Introduction to Plasma-Surface 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.

R. A. Pitts: Burning Plasma Diagnostics Workshop, Varenna, Italy, 24-28/09/20075 of 32

Terminology: limiters and divertors

Core plasma

Core plasma

Scrape-off layer (SOL) plasma: region of open field lines

Divertor targets

Limiter

Vessel walls

Private plasma

LCFS

X-point

“Upstream”

Outermidplane

CL

OuterInner

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 limiterPoloidal 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 flowviewed 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 ionsare accelerated intothe sheath

Ion and electron Density; the electrons are depleted due to the negative potential

Calculation of the sheath potential

2

2( )e i

o

d en n

dx

Start with Poisson’s equation

The electrons have a Boltzmann distribution

ni = no exp(e/T) and we assume the simple form for the ion energy

2 21 1

2 2i i i omv mv e

The sheath potential

21 1 /ln

2 2 1 /o i e

e i e

e m mT T T

Is then given by where is the secondary

electron coefficient

For Ti=Te and =0 -e 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 view of RFA

i sidee side

Grid 20÷350V

Grid 20÷350V

Grid 1-200V

Grid 1-200V

Entrance slit-150V

Entrance slit-150V

Both slits are30 m 3mm

colectors

carbonizedsurface

e- rejectedby slit

Suppresion of secondary e-

due to ion bombardment.

Parallel flow for forward BT direction.

2

17

Upstream side facing outer divertor

Downstream side facing inner divertor

Cutoff for ions with v ||<vcrit

e-

e-

i+

i+

All potential are applied with respect to torus ground

Schematic of double Retarding Field Analyser used on JET

R A Pitts et al

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

P sTe

21 /2 2 1

ln1 2 2 1 /

i eie s e

e i e

m mT

T T TP n c T

The first term is the ion energy, the second the electron energy and the third the energy from the sheath. This reduces to the following equation for a hydrogen plasma where Ti=Te and

In practice is often close to unity and P can be significantly enhanced

The SOL transport

We can write the radial particle balance

s

c

d dn ncD

dr dr L

Simple radial profiles

Assuming DL and cs are independent of radius we can integrate to obtain

n (r) = n(a) exp{-(r-a)/n}

where n =[D Lc/ cs]1/2

The heat balance can be considered in similar way leading to

T (r) = Te(a) exp{-(r-a)/T}

where 15 / 2 /

n

T n TD

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 withconservation of particles and momentum. We thus have:

Where S is the source of particles due to cross field diffusionP=n(Te+Ti) and m is the ion mass

dnv S

dzand

dv dpnmv mvS

dz dz

Density at the sheath

2

2

1

1s

MdM S

dz nc M

Solving the two equations we obtain

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

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

2

( ) 1

(0) 1

n M

n M

Presheath potential

The electron density distribution is given by the Boltzmannequation

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, and p

Estimate of edge density(for limiter tokamaks only)

We define the particle replacement time asnñV/p

We then integrate the flux to the limiter

Calculating p in terms of ionization penetration with vn the neutral velocity and the ionization rate coefficient we get

22 21 31( ) 5 10

4 6i

ep n s n

vn Vn a n x n m

a c v

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), Pericoli-Ridolfini, 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