorbed mainly by the free electrons of thevapor at high temperature and high Z and by theinner shell electrons at lower Z. It can be seenthat the upward radiation is generated in thisregion. However, the radiation power toward thetarget surface Sin is absorbed mainly by vapor

Fig. 7. Spatial distribution of emitted radiation and depositedplasma power in Li vapor.


Fig. 8. Spatial evolution and lifetime of a lithium droplet as it moves in vapor cloud.

surface (Stgt[Be]�230 kW cm−2 vs. Stgt(Li)�300kW cm−2). The lifetime of MPs is determined bythe incoming radiation power and vaporizationenergy; thus, �life(Li)�40 �s, but �life(Be)�240�s, and �life(C)�400 �s [21].

The mechanism and dynamics of a splashing–destruction wave can be described as follows.During the initial phase, the target surface isheated by both plasma particles and photon radi-ation while the surface temperature is achievingthe threshold temperature–energy. Then, asplashing wave propagates into the target bulk.The front wave position xwave inside the target isdetermined by the threshold condition T(xwave)=Tth. All of the target mass behind the wave frontwith x�xwave is emitted in the form of MPs.Depending on material properties and mechanismof splashing–brittle destruction, these MPs ex-hibit certain distributions in size Rdo, velocitiesVdo, and angles of ejection. Detail calculationshave also shown that the initial distribution ofMP size and velocities does not affect the netradiation power to the target surface, only thevaporization path length of the MPs [21].

The process of ablation mass loss can be di-vided into two stages. During the first stage thesplashing wave propagates quickly, because thetarget surface is heated near Tth at a sufficient

depth, and any slight additional radiation poweris enough to achieve threshold conditions. There-fore, sufficient mass is ejected in a short time;both the mass and time are determined by thematerial properties. The time evolution of theberyllium target surface temperature Ts anddroplet and total vapor mass losses are shown inFig. 9. The time history of the splashing erosionwave of beryllium droplets is shown. The targetsurface temperature achieves a quasi-stationaryvalue after a certain time.

During the second stage, after the first ejectionwave, the splashing process is quasi-stationaryand the flux of newly ejected MPs becomes equalto the flux of the vanishing MPs [2]. For a lithiumtarget, this state is quickly achieved in �20 �s,but for materials with higher Tvap such as beryl-lium, this state is achieved at the much later timeof �150 �s. For materials with even higher Tvap,like CBMs, such a state was not achieved in up to600 �s. The total mass loss of beryllium targets isonly �10–15% of the total melting thickness forwell-confined vapor and droplet clouds.

The total mass loss is, therefore, determinedfrom the net radiation flux that arrives at thetarget surface after the double shielding effect thatis due to absorption by both vapor plasma andMPs. After a certain transition time, these fluxes,


as well as the front vapor cloud temperatureachieve the quasi-stationary state. The vapor anddroplet shielding efficiency is �95% for the can-didate materials and the conditions studied in thisanalysis.

5. Results from simulation experiments

Disruption conditions in next-step devices can-not be achieved in existing tokamaks because ofthe large difference in stored energy in the twodevices. Therefore, laboratory experiments (e.g.laser and electron beams, open plasma traps andplasma guns) are used to study and simulatedisruption erosion effects [22–26], The results ofthese experiments are used to validate the above-discussed theories and models, which are cur-rently under development for the purpose ofpredicting effects in a next-step device.

Laser and high-energy electron beam facilitieshave been widely used to test divertor materials,primarily graphite and carbon-based materials[25,26]. These experiments, mainly carried out infacilities without a magnetic field (known toconfine vapor plasma near the surface of theexposed material samples), and thus in the pres-

ence of a poor shielding efficiency, have typicallyshown very high erosion rates (hundreds of �m).In laser beams, this is due to the fact that thebeam size is generally very small (�2–4 mm) andpenetrates the expanding cloud of vaporized ma-terial with little attenuation. In electron beams,because of the high kinetic energy (100–150 keV),the electrons penetrate the vapor and the targetmaterial more than in laser or plasma gun devices.Thus, the vapor cloud is heated to lower tempera-tures than in plasma gun experiments, and thefraction of incident energy that is dissipated viaradiation in the vapor is much lower [13].

Experiments carried out in a particular type ofsimulator devices, e.g. the GOL-3 facility, whichuses a combined hot electron beam (low MeVrange) and low-temperature plasmas (�3–5 eV),led to an explosive-type high erosion of graphitematerials [27]. Approximately 500 �m per shot ofgraphite was eroded by an energy density of 30MJ m−2. The enhanced graphite erosion can beexplained in terms of the volumetric energy depo-sition causing significant bulk damage and theeroded graphite being emitted in the form ofgrains ranging in size between 1 and 40 �m. Theconditions in this facility, however, may not befully relevant to disruption conditions in toka-

Fig. 9. Time evolution of beryllium target surface temperature, droplet mass, and total vapor mass.


maks because there are no such hot electronsduring a tokamak thermal quench disruption.

Plasma gun devices, which typically producelow-temperature plasmas (T�1 keV) and high-energy flux (up to 10–20 MJ m−2 deposited in apulsed duration of �1 ms), are more suitablethan electron or laser beams for simulating rele-vant reactor disruption conditions. These facilitiesare primarily used to study the underlying physicsof the plasma–surface interactions during disrup-tions and quantify the resultant material targeterosion. One relevant gun-facility is the MK-200UG, which can produce hydrogen and deu-terium plasma streams with a total energy of 50kJ and ion kinetic energy �1 keV in a magneticfield of 2–3 T [24]. Target materials can be testedat perpendicular as well as in an oblique plasmaincidence. The main disadvantage of this facility isits very short pulse duration, i.e. t�40–50 �s,which makes it suitable to simulate only the earlystages of a disruption in a next-step tokamak.Quasi-stationary plasma guns such as VIKA andQSPA generate plasma streams with sufficientlylong-pulse duration [22,23]. However, because ofthe relatively low kinetic energy of the ions (Ei=100–300 eV), and large plasma densities (�1022

m−3), a shock wave may arise during plasmadeposition and this could lead to a deceleration ofthe plasma stream and to a ‘self-shielding’ effectthat mitigates the energy flux that reaches thematerial surface and leads to an underestimationof erosion when compared with actual tokamakconditions.

Several experiments have been performed invarious plasma gun facilities, primarily to studyphysical properties and shielding efficiency ofplasma vapor shields and the resultant materialerosion. In these experiments, the plasma temper-ature and density distributions in the vaporshielding layer are measured along with the lateralleakage of radiation by Thomson scattering andoptical and soft X-ray interferometry. Materialerosion damage is generally measured by surfaceprofilometry and mass loss. Vapor shielding re-duces erosion, at least to some extent, in mostdisruption simulation facilities. The dependence ofthe density and temperature of plasma vapor onthe incoming plasma flow and the target material

is generally in good agreement with theory [13].At perpendicular plasma impact, the targetplasma expands upwards toward the plasmastream along the magnetic field lines, and trans-verse motion is inhibited by the strong magneticfield. At oblique incidence, the vapor shield ofcarbon material drifted in the direction of themagnetic field lines, along the inclined target sur-face, and the oblique magnetic field does nottotally prevent transverse plasma motion [28].This mechanism depletes the shielding propertiesand increases the erosion of a graphite target by�50%. This finding was in agreement with mod-eling predictions, carried out prior to the experi-ments, to model the effect of vapor loss due toinstabilities [20]. Additional analysis is needed todetermine the underlying cause of this drift.

Recent gun experiments have also shown collat-eral damage of nearby surfaces from radiationemitted from the outermost regions in a well-confined vapor cloud [28]. A graphite erosion of0.35 �m per shot was caused by radiation emittedfrom a plasma vapor that formed in front of atungsten target (�1 MJ m−2). This erosion issimilar to that observed for direct plasma impact(0.4 �m per shot) at much higher heat flux (�15MJ m−2). This finding is in agreement with re-sults of modeling [29], and is attributed to the factthat the shielding efficiency is lower under radia-tion heat loads than under direct plasma impact.The secondary radiation is, therefore, an impor-tant consideration for the choice of divertor mate-rials and geometry in future tokamak devices.

For CBMs, strong erosion with considerablemass losses that exceed those from surface vapor-ization is also observed in plasma-gun devices.Experiments in the MKT facility have shownemission of MPs [30]. Recently, experiments per-formed in MK-200UG [31] and QSPA [32] havealso revealed macroscopic erosion mechanisms.

Several studies have also been carried out inrecent years to investigate the macroscopic ero-sion of metals under disruption conditions [33].Preliminary analysis of the microstructure of theexposed metal surfaces has clearly shown the for-mation of high-volume-bubble densities [34], withtraces of melted-metal droplets of light-Z materi-als (e.g. aluminium) up to a few meters away from


Fig. 10. Time dependence of tungsten melting and splashingfront with droplet shielding effect.

It was shown that decreasing Srad from 0.3 to0.1 MW cm−2 increases the delay time from 60 to600 �s, respectively [37]. This finding has twosignificant implications. The first is that the levelof radiation power substantially increases the MPerosion rate (from 100 �m at 0.1 MW cm−2 to900 �m at 0.3 MW cm−2, without droplet shield-ing). Second, it can explain why in some simula-tion experiments, particularly with high-Z targetssuch as tungsten, significant splashing was notseen because the time duration of these simulationdevices is short, i.e. less than the time delayrequired for Srad associated with such experi-ments. Therefore, to adequately model and simu-late the effect of tokamak instability events onerosion lifetime, facilities with a time duration�300 �s is needed. In the VIKA disruption simu-lation facility [36], it was shown that for differenttarget materials, significant erosion starts after adelay time similar to that predicted by models inHEIGHTS [37].

Therefore, mass losses of divertor plate andnearby components depend strongly on the dy-namics and evolution of the vapor cloud anddroplets or MPs. The main concern is the time tostart ablation and the existence of both vapor anddroplet shielding. Mass losses and lifetime ofPFMs due to vaporization and ablation dependstrongly on interaction conditions that dictate theexistence or absence of both vapor cloud anddroplet shields. The vapor shield exists if thevapor cloud is well confined by a strong magneticfield. For a divertor plate, the existence of vaporshielding depends on MHD instabilities in thevapor cloud, which can lead to turbulent diffusionacross the magnetic field. In an inclined magneticfield, turbulent diffusion leads to vapor flow andloss (‘the vapor wind’) along the poloidal direc-tion that decreases the efficiency of vapor shield-ing. The blowing away of droplets or MPs by thevapor wind is more serious because decreasing thedroplet shielding significantly enhances dropletemission. For nearby components of the divertorsystem, existence of shielding depends, in addi-tion, on the geometrical locations relative to mag-netic field structure.

Four erosion scenarios are possible duringplasma– target interaction [37]. Fig. 11 shows the

the target area. Bubble formation was also foundin electron-beam experiments [35]. Careful analy-sis of the irradiated samples has also suggested thepossibility that hydrodynamic instability is a melt-layer erosion mechanism that is in addition to thevolume bubble vaporization. Near the central ar-eas of the sample where the velocity of the inci-dent plasma stream along the sample surface isnear zero, the volume bubbles are seen clearly.Near the sample peripheral areas, however, onecan see liquid droplets with long tracks, formedbecause of the high velocity of the plasma stream.

Melt-layer erosion of much heavier materials,such as tungsten, was shown to be very low inplasma gun experiments [36] but is more likely tobe greater for longer (�1 ms) heat pulse dura-tion. The HEIGHTS package is used to explain thisphenomenon in recent plasma-gun disruption sim-ulation experiments. Fig. 10 shows the time de-pendence of tungsten melting andsplashing-erosion depth for a low radiation powerlevel of 0.1 MW cm−2 on a tungsten surfacewithout the effect of droplet shielding (anticipatedin all laboratory simulation devices). The time�delay required to heat the surface to a temperatureabove the splashing condition (T�Tvap [Pv],where Pv is plasma pressure above the targetsurface) inversely depends on the square of in-coming radiation power.


erosion depth of both beryllium and graphitetargets for these cases with and without bothvapor shielding and droplet shielding. In Case 1,i.e. absence of both shielding mechanisms (novapor shielding, i.e. vapor is not well confined andthere is no droplet shielding, so droplets aresplashed away from the incoming plasma), allincoming power will be spent in splashing erosionof the liquid surface. Erosion loss is very high,and this case may represent a disruption simula-tion device in which the incident plasma has avery high dynamic pressure that exceeds the mag-netic field pressure that is capable of blowing offthe initial vapor cloud and liquid layers. Case 1may also resemble a tokamak condition in whicha strong MHD vapor turbulence develops andleads to fast removal of vapor and droplets alongthe target surface. In Case 2, without vaporshielding and splashing (or ablation), all incomingpower will be spent in vaporizing the target sur-face. This may occur if the vapor cloud is re-moved for any reason and the target materialdoes not melt or splash–destruct.

In Case 3, with vapor shielding but withoutdroplet shielding (droplets are removed from in-coming power), the net incoming radiation powerto the target surface is spent in splashing. Thissituation can occur on nearby components duringa divertor plate disruption, in which the intensephoton radiation from the hot vapor cloud de-

posits its power at locations with different orien-tations to the magnetic field lines; as a result, thevapor cloud is not well confined. This may also betrue in many of the disruption simulation devices,such as plasma guns and electron beams wherethe cross section of the plasma or particle flow issmall and the MPs flight time in the vapor cloudis inadequate to absorb the incoming radiationpower and further shield the target surface. Thiscan also occur under tokamak conditions withmoderate levels of turbulence, in which the vaporwind is strong enough to blow away droplets butnot strong enough to remove all vapor; thus, theremaining vapor cloud has enough depth to stopmost incoming plasma particles and radiate backthe deposited power. Ablation can increase masslosses by �4–5 times. Therefore, droplet removalis critical because the result of droplet shielding isthat all of the radiation from the vapor cloud goesto the target surface to be spent in vaporization,mostly through the intermediate process ofdroplet emission and further vaporization duringdroplet flight across the vapor cloud.

The fourth Case is the most desirable and canbe realized in a tokamak device if the vapor cloudis well confined and without MHD effects. Undersuch conditions, a well-confined vapor anddroplet cloud can reduce erosion losses by up totwo orders of magnitude. It should be noted thatthese results are valid at longer time t��delay, i.e.when the surface temperature achieves its quasi-stationary value in stable vapor plasma. Forshorter times, vaporization losses in the case ofvapor and droplet shielding can be calculateddirectly. However, the liquid droplets or pieces ofCBMs, simply stated as MPs, that are ejected neartarget edges and/or are large or moving withhigher velocities will not have sufficient time tocompletely vaporize and shield the target surface,therefore, erosion lifetime is lower. In addition,higher droplet velocities due to the drag force ofthe fast-expanding vapor, or due to the highexplosive pressure in the brittle destruction mech-anism, can increase mass loss because the dropletswill spend less time in the hot vapor cloud.

The observed increase in the eroded area, whichis larger than the footprint of the incident plasmaflow in some simulation experiments, can be ex-

Fig. 11. Erosion depth of berylium and carbon targets forvarious cases with and without vapor and droplet shieldingeffects.


plained as the result of the interaction of vaporradiation with the target surface outside theplasma flow spot [33] or as being due to thedeveloped MHD instabilities in the vapor cloud[20]. In addition, slight shifting of the vapor clouddue to the [Eb ×Bb ] force may also occur along thetarget. However, these problems have not beenwell investigated and require more analysis andsimulation.

To summarize the simulation results, we maysay that overheating the plate surface causes MPsand droplets to be ejected–splashed upstream andaway from the surface. These particles then ab-sorb some part of the incoming vapor radiation.The net fraction of radiation power that reachesthe divertor surface is determined mainly by theratio of the vaporization to splashing energies.The distance L at which MPs or droplets arecompletely vaporized is �1 cm. Therefore, themixture of vapor and MPs exists only very nearthe divertor surface. Despite initial large splashingerosion, total erosion of the divertor plate isdefined only by vaporization losses, includingboth divertor plate vaporization and MP vapor-ization. Again, this is true only if both the vaporcloud and the splashed droplets are well confinedin front of the disrupting plasma. However, lossof vapor confinement can occur as a result of theMHD instability that arises from distortion of theoblique magnetic field lines by the expanding va-por plasma [20]. In this case, the developed turbu-lence leads to vapor flow along the divertor platesurface. Due to this flow, K–H instability ofunstable surface waves occurs and leads tosplashing.

This vapor flow blows both vapor and dropletsalong the target surface, reducing vapor shieldingefficiency because of vapor cloud removal. Inaddition, efficiency of droplet shielding is reducedbecause droplet exposure time in the depletedvapor is decreased. Efficient vapor shielding thatprotects the divertor plates from high heat loadsmeans that �90% of incoming power is radiatedto nearby locations. Therefore, the problem oferosion of other parts in a closed divertor systembecomes more serious. It was shown both experi-mentally [28] and theoretically [29] that interac-tion of this ‘secondary’ radiation with other

components leads to the same consequences as theprimary interaction of the SOL plasma, i.e. vaporcloud formation, splashing, etc. Moreover, it maybe very difficult for such vapor clouds to be wellconfined, especially if the magnetic field angle ofinclination with variously oriented surfaces is verylow. Erosion of such nearby components could beestimated, as done in Case 1 on Fig. 11, becauseof the absence of both shielding effects.

6. Effects of long-duration plasma instabilities

Thermal-quench disruptions and ELMs haveno significant thermal effect on structural materi-als and coolant channels, because deposition timeis short (�10 ms). However, VDEs (duration100–300 ms), and runaway electrons (deeper pen-etration depth), in addition to causing severe sur-face melting and erosion, can substantiallydamage these components [2]. One concern is thehigher temperature observed in the structural ma-terial, particularly at the interface with the coatingmaterials. Elevated temperatures and high ther-mal stresses in the structure seriously degrade theintegrity of the interface bonding; this may lead todetachment of the coating from the structuralmaterial.

The surface temperature of the copper-structureduring a VDE has been calculated for differentsurface coated materials such as tungsten, beryl-lium, and carbon tiles. As an example, Fig. 12shows the surface temperature of a 5-mm-thickcopper substrate at its interface with 5-mm-thicktungsten and beryllium coatings and 20-mm-thickcarbon tiles during a typical VDE releasing to thesurface about 60 MJ m−2 in 300 ms [1]. Underreactor conditions, the tile thickness is determinedby the surface temperature limitations during nor-mal operation. With a tungsten coating, the cop-per surface interface can actually melt. For thegiven conditions, only beryllium coatings of rea-sonable thickness (�5–10 mm) or very thickcarbon tiles (�20 mm) can withstand the accept-able temperature rise in the copper structure, be-cause most of the incident plasma energy isremoved by beryllium’s higher surface vaporiza-tion rate, which leaves little energy to be con-


Fig. 12. Time evolution of surface temperature of coppersubstrate with various surface coating materials.

processes that lead to vapor and droplet forma-tion and shielding. Two separate mechanisms ofmaterial erosion occur during plasma disruptions,atomic vaporization from the target surface andablation in the form of MPs (i.e. liquid metaldroplets or macroscopic pieces of CBMs). Abla-tion can be attributed to hydrodynamic instabili-ties, volume-bubble boiling (metallic materials),thermal stresses, and pore explosion (brittle mate-rials), A HEIGHTS-package numerical simulationwas carried out with new models for dynamicevolution and interaction of MPs with an inho-mogeneous vapor cloud.

The ablation mechanism plays a more impor-tant role because the required threshold energyneeded for ablation is much less than the energyof vaporization. It can lead to significant masslosses if the ejected MPs are removed quicklybefore they are completely vaporized. In the ab-sence of strong plasma and vapor wind or vaporturbulence diffusion, a new process, named‘droplet shielding’, takes place and leads to signifi-cant reduction in total mass losses from the targetsurface. The shielding efficiency of both vaporand droplet shielding in well-confined vaporplasma can exceed 95% for candidate materialslike lithium, beryllium, and carbon.

In a typical disruption of an ITER-like ma-chine, of �d�1 ms; the predicted mass losses perdisruption are on the order of Xloss(Li)�750 �m,Xloss(Be)�30 �m, and Xloss(C)�22 �m. Thesevalues may seem acceptable from an engineeringpoint of view; however, one should note that allof the above analyses assumed no vapor–plasmawind or turbulence diffusion along the divertorplate surface. In such a case, the actual erosionvalues of the divertor plate and nearby compo-nents will be significantly increased. In addition,the deposition of eroded and splashed materialson reactor components can adversely affectplasma performance. The use of a renewable ma-terial such as free-surface liquid lithium may sig-nificantly extend the lifetime of PFMs andsubstantially enhance the tokamak concept forpower-producing reactors. In general, majorplasma instabilities must be avoided or their fre-quency be significantly reduced.

ducted through the structural material [1]. There-fore, beryllium and carbon coating materials willsuffer significant surface erosion while protectingthe structural copper substrate. A thin (�1–2-cm-thick) free-surface layer of a liquid metal suchas lithium would be ideal to completely protectthe structure and offer unlimited PFC erosionlifetime. Lithium is shown in Fig. 12 only forcomparison. The temperature rise in copper struc-ture is very small when lithium is used. Thestructural materials will, therefore, exhibit nohigh-temperature effects during the VDE becausethe liquid metal will remove the heat by eitherconvection (moving film) or intense vaporization(stationary film). However, problems related toplasma– free-surface liquid–metal interactionsduring normal operations must be carefullyexamined.

7. Summary and conclusions

Mechanisms of material erosion and lifetimeduring plasma disruptions are modeled in detail.Erosion of plasma-facing materials is governed byboth the characteristics and distribution of inci-dent plasma particles from the SOL, as well as by


Acknowledgements

Work is supported by the US Department ofEnergy, Office of Fusion Energy, under ContractW-31-109-Eng-38.

References

[1] A. Hassanein, I. Konkashbaev, Fusion Eng. Des. 51–52(2000) 681.

[2] A. Hassanein, Fusion Technol. 30 (1996) 713.[3] A. Hassanein, G. Federici, et al., Fusion Eng. Des. 39–40

(1998) 201.[4] A. Hassanein, I. Konkashbaev, J. Nucl. Mater. 273 (2000)

326.[5] A. Hassanein, I. Konkashbaev, ‘‘Physics of collisionless

scrape-off-layer plasma during normal and off-normaltokamak operating conditions,’’ Argonne National Labo-ratory Report ANL/FPP/TM-296, March 1999.

[6] A. Hassanein, I. Konkashbaev, Suppl. J. Nucl. Fusion 5(1994) 193.

[7] A. Hassanein, I. Konkashbaev, J. Nucl. Mater. 290–293(2001) 1074.

[8] A. Hassanein, V. Belan, et al., J. Nucl. Mater. 241–243(1997) 288.

[9] A. Hassanein, Response of Materials to High Heat Fluxesduring Operation in Fusion Reactors, ASME, 1998 88-WA/NE-2.

[10] A. Hassanein, Fusion Technol. 15 (1989) 513.[11] A. Hassanein, et al., in: K. Herschbach, W. Maurer, J.E.

Vetter (Eds.), Fusion Technology, 1994, p. 223.[12] A. Hassanein, I. Konkashbaev, Fusion Eng. Des. 28

(1995) 27.[13] A. Hassanein, I. Konkashbaev, Plasma Devices Opera-

tions 5 (1998) 297.[14] L.L. Lengyel, et al., Nucl. Fusion 36 (1996) 1679.[15] L.L. Lengyel, V.A. Rozhansky, J.Yu. Veselova, Drift

motion in the scrape-off-layer during hard disruptions,Proceedings 24th European Physical Society Conf. onContr. Fus. and Plasma Phys., (Berchtesgaden, Germany,1997), Ed. Eur. Phys. Soc., Geneva, Vol. 21A-pan 4, 19971549.

[16] I.S. Landman, H. Wuerz, Electric stopping in hot-plasma-wall interactions, Proceedings 24th European PhysicalSociety Conf. on Contr. Fus. and Plasma Phys., (Bercht-esgaden, Germany, 1997), Ed. Eur. Phys. Soc., Geneva,Vol. 21A-part 4, 1997 1821.

[17] R. Vassen, A. Kaiser, D. Stover, J. Nucl. Mater. 233–237(1996) 713.

[18] S. Pestchanyi, N. Usov, H. Wuerz, Numerical simulationof brittle destruction of carbon-based materials due topulse plasma heating, Proceedings 20th Symp. Fus. Tech-nol. (Marseille, France, 1998), Beaumont, B., et al. (Eds.),Vol. 1, 1998 275.

[19] M. Guseva, et al., J. Tech. Phys. 66 (6) (1966) 106.[20] A. Hassanein, I. Konkashbaev, J. Nucl. Mater. 258–263

(1998) 645.[21] A. Hassanein, Effect of Macroscopic Eroded Debris on

Lifetimes of Plasma-Facing Components during PlasmaInstabilities, presented at 21st European Symposium onFusion Technology (SOFT), 11–18 September 2000,Madrid, Spain. Accepted for publication in Fusion Eng.Des. 56–57 (2001) 409.

[22] V. Belan, et al., J. Nucl. Mater. 233–237 (1996) 763.[23] V. Litunovsky, et al., in: B. Beaumont, P. Libeyre, B. de

Gentile, G. Tonon (Eds.), Fusion Technology, 1998, p.59.

[24] N.I. Arkhipov, et al., J. Nucl. Mater. 233–237 (1996) 767.[25] J. Linke, et al., in: B. Keen, M. Huguet, R. Hemsworth

(Eds.), Fusion Technology, 1991, p. 428.[26] J. Van der laan, J. Nucl. Mater. 162–164 (1989) 964.[27] A.V. Burdakov, et al., J. Nucl. Mater. 233–237 (1996)

697.[28] V. Safronov, N. Arkhipov, et al., in: B. Beaumont, P.

Libeyre, B. de Gentile, G. Tonon (Eds.), Fusion Technol-ogy, 1998, p. 105.

[29] A. Hassanein, I. Konkashbaev, in: C. Varandas, F. Serra(Eds.), Fusion Technology, 1996, p. 379.

[30] Y.V. Martynenko, et al., J. Nucl. Mater. 258–263 (1998)1120.

[31] V. Safronov, et al., J. Nucl. Mater. 290–293 (2001) xxx.[32] V. Belan, et al., J. Nucl. Mater. 233–237 (1996) 763.[33] A. Hassanein, I. Konkashbaev, Disruption simulation

experiments and extrapolation to reactor conditions,Proc. 20th Symp. Fusion Technology (Marseille, France,1998), B. Beaumont, et al. (Eds.) Vol. 1, 1998 245.

[34] N.I. Arkhipov, V.P. Bakhtin, V.M. Safronov, D.A. To-porkov, S.G. Vasenin, H. Wurz, A.M. Zhitlukhin, Plasmatemperature measurements in disruption simulated experi-ments, in: K. Herschbach, W. Maurer, J.E. Vetter (Eds.),Proceedings 18th Symposium Fusion Technology, (Karl-sruhe, Germany, 1994), vol. 1, Elsevier, Amsterdam,1995, p. 395.

[35] A.V. Burdakov, et al., J. Nucl. Mater. 233–237 (1996)697.

[36] V. Litunovsky et al., Proceedings 20th Symposium onFusion Technology (SOFT), 7–11 September, Marseille,France, Vol. 1, 1998 59.

[37] A. Hassanein, I. Konkashbaev, J. Nucl. Mater. 290–293(2000) 1171.

prediction of material erosion and lifetime during major ... · fusion engineering and design 60...

Documents