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Introduction to PlasmaSurface Interactions
G M McCracken
Hefei, October 2007
6 lectures comprising:
1 Basic boundary physics
2 Recycling
3 Atomic and molecular physics
4 Wall conditioning
5 Sputtering physical and chemical
6 Divertor physics
Problems in early magnetic
confinement devices
• The study of surface interactions was forced upon early fusion
researchers because of the problem of impurities.
• Many of the early containment vessels were made of glass or
ceramic and when the unstable plasma interacted with these
materials many impurities were released in the form of gases
like water CO2 and CH4.
• Low Z impurities were ionized and radiated so much energy
that it was not possible to heat the plasma at all. There was a
so-called radiation barrier which prevented getting the
temperature above about 50 eV.
• Strategies to remove impurities baking and discharge
cleaning, gettering, carbonization, divertors.
• We must first understand the basic physics in the edge
plasma in order to try to control the outflow of plasma with
minimum release of impurities and without damaging the walls
of the vessel.
Purpose of limiters
• For plasma diffusing across the field the limiter is
the first point of contact with a solid surface
• It serves primarily to protect the vacuum vessel,
particularly from disruptions, runaway electrons
etc.
• Another important function is that it localizes the
plasma interaction which leads to faster cleaning
up of the surface
• Even a point contact serves as a limiter but the
larger the surface in contact with the plasma the
shorter the scrape-off layer
Types of limiter
Poloidal
Rail
Toroidal
Discuss 5 simple calculations
• The calculations apply to the low density
limit and mainly to limiter conditions
•
•
•
•
•
Sheath potential
Power transmitted to the limiter
Radial profiles of ne and Te
Density at sheath edge
Presheath potential
2-D schematic of boundary flow
viewed from the top
Schematic diagram of the plasma flow from the confined plasma into
the SOL by cross-field diffusion and along the field in the SOL to the
limiters or divertor target
The plasma sheath
• Because the velocity of the electrons is higher
than the ions, charge builds up on the surface
• This induces an electric field which balances the
flow of ions and electrons
• This is the origin of the plasma sheath
• The electric field is located in a narrow layer
near the surface
• Its width is several Debye lengths
Spatial variation of the electric potential, ion velocity and the
ion and electron densities across the plasma sheath
Potential; note the
presheath potential
Ion velocity; the ions
are accelerated into
the sheath
Ion and electron
Density; the electrons
are depleted due to
the negative potential
Calculation of the sheath potential
Start with Poisson’s equation
d e
 (ne  ni )
2
dx
o
2
The electrons have a Boltzmann distribution
ni = no exp(e/T) and we assume the simple form
for the ion energy
1
1
2
mi vi  mi vo 2  e
2
2
The sheath potential
Is then given by o where  is the secondary
electron coefficient
eo
1  1 2 mi / me 


 ln 
Te
2  2 1Ti /Te  


For Ti=Te and =0 -e o 2.8Te
Edge diagnostics
•
•
•
•
•
•
Surface temperatures, ir, TCs
Langmuir probes in limiters and divertors
Atomic beam techniques, eg Li beam (ne)
Thomson scattering for ne,Te
Microwave interferometry ne
Laser resonance fluorescence
Double langmuir probe
Two probes, one facing each direction. Each consists of a post about
1mm diameter with a plate behind it
Example of langmuir probe
distribution in a divertor
Measurement of ion and electron
energy distributions
• Generally difficult. The only way is with energy
analysers.
• It is necessary to exclude plasma from the
analysis region
• This can be done by having a very fine slit,
comparable with the Debye length, but this
makes the instrument very delicate
• In order for there to be minimum interaction with
the edge of the slit it has to be very thin
Schematic of double Retarding Field Analyser used
on JET
Schematic view of RFA
All potential are applied with respect to torus ground
Entrance slit
Grid 2
-150V
0÷350V
Grid 1 colectors Grid 1 Grid 2
-200V
-200V 0÷350V
2
carbonized
surface
e-
i+
e-
i+
17
Both slits are
30 m 3mm
Downstream side
facing inner divertor
e side
e- rejected
by slit
i side
Suppresion of secondary e due to ion bombardment.
Parallel flow for forward BT direction.
R A Pitts et al
Entrance slit
-150V
Cutoff for ions
with v ||<v crit
Upstream side
facing outer divertor
Photograph of the JET retarding field analyser
The full probe head assembly before adding the protective end-cap. Note
the narrow Aluminium defining slit diffusion bonded onto the back of a
stainless steel slit plate. The Nickel grid plates can just be seen.
Integral ion and electron energy distributions
Plasma boundary of the DITE
tokamak (a) ions, (b) electrons.
(Pitts, R.A. Physics of Fluids 3,
2871 (1991).)
Effect of sheath on sputtering
Because of the sheath acceleration the charge
state of the impurity ions is very important. A
three times charged ion will have three times
the energy of a singly charged ion.
We discuss charge state in the third lecture.
Energy transported to a surface
P  ne csTe


2


 2Ti  2  1 ln  1  mi / me  
 T 1 2  2 1T /T   
i e 

 e

The first term is the ion energy,
the second the
P 
electron energy and the third the energy from the
sheath. This reduces to the following equation for a
hydrogen plasma where Ti=Te and 0
P   sTe
In practice  is often close to unity and P can be
significantly enhanced
The SOL transport
We can write the radial particle balance
d  dn  ncs
D


dr  dr  Lc
Simple radial profiles
Assuming DL and cs are independent of radius we can
integrate to obtain
n (r) = n(a) exp{-(r-a)/ln}
where
ln =[D Lc/ cs]1/2
The heat balance can be considered in similar way
leading to
T (r) = Te(a) exp{-(r-a)/lT}
where
ln

1

lT 5 / 2   ln / DlT
Calculation of transport along the field
lines in the SOL
The simplest model to reproduce the main features
is the steady state, inviscid isothermal model with
conservation of particles and momentum. We thus have:
d
 nv   S
dz
and
dv
dp
nmv    mvS
dz
dz
Where S is the source of particles due to cross field diffusion
P=n(Te+Ti) and m is the ion mass
Density at the sheath
Solving the two equations we obtain
2
dM
S 1  M 

dz ncs 1  M 2 
Where M =v/cs is the Mach number. As M , dM/dz
and the plasma solution breaks down. M=1 indicates
the start of the plasma sheath. We also obtain
n( M )
1

n(0) 1  M 2
where n(0) is the density at the stagnation point v=0.
It is seen that n(M)/n(0) tends to 0.5 as M tends to 1
Presheath potential
The electron density distribution is given by the Boltzmann
equation
n(M)=n(0)exp(e/Te)
Substituting in the previous equation we obtain
(M) = -[Te/e]ln(1+M)2
As M tends to 1 the presheath potential  tends to 0.69Te/e
We have also shown that the sheath is =2.8 Te/e
Summary of n,, M and p
Estimate of edge density
(for limiter tokamaks only)
We define the particle replacement time as
n  ñV/tp
We then integrate the flux to the limiter
Calculating tp in terms of ionization penetration with
vn the neutral velocity and the ionization rate
coefficient we get
n( a ) 
nV
tp
 vi
1

l n
4 alncs 6 vn
2
5 x10
21
2
ne m
3
Dependence of edge density on
line average density
Relationship between the
edge density ne (a) and line
average density ne for a
range of tokamaks with
limiters. The line represents
the model of eqn (Erents,
S.K., et al., Nuclear Fusion
28, 1209 (1988), PericoliRidolfini, V. Nuclear Fusion
31, 127 (1991), Matthews, G.
F., et al., Nuclear Fusion 28,
2209 (1988).)
Summary
• Types and purpose of limiters
• Sheath potential
• Measurement of ion and electron energy
distributions at the limiter
• Energy transported to the limiter
• SOL transport, radial profiles, presheath
• Some of this analysis applies to divertors
in the low density limit