2 Experiment and data analysis

As mentioned, data from the experiments conducted at the TEXT and FTU tokamaks have been used in the present paper. The former experiment has been described by Lippmann et al. ([1987]), Finkenthal et al. ([1986]) and Finkenthal et al. ([1987]). The details of both experiments will be briefly mentioned here.

2.1 Spectroscopic instrumentation

The spectra were recorded by a 1 meter Rowland circle grazing incidence time-resolving spectrometer (GRITS) (Hodge et al. [1984]). In both experiments, GRITS had a spectral resolution of 0.8 Å (full width at half maximum (FWHM) of 0.7 Å). Temporal resolution (detector integration time, called a frame) was 5.4 ms in the TEXT experiment and 11 ms in the FTU experiment. A spectral range 60 to 80 Å wide was covered by the detector during each tokamak discharge. The wavelength calibration was done using resonant lines of intrinsic and seeded tokamak impurities and is considered to be accurate to 0.2 Å. In both experiments, GRITS image intensified photodiode array detector was absolutely calibrated in the spectral range of 20 - 350 Å using synchrotron radiation from the NIST SURF II electron storage ring. The uncertainty in the absolute brightness measurements was estimated to be $\sim 30 \%$, whereas relative brightness of two lines widely separated in wavelength was estimated to be $\leq 20 \%$. In the TEXT experiment, the edge plasma was monitored by a normal incidence time-resolved spectrometer (NITS) (Bell et al. [1981]), covering the range between 300 and 2200 Å. At FTU, a SPRED (survey poor resolution extended domain) spectrometer (Fonk [1982]) was used for measurements in the 200 - 1700 Å range.

2.2 Plasma diagnostics

TEXT was a medium-size tokamak with a central electron temperature about 1 keV and central electron density $\simeq~6~10^{13}$ cm^-3 (Gentle [1981]). The electron temperature was measured in the steady state by radially resolved Thompson scattering, and far infrared (FIR) interferometry was used for electron density diagnostics. The TEXT temperature and density profiles and other plasma parameters are given in Lippmann et al. ([1987]). FTU is a compact high magnetic field, high density tokamak (Andreani [1993]). Typical time histories of its density and temperature profiles are shown in Fig. 1, as measured by FIR and electron cyclotron emission (ECE) interferometers, respectively. Thomson scattering measurements of $T_{\rm e}$ and $n_{\rm e}$ were also available. The accuracy of $T_{\rm e}$ measurements decreases with distance from the plasma center and is only good to $\pm 50$ eV in the plasma periphery. Calcium fluoride (CaF₂) was injected into the plasma in both experiments using a laser blow-off (LBO) technique (Terry et al. [1983]). This method caused controlled perturbation to the plasma. The central electron temperature decrease was 14% at TEXT and 25% at FTU. The electron density increased by $\sim 18\%$ at TEXT and 10% at FTU. The overall reproducibility of the plasma parameters and those of CaF₂injections was estimated to be within $10\%$ in both experiments.

   
2.3 Spectra interpretation

Some of the recorded spectra are presented in Figs. 3 and 4. The TEXT spectrum was composed of six overlapping spectra obtained from reproduceable consequent discharges. Emission from intrinsic tokamak impurities (such as oxygen, carbon, iron, titanium) was integrated over several detector time frames preceding the CaF₂ injection and subtracted from the injection spectrum. This procedure also helps to correct for the scattered light contribution to the recorded spectra. Line identifications were made using wavelength values compiled by Kelly ([1987]). Line intensities were obtained by piece-wise fitting of a multi-Gaussian function to the data using the wavelength from Kelly ([1987]). Analysis of the recorded spectra included: (i) interpretation of spectral line intensities of individual charge states and (ii) interpretation of full spectra. Line-integrated intensities are characteristic of plasma conditions at the maximum abundance (MA) location of each ion (Fig. 2). Therefore, local plasma conditions ($T_{\rm e}$ and $n_{\rm e}$) and emissivity distribution of each ion must be known. To achieve this, measurements were performed along different LOS over a number of reproduceable discharges in the TEXT tokamak.

Figure 4: LOS-integrated Ca spectrum, recorded at FTU

Figure 5: TEXT spectra taken along three different lines of sight a) - through Ca XVI MA location b) - through Ca XIV MA location, and c) - through Ca XII MA location

 

 

Table 1: Electron temperature and density at the maximum abundance location of Ca XVIII - Ca XII ions in TEXT and FTU tokamaks

		$k\,T_{\rm e}$ (eV)		$n_{\rm e}$ ( $\times10^{13}\ {\rm cm}^{-3}$)
Ion	I. P. a (eV)	TEXT	FTU	TEXT	FTU
Ca XVIII	1157	1000 c	650 c	5.4 c	3.0 c
Ca XVII	1087	800 b	550 c	4.0 b	2.8 c
Ca XVI	974	650 b	500 c	3.3 b	2.7 c
Ca XV	895	450 b	430 c	2.9 b	2.6 c
Ca XIV	818	350 b	360 c	2.4 b	2.4 c
Ca XIII	727	230 b	240 c	1.8 b	2.2 c
Ca XII	657	130 b	160 c	1.2 b	2.0 c

• ^aIonization potential, from Kelly (1987).
• ^b From measured ion emissivity profiles and measured $T_{\rm e}$ and $n_{\rm e}$ profiles as described in Sect. 2.
• ^c Calculated as described in Sect. 2.

Line-integrated brightnesses of most intense spectral lines were Abel-inverted and species' radial distribution profiles were inferred (Fig. 3 in Lippmann et al. [1987]). Relative line intensities of the considered $\Delta n=0$transitions are practically temperature independent. Tables 2, 3 and 4 compare measured and calculated line intensities, normalized to the intensity of some resonant representative line of the same ion. The chosen normalization is fairly arbitrary, and meaningful comparisons are made on a case to case basis.

Spectral line blending presented problems in some cases. The blends can be classified as follows: calcium-specific blends (two or more close lines, emitted by calcium ions); blends due to the limited instrumental resolution; and blends, specific to the CaF₂ injection. The spectral blend separation techniques used were similar to those described by Huang et al. ([1987]). Time behavior of LBO-injected impurities in a tokamak plasma is characterized by line brightness decay time. It is therefore possible to separate lines from different ionization stages by comparing time histories of adjacent detector pixels. In the cases where the measured lines originate from the same upper level, branching ratios of the corresponding transitions were used to estimate blended line intensities. Also, spectra recorded at different spatial locations (and therefore at different temperatures), were used in the analysis. For example, Ca XII lines $\lambda141.0$ and $\lambda147.3$ are strongly blended with the brighter lines of Ca XV and Ca XIV on a spectrum recorded along the near-central line of sight (LOS) (Fig. 5). The spectrum with the LOS passing through the Ca XII emissivity peak was used to derive the $\lambda141.1$ and $\lambda147.3$ line brightnesses. The radial position, according to the measured temperature profile, corresponds to $\sim 130$ eV. In some cases (such as the Ca XVIII lines recorded at TEXT, and the FTU spectra (Fig. 4)), spatial measurements were not performed. The predicted ground state density distributions were used to estimate the ion MA temperature and density, as described below.

In a tokamak discharge, ground state densities of impurity ions are constrained by radial temperature and density gradients and the radial particle transport. The tokamak plasma is optically thin, and the main inter-species processes are recombination (radiative, dielectronic) and ionization (direct, autoionization). In a typical ohmically heated tokamak plasma after an LBO impurity injection, ion species evolve toward a steady state equilibrium. This was confirmed in many experiments: for example, Horton & Rowan ([1994]) extensively studied transport phenomena in the TEXT tokamak, using Sc and Ti , LBO-injected into plasma. However, ion maximum abundance temperatures differ from the coronal ionization-recombination equilibrium case due to inward radial plasma transport. The ion fractional abundance peaks are shifted toward higher temperatures (Table 1). Time evolution of the ground level density n_q of injected impurity ion species qcan be obtained by solving a set of differential equations:

$$\frac{{\rm d}n_q}{{\rm d}t}= -\frac{1}{r}\frac{\partial}{\partial r} r \Gamma_q - \frac{n_q}{\tau_q}+S_q+$$ (1)

$I_{q-1}n_{q-1}-(I_q+R_q)\,n_q+R_{q+1} n_{q+1},$

where q is ion charge ( $0 \le q \le 20$ for calcium), $\Gamma_q$ is radial particle flux, S_q and $-\frac{n_q}{\tau_q}$are impurity source and sink terms, respectively, and I_q, R_q are total ionization and recombination rates. To obtain fractional abundances, the set of equations was solved by the transport code MIST (Hulse [1983]). Measured $T_{\rm e}$ and $n_{\rm e}$ profiles were used as input for this calculation. Transport parameters, such as diffusion and convection coefficients, which enter the equations through the particle flux quantity $\Gamma$, were adopted from the dedicated transport experiments (Horton & Rowan [1994]).

 

 

Table 2: Observed and calculated relative line intensities of Ca XVIII, Ca XVII, Ca XVI, Ca XV in TEXT tokamak

							Relative Intensity a
	Lower level			Upper level			Measured	Calculated d
Ion	Term	Label b		Term	Label b	$\lambda$ (Å) c		HULLAC	CHIANTI
Ca XVIII	2s2S1/2	1		2p2P3/2	3	302.2	100	100.0	100.0
	2s2S1/2	1		2p2P1/2	2	344.8	32	51.5	51.1
Ca XVII	2s $^{2}\,^{1}$S0	1		2s2p1P1	5	192.9	100	100.0	100.0
	2s2p3P1	3		2p $^{2}\,^{3}$P2	8	218.8	1.0	0.93	0.85
	2s2p3P0	2		2p $^{2}\,^{3}$P1	7	223.0	1.1	0.75	0.73
	2s2p3P1	3		2p $^{2}\,^{3}$P1	7	228.7	1.1	0.51	0.50
	2s2p3P2	4		2p $^{2}\,^{3}$P2	8	232.8	2.0	2.15	1.95
	2s2p3P2	4		2p $^{2}\,^{3}$P1	7	244.0	1.4	0.70	0.69
	2s $^{2}\,^{1}$S0	1		2s2p3P1	3	371.0	$\cdots$	2.80	2.92
Ca XVI	2s22p2P1/2	1		2s2p $^{2}\,\,^{2}$P3/2	10	154.9	18	17.8	17.7
	2s22p2P1/2	1		2s2p $^{2}\,\,^{2}$P1/2	9	157.8	10	17.2	13.3
	2s22p2P3/2	2		2s2p $^{2}\,\,^{2}$P3/2	10	164.2	100	100.0	100.0
	2s22p2P3/2	2		2s2p $^{2}\,\,^{2}$P1/2	9	167.4	34	39.8	47.9
	2s22p2P1/2	1		2s2p $^{2}\,\,^{2}$S1/2	8	168.9	26	48.3	67.4
	2s22p2P1/2	1		2s2p $^{2}\,\,^{2}$D3/2	6	208.6	32	54.8	67.3
	2s22p2P3/2	2		2s2p $^{2}\,\,^{2}$D5/2	7	224.6	40	71.3	73.5
Ca XV	2s22p $^{2}\,\,^{3}$P0	1		2s2p $^{3}\,\,^{3}$S1	13	137.2	20	15.8	15.6
	2s22p $^{2}\,\,^{3}$P1	2		2s2p $^{3}\,\,^{3}$S1	13	140.6	42	45.7	45.7
	2s22p $^{2}\,\,^{1}$D2	4		2s2p $^{3}\,\,^{1}$P1	15	141.7	51	47.9	48.8
	2s22p $^{2}\,\,^{3}$P2	3		2s2p $^{3}\,\,^{1}$D2	14	144.3	107	85.5	86.2
	2s22p $^{2}\,\,^{1}$D2	4		2s2p $^{3}\,\,^{1}$D2	14	161.0	100	100.0	100.0
	2s22p $^{2}\,\,^{3}$P0	1		2s2p $^{3}\,\,^{3}$P1	11	171.6	35	18.9	17.9
	2s22p $^{2}\,\,^{3}$P1	2		2s2p $^{3}\,\,^{3}$P2	12	176.0	8	12.2	11.8
	2s22p $^{2}\,\,^{3}$P1	2		2s2p $^{3}\,\,^{3}$P1	11	176.9	47	31.3	29.8
	2s22p $^{2}\,\,^{3}$P1	2		2s2p $^{3}\,\,^{3}$P0	10	177.3	20	23.5	23.8
	2s22p $^{2}\,\,^{3}$P2	3		2s2p $^{3}\,\,^{3}$P2	12	181.9	60	95.9	94.2
	2s22p $^{2}\,\,^{3}$P2	3		2s2p $^{3}\,\,^{3}$P1	11	182.9	15	19.8	18.0
	2s22p $^{2}\,\,^{3}$P0	1		2s2p $^{3}\,\,^{3}$D1	8	201.0	29	41.2	38.8
	2s22p $^{2}\,\,^{3}$P1	2		2s2p $^{3}\,\,^{3}$D2	7	208.7	82	82.3	77.9
	2s22p $^{2}\,\,^{3}$P2	3		2s2p $^{3}\,\,^{3}$D3	9	215.4	95	106.0	101.4

• ^aLine intensity, relative to some representative line in each isosequence.
• ^bLabels refer to Fig. 7.
• ^cFrom Kelly ([1987]).
• ^dFor $T_{\rm e}$ and $n_{\rm e}$ values, corresponding to the measured MA location of the ion.

 

 

Table 3: Observed and calculated relative line intensities of Ca XIV, Ca XIII, Ca XII in TEXT tokamak

							Relative Intensity a
	Lower level			Upper level			Measured	Calculated d
Ion	Term	Label b		Term	Label b	$\lambda$ (Å) c		HULLAC	CHIANTI
Ca XIV	2s22p $^{3}\,^{2}$D3/2	2		2s2p $^{4}\,^{2}$P1/2	13	128.2	15	12.0	17.0
	2s22p $^{3}\,^{2}$D3/2	2		2s2p $^{4}\,^{2}$P3/2	12	132.9	12	9.1	13.5
	2s22p $^{3}\,^{2}$D5/2	3		2s2p $^{4}\,^{2}$P3/2	12	134.3	34	46.1	67.5
	2s22p $^{3}\,^{2}$P3/2	5		2s2p $^{4}\,^{2}$P1/2	13	142.4	10	12.5	19.7
	2s22p $^{3}\,^{2}$P1/2	4		2s2p $^{4}\,^{2}$S1/2	11	153.2	6	9.0	13.6
	2s22p $^{3}\,^{2}$D3/2	2		2s2p $^{4}\,^{2}$D3/2	9	165.3	39	38.0	53.3
	2s22p $^{3}\,^{2}$D5/2	3		2s2p $^{4}\,^{2}$D5/2	10	167.0	60	51.6	67.7
	2s22p $^{3}\,^{4}$S3/2	1		2s2p $^{4}\,^{4}$P1/2	8	183.5	26	32.7	33.9
	2s22p $^{3}\,^{4}$S3/2	1		2s2p $^{4}\,^{4}$P3/2	7	186.6	43	65.4	66.0
	2s22p $^{3}\,^{2}$P3/2	5		2s2p $^{4}\,^{2}$D5/2	10	189.0	10	10.3	14.1
	2s22p $^{3}\,^{4}$S3/2	1		2s2p $^{4}\,^{4}$P5/2	6	193.9	100	100.0	100.0
Ca XIII	2s22p $^{4}\,\,^{1}$D2	4		2s2p $^{5}\,\,^{1}$P1	9	131.2	69	63.2	68.7
	2s22p $^{4}\,\,^{3}$P2	1		2s2p $^{5}\,\,^{3}$P1	7	156.7	48	34.3	34.0
	2s22p $^{4}\,\,^{3}$P1	2		2s2p $^{5}\,\,^{3}$P0	8	159.8	20	23.7	24.4
	2s22p $^{4}\,\,^{3}$P2	1		2s2p $^{5}\,\,^{3}$P2	6	161.7	100	100.0	100.0
	2s22p $^{4}\,\,^{3}$P1	2		2s2p $^{5}\,\,^{3}$P1	7	162.9	18	18.0	18.0
	2s22p $^{4}\,\,^{3}$P0	3		2s2p $^{5}\,\,^{3}$P0	8	164.1	35	22.9	22.9
	2s22p $^{4}\,\,^{3}$P1	2		2s2p $^{5}\,\,^{3}$P2	6	168.4	24	30.5	30.5
Ca XII	2s22p $^{5}\,^{2}$P3/2	1		2s2p$^6\,^{2}$S1/2	3	141.0	100.0	100.0	100.0
	2s22p $^{5}\,^{2}$P1/2	2		2s2p$^6\,^{2}$S1/2	3	147.3	40	43.6	43.1

• ^aLine intensity, relative to some representative line in each isosequence.
• ^bLabels refer to Fig. 7.
• ^cFrom Kelly ([1987]).
• ^dFor $T_{\rm e}$ and $n_{\rm e}$ values, corresponding to the measured MA location of the ion.