The Curved Crystal Spectrometer for Ignitor

Transcription

1 The Curved Crystal Spectrometer for Ignitor F. ombarda, ENEA Fusione, Frascati (Italy) MIT RLE Report PTP 02/02 Cambridge, MA March 2002

2 1. Introduction In the next generation of magnetically confined burning plasma experiments, an increasingly important role will be played by neutron diagnostics. For the measurement of the ion temperature, X-ray spectrometers measuring the Doppler width of impurity lines are also envisaged. This technique can survive in an ignition experiment environment, since the diffracting crystal provides a mean of removing the detector from the direct neutron flux produced by the plasma. Especially in the case of a compact, high field device such as Ignitor, methods based on charge exchange recombination spectroscopy, which requires a neutral beam, or neutral particle analysis are not effective given the high plasma density. High resolution curved crystal spectrometers have become standard diagnostics for plasmas with temperatures above ~1 kev [1,2,3,4]. A convenient range of observation is between 1.5 and 4 Å, where the resonance spectra of H-like and He-like elements from argon to nickel are located, as well as lines from highly ionized molybdenum. In Ignitor, the first wall will be covered with Mo tiles; therefore trace levels of this metal can be expected to be found in the core plasma. Otherwise, the spectroscopy measurement for the ion temperature can rely upon impurity injection, chosen to suit the plasma parameters to be measured. Usually, very small impurity amounts ( ne) are adequate for this kind of measurements, given the relatively high luminosity of curved spectrometers. In particular, the Johann configuration is a very suitable instrument to operate in a high background radiation environment, because it allows the positioning of the crystal at a considerable distance from the plasma (the throughput scales only as the inverse of the distance rather than the more typical inverse square), where the detector can easily be shielded. Focal lengths of the order of 20 m have been achieved [5]. The measurement of the ion temperature spatial distribution is more difficult than that of the electron temperature profile. This is likely not to be a serious problem for Ignitor because, owing to the very high plasma density expected in this experiment, the values of the two temperatures should be very similar. Nevertheless, an independent assessment of the ion temperature profile is highly desirable, and 2-D versions of the Johann spectrometer have been successfully implemented [6,7]. Their possible applications to Ignitor are considered. Other plasma parameters can be derived from different features of the high resolution X- ray spectra. For example, the electron temperature has been obtained by the line intensity ratio of 1

3 dielectronic satellites to the resonance line [8,9]; the impurity ion concentration was derived by the absolute line brightness [10], and the plasma rotation is measured by the line Doppler shift with appropriate line-of-sights [11]. All of these quantities should also be measurable on Ignitor, although with possible restrictions on the accessible parameter ranges. 2

4 2. Instrument lay-out The principle of operation of ragg spectrometers in the Johann configuration is illustrated in Fig. 1: a flat crystal bent to a radius of curvature 2R determines a focusing Rowland circle of radius R. X-ray photons of wavelength λ incident on the crystal at an angle θ ( λ d) = asin 2 relative to the diffracting planes are focused on the Rowland circle. Photons of different wavelengths are focused at different positions and a position sensitive detector allows the simultaneous measurement of the spectrum in a given wavelength range. Typical ragg angles are between 35 and 65. The input arm, connecting the machine to the crystal, is usually fixed, whereas the output arm can have the possibility of pivoting to some extent around the crystal, to allow more freedom in the choice of spectral range to be observed according to the plasma conditions and the available impurities. In the case of Ignitor, the high neutron fluxes expected in the D-T phase of the experiment suggest the positioning of both crystal and detector outside the torus hall, in a configuration similar to that adopted for JET [5], for ease of access and maintenance. On the other hand, in the preliminary experimental campaigns in H, He, or even D, a more compact instrument located inside the torus hall could be more effective, as it will provide higher throughput and more spatial coverage. Given the fact that the input and output arms are only needed to provide a vacuum path to the X-ray photons, changing from one configuration to the other would only involve a relatively minor upgrade. In its simplest form, a single diffracting crystal (quartz) and a Multiwire Proportional Chamber (MWPC) can provide a measurement of the ion temperature along a single line of sight, with spatial resolutions determined either by the dimension of the emitting region in the plasma or by the relative sizes of the crystal and the detector, usually of the order of cm. Spatial resolution in the vertical plane can be improved by inserting a horizontal slit before the crystal or before the detector (see Fig. 2) and adopting a two-dimensional read-out of the MWPC [6]. Movement of neither the crystal nor the detector is required, and the spectra for all the chords are collected simultaneously. This extremely simple scheme can be improved upon, for example by adopting spherical crystals, which provide a self-imaging configuration, without the need for the additional slit [7]. Since the latter configuration has only recently started to be adopted as a diagnostic in fusion experiments, for the present we will consider primarily the 3

5 traditional cylindrical configuration for the determination of the basic instrument parameters, but this option will be considered at a later time. Given the present dimensioning of the Ignitor torus hall, a possible layout for the curved crystal spectrometer is shown in Fig. 3. To avoid blocking the view of other horizontal ports, in may be necessary to tilt the whole Rowland circle by few degrees. For the high neutron phase of the experiment, ragg angles 60 will be best, but for the earlier phase θ 65 will provide better results. Possible elements to monitor and crystal cuts to use for the various ranges of expected temperatures are listed in Table I. These ions may not necessarily be naturally present in the plasma, thus they may have to be injected into it. Quartz crystals have a lower reflectivity than germanium, but they have superior bending properties, so they are our first choice, unless luminosity turns out to be a very limiting factor. Table I Ion, λ (Å) Quartz (hkl) 2d (Å) R i, θ i (10-5 ) θ Temperature Range (kev) Ar 16+, , , Ar 17+, , , Ti 20+, , Cr 22+, , , Fe 24+, , , Ni 26+, (Ge) Mo 32+, 3.74 Same as Ar Mo 40+, TD > 10 Tentative list of candidate ions for ion temperature measurements. 4

6 3. Detector The spectrometer relies on the availability of large area, high resolution, space sensitive detectors. Multiwire Proportional Counters (MWPC) have been the preferred choice in most cases. Their only major drawback is a limit of approximately 1 MHz in total counting rate for detectors based on delay-line read-outs, and 1 MHz/ch for direct, single wire read-out. A new generation of detectors is being developed (see the list, for example, in ref. 7 and the new GEM detectors [12]), but their suitability still needs to be investigated, especially with regard to increased dimensions. for now we will pursue the more conservative but well tested approach provided by MWPCs with delay-line read-out, as done for the crystal diffracting element. This detector offers in fact the possibility of discriminating the gamma and neutron-induced background [13]. In particular, we refer to the two-dimensional camera built for the ragg spectrometer of FTU [6], whose characteristics are summarized in Table II. The wider dimension is desirable in order to match the width of the port and thus being able to cover the largest spectral range. On the other hand, the signal-to-noise ratio deteriorates the longer the signal has to travel along the delay line, so the final choice will be determined by the optimal compromise between these two requirements. Table II Detector effective area Detection gas Resolution in x-direction Resolution in y-direction Max. Counting Rate mm mm 75% Ar ( or Xe) 25% Ethane <0.4 mm 5-20 mm (programmable) 500 KHz 5

7 4. Spectrometer Resolution and Throughput The relative Doppler broadening of spectral lines is given by λ λ D 3 i( kev) = T A ( amu) In the range of temperature and ion mass of interest this value is typically ~ The spectrometer resolving power needs therefore to be of the same order. Other broadening mechanisms are usually negligible for the X-ray radiation emitted by the core plasma, except for the natural width of the line, which can easily be taken into account. Detector and analyzing crystal both contribute to the total instrument resolution, in the way detailed in Table III. Not all contributions are symmetrical broadenings, and for this reason is somewhat important to keep the instrumental function narrower than the observed line, so that the its shape does not need to be known in detail and it can be simply assumed to be gaussian, like the thermal broadening. In Table III two possible configurations are analyzed, one corresponding to θ = 68 and a shorter crystal curvature radius, the second one to θ = 49 and longer arms. In both cases the assumption is made that the crystal dimensions can be as large as those used for JET ( mm) and of similar quality. If the instrumental resolution is adequate, the final uncertainty on the ion temperature is determined mainly by statistical errors. The global throughput of the instrument will be estimated to assess the level of impurity density in the plasma that can provide the required signal. The spectrometer luminosity can be evaluated according to two basic conditions: i) the plasma represents an extended source in the vertical direction ( θ + ) h h 2Rsin d 2Rsinθ and the s D signal is integrated over the height of the detector; ii) the slit configuration is adopted and the signal is binned into 8 vertical channels of the detector. The overall detection efficiency η is estimated for an equivalent depth of 7.5 mm of argon and 2.5 mm of ethane in the detector. The transmission efficiency is for a 150 µm thick beryllium window ( 0.8 to take into account the shade of supporting ribs), 250 µm mylar, 1.5 mm of argon and 0.5 mm of ethane, representing the absorbing materials along the photon path. 6

8 5. Spatial Resolution With the Johann spectrometers is always convenient to locate the focal circle at the mouth of the viewing port, which is typically the narrowest section along the optical path. Thus, the light can be collected from a relatively extended region in the plasma. Given the astigmatism of the cylindrical mounting, the spatial resolution is provided by the region over which the observed ions live, usually ranging between 1/3 and 1/2 of the minor radius. When higher spatial resolution is required, than a proper imaging set-up needs to be used. The simplest one, shown in Fig. 2, makes use of a variable horizontal slit to image the plasma onto a 2-D detector. The horizontal port vertical aperture allows a direct view of little more than 60 % of the plasma (about 0.5 m above and below the midplane). Given a port height of 80 cm and a crystal height of 5 cm, the resulting image at the detector would be 70 cm high. This is too much to be covered by a single MWPC, but the use of two, or even three detectors (with a single crystal) could have the additional advantage of being able to monitor spectral lines from adjacent ionization stages, at slightly different ragg angles, to optimize the line brightness over the temperature radial profile. The use of multiple crystals would also add flexibility. The detector resolution in the vertical direction is arbitrary but, for example, a 1.5 cm channel at the detector will view less than 2 cm of plasma. The advantage of the slit-2d MWPC solution is that of offering the possibility of a very easy adjustment of these parameters according to the experimental conditions. The combination of the numbers presented lead to the conclusion that the ion temperature in Ignitor could be measured in the range from 0.8 to above 10 kev to within ~ 10 %, with a spatial resolution of about 2 cm and a (variable) time resolution of approximately 50 ms. 7

9 Table III Contributing factors Crystal length 2 λl lc 1 = λ 4R 2tan2 θ Crystal height 2 λh hc 1 = λ 4R 2sin2 θ Detector resolution λ λ Crystal angular λ width λ Curvature defects Instrument resolution x cotθ = 2R sinθ D D ω λ λ CD ω = tanθ l = r c ( 2R) 2 2 cot 2 λ λ λ λ = λ + λ λ + λ 2 2 λω λ CD + + λ λ 2 2 Inst l h D R θ 1/2 θ =68, 2R=6 m θ =49, 2R=22.5 m Throughput ( f η Rlhh i c c Dsinθ L = = (sr m 2 ) source) εds 4π 2Rsinθ + D Throughput (slit L configuration) y η Rlhh = 4π 2Rsinθ sinθ ' i c f D D cf (sr m ) 8

10 6. Rotation Measurements The phenomenon of spontaneous rotation in non-n heated tokamak plasmas has recently been observed for the first time on Alcator C-Mod [14] and its relation to the confinement properties of the plasma has been theoretically investigated [15]. A scaling of the spontaneous rotation with plasma size and parameters is not available yet, thus we shall assume that the toroidal rotation in Ignitor will be of the same order of what presently observed on Alcator C-Mod, about 10 Km/s or higher. The spectrometer layout shown in Fig. 2 can also detect, in principle, a poloidal ion flow, but the detection of toroidal flows requires the observer (i.e., the resolving crystal) to be positioned off the normal viewing line. Given the geometry of the horizontal ports in Ignitor, the maximum angle that can be used is α = atan160/1840 = The relative Doppler shift of the line λ λ Φ vφ = sin α is about two orders of magnitude less than the thermal width of the c line, and its detectability relies entirely on the detector spatial resolution x D. The condition that needs to be verified is λ λ Φ xd cotθ >. 2R sinθ From this expression it is clear that larger ragg angles and longer curvature radii are more favorable. For θ = 68, and values of the ratio x 2R , the minimum toroidal rotation speed that can be detected is ~ m/s. Unfortunately the port geometry does not leave much room for optimizations, so the path to follow to improve the sensitivity is essentially that of improving the detector resolution. The new GEM detectors seem very promising in this respect. y similar calculations, the minimum flow velocity in the poloidal direction that can be detected is ~ m/s, since in this case the viewing line is essentially parallel to the velocity vector. There is little expectation to find such flows in the central core of the plasma, but it could be present, for some regimes, in the outer part of the plasma column. D 9

11 CRYSTAL θ ROWLAND CIRCLE λ 1 2R λ 2 λ 1 PLASMA λ 2 FIG. 1. Optical scheme of the Johann mounting. 10

12 Plasma e Window Crystal Slit Detector d s hc hf D 2Rsin θ D cf FIG. 2. Spectrometer cross section in the spatial imaging configuration. 11

13 FIG. 3. Possible lay-outs for the curved crystal spectrometer. 12

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