SPECTROSCOPIC DIAGNOSTICS OF TOKAMAKS

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SPECTROSCOPIC DIAGNOSTICS OF TOKAMAKS

C. de Michelis

To cite this version:

C. de Michelis. SPECTROSCOPIC DIAGNOSTICS OF TOKAMAKS. Journal de Physique Collo-

ques, 1988, 49 (C1), pp.C1-165-C1-174. �10.1051/jphyscol:1988132�. �jpa-00227452�

JOURNAL DE PHYSIQUE

Colloque C1, S u p p l 6 m e n t au n 0 3 , Tome 4 9 , M a r s 1988

S P E C T R O S C O P I C D I A G N O S T I C S OF TOKAMAKS

C. DE MICHELIS

Association Euratom-CEA sur la Fusion, Departement de Recherches sur la Fusion Contr6lee, CEN de Cadarache, F-13108 Saint-Paul-lez-Durance Cedex, France

RESUME

Les impuretes ayant un grand intCrCt dans les tokamaks, la spectroscopie joue un r61e important pour la comprehension de leur comportement. Les techniques utilisees pour Cvaluer leurs densitis, les pertes par rayonnement, et les proprietes du transport sont discut6es ; quelques developpements recents sont aussi esquissCs.

ABSTRACT

Impurities being an important concern in tokamaks, spectroscopy plays a key role in their understanding. Techniques for the evaluation of concentrations, power losses and transport properties are surveyed, and a few developments are outlined.

1. INTRODUCTION

Plasma spectroscopy is the study of the electromagnetic radiation emitted by ionized media, and is therefore a non perturbing technique. Due to the large value of the electron temperature T of present tokamak plasmas (values in excess of 5 keV have been obtained), the main part of the emitted radiation (due to impurities) occurs at large photon energies, in the vuv and soft x-ray spectral regions.

Since in tokamak plasmas T and the electron density Ne are independently measured (e.g., by laser scattering and interferometric techniques), spectroscopy is used to study impurity effects ; in particular, it is asked to evaluate the impurity density NT, the effective charge Z = 2 NZZ 2 /Ne, and the radiated power PR, as well

eff

as to understand the impurity transport. Additionally, as we shall see, it is increa- singly used to measure the ion temperature T. and the plasma rotation velocity v

r.

Beside the basic gas (protons or deuterons), tokamak plasmas always contain traces of impurity ions, produced by their interaction with limiters and walls. In- trinsic impurity elements are : i) desorbed elements (C, N, 0 , and C1, generally called light impurities), having relative concentrations up to a few % ; and ii)

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988132

C1-166

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eroded elements (Ti, Fe, Cr, and Ni being the most abundant in present tokamaks _; they are generally referred to as heavy impurities), with typical concentrations one order of magnitude lower. The main difference between these two classes of impurities is that light impurities are completely ionized in the plasma center and do not therefore emit any central line radiation, whereas heavy impurities are everywhere only partially ionized (since the ionization potential,

xZ,

of their last, H-like, ion is much larger than the central electron temperature), and radiate strongly.

Since the

Te

profile is centrally peaked, incoming impurity ions are ioni- zed by electron impacts to successively higher charge states as they penetrate pro- gressively into the plasma, and develop a characteristic shell structure having a

DA =10000cm2~' ,VI =200 crn

2

radial location depending on Te and

T ~ ( o ) = s ~ ~ v . N ~ ~ O ) = S ~ ~ ~ " ~ ~ ~ , N , ( O ) ~ ~ ~ l ~ ~ ~ , , i ~ diffusion properties (see figure 1 as an example). This shell structure is main-

-->..

^N, tained throughout the discharge by a

t ^\.- .

\',,

I

continuous impurity influx, balanced by

'. ..

a comparable outward movement of highly charged central impurities, thus gene- rally preventing accumulation of impuri- ties in the discharge. For sufficiently ionized ions, impurity ions are unifor- mily spread on the magnetic surfaces ; the impurity emission is therefore uniform around the torus.

0 20 40 60 80 100 120

r [ c m l

Fig. 1 In the following, we shall discuss the procedure followed by plasma spectrosco- pists to interpret the experimental data, and outline a few recent developments. More details can be found in recent review papers [ I - 3 1 .

2. INTERPRETATION OF SPECTROSCOPIC DATA

Impurities have profound effects on the plasma, the most important being their deleterious contribution to the energy balance through radiation losses. A complete study of impurity concentrations and radiative losses in a given plasma would require extensive spatially resolved spectroscopic measurements of at least the strongest transitions of all ions for each important impurity element. This is of course an endless task, and the study is always limited to a few strong lines of a few ions, a model being subsequently used to deduce the complete impurity properties.

The procedure generally followed is schematically shown in figure 2, and it will be discussed below. However, it is impractical to attempt to use the full procedure on a day-to-day basis, and very often, when impurities are not the main concern of the

F i g . 2

C1-167

NUMERICAL COMPUTATION EXPERIMENTAL DATA

Transport code

Homogeneous Te ( r , t )

ff.

S

cylindrical Ne ( r , t l

plasma

Ne [%-,~,1-~zf

+ ~ , + 1

az+, - ~ z " z I

2 . 0 . . , Z N

Nz ( r , t ) N,(r,t)

I coronal hypothesis

Q: , N e ( r , t ) -

E; ( r a t ) = Ne ( r , t ) N, ( r , t ) Q:' $, * DA,VA+ E;J ( r , t 1

Zeff ( r , t l =

Pz = P; +Pi +p,b PR (r,tl=EZPz(r,tl t

li

1

Bz ( h , t l = - J E : ( r , t ) d r - ^DA - 8: I h , t )

2n absolute

1 calibration

1; ( h , t ) Spectroscopy t

1

A bel

inversion

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experimental program, the central chord emission of a few, well chosen, lines is only taken, complemented by a non-specific evalua- tion of the contamination and measurements of the bolometric losses.

A necessary pre-requisite for the analysis of spectroscopic data is knowledge of the relevant atomic cross-sections (ioni- zation, recombination and excitation). Since very few of them are experimentally known, theoretical or semi-empirical expressions are generally used. We shall not discuss this problem here, apart from noting that a large part of the uncertainties on spectroscopi- cally deduced parameters comes from the poor

I .

knowledge of atomic data [ I ] .

, ,

Figure 3 shows four impurity ion vuv radiance profiles obtained on TFR. The first step in the analysis of experimental data is the Abel inversion of the radiance profiles in order to obtain the emissivity

l - -

^profiles

- ^{' : E}

^{( G ,}

-

^t)

^.

Although this is generally

. - L

-

done in cylindrical geometry, it is still possible to invert non-cylindrical radiance profiles (D-shapes are current) if several lines of sight are available or if the magne- tic surface topology (i.e., the plasma shape) is known. E , ) is the quantity which is ) generally compared with numerical computation 10 15 /1J

results. However, the ion densities N (r,t) 0 0 5

'

can be easily derived from it, taking idvan-

1

tage of the fact that, for the strongest Fig. 3

lines emitted at tokamak conditions, the coronal hypothesis is satisfied, i.e., exci- tation by electron collisions from the ground state (having a density practically equal to the total ion density) with rate coefficient Q~~

(T

) , followed by radiative

z e

decay, with branding ratio T.. (but care must be taken with ions having highly popu- 1 3

lated metastable levels).

The experimental results are then compared with the results of a numerical code. The transport code solves the impurity transport system (box.in figure 2). The analysis of the impurity behaviour reduces to finding solutions of this system of equations (one for each important impurity), with given N and Te ~rofiles (thus decoupling it from the plasma MHD equations), which agree with the few available emissivity profile measurements. The scrape-off problem is very often by-passed by using ad-hoc boundary conditions at the limiter radius, since in this region both atomic rate coefficients and T and Ne values are poorly known. The main problem in the solution of the transport system is the expression to be used for the impurity flux TZ, which of course depends on diffusion properties. Indeed, neoclassical trans- port calculations yield expressions which cannot generally explain the experimental data. Since the anomaly is generally very large, it has become customary to neglect the neoclassical terms and write the flux as the sum of a diffusive and a convective parameter (D and VA, respectively ; see figure 2). Generally speaking, the V term

A A

- - - c o d e : OA=LWOcm1i'.V :400cm i' describes the denree of peakinn of the total - -

impurity profile (VA > ^{0 ,} centrally peaked ; l o

VA = 0, radially constant ; V < ^0, centrally

-

^A

;

hollow). The results of the comparison between

,5? the TFR transport code and impurity emissi- 5 ; vity profiles in TFR [4] are shown in figure 4

(dashed lines represent calculated quantities).

The most satisfying point in these simulations is that heavy and light intrinsic impurities (as well as purposely injected ~mpurities) require the same transport coefficients to be correctly simulated. Once the transport coefficients have been evaluated, it is straightforward to calculate the total impu- rity density NT, the effective charge Z

eff'

0 5 10 1s 20 and the total radiated power P R '

r l c m l

F i g . 4

Although the procedure outlined above is well established, a few comments must be added.

i) Analysis of intrinsic impurity transport by the above method is often unsatisfactory, since the source functions are largely unknown and uncontrollable. A way around this problem is to inject into the plasma, in a controlled way, a small (not perturbing the base plasma), known amount of an impurity which is not naturally present. Although pulsed noble gas injection has been used, the preferred method

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involves laser injection of metallic impuri-

51 ~ n j e c t ~ o n ~ n t o Atcator ties [5], for which the injection time is

Te (0)=8S0e4,We = 3 5 ~ 1 0 ' t m ' ~

short compared to relevant atomic and dif- fusion times. An example is shown in figure 5 for Si injection into Alcator deuterium plasmas (Te(0) = 850 eV,

%

^{= 3.5} x 1014 ~ m - ~ )

[ 6 ] . Figure 4a) shows the time evolution of the Si XII, XIII, and XIV radiances. They are compared with the predictions of neoclassical theory (which, as expected, indicates central Si accumulation, in complete disagreement with the experimental intensity decays) in figure 4b). Figure 4c) is obtained by adding an order of magnitude larger anomalous term, and shows satisfactory agreement.

ii) Although the analysis outlined in figure 2 allows the incoming impurity fluxes to be evaluated, it is also possible to deduce the incoming flux at steady state from chord-integrated line radiance values

BY

of peripheral spectral lines [2]. Howe- ver, this evaluation must be employed with

0 10 20 30 great care, since peripheral impurities are

Tlme a f t e r ~njectian (ms) very often affected by poloidal and/or toroi-

Fig. 5 dal asymmetries, originating from localized impurity sources (since low ionization poten- tial ions have no tirne to spread out uniformily over the magnetic surfaces).

Oxyqrn iii) At steady state (aN /at = O),

if diffusion effects can be neglected

(r

^{= O ) ,}

the transport equation reduces to the corona IE model, i.e., a balance between colli- sional ionization and recombination. Two neighbouring ionization states are then

connected by :

NZ / ^NZ+l

- -

(Te9 Ne> NH) SZ (Te)

The solution of this equation for 10 m lo*

oxygen and nickel, gi.ven by the fractional Fig. 6

abundances f = N / 2 N as functions of Te, is shown in figure 6 [7]. Note that

z z

these data, for a particular plasma for which the electron temperature profile Te(r) is known, can also be plotted as ion density profiles N (r). This type of calcula- tions is much easier than solving the full transport system, and it is therefore still used sometimes to have a rough idea of impurity concentrations. Comparisons of IE models with experimental data invariably show that light impurities are far from IE ; at a given radius (i.e., given Te), light atomic species are considerably less ionized than at IE, a consequence of their inward movement. Heavy impurities, howe- ver, generally have ion density profiles which are only slightly displaced towards higher Te (i.e., inwards) with respect to IE predictions, and are somewhat broader due to diffusion.

3. PRESENT DEVELOPMENTS

The procedure outlined above has been successfully used on all medium size tokamaks to interpret vuv spectroscopic data. However, for the present generation of large tokamaks (characterized by large temperature values) it needs to be updated by the use of additional spectroscopic data. Two additional measurements will need to be performed almost routinely.

i) Since light impurities are fully ionized in the plasma core (and do not therefore emit any line radiation, thus not being detectable by conventional spectros- copy), the transport code has been used to evaluate the central light impurity content and behaviour. However, this has now become unreliable, since the observed radiances are very far from the plasma center (see figure 1, showing the results of the TFR code for a JET plasma having Te(0) = 5 keV). This problem is now experimentally solved by using the optical excitation of fully stripped light ions via charge- exchange recombination with neutral hydrogen (deuterium) from neutral beams. However,

code Oh =h000cm2i1 ,v,

=I$:

c m i l z < high power neutral beams (such as those used

I I for additional plasma heating) also modify

IT

⁰⁸⁺

I

considerably the base plasma to be studied ;

0

-I

1 radiation can be detected in the conventional

0 s 10 1s 20

r [ c m l vuv spectral region, it has the great advanta-

.

⁷ ge for present and future tokamaks that

'?E -

z? 's

-

_{A. 0.5}

_--

Z

\

it is therefore preferred to employ low power, non perturbing, auxiliary sources of neutrals to induce charge -exchange reac- tions. Figure 7 shows the profile of fully ionized oxygen ions in TFR, obtained by using an auxiliary neutral beam and detecting the

0

Ha (n = 3 to 2, 102 A) transition of charge- exchange 07+ [8]. Although charge-exchange

'21-172 JOURNAL DE PHYSIQUE

several strong lines also exist in the visible. Indeed, the electron capture occurs preferentially on an excited level with quantum number

n

^{= z ~} ; ^.for oxygen, ^{~ ~}

n

^{= 5,}

and therefore line emission from large n value levels (occuring in the visible) is relatively important [ 9 ] . The fact that it is possible to work in the visible will be very important in t.he future, since it is then possible to put all the radiation sensitive equipment behind the biological radiation shield, using light guides to transfer the plasma emission.

ii) In present, large Te, tokamaks, central heavy impurities are ionized to the He-like and H-like states. Line emission from these one- and two-electron ions occurs

"

in the soft x-ray spectral region (below 10 A), where crystal spectrometers must be used. A considerable amount of work in this spectral range has already been carried out. As an exemple, figure 8 shows a chromium crystal spectrum, obtained in TFR [lo].

In this case one observes the satellites to the K, lines of highly ionized ions.

These satellites (on the long wavelength side of the He-like resonance line) are due to line emission from radiative decay of excited states lying above the first ioniza- tion limit (the upper states being produced by impact excitation of inner-shell elec- trons and by dielectronic capture of the T e ( 0 ) = 1 5 keV

200 incident electron in a highly excited state

after excitation of a bound electron from the

-

w c ground state). The most prominent peaks in 5

s

100 figure 8 belong to the He-like w,x,y and z

-.

"7

+ lines and to the Li-like t, q, (k,r) and j

C

u 0 satellites. At still longer wavelengths,

0 satellites to Be-like and less ionized ions

2 17 2 18 2 19

A ~ A I

²²⁰ are also found. The He-like w (resonance) F i g . 8 line intensity (if possible spatially resolved)

is used as an additional data in the trans- port studies. However, the intensity of the satellites with respect to the resonance transition can also be used to have an insight on additional plasma parameters. In particular, dielectronic satellites of heavy ions have intensities comparable to the resonance transition (since their intensity is proportional to Z 4 ) . The ratio 1.11

N J W

is practically only T -dependent, and, since Te is independently known, can be used to verify the atomic physics. On the oth'er hand, inner-shell satellite intensities are proportional to the recombined ion densities ; their ratios I /I IB/Iw, etc

...

9 w'

are therefore proportional to NLi/NHe, NBe/NHe, etc

...,

respectively, and can be used as additional inputs in the comparison with the transport code.

4. PLASMA DIAGNOSTICS APPLICATIONS

The use of spectroscopy to diagnose particle densities and temperatures in

5 : CONCLUSIONS

astrophysical and laboratory plasmas is well established [I]. However, its utility in tokamak plasmas has been superseded by more satisfactory, more flexible, and more direct techniques. As a result, present tokamaks are equipped with a large variety of state of the art instruments [ll], and they do not rely strongly on spectroscopy for energy confinement studies. Spectroscopy is therefore devoted to studying the impuri- ties themselves, as we have shown above ; however, it is also increasingly used for ion temperature profile measurements from the Doppler broadening and for plasma rotation velocity measurements from the Doppler shift of emitted lines. It so hap- pens that the soft x-ray and visible spectral regions (which we have discussed above) are those in which it is easier to get the

We have shown here how it is possible, starting from a few spectroscopic measurements, to deduce the impurity properties of tokamak plasmas. Although the understanding of impurity transport is of importance, spectroscopy is also used to evaluate plasma parameters otherwise difficult to obtain.

The diagnostic possibilities of spectroscopy in tokamaks are by now well assessed ; however, several instrumental developments are presently sought after.

Firstly, present tokamaks are characterized by low repetition rates (but long dis- charges) ; it is therefore necessary to have spectroscopic diagnostic techniques capable of adequate space and time resolution during a single discharge. Time reso- lution must also include the possibility of analysing the important spectral regions with either high (for individual line scanning) or low (to have a survey of an entire spectral region) spectral resolution. Additionally, due to the use of D-T mixtures, the instruments will need to be protected behind a biological shield (this is parti- cularly easy in the visible, since radiation can then be transferred by light gui- des). Finally, present T values result in the interesting emitted radiation being at shorter wavelengths, thus requiring sophisticated crystal spectrometers. Moreover it will probably be possible to diagnose a particles by charge-exchange effects.

necessary resolving power. Indeed, both the Doppler shift and width are proportional to

A

and (the tokamak central conditions line emission require wavelength), instrumenta- tion having a resolving power A/&

2

10 4

.

0

Near vuv (above 1200 A) and visible Doppler spectrometers allow peripheral ion tempera-

bo.Oc.,

Y)

220 2 ~ 0 260 280 3 ; ~ 320 tures and rotation to be obtained, central

CHANNELS

values being accessible both in the visible F i g . 9 (charge-exchange lines) and in the soft x-ray region (see figure 9 for an example 1123). Intermediate ions have not been accessible to Doppler spectroscopy until it was discovered that it is possible to observe long wavelength (in the near vuv region) forbidden transitions from heavy impurity ions.

H e - l l k e A r w ( l = 3 9 t b * l To = X X ) 1 3 5 e V 1 . ~ . = 3 . 6 chamdr

z E f

\

. .. .-.... - . . ^.. .--.--....

JOURNAL DE PHYSIQUE REFERENCES

[I] DE MICHELIS, C. and MATTIOLI,

M.,

Nucl. Fusion

11

(1981) 677 [2] DE MICHELIS, C. and MATTIOLI, M., Rep. Prog. Phys.

3

(1984) 1233 [3] ISLER, R.C., Nucl. Fusion 2r, (1984) 1599

[4] TFR GROUP, Nucl. Fusion

23

(1983) 559

[5] MARMAR, E.S., CECCHI, J.L. and COHEN, S.A., Rev. Sci. Instrum.

46

(1975) 1149 [6] MARMAR, E.S., RICE, J.E. and ALLEN, S.L., Phys. Rev. Letters

2

(1980) 2025 [7] BRETON, C., DE MICHELIS, C. and MATTIOLI, M., J. Quant. Spectrosc. Radiat. Trans-

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(1978) 367

[8] TFR GROUP, Phys. Letters (1985) 29

191 FONCK, R.J., DARROW, D.S. and JAEHNIG, K.P., Phys. Rev. A

2

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[lo] TFR GROUP, DUBAU, J. and LOULERGUE,

M.,

J. Phys. B. : At. Mol. Phys.

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[ll] EQUIPE TFR, Nucl. Fusion

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Proceed. 11th Europ. Conf. Controlled Fusion Plasma Physics (Aachen, Sept. 1983), EPS (1) (1983) 89