Optical tomography diagnostic for study of neutral plasma component in the gas dynamic trap
PPrepared for submission to JINST
Optical tomography diagnostic for study of neutralplasma component in the gas dynamic trap
A. Lizunov, A. Khilchenko, D. Moiseev and P. Zubarev
Budker Institute of nuclear physics,630090 Novosibirsk, Russia
E-mail: [email protected]
Abstract: The optical diagnostic observing D- 𝛼 line emission along multiple chords in the bound-ary region close to the plasma absorber, is recently installed at the gas dynamic trap. The imple-mented pattern of viewing lines is suitable for a tomographic reconstruction of local emissivityprofiles, although steps towards increasing the channel count and extending of angular plasmacoverage must be taken. The optical registration system of a modular design uses avalanche photo-diodes with wideband amplifiers for a large signal dynamic range and the effective time resolutionof 1 𝜇𝑠 . The iterative backward projection technique based on the maximum likelihood principle,demonstrates an acceptable computation accuracy. Images of plasma evolution in the cross sectionwere obtained. Tools for the correlation analysis were also developed and first results of study ofthe plasma turbulence are presented.Keywords: Plasma diagnostics - interferometry, spectroscopy and imagingArXiv ePrint: 1234.56789 Corresponding author. a r X i v : . [ phy s i c s . p l a s m - ph ] F e b ontents Linear open-ended systems have direct contact of confined plasmas with the end wall due tothe magnetic field geometry. The axial heat conductivity is therefore a major issue which mustbe addressed in an improved confinement concept basing on the linear "magnetic bottle" fieldconfiguration. As one of them, the axially symmetric gas dynamic trap (GDT) [1] utilizes severaltechniques to increase the lifetime of particle and energy in the central cell. Strongly expandingmagnetic flux beyond the mirror prevents a flyover penetration of cold electrons emitted by the wallback to central plasma thus allowing for a radical depression of heat conductivity comparing tothe classical Spitzer [2] case. Study of axial transport [3] is one of ongoing physical objectivesof the GDT research program. In high-beta regimes [4] with electron cyclotron resonance heating(ECRH) [5], extra efforts must be spent to stabilize the plasma against magneto-hydrodynamic(MHD) perturbations. This line of experimental and theoretical activities has led to establishing ofthe so called vortex confinement [6] method of MHD modes suppression which is now a standardattribute of experimental scenarios in GDT. A specific plasma equilibrium called vortex, is drivenby biasing radial limiters and plasma absorber sections. It is also realized that the approach is viableif the particle density is above the certain threshold in the expander region. Normally this density ismaintained by the hydrogen or deuterium puff in the expander tank. The neutral plasma componentformed both by the gas puff and plasma flux neutralisation on the end wall, therefore represents asignificant fraction bound to the physics of ion and electron transport in the expander. A productiveway of study is detection of light emitted along multiple lines of sight (LOS) distributed acrossthe plasma diameter. Then a tomography reconstruction can be used to obtain the local emissivitydistribution. Various tomography diagnostics in optical to soft X-ray range are being widely usedin experiments with magnetically confined plasmas for decades [7–15]. The paper discusses therecently developed visible range optical diagnostic, which is installed in the GDT expander tomonitor dynamics of atomic plasma component spatial profile.– 1 –
Diagnostic description
Figure 1 shows the gas dynamic trap layout. The diagnostic LOS are arranged in the plane , Figure 1 : Gas dynamic trap schematic: 1 – central cell, 2 – right expander tank, 3 – magneticcoil of central solenoid, 4 – atomic beam injector, 5 – deuterium beam, 6 – beam dump, 7 – arcdischarge plasma source, 8 – plasma dump in the left expander tank, 9 – radial limiter, 10 – left gasbox, 11 – right gas box, 12 – waveguides of ECRH system, 13 – diamagnetic loop, 14 – Thomsonscattering diagnostic, 15 – hot-ion plasma, 16 – plane of observation of tomography diagnostic.which is offset at 50 mm from the plasma absorber surface . The viewing geometry is presented inFigure 2. In its current state, the diagnostic has two LOS bundles of a fan beam structure both. Thedeveloper team bears plans to install several (four) bundles similar to the bundle-1 to cover all anglesnearly uniformly. Unfortunately the vacuum port availability was a severe limiting factor duringthis period of time, which has defined a suboptimal plasma coverage with LOS. The bundle-2 isinstalled in the tangent view port having accordingly smaller aperture angle. Undoubtedly this LOSpattern would sacrifice the Abel inversion accuracy which degree is estimated below in the paper.Up to now, the optical system counts 42 LOS numbered as shown in Figure 2. The whole opticalregistration system is comprised of 14 identical detector modules with three avalanche photodiodes(APD) sharing the same lens and interference filter. The optical and mechanical module design isdiscussed in the previous paper describing the prototype diagnostic [16] along with consideration ofthe two-stage transimpedance operational amplifier (OPA) and the procedure of absolute intensitycalibration. The current version uses narrowband interference filters centred at 656.2 nm with theFWHM of 1 nm to observe both H- 𝛼 and D- 𝛼 emitted by the plasma majority and gas puffed intothe expander. In principle, one can switch to an impurity line (within the wavelength range of arespectable APD quantum efficiency) simply replacing the set of filters. Filter-lens interchangeableassemblies are mounted in the aluminium body part 5 (see Figure 2) which is provided withwater cooling flowing in the recirculating chiller system for the working temperature set point of20 ◦ C. Detector modules are attached to this cooled part having approximately the same temperature 𝑇 𝐴𝑃𝐷 = ± ◦ C. Prior to installation, each detector module is tuned to the optimal APD bias voltageindividually and calibrated at this voltage. This aim of this procedure is to adjust the avalanche gain– 2 – igure 2 : Diagnostic layout: 1 – left GDT expander tank, 2 – diagnostic bundle-1, 3 – diagnosticbundle-2, 4 – detector module, 5 – interference filter nest, 6 – angle alignment unit, 7 – vacuumwindow, 8 – line of sight, 9 – projection of radial limiter, 10 – maximum observable plasma size,11 – electronics box, 12 – gas puff cloud.in order to reach the maximum signal-to-noise ratio (SNR). On incident light signals close to whatexpected in GDT measurements, all acquisitions channels have shown
𝑆𝑁 𝑅 = ÷
120 within thebandwidth of 0...5 MHz. The APD-OPA performance parameters are competitive to that reportedfor similar devices developed for high-speed low light plasma diagnostics, see for example [17].Lab tests have shown that both the SNR of the APD-OPA circuit and therefore the signal acquisitionsystem effective dynamic range are defined by the Poisson shot noise and the APD excess noise butnot the amplifier noise. On the machine, two custom made precision multi-channel high voltagepower supplies serves detector units in the bundle-1 and bundle-2. The output voltage is traced andrecorded for every channel indicating that the set voltage stability (including both the ripple and thelong-term drift) is (cid:27) − . Power supply units are placed in the electronics box (see Figure 2),where signal loggers are homed as well. A compact arrangement of hardware minimises cablelengths and permits to have all electronics be grounded in the single point at the GDT port flange.For the described tomography diagnostic, we used the BINP made synchronous multi-channel ADCsystem with the sampling frequency of 50 MSample/s and 12 bit vertical resolution. The recordersystem has the System-on-Chip controller with the integrated Ethernet onboard and collected datais available on the remote server via the dedicated high-speed transfer protocol over TCP. In allmeasurements, the data acquisition system was delivering the actual time resolution of 1 𝜇𝑠 with– 3 –he oversampling of 50 samples per data point. Such a provision is effective for smoothing outshot noise and APD excess noise at the price of bigger data rate through the connection line. Infuture ADC designs, an onboard Field Programmable Gate Array (FPGA) will be introduced foronline data processing and reduction. Table 1 summarises the main parameters of the tomographydiagnostic on GDT. Table 1 : Main parameters of the optical tomography diagnostic.
Viewing geometry
Inteference filters Centre 656.2 nm, FWHM 1 nm (1 filter for 3 LOS)Optical lens Single lens (cid:31)
Signal registration system
Sensor APD Hamamatsu S12053-10 (cid:31) ÷ (cid:27) · 𝑉 / 𝐴 Amplifier bandwidth 0...5 MHzADC sampling rate 50 MSample/sADC vertical resolution 12 bitSNR 85 ÷ 𝜇𝑠 Measurement of absolute intensity.
With the absolute calibration made, each LOS deliversthe optical power in Watts or number of collected photons per second per unity of volume. Theultimate physical task is to recover the local density of atomic hydrogen and deuterium fractions.This task would require a collisional-radiative model with a number of inputs. First of all, the data onelectron temperature and density is necessary. The plasma absorber has a set of probes acquiring thetotal particle flux, ion current, incident energy and electron temperature. Upon the commissioningof these probes distributed across the entire absorber surface, arrays of parameters will be enabled formodelling of particle interactions in the sheath and expander volume. The theoretical model itselfis under development as well. Not having a comprehensive description of the plasma equilibrium,one can derive a simple estimation of the excited state density 𝑛 ∗ = 𝜖 𝜏 𝑟 𝑎𝑑 · 𝑘 − , where 𝑛 ∗ is thedensity of hydrogen or deuterium atoms in the 𝑛 = 𝜖 is the calculated local emissivity( 𝑐𝑚 − 𝑠 − ), 𝜏 𝑟 𝑎𝑑 is the radiative decay time of the 𝑛 = 𝑘 − is the branching ratio forH- 𝛼 optical transition.Figures 3a and 3b show typical acquired signals of intensity integrated along the LOS, nor-malised on the observation solid angle and the light collection volume. Most plasma confinementregimes are accompanied with intensity oscillations visible in Figures 3a and 3b. Oscillations aremore prominent in edge plasmas. First attempt of the time-domain and space-domain analysis ofoscillations is discussed in the Section 5. Note that the detector noise is approximately two ordersof magnitude smaller than small-scale fluctuations in Figure 3b.– 4 –
400 5100 6800 8500 10200 11900 136000.00E+0008.90E+0101.78E+0112.67E+0113.56E+0114.45E+0115.34E+011 I n t en s i t y ( / s / c m ^ ) Time (mks)
LOS9 LOS21 a) (a) Signals from LOS-9 (bundle-1 central) andLOS-21 (bundle-1 edge) in GDT shot 49617 il-lustrating jumps and oscillations of intensity. I n t en s i t y ( / s / c m ^ ) Time (mks)
LOS9 LOS21 b) (b) Signal of LOS-21 scaled (boxed piece inFigure a). Figure 3 : Examples of signals of intensity integrated along LOS.
Given pattern of LOS provides insufficient data and so the geometry matrix connecting the unknownemissivity distribution with the measured one, is underdetermined in our case. Generally speaking,the mathematical problem can be qualified as ill-posed. Reconstruction techniques operating withthe Fourier transform and matrix inversion methods [18–24], face difficulties. For such underde-termined systems, regularisation or iterative fitting methods can be used [25, 26]. For our purpose,we have employed the iterative algorithm of maximum likelihood with mathematical expectationmaximisation (ML-EM) [21, 22, 27, 28]. This algebraic method exhibits great advantages of goodhandling of sparse sampling, cone or fan beams and a limited viewing angle [27, 28]. No symmetryassumptions involved in the scheme, which is mandatory. However, this approach is a relativelydemanding to computational resources.The iterative sequence of the objective function maximisation is performed via the equation 𝜖 ( 𝑛 + ) 𝑖 = 𝜖 ( 𝑛 ) 𝑖 · (cid:205) 𝑘 𝑊 𝑖𝑘 · ∑︁ 𝑘 𝑊 𝑖𝑘 𝐽 𝑘 (cid:205) 𝑙 𝑊 𝑙𝑘 𝜖 ( 𝑛 ) 𝑙 , (3.1)where 𝜖 ( 𝑛 ) 𝑖 is the emissivity in the grid cell- 𝑖 on the iteration step 𝑛 , 𝐽 𝑘 is the line integrated intensityof the LOS- 𝑘 , 𝑊 𝑖 𝑗 is the weight matrix defined by the geometry only. The computation starts fromthe flat distribution as an initial guess. On every step, (1) the forward projection is performed fromthe estimate as 𝐽 𝑠𝑖𝑚 ( 𝑛 ) 𝑖 = (cid:205) 𝑘 𝑊 𝑘𝑖 𝜖 ( 𝑛 ) 𝑘 , then (2) it is compared to the measured one via the ratio 𝑅 𝑖 = 𝐽 𝑠𝑖𝑚 ( 𝑛 ) 𝑖 / 𝐽 𝑖 and then (3) the previous estimate is improved using (3.1). The sequence iteratesupon convergence. After some optimisation, the square XY grid of 20 ×
20 cells was adapted,where
𝑋, 𝑌 ∈ [− , ] mm. The axis direction is indicated in Figure 2. The computation box isprojected to the GDT central plane radius of 𝑟 ( 𝑚𝑎𝑥 ) ≈ . (a) Example of synthetic Gaussian profile usedfor validation, centre: 𝑋 = 𝑌 =
150 mm. (b) Backward reconstruction of synthetic profilein Figure a).
Figure 4 : Example of validation of tomography reconstruction algorithm on synthetic profiles.similar results. A trapezoid distortion is present in the computed image as one would expectfrom the current limited angle optical registration system. We believe reconstruction artefacts willbe significantly depressed in the planned advanced setup with four LOS beams and more evenangular separation. Considering measurements taken in GDT plasmas so far, a certain cautionmust be adhered to quantitative conclusions regarding spatial distributions of the local emissivity.Nevertheless, reconstructed profiles are useful to observe their behaviour during the shot.
Figure 5 demonstrates the series of reconstructed emissivity images in the GDT shot 46617 coveringthe plasma heating phase and decay. Each frame’s duration is 𝜏 𝑒𝑥 𝑝 = 𝜇𝑠 (single time point) withoutaveraging, the separation is 740 𝜇𝑠 . The time stamp indicate the moment after the plasma startup.The emissivity is shown in a colour pattern, which is scaled to the maximum in every image. Thiswould simplify tracing profile evolution. The absolute intensity ramps up during first six framesand then ramps down as it seen in Figure 6, where the total number of emitted D- 𝛼 line photons persecond at corresponding time moments is shown. Thus, the brightest frame No. 6 has ≈
100 timesmore light than the first frame. In this confinement regime, deuterium plasma is created by thearc-discharge source located in the opposite (right) expander, see Figure 1. Eight 25 keV deuteriumbeams fire at 3.5 ms with the injection pulse duration of 5 ms. The D- 𝛼 emissivity distributionremains sharp and relatively symmetric during first 4.4 ms after startup. Afterwards, the profilebroads with a more evident asymmetry and an increasing shift to the left. Basically, this effect isconsistent with the expander gas puff in Figure 2. After the heating beam pulse is finished (frameNo. 8 at 𝑡 = .
88 ms and further), the emissivity profile evolves to a more compact shape with agradually decreasing X-offset. – 6 – igure 5 : D- 𝛼 emissivity profile dynamics in GDT shot 46617. Intensity I n t en s i t y ( / s ) Time (ms)
Figure 6 : Dynamics of total D- 𝛼 intensity in GDT shot 46617.Another set of reconstructed emissivity images in Figure 7 taken in the GDT shot 46612,exhibits an example of fast dynamics associated with the MHD plasma instability during the neutralbeams injection. Images are plotted with the time step of 120 𝜇𝑠 at the same intensity scale, whichis shown in Figure 7. – 7 – igure 7 : Fast dynamics of D- 𝛼 emissivity profile during MHD event in GDT shot 46612. Evolution of plasma flow in the boundary region of the absorber indicate the presence of fluctuations.They appear as on oscillating signal component in Langmuir probes data, magnetic coils andmeasurements of line emission intensity as well. Typical edge LOS signals (see Figures 3a and 3b)give evidence of the plasma turbulence that is probably expressed in fluctuations of electron and iondensity. Some of transient events observed by the optical diagnostic, are clearly connected to lowmodes of MHD instability with azimuthal wavenumbers 𝑚 = ÷ 𝛼 emissivity reaches ∼ 𝛼 line intensity correlation measurements in the GDT expanderplasma not delving into the underlying physics.A similarity of two signals in time domain is defined by the cross-correlation function 𝜌 𝑥𝑦 ( 𝑡 ) = ∫ ∞−∞ 𝑠 ∗ 𝑥 ( 𝜏 ) 𝑠 𝑦 ( 𝑡 + 𝜏 ) 𝑑𝜏, where 𝑠 𝑥 ( 𝑡 ) , 𝑠 𝑦 ( 𝑡 ) are time traces (complex conjugate makes no difference in our case of real-valueddata). Figure 8 illustrates the example of 2-d correlation function 𝜌 ( 𝐿𝑂𝑆 − ) ( 𝑡, 𝑦 ) between the LOS-1 and the full set of LOS, 𝑦 = ÷
42. Two time scales are apparent in this periodic correlationfunction. The bigger frequency of 𝑓 𝑀 𝐻 𝐷 (cid:27)
14 kHz is associated with the MHD interchange mode 𝑚 =
1, the smaller one of 𝑓 𝑟𝑜𝑡 ≈ 𝑃 𝑥𝑦 ( 𝑓 ) = F ( 𝑠 𝑦 )F ∗ ( 𝑠 𝑥 ) , where F ( 𝑠 ) denotes the signalFourier transform. The function of coherence 𝛾 𝑥𝑦 ( 𝑓 ) = | 𝑃 𝑥𝑦 ( 𝑓 )| 𝑃 𝑥𝑥 ( 𝑓 ) 𝑃 𝑦𝑦 ( 𝑓 ) – 8 – igure 8 : Correlation between LOS-1 and other LOS in GDT shot 46933.estimates a stability of the cross-phase between two signals in time and space for the given frequency.Figure 9a shows the autopower spectrum calculated by the signals in LOS-10 and LOS-33. Compar- (a) Autopower spectrum of signals LOS-10(chord radius 64 mm) and LOS-33 (chord radius495 mm). (b) Cross-power spectrum of signals LOS-7 andLOS-21 (chord radii 256 and 592 mm), LOS-31and LOS-32 (chord radii 430 and 465 mm). Figure 9 : Power spectrum of turbulence in shot 46933.ing the two plots, one may point out a remarkably larger fluctuation level on the plasma peripherythan in the core (LOS-33 has the radius of 495 mm which projects to the limiter radius of 150 mm inthe central plane coordinates – the plasma boundary). The whole fluctuation spectrum spans overthe range 1 ÷
100 kHz or even further with the prominent peak at the frequency of (cid:27)
14 kHz, whichis linked to large-scale MHD instability modes. Same comparison between two curves in Figure 9bqualitatively demonstrates an observable degree of correlation in two neighbouring viewing chordsat the plasma edge: LOS-31 and 32 with the radii of 430 mm and 465 mm over the spectral rangeof approximately 5 ÷
100 kHz (red curve). A relative drop in the blue curve in Figure 9b witnessesthat such correlations vanish between intermediate radii (LOS-7, 256 mm) and the edge (LOS-21,– 9 –92 mm). To highlight the broadband frequency spectrum of the plasma turbulence, Figures 10a (a) Coherence between four pairs of LOS. (b) Cross-phase between four pairs of LOS.
Figure 10 : Illustration of spatial coherence of line-integrated intensity in different observationchords.and 10b are provided with the linear axis scale. Coherency and cross-phase of four LOS pairs areshown: LOS-38 and LOS-39 ( 𝑟 =
630 mm, 𝑟 =
659 mm – edge); LOS-3 and LOS-4 ( 𝑟 = . 𝑟 = . 𝑟 =
126 mm, 𝑟 =
64 mm – core); LOS-10 andLOS-22 ( 𝑟 =
64 mm, 𝑟 = . The described optical tomography diagnostic is remaining at the commissioning stage at GDT. Arobust modular design of the optical registration system and signal acquisition electronics allowsfor a gradual build-up of channels, while the system is already capable of delivering the valuablephysical data. The nearest future objective is to introduce three more LOS beams similar to theinstalled bundle-1 (see Figure 2). The diagnostic is routinely working in experiments for the studyof axial particle and energy transport in the axially symmetric gas dynamic trap. A part of this work– 10 –ackage, is examination of a massive gas injection in the expander and its impact on the centralcell electron temperature and plasma MHD stability. The preliminary results reported in this paper,encourage to expand the task list with the study of the discovered broadband plasma turbulence.
Acknowledgments
This work is supported by the Russian Science Foundation, project No. 18-72-10084 issued on31.07.2018.
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