Transcript Introduction to Plasma

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 DIII 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 model
no energy or momentum sinks in SOL
specifically, no radiation
Geometry of the 1-D 2-point fluid model
Poloidal cross-section
Upstream density and
temp nu and Tu are
assumed to be at the Xpoint.
Downstream density
and temp nt and Tt are at
the target
Geometry along the field line
Modelling the divertor - 1
Model using the following assumptions
Momentum conservation along the field line requires


nT 1  M 2  constant
Heat transfer along field line is by conduction
dTe
5/2



T
qII  
where
dz
Heat transmitted across the sheath is given by
qII   s nt Tt cs
Where  s 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
Modelling the divertor - 2
The solutions are messy but when we have a sufficiently high
temperature gradient so that Tu7/2>> Tt7/2 then we can obtain
the simple forms
L  s nu
nt  2.7x10
8/7
AqII
6/7
2
3
33
And
10/7
Aq
28
II
Tt  3.1x10 4/7 2 2
L  s nu
m-3
keV
Note the nu3 and nu-2 dependence of target density and
temperature respectively
Target temperature and density vs
upstream density
qII =1000MW m2
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 >> Tt7/2 the ratio of the upstream to
down stream temperatures can be calculated
8/7
Aq
Tt
32
 1.9 x10 6/7 2 2
Tu
L  s nu
From which it can be noted that a large
temperature gradient requires low power, a long
connection length or a high density
Effect of recycling at the target
Assumed 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
Divergence of heat flux must be zero
.q  .q  .q  0
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
 p  5 x1016
L4/9    ns 
q s 5/9
7/9
m
5/9
14/9
L
q
2
s
q t  2 x1015
Wm
7/9

n
  s
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 power
The SOL is very thin, determined by the relative rates of parallel
and cross field transport
Upstream widths are p ~3 mm in present devices, C-Mod, AUG, JET
- estimated to be p ~ 100mm in ITER leading to qu ~ 2000 MW/m2
Divertor plates have a limit of ~ 10 MW /m2
requiring a factor of 200 reduction
Methods of reducing power flux
1. 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
Pr   nm ne R Te  dV
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%
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 ash
Pressure 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 h is
h
nHe, g / nHe, p
2nmol / ne
0.1  0.8
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 ~2030 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)