Introduction to Plasma-Surface Interactions

Lecture 3

Atomic and Molecular Processes

Ionization and charge exchange

• Neutral atoms entering the plasma from the boundary meet the plasma and are subject to ionization, excitation and charge exchange

• The reaction rates are a function of Te and ne and so vary with radius

• These lead to radiation which tends to cool the edge

• The processes are thus interactive

Neutral atoms entering plasma

• H +e →H∗ + e excitation

• H +e →H++ 2e ionization

• H++H →H +H+ charge exchange.

Consider a neutral atom coming back into the plasma

These are the atomic processes involved.

Molecules entering plasma

• Neutral molecules

• H2 +e → H + H +e dissociation • H2 +e → H++ H +2e dissociative ionization • H2 +e → H2

++ 2e molecular ionization

• Molecular ions

• H2 ++ e → H +H dissociative recombination

• H2+ +e → H++ H++ 2e dissociative ionization.

For a molecule entering the plasma the reactions are:

Rate coefficients for hydrogen atoms and molecules

Dissociation

ionization

ionization

Charge exchange

ionization

1-D Model of ionization

The collision rate is given by

The flux of neutrals F(r) as a function of radial position is thus given by

Where F(a) is the initial flux and is determined by the local temperature

The local source function S is

F(r)F(a) 1 ne vo

drr

a

sdF r dr

Rneno

Ionization and Charge exchange

• If the plasma conditions were known it would thus be possible to calculate ionization rates.

• However since the impurities modify the boundary and so more sophisticated models have to be used to obtain a self consistent solution

• Charge exchange is an additional complication• Because rate coefficients for CX are greater than for

ionization the penetration of neutral is dominated by charge exchange.

• The behaviour of neutrals has to be calculated either by transport codes or Monte Carlo techniques

Impurities• Impurities have the additional complication

of multiple ionization• Simultaneously they become heated by

collisions with the background plasma• The classical thermalization time is given

by

• Ionization time is given by

th 2.2x1017mITB

3/2

mB1/2nBZB

2Z I2 ln

ne vion 1

Ionization state

• The temperature which an ion reaches before being ionized to the next state is determined by

•

• which is independent of density

• At low Te the ions are thermalized before ionization to the next stage

• At high Te they are ionized before they are thermalized

ion / th

Calculated impurity temperature before further ionization

The temperature reached before ionization occurs depends on the ratio

It is independent of density

ion th

Excitation

• The ratio of the excitation to ionization rate for a given ionization state can be calculated for a given Te and ne

• This gives the photon efficiency I.e. the number of of photons emitted per ionization event.

• Together with a measured photon flux the photon efficiency allows the influx of impurity ions to be calculated.

• The inverse photon efficiency can be calculated for a given transition and is plotted next

Inverse photon efficiency of impurities

Ion

izat

ion

even

ts p

er p

hoto

n

Impurity atoms entering the plasma are first excited before ionization

The number of photons emitted can be used as a measure of the influx

Many of the emitted photons are in the visible and can be easily detected with spectrometers or filters.

These curves can be obtained from basic atomic data (ADAS Users manual, Summers 2000) and they can be used for measuring absolute impurity or hydrogen fluxes

The photons/ionization are only weakly dependent on density

Measuring impurity influxes

• A variety of low charge states can be used to experimentally measure impurity influx, CI,CII, CIII, He I, HeII and neutral or singly charge metal atoms, e.g. MoI, CrI

• Individual transitions can be measured with spectrometers or optical filters

• Photon efficiency is more difficult to calculate for complex heavy atoms e.g. W but progress in theoretical calculations is being made

Charge state

• The charge state can be calculated as a function of Te for coronal equilibrium conditions

Oxygen ionization state distribution in coronal equilibrium

Calculated charge states in equilibrium conditions as a function of electron temperature (Carolyn and Piotrowitz 1983)

Charge state in the boundary

• The charge state in the boundary is very important as the impurities are accelerated in the sheath and a high charge state leads to high energy

• The charge state is not necessarily the equilibrium one for the local Te as high charge states can diffuse out from the core

• The charge state in the boundary is difficult to measure but G Matthews has developed a mass spectrometer technique

Cycloidal mass spectrometer for impurity charge and mass measurements in the SOL

Design of an ExB mass spectrometer developed to measure mass and ion charge state in the tokamak boundary plasma.

It is necessary to line it up very carefully with the magnetic field. It was used successfully on the DITE and Julich tokamaks.

Matthews NF31(1991) 1498

Impurity charge state distribution

Mass spectrum of impurity ions in the SOL of the DITE tokamak

Measured with a cycloidal (ExB)mass spectrometer (Matthews 1991)

Ions from singly charged up to 6+ carbon and 8+ oxygen are observed

Mass/charge ratio

Impurity injection

• Impurities are sometimes injected to enhance radiation• This distributes the power from the plasma more

uniformly over the vessel wall• It reduces the power deposited on limiters or divertors • It is important that the impurities cool the edge without

cooling the centre and reducing the fusion reaction rate. • The impurity species therefore needs to be carefully

chosen. • A disadvantage of this technique is that multiply charged

impurity species may sputter the limiter and divertor thus enhancing erosion

The radiating edgeThe objective of a radiation is to get the edge as cool as possible in order to reduce sputtering Possible radiating impurity species:

He Ne Ar Xe

These are the only species that will recycle at the boundary and therefore do not have to be fed in continuously

The problem is that the sputter threshold energy is lower for impurities than H isotopes

It is better not to have too high a Z impurity

Much effort has been given to the radiating edge and up to 70% of the plasma energy has been radiated

Atomic physics Summary - 1

• Atomic physics is complex but is well understood and reliable data are available

• For hydrogen atoms entering the plasma the dominant process is charge exchange and neutrals undergo a “random walk” which can be analysed by Monte Carlo methods

• For impurity ions the dominant process is ionization

• The dominant charge state of the impurities is determined by the local Te and ne and the time for which the impurity has been in the plasma

Atomic physics Summary - 2

• Higher charge states than the expected equilibrium are observed in the boundary due to diffusion from the core

• Photon efficiency is an important concept for experimental measurements of the impurity influx.

• Influx can be measured with a variety of low ionization states

Atomic physics Summary - 3

• Impurity injection is a possible way of enhancing radiation

• However it has a number of deleterious side effects