Introduction to Plasma-Surface Interactions

Lecture 6

Divertors

Divertor functions• 1. Removes plasma surface interactions from the confined

plasma: hence reduces the impurity flux back into the plasma

• 2. Removes deposited power to a region where it is easier to remove using a heat transfer fluid

• 3. Reduces the flux of fast CX neutrals to the main chamber walls by reducing the flux of neutrals which can reach the main plasma

• 4. Impurities ionized in the SOL will flow into the divertor

• 5. Pumps helium. The divertor maintains a higher neutral pressure than the SOL and therefore it is easier to pump the helium out. (Important in DT burning devices)

Potted history of divertors• A form of divertor was part of the early

stellerators designed by Spitzer in the 1950’s• Much later, divertors were designed for tokamaks,

DIVA (1974), DITE (1976), T12, PDX and ASDEX

• Early divertors used a separate chamber but in D-III it was discovered that they worked well with the target in the same chamber

• ASDEX discovered the H-mode during divertor operation

Typical poloidal divertor

Poloidal cross-section of tokamak with typical field lines.

The poloidal fields are used to produce a null which causes the field lines to diverge and flow out into a separate chamber remote from the confined plasma

The null is known as the X-point

Simple analytical modelling of the divertor

• Consider only region between X-point and the target

• Energy flow comes across the LCFS from the confined plasma

• Assume a 1-dimensional modelno energy or momentum sinks in SOLspecifically, no radiation

Geometry of the 1-D 2-point fluid modelPoloidal cross-section

Geometry along the field line

Upstream density and temp nu and Tu are assumed to be at the X-point.

Downstream density and temp nt and Tt are at the target

Modelling the divertor - 1Model using the following assumptions

Momentum conservation along the field line requires

constant

Heat transfer along field line is by conduction

where

Heat transmitted across the sheath is given by

Where is the sheath transmission factor and cs is the ion sound speed

Taking qII to be known we can solve the 3 equations for Tt. Tu and nt in terms of nu

nT 1M 2

qII dTedz

T 5/2

qII sntTtcss

Modelling the divertor - 2

The solutions are messy but when we have a sufficiently high temperature gradient so that Tu

7/2>> Tt7/2 then we can obtain the

simple forms

m-3

And

keV

Note the nu3 and nu

-2 dependence of target density and temperature respectively

nt 2.7x1033 L6/7s

2nu3

AqII8/7

Tt 3.1x1028 AqII10/7

L4/7s2nu

2

Target temperature and density vs upstream density

qII =1000MW m-2

L=50m

A=2

Note the nu3

dependence of nt

And the nu-2

dependence of Tt

At low nu target density nt is linear with nu

Calculated with the simple analytical 1-D model described

High density limit

When Tu7/2 >> Tt

7/2 the ratio of the upstream to down stream temperatures can be calculated

From which it can be noted that a large temperature gradient requires low power, a long connection length or a high density

8/732

6/7 2 21.9 10t

u s u

AqTx

T L n

Effect of recycling at the targetAssumed plasma source function due to recycling

Ti = Te

ne

Mach number

Plasma due to recycling enhances the flow back to the target

At high densities when flow across the separatrix is small this is the dominant source

Ionization and density peak near the target plate and T falls

Flow accelerates near the target due to the source

Radial power distribution in the SOL

. . . 0q q q

Divergence of heat flux must be zero

Where qs are heat flux vectors. From this an expression for the parallel heat flux at the target and the power scrape off thickness can be derived

7/94/916

5/9

5/9 14/915 2

7/9

5 10

2 10

sp

s

st

s

L nx m

q

L qq x Wm

n

For qII =0.5 MWm-2, L=150m, =1 m2s-1 and nu=1x10 m-3 we obtain p=0.01 m and qII=7 GW m-2

Dispersal of divertor powerThe SOL is very thin, determined by the relative rates of parallel and cross field transportUpstream widths are p ~3 mm in present devices, C-Mod, AUG, JET- estimated to be p ~ 100mm in ITERleading to qu ~ 2000 MW/m2

Divertor plates have a limit of ~ 10 MW /m2

requiring a factor of 200 reduction

Methods of reducing power flux1. Mid-plane pitch angle (~x7)2. Flux surface expansion (~x3)3. Tilted divertor plate (~x3)4. Divertor/SOL radiation requires a further factor of 3

Volume losses of power in the divertor by impurity radiation, simple calculation

Impurity radiation can be written

Where nm is the impurity concentration an R(Te) is the radiation parameter which depends on species. Maximum values of R are ~1031 Wm3

Considering average values, to radiate 1GW requires

nmneV> 1040m-3

For V= 103 m3 and ne=~1020 m-3, the impurity fraction

nm//ne~10%

r m e eP n n R T dV

Power loss mechanisms

Radiation: Such high concentrations could lead to impurities flowing back into the confined plasma. It may also cause an unacceptable sputter rate of the target

Charge exchange: The ratio of charge exchange to ionization rate coefficients indicate that the temperature must be already low (<10 eV) to obtain a significant energy loss by charge exchange

The answer appears to be to have radiating mantle in the main plasma. Up to 70% of the plasma power has been radiated in experimental tokamaks but it is still uncertain whether this much power can be radiated in ITER

Removal of helium ashPressure is very low at the boundary of the plasma and would require an enormous pumping speed to remove it

The gas pressure in the divertor has to be optimized by operating at high density and improving the baffle geometry

He pressure tends to be proportional to H pressure, experimentally the enrichment factor is

, ,/0.1 0.8

2 /He g He p

mol e

n n

n n

Experimentally the effect of baffles tends to be small (<2 in JET and C-Mod )

2D effects: schematic of particle flow in the divertor

While the region near the separatrix tends to be at high density and in the recycle mode, further out it is low density with low tempoerature and little recycle

General design considerations

• Tile geometry needs to be very carefully controlled. Because of the very high parallel power density any surface not at grazing incidence will suffer serious damage.

• Flat plate geometry has the advantage of simplicity, good diagnostic access and a simple rigid structure can be used

• Because of the high powers there is significant thermal expansion and non-uniform heating

• To minimize stress in the tiles they are normally small ~20-30 mm• The angle of the tiles wrt field lines has to be as small as possible to

increase the effective area• At very low angles the tile edge can become exposed. This is

overcome displacing each tile wrt its neighbour

Example of target tile geometry

With this geometry, in order to prevent tile edges being exposed, the tile accuracy has to be high (~0.1 mm)

Divertor analysis

• Divertors are very complicated and still not fully understood

• Although these 1-D analytical models are helpful in understanding the important parameters it is necessary to use 2-D codes

• These have analytical sections for the plasma fluid and Monte Carlo codes for the neutrals. The two parts have to be coupled which is complex.

• Examples of these B2-Eirene Braams and Reiter (Julich)and EDGE2D-Nimbus (JET)