Charge exchange radiation diagnostic with gas jet target for measurement of plasma flow velocity in the linear magnetic trap
PPrepared for submission to JINST
Charge exchange radiation diagnostic with gas jet targetfor measurement of plasma ๏ฌow velocity in the linearmagnetic trap
A. Lizunov
Budker Institute of nuclear physics,630090 Novosibirsk, Russia
E-mail: [email protected]
Abstract: The ambipolar electrostatic potential rising along the magnetic ๏ฌeld line from thegrounded wall to the centre in the linear gas dynamic trap, rules the available suppression of axialheat and particle losses. In this paper, the visible range optical diagnostic is described using theDoppler shift of plasma emission lines for measurements of this accelerating potential drop. Weused the room temperature hydrogen jet pu๏ฌed directly on the line of sight as the charge exchangetarget for plasma ions moving in the expanding ๏ฌux from the mirror towards the wall. Both bulkplasma protons and ๐ป๐ + ions velocity distribution functions can be spectroscopically studied; thelatter population is produced via the neutral He tracer pu๏ฌ into the central cell plasma. This way,potential in the centre and in the mirror area can be measured simultaneously along with the iontemperature. A reasonable accuracy of 4 รท
8% was achieved in observations with the frame rateof โ ๐ ๐ป๐ง . Active acquisitions on the gas jet also provide the spatial resolution better than 5 mmin the middle plane radial coordinate because of the strong compression of the object size whenprojected to the centre along the magnetic ๏ฌux surface. The charge exchange radiation diagnosticoperates with three emission lines: H- ๐ผ Corresponding author. a r X i v : . [ phy s i c s . p l a s m - ph ] F e b ontents Linear magnetic systems for plasma con๏ฌnement, also frequently referred as open-ended traps, havethe common issue of ๏ฌeld lines facing the grounded metallic wall somewhere beyond the mirror. Theparticular magnetic ๏ฌeld con๏ฌguration for di๏ฌerent devices varies. In order for these con๏ฌnementconcepts to be attractive for real applications, the axial heat ๏ฌux through the direct contact withthe wall must be radically depressed comparing to the classic Spitzer [1] heat conductivity. Thegas dynamic trap (GDT) [2] utilizes a strongly expanding magnetic "fan" beyond the mirror with astraight or curved inwards ๏ฌeld line shape. The axial pro๏ฌle of the plasma electrostatic potentialplays a crucial role forming the actual heat transport physics. In a steady state, this ambipolarpotential equalises the electron and ion currents onto the wall. Study of the axial particle andenergy transport [3] is one of the top priorities in the GDT scienti๏ฌc task list. This activityembraces new diagnostics development as well as experimental and theoretical research.Layout of the GDT device in the Budker Institute is shown in the Figure 1. The detaileddescription of plasma heating and sustainment scenarios can be found in [2], [4]. The current GDTscenario employs electron cyclotron resonance (ECR) discharge for the plasma startup, but does notinvolve ECR heating. Only one of gyrotrons and waveguides (12) drawn in the Figure 1, is used.In this scenario, the energetic ion population and bulk plasma heating is produced via the neutralbeam injection.
The analysis of the velocity distribution function for ions streaming out of the magnetic mirror,would bring the desired information about the electrostatic potential drop along the trajectory and theion temperature. In GDT plasmas, the particle ๏ฌow through the mirror towards the absorber surface,is e๏ฌectively collisionless. The ion energy and magnetic moment conservation in a collisionlessregime is expressed as ๐ ๐ ๐ฃ = ๐ ๐ ๐ฃ + ฮ ๐ ( ๐ง ) , ๐ฃ โฅ = ๐ฃ โฅ ๐ป ( ๐ง ) ๐ป โ . (2.1)โ 1 โ igure 1 : The gas dynamic trap: 1 โ central cell, 2 โ right expander tank, 3 โ magnetic coil ofcentral solenoid, 4 โ atomic beam injector, 5 โ deuterium beam, 6 โ beam dump, 7 โ arc dischargeplasma source, 8 โ plasma dump in the left expander tank, 9 โ radial limiter, 10 โ left gas box, 11 โright gas box, 12 โ waveguides of ECRH system, 13 โ diamagnetic loop, 14 โ Thomson scatteringdiagnostic.Here in (2.1), ๐ฃ and ๐ฃ is the ion velocity in the measurement point in the expander and in thecentral cell, ๐ ( ๐ง ) = ๐๐ ( ๐ง ) is the potential energy for the ๐ -charged ion in the electrostatic potentialdistribution ๐ ( ๐ง ) . The ๐ง = ๐ป ( ๐ง )/ ๐ป (cid:28) ๐ฃ (cid:117) ๐ฃ ๐ง . The one halfof the Maxwellian ion distribution function (IDF) with ๐ฃ ๐ง โฅ ๐ ๐ = ๐ (cid:18) ๐ ๐ ๐๐ ๐ (cid:19) / ๐ ๐ / ๐ ๐ exp (cid:18) โ ๐ ๐ ๐ฃ ๐ ๐ (cid:19) . (2.2)Acceleration in the potential drop means that (2.2) is not zero only for the axial velocity above thevalue de๏ฌned by the expression ๐ ๐ ๐ฃ ๐ง ๐๐๐ = ๐ ฮ ๐. (2.3)The equation (2.3) already provides the measurement approach. A natural and commonly used wayto measure the axial ion velocity (or energy) in the plasma ๏ฌux is by means of a grid electrostaticanalyser, where the scanning analysing voltage is applied to decelerate ions. In past experimentsin GDT, such experiments were successfully done [2] (page 26). There are some ๏ฌaws though inthis technique. For example, it is typically tricky to arrange measurements in multiple radial pointswith the grid energy analyser. A special high voltage power supply for such an analyser can becomplex and expensive. In this paper, we are considering a spectroscopic approach to the task. Themethod relies on charge exchange conversion of streaming ions into atoms with the subsequent lightemission, which implies the classical Charge eXchange Radiation Spectroscopy (CXRS) scheme: ๐ด ๐ + + ๐ป โ ๐ด โ( ๐ โ )+ + ๐ป + โ ๐ด ( ๐ โ )+ + ๐ป + + โ๐. (2.4)โ 2 โhe neutral hydrogen target is used in (2.4), which is typical for CXRS. The emitted light spectrumshape encodes the IDF parameters. The ion temperature can be calculated by the Doppler FWHM(Full Width Half Maximum) as ๐ ๐ = ๐ ๐ ๐ (cid:18) ๐ฟ๐ / ๐ (cid:19) , (2.5a)where ๐ is the unshifted wavelength. In turn, the accelerating potential drop is linked to theDoppler line shift as ฮ ๐ = ๐ ๐ ๐ ๐ (cid:18) ฮ ๐ ๐ท ๐ (cid:19) ฮ , (2.5b)where ฮ is the angle between the ion velocity and the Line of Sight (LOS) direction.Diagnostics for CXRS in a tokamak or other magnetic plasma con๏ฌnement device, are typicallyassociated with the atomic (hydrogen or deuterium) beam acting as a target. Indeed it is generallya crucial requirement to deliver a substantial target atom density to the certain point inside the bulkof the plasma. The major performance criterion here is the signal-above-background ratio (S/B).In the simplest case, it is given by the relation between the active CX signal recorded on the target,and the passive emission collected along the LOS. A respectable ๐ / ๐ต (cid:38) ๐ = ๐ป ( ๐ง )/ ๐ป roughly linear. In the region under study, it is50 รท
100 less than that in the central cell, which poses a certain diagnostic challenge. On the otherhand, restrictions against perturbing the plasma parameters are mild. It is proven [11] that even astrong emission of cold electrons downstream in the expander do not a๏ฌect the central cell plasma.Then it is advantageous to use a gas jet pu๏ฌng from the narrow capillary placed directly on the LOSinstead of the energetic atomic beam because a much larger local atomic density (and the rate of CXevents) can be achieved. The CXRS gas target assembly is a 2 mm-diameter quartz tube insertedvia the vacuum feedthrough and connected to the pulsed fast electromagnetic valve. The valveopen delay relative to the measurement time window, is adjusted to the minimum while it is stillsu๏ฌcient to generate an e๏ฌective CX target. The main concern is to reduce the additional gas loadin the expander tank during the plasma discharge and so to less contaminate other measurementsin the expander. The estimated molecular hydrogen density of ๐ ( ๐ป ) (cid:27) ๐ โ is observedsu๏ฌcient for an ample optical signal of CX emission, as it is shown below in the paper. Thelocal observation volume (gas cloud) has the size of โ ๐๐ , but the actual space resolution isde๏ฌned by the cloud size mapped onto the GDT central plane along the magnetic ๏ฌux surface: ๐ฟ๐ โ ๐ฟ๐ ๐๐๐๐ข๐ โ๏ธ ๐ป ( ๐ง )/ ๐ป โ รท ๐๐ . In the paper, radii are expressed in the device mid-plane ifnot otherwise speci๏ฌed. As the Figure 2 illustrates, the diagnostic LOS is ๏ฌxed. The gas tube tip isโ 3 โ igure 2 : Layout of CXRS measurements in the left GDT expander: 1 โ cone part of the GDTcentral cell, 2 โ magnetic coil, 3 โ mirror magnetic coil assembly, 4 โ gas pu๏ฌ volume, 5 โ boundarymagnetic ๏ฌeld line, 6 โ expander tank, 7 โ plasma dump, 8 โ translation vacuum feedthrough of thegas feed tube, 9 โ quartz tube 2 mm diameter, 10 โ charge exchange gas target, 11 โ ๐ป reservoir andthe feed line with the pulsed electromagnetic valve, 12 โ 2-inch lens for light collection, 13 โ lightcollection solid angle, 14 โ optical ๏ฌbre optic, 15 โ spectrometer coupled with the CCD camera.movable between the axis and the plasma periphery along the LOS allowing for pro๏ฌle acquisitionin a series of shots. One should keep in mind that both the radius and the z-coordinate are changedat the same time along the LOS.The optical system (12) (see Figure 2) collects the light, which comes to the spectrometer(15) via the ๏ฌbre optical light guide (14). The Table 1 summarizes the main parameters of theregistration system. The spectrometer we used is the factory LOMO MDR-23 model with thecustom cylindrical output lens for the astigmatism correction. It is coupled with the PrincetonInstuments PyLoN CCD camera [12] which has a small dark current and readout noise. The CCDis con๏ฌgured in the "Kinetics" mode (see [12]) featuring multiple exposures on the sensor withinthe single digitization and the readout cycle. This regime provides a trade-o๏ฌ for a reasonably fastframe rate in the kHz region with a limited number of exposures at the price of sacri๏ฌcing the lightthroughput. We set ten exposures of 0 . ๐๐ duration and the e๏ฌective frame rate of 1.1 kHz, thespectrometer entrance slit is accordingly enabled only on the 1 /
10 of its height.โ 4 โ able 1 : Main parameters of the optical registration system.
Spectrometer
Optical scheme Czerny-TurnerFocal distance 600 mmF/No. F/6Groove density 1800 g/mmBlaze 550 nmDispersion 0.69 nm/mmSpectral resolution 0.041 nm
CCD
Model PyLoN 2KB eXcelon (LN-cooled to -120 โ )Sensor 2048x512 pixels 13 . ร . ๐๐ Binning
Kinetics , 50 rows verticalExposures on CCD 10Exposure duration 0.5 msFrame rate 1.1 kHzSystem noise โ . ๐ โ Hydrogen H-alpha spectral line.
The observation geometry shown in the Figure 2 shows thatthe angle between the ion velocity vector and the LOS vector (the latter being directed towards theoptics) ฮ > โฆ . This angle varies from ฮ = โฆ on the axis to the ฮ ๐๐๐๐ = โฆ on the edge๏ฌeld line projecting to ๐ = ๐๐ โ the radial limiter radius. For these angles, the Doppler shift istowards larger wavelengths. In all GDT experimental scenarios, there is a non-negligible hydrogenplasma component even if deuterium is used to create both the bulk plasma and fast ions via neutralbeam injection. Possible explanations of that are some organic residuals inside the vacuum vesseland also micro-leaks of the air with water vapor. Anyway, observation of the Doppler-shifted D- ๐ผ ๐ผ (cid:46) ๐๐ , so one can assume hydrogen ion birth places localized in the left mirror area.We will refer the plasma electrostatic potential calculated by the H- ๐ผ Doppler shift as the "potentialin the mirror" to distinguish from the central potential.
He-I spectral lines.
The diagnostic scheme becomes more versatile with the additional heliumpu๏ฌ in the central GDT part. Helium component is used as a tracer; the net He amount is smallcompared to the deuterium and hydrogen pu๏ฌ and it should be barely enough to create an observableoptical signal. Atoms of He are stripped down to ๐ป๐ + with the characteristic time of โผ . รท . ๐๐ which is smaller than the axial particle loss time ๐ ๐ (cid:27) . ๐๐ . One can expect the prevailing contentof ๐ป๐ + over ๐ป๐ + in the plasma ๏ฌow in the expander, which is useful from the spectral analysisviewpoint due to the larger Doppler shift. One can not however presume the He ion population beingโ 5 โ I n t en s i t y ( A DC c oun t s ) Wavelength (nm)1 2 3
Figure 3 : The spectrum recorded on the axis with the CX gas target in GDT shot 49311 at ๐ก = ๐๐ ,exposure ๐ = . ๐๐ : 1 โ bright D- ๐ผ and H- ๐ผ lines (cut out), 2 โ C-II lines 657.8 nm and 658.3 nm,3 โ He-I line 667.8 nm with Doppler-shifted component.in a local thermodynamic equilibrium with the bulk deuterium or deuterium-hydrogen plasma. Ions ๐ป๐ + are partially converted into ๐ป๐ โ with subsequent emission of He-I lines. In this work, weobserved the He-I lines 587.6 nm and 667.8 nm. The latter option was used in most shots becausethis He-I line ๏ฌts the same working spectral range with H- ๐ผ . In this way, the measurements of themirror potential, the central potential, the hydrogen temperature and the helium temperature werepossible simultaneously. The Figure 3 demonstrates the spectrum sample taken in the GDT shot49311 with the charge exchange gas target switched on. The frame exposure was 0.5 ms recordedat ๐ก = ๐๐ during the plasma heating phase. One may observe both the narrow cold-gas He lineand the broader red-shifted emission responsible for accelerated ๐ป๐ + ions. Fitting CX spectra and measurement of potential and ion temperature.
Figure 4 shows theactive CX H- ๐ผ spectrum (magenta) measured on the axis in the shot 48994 and the backgroundor passive spectrum from the shot 48993 (blue). The ๏ฌt curve is also plotted (black). Note thatthe Doppler-shifted line is almost vanished in the passive sample. With this contrast ratio, we canneglect the passive contribution in the gas target enabled frame thus considering the recorded opticalsignal being the active CX emission. This ensures the spatial resolution considered above. In thisparticular series of shots, the hydrogen bulk plasma feed predominated. This lead to a relativelysmall background D- ๐ผ emission, which is rendered in the passive spectrum as a smoothed dent(2) on the H- ๐ผ wing, see Figure 4. Physical data, namely the temperature and the potential, areobtained via ๏ฌtting recorded spectra with the model function. The model we used, is a superpositionโ 6 โ I n t en s i t y ( A DC c oun t s ) Wavelength (nm)
Gas target No gas target Fit656.1 656.3
12 3
Figure 4 : Spectrum of H- ๐ผ emission on the axis used for calculation of the mirror potential:magenta curve โ active CX frame acquired in the GDT shot 48994, blue curve โ passive frameacquired in the GDT shot 48993, black curve โ model ๏ฌt of the active CX spectrum. Verticaldashed lines mark positions of unshifted D- ๐ผ and H- ๐ผ . 1 โ bright cold-gas D- ๐ผ and H- ๐ผ lines (cutout), 2 โ D- ๐ผ in the passive spectrum, 3 โ part of spectrum corresponding to the accelerated IDF.Acquisition timing parameters: ๐ก = ๐๐ , ๐ = . ๐๐ .of multiple bi-Gaussian lines each having its own set of parameters. Upon the ๏ฌt convergence, linewidth and shift parameters are used for the calculation of the ion temperature and the potential dropvia formulas (2.5a) and (2.5b). The mathematical processing codes are made using the nonlinear๏ฌt libraries provided in the Center Space NMath .NET software package [13]. Error bars shown inall graphs that follow, re๏ฌect the accuracy of the spectrum ๏ฌt with the model function. Recordedspectra of He-I emission on the axis are plotted in the Figure 5. Similar to the Figure 4 with theH- ๐ผ pro๏ฌle, both passive and active CX spectra are shown. There is no prominent Doppler-shiftedsignal above the noise level in the passive spectrum and likewise the H- ๐ผ case, no backgroundsubtraction is needed for processing of the active CX spectrum. Easy to notice, that the cold-gasHe-I line (1) also features the positive Doppler shift ฮ ๐ ๐๐๐๐ ( ๐ป๐ ) (cid:39) . ๐๐ that is a reliable andreproducible e๏ฌect. Such a shift is translated to the velocity ๐ฃ ๐๐๐๐ ( ๐ป๐ ) (cid:39) . ยท ๐ / ๐ which isconsistent with collisions of cold He atoms in the expander with the accelerated plasma particles inthe ๏ฌow. The peak (3) we believe to be responsible for the mirror re๏ฌection of emitted light fromthe plasma dump surface. Due to some oversight, this surface is neither sand blasted nor darkenedand the re๏ฌection would be remarkable indeed giving an approximately opposite Doppler shift as itis observable in the Figure 5. We also admit a partial re๏ฌection of plasma ๏ฌow particles from theโ 7 โ I n t en s i t y ( A DC c oun t s ) Wavelength (nm)
Gas target No gas target Fit667.815
Figure 5 : Spectrum of He-I emission 667.8 nm on the axis used for calculation of the centralpotential: magenta curve โ active CX frame acquired in the GDT shot 49707, blue curve โ passiveframe acquired in the GDT shot 49705, black curve โ model ๏ฌt of the active CX spectrum. Thevertical dashed line marks the unshifted line position. 1 โ cold-gas He-I line, 2 โ active CXspectrum, 3 โ mirror re๏ฌection. Acquisition timing parameters: ๐ก = ๐๐ , ๐ = . ๐๐ .dump surface.Using the spectrum mathematical analysis as explained above, time evolutions of the hydrogenion temperature and ๐ป๐ + ion temperature are plotted in the Figure 6a. The electron temperature ismeasured by the Thomson scattering in the GDT centre. The dashed curve provides the referenceof diamagnetic signal showing the dynamics of the plasma energy content. The Figure 6b showsthe time evolution of the plasma electrostatic potential measured via the H- ๐ผ Doppler shift (blue๏ฌlled triangles) and Doppler shifts of two He-I lines: 667.8 nm (red ๏ฌlled circles) and 587.6 nm(magenta open squares). The former two measurements are done simultaneously in the same shot,the latter one required tuning the spectrometer.
The accuracy of considered CXRS measurements on He-I lines ๐ โ รท
8% is primarily a functionof the active signal intensity, because contribution of the background line emission along the LOSand the continuum light both are small. Mathematical calculations of the Doppler-shifted H- ๐ผ areslightly complicated by the neighbouring cold-gas background line that may be approximately twoorders of magnitude stronger. The exposure duration of 0.5 ms and the frame rate of 1.1 kHz allowโ 8 โ I on t e m pe r a t u r e ( e V ) Time (ms) (a) Ion temperature time evolution close to theaxis. Horizontal error bars show the exposureduration of 0.5 ms. P o t en t i a l ( V ) Time (ms) (b) Time evolution of the plasma electrostaticpotential in two locations (close to the axis).
Figure 6 : Example of application of the CXRS diagnostic for the study of the ion velocity distri-bution function.for resolution of plasma parameters dynamics during the plasma startup, heating and sustainmentin GDT. The spatial resolution of (cid:46) ๐๐ determined by the gas cloud projection onto the middleplane, is su๏ฌcient for the study of spatial pro๏ฌles of the ion velocity distribution function. In thepresent diagnostic design, there is a single line of sight which requires a series of shots for pro๏ฌlemeasurements. A comprehensive investigation of the axial transport of particles and energy in thegas dynamic trap with the intensive CXRS diagnostic involvement is under way.From the viewpoint of R&D of new instrumentation, some valuable experience has beenobtained as well. The basic diagnostic technique using the gas jet target is con๏ฌrmed to be workablein a wide range of central cell plasma parameters and residual gas pressure in the expander vessel.It provides a solid ground for development of a more capable CXRS diagnostic version for thenext-generation linear magnetic system for plasma con๏ฌnement [14], which construction is to bestarted within a couple of years. The improved optical system will have multiple observation pointsdistributed across the plasma fan in the expander area. The charge exchange target should be a morecollimated helium jet with a greater penetration depth, probably a supersonic gas jet like [5, 6]. Acknowledgments
This work is supported by the Russian Science Foundation, project No. 18-72-10084 issued on31.07.2018.
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