gregor morfill max-planck institut für extraterrestrische physik ipp-cas, hefei, 24/1/2008

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Gregor Morfill Gregor Morfill Max-Planck Institut für extraterrestrische PhysikMax-Planck Institut für extraterrestrische Physik

IPP-CAS, Hefei, 24/1/2008IPP-CAS, Hefei, 24/1/2008

Thanks go to my co-authors: S. Ratinskaya, U. de Angelis, C. Castaldo, and to J. Martin, S. Khrapak and M. Horanyi for discussions and further information.

Dust in Fusion ReactorsDust in Fusion Reactors

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contentscontents I. Introduction:I. Introduction: II. ´Dust Physics´ overview:II. ´Dust Physics´ overview:

III. ´Dust Physics´ - High velocity (Hi-V) dust particles in the III. ´Dust Physics´ - High velocity (Hi-V) dust particles in the km/sec range km/sec range

IV. Hi-V dust Particles: Direct measurements IV. Hi-V dust Particles: Direct measurements

V. Could high velocity (Hi-V) dust particle impacts lead to aV. Could high velocity (Hi-V) dust particle impacts lead to a runaway effect? runaway effect?

VI. High velocity (Hi-V) dust particles as a source of VI. High velocity (Hi-V) dust particles as a source of neutrals neutrals

ConclusionConclusion

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Plasma Fusion is one of the most Plasma Fusion is one of the most important topics in safeguarding the important topics in safeguarding the world energy needs in the future.world energy needs in the future.

Advantages:Advantages:

The ´fuel´ is practically inexhaustible.The ´fuel´ is practically inexhaustible.

The energy production per gram is huge.The energy production per gram is huge.

The waste production is low.The waste production is low.

The environmental effects are minimal.The environmental effects are minimal.

The danger of radioactive accidents is The danger of radioactive accidents is minimal.minimal.

I. IntroductionI. Introduction

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Plasma Fusion is one of the most Plasma Fusion is one of the most important topics in safeguarding important topics in safeguarding the world energy needs in the the world energy needs in the future.future.

Problems:Problems:

The technology has proven to be The technology has proven to be much more challenging than much more challenging than initially assumed.initially assumed.

The reactor environment is not The reactor environment is not ´benign´ by any standards.´benign´ by any standards.

The plasma-wall interactions cannot The plasma-wall interactions cannot be avoided and imply limited be avoided and imply limited operation times before repairs are operation times before repairs are necessary.necessary.

I. IntroductionI. Introduction

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That dust exists in tokamaks is well That dust exists in tokamaks is well known.* known.*

That this dust may constitute a hazard That this dust may constitute a hazard for fusion reactors is a concern.for fusion reactors is a concern. What is almost completely unknown is What is almost completely unknown is the scope of the problem – other than the scope of the problem – other than straightforward linear extrapolations.straightforward linear extrapolations.

Consequently there is little (if any) Consequently there is little (if any) thought given to possible reactor thought given to possible reactor design implications.design implications.

ITERITER

Parameters:Parameters:R = 6.2m, r = 2.0mR = 6.2m, r = 2.0mB = 5.3T (on axis)B = 5.3T (on axis)I = 15MAI = 15MAPredicted fusion power of Predicted fusion power of 500MW500MW

* Dust production in ITER * Dust production in ITER is estimated at 750 kg/year (Be)is estimated at 750 kg/year (Be) and 150kg/year (Cu) and 150kg/year (Cu)

Mitsubishi Report (2006)Mitsubishi Report (2006)

I. Introduction: Dust in TokamaksI. Introduction: Dust in Tokamaks

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Size distributionSize distribution (from dust (from dust collection) peaks around 5-10 collection) peaks around 5-10 μμm m and falls off smoothly to beyond and falls off smoothly to beyond 100 100 μμm.m. (Ciattaglia, Rohde, EPS (Ciattaglia, Rohde, EPS Warsaw, 2007)Warsaw, 2007)

Propagation direction Propagation direction of ´small´ of ´small´ dust particles mostly along the dust particles mostly along the plasma rotation. plasma rotation. (Roquemore, (Roquemore, Rudakov, EPS Warsaw, 2007)Rudakov, EPS Warsaw, 2007)

Observed particle velocities Observed particle velocities are 10are 10´s of m/sec up to 0.5 km/sec. ´s of m/sec up to 0.5 km/sec. (Rohde, Rudakov, Hong, (Rohde, Rudakov, Hong, Roquemore, EPS Warsaw, 2007)Roquemore, EPS Warsaw, 2007)


Film provided by F. Lott and G. F. Counsell (2006)Film provided by F. Lott and G. F. Counsell (2006)

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Particle life timesParticle life times,, , in the main , in the main chamber are a few msec, in the chamber are a few msec, in the SOL SOL 100msec100msec (Smirnov, (Smirnov, Roquemore, Hong, EPS Warsaw, Roquemore, Hong, EPS Warsaw, 2007) 2007)

´Rocket force´´Rocket force´ acceleration may acceleration may have been observed? have been observed? (Interaction (Interaction with ELMs - Asakura, SOL/Plasma with ELMs - Asakura, SOL/Plasma boundary - Rudakov, EPS Warsaw, boundary - Rudakov, EPS Warsaw, 2007)2007)



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The ´traditional´ concerns:The ´traditional´ concerns:

Dust sputtering could lead to Dust sputtering could lead to core plasma contamination.core plasma contamination.

Transport and redeposition of Transport and redeposition of dust can roughen surfaces, dust can roughen surfaces, reducing the performance.reducing the performance.

Dust can block gaps in tiles left Dust can block gaps in tiles left for engineering reasons.for engineering reasons.

Dust could contain beryllium Dust could contain beryllium and tritium.and tritium.

Dust can transport impurities Dust can transport impurities around the scrape-off layer.around the scrape-off layer.

Be - dust in the diverter may Be - dust in the diverter may cause H explosion.cause H explosion.


Co-deposited material

e.g. Winter (1999), Rubel et al. (2001), Martin (2006)

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The ´unconventional´ concerns:The ´unconventional´ concerns:

Is there some ´dust physics´ that Is there some ´dust physics´ that has not been considered so far? has not been considered so far?

In what way(s) not considered so In what way(s) not considered so far could dust become a hazard? far could dust become a hazard?

Could ´dust´ become a design or Could ´dust´ become a design or reactor operation driver?reactor operation driver?


Co-deposited material

e.g. Winter (1999), Rubel et al. (2001), Martin (2006)

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Provided by F. Lott and G. F. Counsell (2006)Provided by F. Lott and G. F. Counsell (2006)

Rudakov (2007, priv. comm.)Rudakov (2007, priv. comm.)

II. ´Dust Physics´ - production, II. ´Dust Physics´ - production, charging, transport, destruction, charging, transport, destruction,

impacts…impacts…

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Provided by F. Lott and G. F. Counsell (2006)Provided by F. Lott and G. F. Counsell (2006)


Have we studied the Have we studied the role of dust in Plasma role of dust in Plasma

Fusion Reactors Fusion Reactors sufficiently ?sufficiently ?



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II. ´Dust Physics´ - II. ´Dust Physics´ - productionproduction, , charging, transport, destruction, charging, transport, destruction,


Fresh dust particles Fresh dust particles can be produced by:can be produced by:

plasma surface erosion plasma surface erosion

and flaking, and flaking, nucleation in cooler nucleation in cooler

regions, regions, destruction of interior destruction of interior

elements. elements. The divertor is believed The divertor is believed

to be the main source to be the main source region.region.

Provided by F. Lott Provided by F. Lott and G. F. Counsell and G. F. Counsell (2006)(2006)

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Charging is rapid mainly by electron and Charging is rapid mainly by electron and ion impacts.ion impacts.

Secondary emission and photoeffect may Secondary emission and photoeffect may also contribute.also contribute.

The overall particle potential is expected The overall particle potential is expected to be a few times the electron energy.to be a few times the electron energy.

II. ´Dust Physics´ - production, II. ´Dust Physics´ - production, chargingcharging, transport, destruction, , transport, destruction,


ee

ii

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Charged particle transport is affected by:Charged particle transport is affected by: Electric and magnetic fields, Electric and magnetic fields, Ion drag forces (including Coulomb drag),Ion drag forces (including Coulomb drag), Thermophoretic forces,Thermophoretic forces, Photophoretic forces,Photophoretic forces, ´Rocket effect´,´Rocket effect´, Thermoionic emission,Thermoionic emission, Collective effects.Collective effects.

II. ´Dust Physics´ - production, II. ´Dust Physics´ - production, charging, charging, transporttransport, destruction, , destruction,


ee

ii

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Particle destruction processes:Particle destruction processes: Heat and evaporation, Heat and evaporation, Ion and electron sputtering,Ion and electron sputtering, Photosputtering,Photosputtering, Thermoionic emission,Thermoionic emission, Collisions.Collisions.

II. ´Dust Physics´ - production, II. ´Dust Physics´ - production, charging, transport, charging, transport, destructiondestruction, ,


ee

ii

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Above a critical velocity of Above a critical velocity of ~1km/sec~1km/sec impacts become destructive (cratering).impacts become destructive (cratering).

Below this velocity impacts are mainly Below this velocity impacts are mainly elastic.elastic.


impactsimpacts……

v v ≤ 1km/sec≤ 1km/sec v v ≥ 1km/sec≥ 1km/sec

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High velocity (High velocity (Hi-VHi-V) particles – if they exist ) particles – if they exist – would be a (wall material) source of:– would be a (wall material) source of:

New particles New particles Neutral gasNeutral gas PlasmaPlasma


impactsimpacts……

v v ≥ 1km/sec≥ 1km/sec

The possible implications have not been

investigated for Plasma fusion reactors so far

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Questions:Questions:

1. Why worry about Hi-V particles? 1. Why worry about Hi-V particles? Tiny Tiny μμm-sized dust particles with velocities above m-sized dust particles with velocities above

a (few) km/sec would not have been detected with a (few) km/sec would not have been detected with current ´direct´ observation programmes (too fast, current ´direct´ observation programmes (too fast, not bright enough).not bright enough).

These particles, if they exist, are particularly These particles, if they exist, are particularly troublesome – they produce more ejecta on impact troublesome – they produce more ejecta on impact than their own mass!than their own mass!

For long operation times Hi-V particles can (in For long operation times Hi-V particles can (in principle) cause a runaway effect.principle) cause a runaway effect.

III. ´Dust Physics´ - High velocity (Hi-III. ´Dust Physics´ - High velocity (Hi-V) dust particles in the km/sec rangeV) dust particles in the km/sec range

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2. Could such high velocities be reached before the 2. Could such high velocities be reached before the particles are lost or sputtered away? particles are lost or sputtered away?

High velocities of around 0.5 km/sec have been High velocities of around 0.5 km/sec have been seen for much bigger particles (more than 1000 seen for much bigger particles (more than 1000 times more massive – hence with much higher times more massive – hence with much higher kinetic energies).kinetic energies).

Other (circumstantial) evidence exists – see later.Other (circumstantial) evidence exists – see later.

Numerical simulations, however, indicate that high Numerical simulations, however, indicate that high velocities are unlikely to occur… but has all the velocities are unlikely to occur… but has all the physics been considered?physics been considered?


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3. Are there any other possible Hi-V signatures? 3. Are there any other possible Hi-V signatures? Look for impact craters, acoustic signatures, plasma Look for impact craters, acoustic signatures, plasma

clouds, neutral clouds, debris clouds, plasma clouds, neutral clouds, debris clouds, plasma contamination due to neutrals etc. contamination due to neutrals etc.

4. Could Hi-V particles be generic features of 4. Could Hi-V particles be generic features of Tokamaks?Tokamaks?

Accelerated (larger) particles apparently occur in all Accelerated (larger) particles apparently occur in all devices.devices.


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1. The size of ´visible´ intrinsic dust particles 1. The size of ´visible´ intrinsic dust particles is not known, but:is not known, but:Injected dust of Injected dust of 66μμm was visible at m was visible at vv≤100m/s≤100m/s (Rudakov, EPS Warsaw, 2007) (Rudakov, EPS Warsaw, 2007) and and 40-120 40-120 μμmm particles were also visible particles were also visible (Granetz, EPS Warsaw, 2007).(Granetz, EPS Warsaw, 2007).

2. The observed dust velocities (so far) are 2. The observed dust velocities (so far) are v ≤v ≤ 500 m/sec:500 m/sec:

At 1000f/s the trajectory length per frame is ≤At 1000f/s the trajectory length per frame is ≤ 50cm.50cm. Hi-V particle velocities are Hi-V particle velocities are ≥ ≥ 1 km/sec. 1 km/sec. The trajectory length per frame is ≥ 1m, The trajectory length per frame is ≥ 1m, and and the brightness per pixel a factor the brightness per pixel a factor 100 100 lower.lower. 3. Hi-V particles cannot be detected optically 3. Hi-V particles cannot be detected optically with current technology.with current technology.


IV.IV. Hi-V dust Particles: Direct measurementsHi-V dust Particles: Direct measurementsOptical measurementsOptical measurements

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The plan was to The plan was to expose a surface to expose a surface to the plasma and the plasma and investigate it investigate it afterwards using high afterwards using high resolution microscopy.resolution microscopy.

Three probe positions Three probe positions in the SOL on the axis in the SOL on the axis (r(r11 – r – r33) - plus one ) - plus one each at the SOL edge each at the SOL edge (r(ruu and r and rbb).).

IV. Hi-V dust Particles: Direct measurementsIV. Hi-V dust Particles: Direct measurementsImpacts on a Langmuir probe in FTU*Impacts on a Langmuir probe in FTU*

*FTU (Frascati Tokamak Upgrade) is a *FTU (Frascati Tokamak Upgrade) is a Tokamak with outer radius of 1m, small Tokamak with outer radius of 1m, small radius 33 cm.radius 33 cm.

Impact-like Impact-like signatures were signatures were

observed at positions observed at positions rr11 – r – r33 , not at r, not at ruu and and

rrbb..

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The image shows ´craters´, The image shows ´craters´, possibly due to micron-sized possibly due to micron-sized Hi-V projectiles.Hi-V projectiles.

The crater dimensions are The crater dimensions are compatible with compatible with 11μμm m particles impacting at particles impacting at 10km/sec – or 10km/sec – or 22μμm at m at 3.5km/sec.3.5km/sec.

The image also shows a The image also shows a distribution of small Fe distribution of small Fe particles (particles (≤ 20≤ 20m), m), presumably ejected from the presumably ejected from the steel wall of the tokamak.steel wall of the tokamak.

Their size spectrum is Their size spectrum is compatible with high velocity compatible with high velocity impacts on the walls. impacts on the walls.

*FTU is a Tokamak with outer *FTU is a Tokamak with outer radius of 1m, small radius 33 cm.radius of 1m, small radius 33 cm.

IV. Hi-V dust Particles: Direct measurementsIV. Hi-V dust Particles: Direct measurementsLangmuir probe surface after exposure in Langmuir probe surface after exposure in

FTU*FTU*

Castaldo et al. (2007)Castaldo et al. (2007)

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IV. Hi-V dust Particles – Direct IV. Hi-V dust Particles – Direct measurements:measurements:

Plasma signatures of impacts in FTUPlasma signatures of impacts in FTU Hi-V particle impacts will Hi-V particle impacts will

also produce a cloud of also produce a cloud of high velocity plasma, high velocity plasma, which will (mostly) be which will (mostly) be captured in the SOL. captured in the SOL.

The impact-produced The impact-produced plasma cloud should be plasma cloud should be measurable as a short measurable as a short burst of enhanced plasma burst of enhanced plasma density with Langmuir density with Langmuir probes. probes.

Wall impacts as well as Wall impacts as well as impacts on the probe impacts on the probe might be observable.might be observable.

Castaldo et al. 2007, Ratinskaya et al. 2007Castaldo et al. 2007, Ratinskaya et al. 2007

Castaldo et al. (2007)Castaldo et al. (2007)

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Plasma signatures of impacts in FTUPlasma signatures of impacts in FTU A semi-empirical A semi-empirical

expression for the expression for the impact produced impact produced plasma (total charge) is:plasma (total charge) is:

NNii = 2.8 = 2.8··101077 aaμμ3 3 vv3.213.21

wherewhere aaμμ is in microns is in microns and v in km/secand v in km/sec

Grün 1981, Burchell et al. 1999Grün 1981, Burchell et al. 1999

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Plasma signatures of impacts in FTUPlasma signatures of impacts in FTU A plasma A plasma impactimpact cloud from cloud from

aa 11μμm particle at 10km/sec m particle at 10km/sec – or a 2– or a 2μμm particle at m particle at 3.5km/sec3.5km/sec – – contains about contains about 10101111 to 10 to 101212 ions (charges) ions (charges) released in a few tens of released in a few tens of μμsec – as was observed.sec – as was observed.

Typical event rates as well Typical event rates as well as plasma, neutral gas and as plasma, neutral gas and secondary particle secondary particle production rates in FTU were production rates in FTU were determined.determined.

These were compatible with These were compatible with

the ímpact signaturesón the ímpact signaturesón the Langmuir probes.the Langmuir probes.

Castaldo et al. 2007, Ratinskaya et al. 2007Castaldo et al. 2007, Ratinskaya et al. 2007

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Langmuir probe Langmuir probe signaturessignatures

About 100 éventsAbout 100 évents´ per second.´ per second.

10101111 – 10 – 101212 charges per charges per évent´.évent´.

All évents´have All évents´have exponential time exponential time profiles.profiles.

Évents´ are more Évents´ are more frequent near wall.frequent near wall. Ratinskaya et al. (2007), Castaldo et al. (2007)Ratinskaya et al. (2007), Castaldo et al. (2007)

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Langmuir probe Langmuir probe signaturessignatures

´Events´ nearer ´Events´ nearer the wall are the wall are smaller and have smaller and have shorter duration shorter duration than those further than those further from the wall.from the wall.

Compatible with a Compatible with a wall source.wall source.

Compatible with Compatible with high velocity high velocity impact plasma impact plasma clouds.clouds.

Ratinskaya et al. (2007), Castaldo et al. (2007)Ratinskaya et al. (2007), Castaldo et al. (2007)

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Caveats:Caveats:

1. Are there any other signatures? 1. Are there any other signatures?

Look for Look for impact cratersimpact craters, accoustic signatures, , accoustic signatures, plasma cloudsplasma clouds, neutral , neutral clouds, clouds,

debris clouds, debris clouds, plasma contamination due to neutralsplasma contamination due to neutrals etc. etc.

Impact cratersImpact craters may look like unipolar arc signatures, impact may look like unipolar arc signatures, impact plasma plasma cloudsclouds may look like blobs, may look like blobs, plasma contaminationplasma contamination may be due to other may be due to other sources (e.g. sputtering) sources (e.g. sputtering)

2. Could such high velocities be reached before the particles are lost or 2. Could such high velocities be reached before the particles are lost or sputtered away? sputtered away?

High velocitiesHigh velocities of around 0.5 km/sec have already been seen for much of around 0.5 km/sec have already been seen for much bigger bigger

particles (more than 100 times more massive). particles (more than 100 times more massive).

More research into efficient acceleration processes is necessary – More research into efficient acceleration processes is necessary – velocities velocities

» » 0.5 km/sec would be a concern0.5 km/sec would be a concern


Plasma signatures of impacts in FTUPlasma signatures of impacts in FTU

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There are two concerns:There are two concerns:

1. Runaway wall erosion could imply much shorter operation 1. Runaway wall erosion could imply much shorter operation times, with all the negative cost/effectiveness problems – or times, with all the negative cost/effectiveness problems – or would dictate a reactor operation mode far from the would dictate a reactor operation mode far from the optimum. optimum.

2. Associated with impact erosion there will also be neutral 2. Associated with impact erosion there will also be neutral gas production. This may penetrate into the core plasma, gas production. This may penetrate into the core plasma, contaminate it and lead to efficiency losses.contaminate it and lead to efficiency losses.

V. Could high velocity (Hi-V) dust V. Could high velocity (Hi-V) dust particle impacts lead to a runaway particle impacts lead to a runaway

effect?effect?

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On impact with the walls Hi-V particles will generate new ejecta On impact with the walls Hi-V particles will generate new ejecta with a ratio with a ratio

MMEE/ M/ Mpp ≈ ≈ 5v5v22

where the impact velocity, v, is in km/sec.where the impact velocity, v, is in km/sec.

Dependence of impact crater volume, V, on impact angle size, Dependence of impact crater volume, V, on impact angle size, θθ ::

V V ≈ V≈ V00 cos cosθθ

Ejecta mass distribution isEjecta mass distribution is

dN/dm = CmdN/dm = Cm-1.8-1.8

with the largest ejecta particle having a mass with the largest ejecta particle having a mass mmL L ≈ 0.1≈ 0.1 M MEE

Burchell et al. 1999, Gault 1963; Dohnanyi 1969; Gault and Wedekind 1969Burchell et al. 1999, Gault 1963; Dohnanyi 1969; Gault and Wedekind 1969


effect?effect?

θθ

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We have: We have: dm/dt = m/ dm/dt = m/ ττmm – m/ – m/ττll + + δδ (t)(t)

the time scale of the growth of total ejecta mass, the time scale of the growth of total ejecta mass, ττmm , in , in the absence of losses, would be the absence of losses, would be ττm m == ττ/5v/5v22 , where the , where the factor 5vfactor 5v22 is the ratio of ejecta mass/impact mass (which is the ratio of ejecta mass/impact mass (which can be large, if the impact velocity v(km/sec) is high).can be large, if the impact velocity v(km/sec) is high).

Also, Also, ττll represents losses (e.g. by sputtering) and represents losses (e.g. by sputtering) and δδ (t) is (t) is an initial source (trigger ) term that becomes irrelevant an initial source (trigger ) term that becomes irrelevant after a few after a few ττmm , if , if ττm m is less than is less than ττll .Then we have .Then we have

m(t) = mm(t) = m00expexp[[t (t (ττll - -ττmm) / ) / ττll ττmm]]

Note: the core plasma contamination by neutrals grows at Note: the core plasma contamination by neutrals grows at the same rate, i.e.the same rate, i.e.

SS00(t) (t) ~ ~ expexp[[t (t (ττll - -ττmm) / ) / ττll ττmm]]Morfill et al. 2007Morfill et al. 2007


effect?effect?

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We had: We had: SS00(t) (t) ~ ~ expexp[[t (t (ττll - -ττmm) / ) / ττll ττmm] with ] with ττm m == ττ /5v /5v22

It is easy to see that provided It is easy to see that provided ττl l ≥ ≥ ττmm we obtain a ´runaway´ effect, we obtain a ´runaway´ effect, with the reactor contamination and wall erosion growing with the reactor contamination and wall erosion growing exponentially. Losses are due to e.g. particle destruction or exponentially. Losses are due to e.g. particle destruction or deposition, removal of plasma contaminants in the SOL, neutral deposition, removal of plasma contaminants in the SOL, neutral deposition.deposition.

Let us take particle destruction by sputtering as the dominant loss Let us take particle destruction by sputtering as the dominant loss process, i.e. process, i.e. ττll = = ττsputsput

There are three conditions for starting an erosion and There are three conditions for starting an erosion and contamination chain reaction:contamination chain reaction:

1. the (particle life) time before wall impact 1. the (particle life) time before wall impact ττ ≤ ≤ ττsputsput

2.2. the acceleration time to the the acceleration time to the critical velocity critical velocity vvcritcrit must be ≤ must be ≤ ττ 3. the largest ejecta particle must have a mass m3. the largest ejecta particle must have a mass mLL ≥ ≥ MMp p ++ MMsputsput

Morfill et al. 2007Morfill et al. 2007


effect?effect?

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Hi-V dust particle Hi-V dust particle

critical velocity –critical velocity – sputter losses:sputter losses:

the asymptotic limit the asymptotic limit

for vfor vcritcrit is 1.4 km/secis 1.4 km/sec

acceleration to acceleration to velocities above the velocities above the limits indicated by limits indicated by the lines would lead the lines would lead to an erosion + to an erosion + contami-nation contami-nation chain reaction.chain reaction. 0 1 2 3 4 5 60 1 2 3 4 5 6

aapp((μμm)m)

8 (km/sec)8 (km/sec)

22

33

44

55

66

vvcritcrit

RRsputsput ττ = 1 = 1μμmm

RRsputsput ττ = 2 = 2μμmm

RRsput sput ττ = 0.5 = 0.5μμmm

77

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Summary of the impact physics Summary of the impact physics investigation:investigation:

Hi-V dust particles (if they exist) present a Hi-V dust particles (if they exist) present a particular hazard for continuous reactor safety particular hazard for continuous reactor safety and operation –and operation – i.e. for i.e. for ττl l – – ττmm ≥≥ 0 0 runaway runaway

growth of erosion and contamination becomes growth of erosion and contamination becomes unavoidable:unavoidable:

Wall erosion will grow exponentiallyWall erosion will grow exponentially

MMErosion Erosion ~~ expexp[[t (t (ττll - -ττmm) / ) / ττll ττmm]]

The core plasma contamination by neutrals grows The core plasma contamination by neutrals grows at the same rateat the same rate

SS00(t) (t) ~ ~ expexp[[t (t (ττll - -ττmm) / ) / ττll ττmm]]Morfill et al. 2007Morfill et al. 2007

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Neutral gas production Neutral gas production

Hi-V particles will also produce a cloud of high Hi-V particles will also produce a cloud of high velocity (up to the free expansion speed) neutral velocity (up to the free expansion speed) neutral gas (wall material). The estimates vary greatly, gas (wall material). The estimates vary greatly, practically no measurements exist: practically no measurements exist:

MMGG/ M/ Mpp ≈ 1 – 10≈ 1 – 10

The neutrals may enter the core plasma - by direct The neutrals may enter the core plasma - by direct injection - up to some characteristic distance, the injection - up to some characteristic distance, the ionisation length (e.g. by electron impact).ionisation length (e.g. by electron impact).

Morfill et al. 1983, Morfill et al. 2007Morfill et al. 1983, Morfill et al. 2007

VI. High velocity (Hi-V) dust particles VI. High velocity (Hi-V) dust particles as a source of neutralsas a source of neutrals

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The penetration depth into the plasma depends on the The penetration depth into the plasma depends on the neutral gas velocity, the ejection direction and the neutral gas velocity, the ejection direction and the plasma density n(plasma density n(xx,T). It is typically (ionisation cross ,T). It is typically (ionisation cross section section for Fe by ~ 20eV electrons is ≈ 5for Fe by ~ 20eV electrons is ≈ 5··1010-16-16cmcm22):):

≈ ≈ 1 – 20 cm1 – 20 cm

Further core plasma contamination is then by diffusion Further core plasma contamination is then by diffusion (for a quick estimate use a linear model, x=0 to x=2R) (for a quick estimate use a linear model, x=0 to x=2R)

∂∂nnii//∂∂t – Dt – D∂∂22nnii//∂∂xx22 = = ∂∂//∂∂xx{{SS00(t) exp(-x/(t) exp(-x/))}}

Pindzola et al., 1995, Morfill et al. 1983, Morfill et al. 2007


X=0X=2R

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The source term for neutral gas contamination isThe source term for neutral gas contamination is

∂∂//∂∂xx{{SS00(t) exp(-x/(t) exp(-x/))}}

the the exp(-x/exp(-x/)) represents the ionisation profile with ionisation length represents the ionisation profile with ionisation length . .

The time dependent term The time dependent term SS00(t) represents the temporal evolution of (t) represents the temporal evolution of the source. If this is due to wall impact production by Hi-V particles (if the source. If this is due to wall impact production by Hi-V particles (if they exist), it can be written as they exist), it can be written as

SS00(t) (t) m(t) m(t)

where m(t) is given from where m(t) is given from dm/dt = m/ dm/dt = m/ ττmm – m/ – m/ττll + + δδ (t), (t), i.e. the rate of production of fresh Hi-V particles, dm/dt, is proportional i.e. the rate of production of fresh Hi-V particles, dm/dt, is proportional

to the impacting population, with total mass m(t). The appropriate to the impacting population, with total mass m(t). The appropriate time scale is the (mean) dust particle life time until impact, time scale is the (mean) dust particle life time until impact, ττ.. ( (ττ ≥≥ ττaccacc the acceleration time.) the acceleration time.)



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Results for FTU were a surprise – they are completely Results for FTU were a surprise – they are completely compatible with the Hi-V particle impact physics estimates:compatible with the Hi-V particle impact physics estimates:

Using the measured impact rates from the ´crater counts´ on Using the measured impact rates from the ´crater counts´ on the Langmuir probe and the plasma cloud production rates as the Langmuir probe and the plasma cloud production rates as the source term for neutral gas contamination yields a core Fe the source term for neutral gas contamination yields a core Fe ion density of ~ 10ion density of ~ 101010cmcm-3-3..

The estimates based on UV spectroscopy also gave 10The estimates based on UV spectroscopy also gave 101010cmcm-3-3..

In addition, the measured core concentration of Ni was a factor In addition, the measured core concentration of Ni was a factor 2 lower than the Fe concentration. Under normal conditions 2 lower than the Fe concentration. Under normal conditions (with inconal poloidal limiter) it is expected that sputtering (with inconal poloidal limiter) it is expected that sputtering should produce a higher Ni concentration than Fe – not lower.should produce a higher Ni concentration than Fe – not lower.

This, too, suggests a wall source (the walls are stainless steel), This, too, suggests a wall source (the walls are stainless steel), but not from sputtering, which should be too small.but not from sputtering, which should be too small.



40

Summary: Evidence for Hi-V particles Summary: Evidence for Hi-V particles in Tokamaksin Tokamaks

1.1. Inferred evidenceInferred evidence from impact from impact craters on Langmuir probes in FTU.craters on Langmuir probes in FTU.

2.2. Inferred evidenceInferred evidence from impact from impact generated plasma clouds in FTU. generated plasma clouds in FTU.

3.3. Inferred evidence Inferred evidence from core plasma from core plasma contamination in FTU.contamination in FTU.

4.4. Theoretical investigationsTheoretical investigations of particle of particle acceleration are not conclusive: acceleration are not conclusive:

- critical velocities of - critical velocities of ~~ 2 km/sec 2 km/sec have not been obtained in the have not been obtained in the

model model calculations calculations - there is a question whether the - there is a question whether the

life life times of the particles may be times of the particles may be underestimated (use of SVP not underestimated (use of SVP not appropriate in a plasma appropriate in a plasma

environment)environment)

41

Conclusion: Hi-V particles in Conclusion: Hi-V particles in Tokamaks Tokamaks

FTU measurements have provided some initial evidence FTU measurements have provided some initial evidence that dust in tokamaks may be highly accelerated.that dust in tokamaks may be highly accelerated.

If this is generally soIf this is generally so, it presents a particular hazard - , it presents a particular hazard - because on impact with the walls each ´Hi-V particle´ may because on impact with the walls each ´Hi-V particle´ may generate 100 – 1000 times more dust.generate 100 – 1000 times more dust.

This dust, in This dust, in continuous reactor operationcontinuous reactor operation, will also be , will also be accelerated, impact the walls - and so on…accelerated, impact the walls - and so on…

Impact-produced neutral high velocity gaseous (wall) Impact-produced neutral high velocity gaseous (wall) material will grow accordingly. It may pass through the material will grow accordingly. It may pass through the SOL, enter the core plasma directly and spread by diffusive SOL, enter the core plasma directly and spread by diffusive transport once it has been ionised.transport once it has been ionised.

This scenario inevitably leads to an exponential This scenario inevitably leads to an exponential growth in reactor contamination and wall erosion…growth in reactor contamination and wall erosion…

……unless steps are taken to overcome this problem.unless steps are taken to overcome this problem.

42

To identify the scope of this possible Hi-V problem, To identify the scope of this possible Hi-V problem, the following steps should be taken:the following steps should be taken:

Study the physics of dust production, transport, acceleration, Study the physics of dust production, transport, acceleration, destruction and impacts – both experimentally and destruction and impacts – both experimentally and theoretically.theoretically.

Measure dust in different Tokamaks (e.g. by acoustic sensors Measure dust in different Tokamaks (e.g. by acoustic sensors and by direct capture using aerogels – or whatever works).and by direct capture using aerogels – or whatever works).

Develop solutions for reducing the dust production in critical Develop solutions for reducing the dust production in critical areas in the reactor. areas in the reactor.

Include the Hi-V dust issue in the reactor design Include the Hi-V dust issue in the reactor design considerations…considerations…

……and start well before the ITER design freeze…and start well before the ITER design freeze…

Because we already have visual observations of ~km/sec dust Because we already have visual observations of ~km/sec dust and cannot assume that a magic barrier exists. Certainly we and cannot assume that a magic barrier exists. Certainly we cannot afford to ignore this effect, if we have not even cannot afford to ignore this effect, if we have not even understood it.understood it.

Conclusion: Hi-V particles in Conclusion: Hi-V particles in Tokamaks Tokamaks

43

Thank you for your Thank you for your attentionattention


44

IV. Return to the original question: IV. Return to the original question: Could there be high velocity (Hi-V) Could there be high velocity (Hi-V)

dust particles?dust particles? To answer this question let us To answer this question let us

summarise the evidence:summarise the evidence:

1. Direct measurements1. Direct measurements – what are Hi- – what are Hi-V particle signatures? Can these V particle signatures? Can these particles be seen/captured?particles be seen/captured?

2. Trajectory calculations2. Trajectory calculations – can high – can high velocities be reached? Can we scale velocities be reached? Can we scale the results to different Tokamaks – i.e. the results to different Tokamaks – i.e. how relevant is this for ITER? how relevant is this for ITER?

3. Rocket effect 3. Rocket effect – what is the role of – what is the role of this process?this process?


??

45

2. Hi-V dust Particles: Trajectory calculations.2. Hi-V dust Particles: Trajectory calculations. Solve the ´Equation of Motion´ taking into Solve the ´Equation of Motion´ taking into account all electromagnetic and plasma drag account all electromagnetic and plasma drag forces, e.g.:forces, e.g.:

Lorentz force Lorentz force GravityGravity

(Geometrical) Flow Pressure(Geometrical) Flow Pressure

gmvvvvnmaBvEqdt

vdm ddpdpdd

dd )(||)( 2 +…+…

etc.etc.

Scale the results to different TokomaksScale the results to different Tokomaks

46

2. Hi-V dust Particles: Trajectory 2. Hi-V dust Particles: Trajectory calculationscalculations – Plasma and field model – Plasma and field model Use Use B2-solps5.0:B2-solps5.0:

Standard European code Standard European code to build plasma profiles to build plasma profiles for the SOL.for the SOL.

B2 is a dual fluid code B2 is a dual fluid code with Braginskii Transport.with Braginskii Transport.

Either fluid neutrals or Either fluid neutrals or EIRENE Monte-Carlo EIRENE Monte-Carlo code.code.

Can build up profiles for Can build up profiles for many tokamaks many tokamaks worldwide, including ITERworldwide, including ITER

From James Martin From James Martin (2006)(2006)

47

2. Hi-V dust Particles: Trajectory 2. Hi-V dust Particles: Trajectory calculationscalculations – B2-solps5.0 plasma and field model - – B2-solps5.0 plasma and field model - scalingscaling

MASTMAST ITERITER


48

2. Hi-V dust Particles: Trajectory 2. Hi-V dust Particles: Trajectory calculationscalculations

(Geometrical) flow pressure (Geometrical) flow pressure is the most important force is the most important force

EE and and v vxxBB become become important as the grain important as the grain evaporatesevaporates

Coulomb collisions were not Coulomb collisions were not included. This can increase included. This can increase the drag cross section (by a the drag cross section (by a factor 10 – 100)factor 10 – 100)

Rocket effect not includedRocket effect not includedFrom James Martin From James Martin (2006)(2006)

Comparison of forces for a typical trajectory where the Comparison of forces for a typical trajectory where the

dust particle (1 dust particle (1 m) evaporates:m) evaporates:

49

THANK YOU THANK YOU FOR YOUR FOR YOUR ATTENTIONATTENTION

50

Tiny dust particles with velocities above a few km/sec would Tiny dust particles with velocities above a few km/sec would not have been detected with current ´direct´ observation not have been detected with current ´direct´ observation programmes (too fast, not bright enough).programmes (too fast, not bright enough).


1. Can plasma drag or other processes be sufficiently effective 1. Can plasma drag or other processes be sufficiently effective to accelerate dust particles to velocities in the Hi-V range to accelerate dust particles to velocities in the Hi-V range (above ~1 km/sec)? (above ~1 km/sec)?

2. Could such high velocities be reached before the particles 2. Could such high velocities be reached before the particles are lost or sputtered away? are lost or sputtered away?

3. What happens when Hi-V particles impact the reactor walls?3. What happens when Hi-V particles impact the reactor walls?

Hi-V dust particles present a Hi-V dust particles present a potential hazard for reactor safety potential hazard for reactor safety and operation that has not been and operation that has not been

taken into account so far.taken into account so far.

II. ´Dust Physics´ - High velocity (Hi-V) II. ´Dust Physics´ - High velocity (Hi-V) dust particles in the km/sec rangedust particles in the km/sec range

51

2. Hi-V dust particles: The gravity 2. Hi-V dust particles: The gravity constraintconstraint

A constraint:A constraint: In order to achieve dust In order to achieve dust acceleration to velocities acceleration to velocities vv00 ≥ ≥ 1 km/s 1 km/s the azimuthal acceleration, the azimuthal acceleration, ώώ, must be , must be sufficiently large so that gravity does sufficiently large so that gravity does not remove the particle firstnot remove the particle first**::

v = Rv = Rώώt t ≥ v ≥ v00 and and ΔΔz = z = ½½gtgt22 ≤ ≤ ΔΔHH

RRώώ/g /g ≥ v≥ v00/√2g/√2gΔΔHH For For vv0 0 = 1 km/s and = 1 km/s and ΔΔH= H=

50cm this gives:50cm this gives: RRώώ/g /g ≥ 300 , t ≥ 300 , t ≤ 0.3 s≤ 0.3 s


ΔΔHH

*Possible electrostatic, photophoretic, thermophoretic etc. forces not yet *Possible electrostatic, photophoretic, thermophoretic etc. forces not yet considered.considered.

52

2. Hi-V dust Particles: Trajectory 2. Hi-V dust Particles: Trajectory calculationscalculations

– Plasma Plots (electron temperature - – Plasma Plots (electron temperature - eV)eV)

MASTMAST ITERITERFrom James Martin From James Martin (2006)(2006)

53

4. Hi-V dust particles present a particular 4. Hi-V dust particles present a particular hazard for reactor safety and operation –hazard for reactor safety and operation – sputter losses:sputter losses:

A short numerical example:A short numerical example: We use a typical sputter loss rate RWe use a typical sputter loss rate Rsputsput of 10 of 10μμm/sec*. m/sec*. From condition 3 we require that the largest ejecta particle mass From condition 3 we require that the largest ejecta particle mass

is:is:

mmL L ≈ 0.1≈ 0.1 M ME E ≥≥ M Mp p ++ MMsputsput

From the empirical relation** From the empirical relation** MMEE/ M/ Mpp ≈ ≈ 5v5v22 (v in km/sec)(v in km/sec) we get after some algebra we get after some algebra mmLL / M / ME E == 0. 0.5v5v2 2 ≥≥ (1+ R (1+ Rsput sput ττ /a /app))33

For e.g. For e.g. RRsput sput ττ = = 11μμm and m and aap p = = 11μμmm we obtain the minimum we obtain the minimum condition for self-sustained erosion growth (and plasma condition for self-sustained erosion growth (and plasma contamination)contamination)

vvcritcrit = = 4.0 km/sec4.0 km/sec

provided the acceleration time is shorter than provided the acceleration time is shorter than ττ (= 0.1 sec). (= 0.1 sec).

*J. Martin, 2007, ** Gault 1963; Dohnanyi 1969; Gault and Wedekind 1969*J. Martin, 2007, ** Gault 1963; Dohnanyi 1969; Gault and Wedekind 1969

54

Summary – FTU measurements and Summary – FTU measurements and impact physics calculationsimpact physics calculations

Conservative estimates for the growth time, Conservative estimates for the growth time, ττmm (FTU), are 10(FTU), are 10-3 -3 – 10– 10-1-1 sec. This is shorter than the sec. This is shorter than the sputter loss (or life) time for a 1sputter loss (or life) time for a 1μμm particle (typically m particle (typically 100msec in the SOL).100msec in the SOL).

These same conservative estimates have shown that These same conservative estimates have shown that for a 1 second FTU reactor operation, the particle for a 1 second FTU reactor operation, the particle (and neutral gas) contamination increases by a (and neutral gas) contamination increases by a factor 10factor 104-64-6. .

This is based on the impact rate measurements This is based on the impact rate measurements deduced using Langmuir probe measurements and deduced using Langmuir probe measurements and crater counts*.crater counts*.

This result is consistent with the typical measured Fe This result is consistent with the typical measured Fe contamination of the main plasma in FTU**.contamination of the main plasma in FTU**.

*Castaldo et al, 2007, **Ratinskaya, priv. comm., Morfill et al, 2007 *Castaldo et al, 2007, **Ratinskaya, priv. comm., Morfill et al, 2007

55 0.5 0.6 0.7 0.8 0.9 1.00.5 0.6 0.7 0.8 0.9 1.0

101044

101055

101066

TTee

M(t)/MM(t)/M00101033

3. Hi-V dust Particles: The ´Rocket 3. Hi-V dust Particles: The ´Rocket EffectÉffect´

vvee vvpp

Condition that ejecta Condition that ejecta mass is larger than mass is larger than initial particle mass, initial particle mass,

MM00, is satisfied , is satisfied provided sufficiently provided sufficiently high velocities are high velocities are

reached (ie. Provided reached (ie. Provided enough mass has enough mass has

been évaporated´).been évaporated´).

MMEE≥M≥M00

FeFe particles particles

56

The ´rocket effect´ is seen in the data. Particles are accelerated The ´rocket effect´ is seen in the data. Particles are accelerated away from ´hot´ regions due to photosputtering, photophoresis, away from ´hot´ regions due to photosputtering, photophoresis, anisotropic impact sputtering (in steep gradients) etc. anisotropic impact sputtering (in steep gradients) etc. This effect This effect tends to confine particles to the cooler SOL.tends to confine particles to the cooler SOL.

The equations to be solved are:The equations to be solved are:

dp/dt = vdp/dt = vppdM/dt + MdvdM/dt + Mdvpp/dt = v/dt = veedM/dtdM/dt and and dM/dt = dM/dt = -R-R00(M/M(M/M00))

ααAmAmpp

withwith αα = 2/3 and v= 2/3 and vee= (2kT= (2kTee/Am/Ampp))½½

RR0 0 is the initial atomic erosion rate (particle mass Amis the initial atomic erosion rate (particle mass Ampp) )

3. Hi-V dust Particles: The ´Rocket 3. Hi-V dust Particles: The ´Rocket Effect´ Effect´

vvee vvpp

57

The solution of these equations yield:The solution of these equations yield:

Particle velocity evolution: Particle velocity evolution: vvpp = v = vee[[MM00/M(t)-1/M(t)-1]]

Characteristic time scale: Characteristic time scale: = M = M00/[/[RR00AmAmpp(1-(1-αα))]]

Characteristic distance: Characteristic distance: x = 2x = 2vve e MM00/[/[RR00AmAmpp]]

Condition that on impact MCondition that on impact ME E ≥≥ MM00: : MM0 0 /M(t) + M(t)/M/M(t) + M(t)/M0 0 ≥ 2 + ≥ 2 + 1/(5v1/(5vee

22)) with vwith ve e in km/sec.in km/sec.


vvee vvpp

58 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.01.0

22

33

44

55

66

vvpp/v/vee

77

M(t)/MM(t)/M00

11


vvee vvpp

vvee corresponds typically corresponds typically to ´sputter temperatures´ to ´sputter temperatures´ of a few eV (for Fe of a few eV (for Fe particles a few km/sec).particles a few km/sec).

59

Could there be high velocity (Hi-V) Could there be high velocity (Hi-V) dust particles?dust particles?

To answer this question we To answer this question we proceed in the following way:proceed in the following way:

1. Direct measurements1. Direct measurements – what – what are Hi-V particle signatures? Can are Hi-V particle signatures? Can they be captured?they be captured?

2. Trajectory calculations2. Trajectory calculations – can – can high velocities be reached? high velocities be reached? Where? How fast? Before the Where? How fast? Before the particle is sputtered away? What particle is sputtered away? What size particles are involved? size particles are involved?


ΔΔHH

60


Dust particles in the 10´s km/sec range would not Dust particles in the 10´s km/sec range would not have been detected with current observation have been detected with current observation programmes.programmes.

Hi-V dust particles present a particular hazard for Hi-V dust particles present a particular hazard for reactor safety and operation.reactor safety and operation.

Plasma azimuthal flow velocities are in this range.Plasma azimuthal flow velocities are in this range.

If plasma drag were sufficiently effective, could If plasma drag were sufficiently effective, could dust particles be accelerated to corotation with dust particles be accelerated to corotation with the plasma and possibly reach 10s of km/sec?the plasma and possibly reach 10s of km/sec?

61


In order to achieve dust acceleration In order to achieve dust acceleration to velocities to velocities vv00 ~ ~ 10 km/s, the 10 km/s, the azimuthal acceleration, azimuthal acceleration, ώώ, must be , must be sufficiently large so that gravity sufficiently large so that gravity does not remove the particle first:does not remove the particle first:

v = Rv = Rώώt t ≥ v ≥ v00 and and ΔΔz = z = ½½gtgt22 ≤ ≤ ΔΔHH

RRώώ/g /g ≥ v≥ v00/√2g/√2gΔΔHH For For vv0 0 = 10 km/s and = 10 km/s and ΔΔH= 50cm H= 50cm

this gives:this gives: RRώώ/g /g ≥ 3000 , t ≥ 3000 , t ≤ 0.3 s≤ 0.3 s


ΔΔHH

62

IR camera IR camera measurements in measurements in ´MAST´ show that the ´MAST´ show that the dust mostly (co)rotates dust mostly (co)rotates in the direction of in the direction of plasma rotation.plasma rotation.

There is also visual There is also visual evidence of the evidence of the ´rocket effect´ ´rocket effect´ acceleration.acceleration.

The dust particles may The dust particles may achieve achieve high speedshigh speeds – – particle velocities in particle velocities in this movie are 10´s of this movie are 10´s of m/sec.m/sec. Provided by F. Lott and G. F. Counsell (2006)Provided by F. Lott and G. F. Counsell (2006)


67

Dust particle acceleration in Tokamaks Dust particle acceleration in Tokamaks – – conclusions so farconclusions so far


1.1. Particle acceleration Particle acceleration to azimuthal to azimuthal velocities of 1 - 10 velocities of 1 - 10 km/sec seems km/sec seems possible (with ion possible (with ion drag Coulomb drag Coulomb enhanced).enhanced).

2.2. Particularly if the Particularly if the injection into the injection into the SOL has a SOL has a substantial Rsubstantial Rω ω alreadyalready..

3.3. Particle life times Particle life times against sputtering against sputtering can be larger than can be larger than the required the required acceleration times acceleration times (a (a ≥≥ 22μμm).m).

70

MASTMAST

ParametersParameters

R = 1.0m, r = 0.5–0.65mR = 1.0m, r = 0.5–0.65m

B = 0.5T (on axis)B = 0.5T (on axis)

I = 2MA (max)I = 2MA (max)

gregor morfill max-planck institut für extraterrestrische physik ipp-cas, hefei, 24/1/2008

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