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 CO 2 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 PoloidalRail 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 n e and T e 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 The electrons have a Boltzmann distribution n i = n o exp(e  /T) and we assume the simple form for the ion energy

The sheath potential Is then given by   where  is the secondary electron coefficient For T i =T e and  =0 -e    2.8T e

Edge diagnostics Surface temperatures, ir, TCs Langmuir probes in limiters and divertors Atomic beam techniques, eg Li beam (n e ) Thomson scattering for n e,T e Microwave interferometry n e 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 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 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 T i =T e and  In practice   is often close to unity and P can be significantly enhanced

The SOL transport We can write the radial particle balance

Simple radial profiles Assuming D L and c s are independent of radius we can integrate to obtain n (r) = n(a) exp{-(r-a)/ n } where n =[D  L c / c s ] 1/2 The heat balance can be considered in similar way leading to T (r) = T e (a) exp{-(r-a)/ T } where

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: Where S is the source of particles due to cross field diffusion P=n(T e +T i ) and m is the ion mass

Density at the sheath Solving the two equations we obtain Where M =v/c s 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

Presheath potential The electron density distribution is given by the Boltzmann equation n(M)=n(0)exp(e  /T e ) Substituting in the previous equation we obtain  (M) = -[T e /e]ln(1+M) 2 As M tends to 1 the presheath potential  tends to 0.69T e /e We have also shown that the sheath is =2.8 T e /e

Summary of n,  and p

Estimate of edge density (for limiter tokamaks only) We define the particle replacement time as  n  ñV/  p  We then integrate the flux to the limiter Calculating  p in terms of ionization penetration with v n the neutral velocity and the ionization rate coefficient we get

Dependence of edge density on line average density Relationship between the edge density n e (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