Preparation of a beam emission spectroscopy diagnostic based on a Lyman-alpha line to diagnose core and edge-plasma density fluctuation on the HL-2A tokamak

In this article,the design of a Lyman-alpha-based beam emission spectroscopy(LAB)diagnostic on the HL-2A tokamak has been proposed for the first time.The purpose of this novel diagnostic is to measure density fluctuations of tokamak plasma.The light-collection system of LAB,which consists of the first mirror and two groups of coaxial double-mirror telescopes,can realize a twosegmented viewing field ofρ=0–0.2 andρ=0.75–1,which is optimized to measure plasma density fluctuation,not only in the edge transport barrier region but also in the internal transport barrier region,to investigate the underlying physics of turbulence in tokamaks.Spectrometers are developed to separate out the Doppler-shifted target line(122.03 and 122.17 nm)from the background Lyman-alpha line(121.53 nm).Here,30 Core-LAB channels and 30 Edge-LAB channels are under development on the HL-2A tokamak.It has high radial spatial resolutions of about 2.7 mm and 3.3 mm for the core and edge channels,respectively.Taking the high light intensity of this Lyman-alpha line into account,temporal resolution of 200 k Hz can be ensured by broad bandwidth amplifiers.This high spatio-temporal resolution makes LAB a potential keen tool to experimentally investigate tokamak plasma physics.

High Wavenumber Density Fluctuation Measurement in the HT-7 Tokamak

A three channel CO2 laser forward scattering diagnostic system was set up to study the core plasma density fluctuation in the HT-7 tokamak. The range of the wavenumber measurement in the poloidal direction was kθ= 12 cm^-1 to 34 cm^-1 and the wavenumber resolution was △k = 2.5 cm^-1. The wavenumber spectrum, the coexisting modes and the micro-instability eruption in experiments are presented.

Plasma edge density fluctuation measurements via lithium beam emission spectroscopy on EAST

Accurate and stable measurements of edge density fluctuation with high spatio-temporal resolution have been achieved by the lithium beam emission spectroscopy(Li-BES)diagnostic on experimental and advanced superconducting tokamak(EAST).The new narrower band interference filter exhibits good ability to suppress background emission signal even under strong lithium coating of the tokamak.The raw data measured by channels at different spatial locations in avalanche photo diode camera with high chopping frequency show good consistency.Based on the detected experimental data,detailed information of density profile and fluctuation structures is obtained.A clear edge coherent mode in the auto-power spectrum is observed in pedestal region,which is regarded as the dominant factor for the strong pedestal density fluctuation amplitude.The cross-power spectrum analysis further excludes the additional effects of common-mode noises and non-local perturbation,demonstrating that the detected fluctuation is only caused by local density fluctuation.The normalized radial and poloidal wave-number spectra can specify the quantitative changes of radial wavenumber(k_(r))and poloidal wavenumber(k_(θ)) during the pedestal density fluctuation phase.This new Li-BES system,which can provide more accurate experimental data,allows further studies of edge density fluctuation and complex transport process on EAST.

Two Dimensional Density FlUCtuation Measurements During the Non-Inductive Current Ramp-up Phase in the Compact Plasma Wall Interaction Experimental Device CPD

Two-dimensional structure of density fluctuations is examined during the current jump phase, indicating a change from the open magnetic fields to the closed ones. During the smooth current ramp-up phase the two-dimensional contour of the LiI intensity shows vertically alignment, consistent with the magnetic surfaces. At the inflection point in Ip ramp-up the LiI intensity contour becomes flat in the observation regime and then suddenly a steep gradient and higher intensity regime are formed in the vertical direction. This higher intensity corresponds to a burst of LiI waveform. According to these changes in the contour, it is found that, within ~1 ms around the burst of LiI, a low frequency coherent wave with a long wavelength rapidly grows. The relations with other signals （magnetic flux and microwave stray power） are discussed with respect to the topological change in the magnetic configuration and mode conversion of the incident electromagnetic waves.

Properties of Density Fluctuations Induced by Geodesic Acoustic Mode in the Edge of HT-7 Tokamak

Properties of the geodesic acoustic mode （GAM） density fluctuations are studied using two toroidally separated Langnmir triple-probe arrays on the top of HT-7 tokamak. The GAM scenario is identified in the potential fluctuations with the toroidally symmetric structure （n =0） and satisfying the temperature scaling of GAM mode frequency. Some theoretical predictions about the mode features of GAM density fluctuations are verified in our experiments： the toroidal mode number of GAM density fluctuations is n = 0; its amplitude is consistent with the theoretical prediction in a factor of 2; the density and potential fluctuations of GAM is in anti-phase at the top of plasma cross-section. Strong nonlinear interactions are found between GAM density fluctuations and ambient turbulence （AT）. The results support the conclusions that the envelope modulation of potential fluctuations is dominantly caused by the direct regulation of GAM in the generation processing, and the envelope modulation of density fluctuation is due to the GAM shear effect.

Density fluctuation of the ^3He reaction-diffusion model in nonextensive statistical mechanics

In this paper the time-space correlation of density fluctuation of the 3He reaction-diffusion model is investigated where the equilibrium distribution is described by the generalized Maxwell Boltzmann distribution in the framework of Tsallis statistics. By using the density operator technique, the nonextensive pressure effect is introduced into the master equation and thus the generalized master equation is derived for the nonextensive system. This paper uses the ^3He reaction diffusion model to analyse the effect of nonextensive pressure on the fluctuation and finds that the nonextensive parameter q plays a very important role in determining the characteristics of the fluctuation waves.

Vortical structures and density fluctuations analysis of supersonic forward-facing step controlled by self-sustaining dual synthetic jets

Shock wave/boundary layer interaction(SWBLI)is still one of the unresolved bottlenecks that restrict the development of more advanced flight vehicles.Supersonic forward-facing step(FFS),an extreme case of compression ramp,often occurs severe SWBLIs with a large separation bubble.In this paper,experimental investigations on vortical structures and density fluctuations characteristics of supersonic FFS controlled by self-sustaining dual synthetic jets(SDSJ)are carried out in a Mach number 2.95 wind tunnel.High spatial–temporal resolution flowfield images of FFS without/with active flow control are captured by adopting nano-particle-based planar laser scattering technique.The control effects of the distance between the actuator and the step are mainly compared.The paper finds that the SDSJ can effectively change the feature of flowfield,eliminate the separation shock and the reattachment shock,compel the original shock induced by the step leading edge to distort and reduce its intensity finally.Density fluctuations analysis demonstrates that the whole flows seem to move upstream with the increase of distance(dS-J).Discrete Fourier transformation spectrums results reveal that the fluctuations are mainly located in the low-frequency region at first.High-frequency components and frequency bandwidth increase slightly after the SDSJ are applied.

Multi-resolution Analysis of Density Fluctuation of Coherent Structures About Supersonic Flow over VG

The density field around a vortex generator （VG） in supersonic flow is studied with a nanoparticle-based planar laser scattering （NPLS） method. Based on the calibration, i.e., the density distribution of the supersonic flow around a wedge, the density field of a supersonic VG is measured. According to movement characteristics of coherent structure in VG’s flow fields and the basic concepts of wavelet, the density fluctuating signals and multi-resolution characteristics of density field images are studied. The multi-resolution characteristics of density fluctuation can be analyzed with wavelet transformation of NPLS images. The wavelet approximate coefficients of density fluctuating signals exhibit their characteristics at different scales, and the corresponding detail coefficients show the difference of diverse layer smooth approximation in some way. Based on 2D wavelet decomposition and reconstruction of density field images, the approximate and detail signals at different scales are studied, and the coherent structures at different scales are extracted and analyzed.

Density Profile and Fluctuation Measurements by Microwave Reflectometry on EAST

A microwave reflectometry system operating in the V-band frequency with extraor- dinary mode polarization has been developed on the EAST tokamak. The reflectometry system, using a voltage-controlled oscillator （VCO） source driven by an arbitrary waveform generator with high temporal resolution, can operate for the density profile measurement. The result of the bench test shows that the output frequency of the VCO has a linear dependence on time. The dispersion of reflectometry system is determined and reported in this paper. The evolution of a pedestal density profile during the L-H transition is observed by the reflectometry in H-mode discharges on EAST tokamak. A frequency synthesizer is used to replace the VCO as microwave source for density fluctuation measurements. The level of density fluctuation in the pedestal shows an abrupt decrease when the plasma enters into H-mode. A coherent mode with a frequency of about 100 kHz is observed and the mode frequency decreases gradually as the pedestal evolves.

Charge density fluctuation of low frequency in a dusty plasma

The charge density fluctuation of low frequency in a dusty plasma, which is derived from the longitudinal dielectric permittivity of the dusty plasma, has been studied by kinetic theory. The results show that the P value, which describes the relative charge density on the dust in the plasma, and the charging frequency of a dust particle Ωc, which describes the ratio of charge changing of the dust particles, determine the character of the charge density fluctuation of low frequency. For a dusty plasma of P<<1, when the charging frequency Ωc is much smaller than the dusty plasma frequency wd, there is a strong charge density fluctuation which is of character of dust acoustic eigen wave. For a dusty plasma of P>>1, when the frequency Ωc, is much larger than wd there are weaker fluctuations with a wide spectrum. The results have been applied to the ionosphere and the range of radius and density of dust particles is found, where a strong charge density fluctuation of low frequency should exist.

Progress of Lyman-alpha-based beam emission spectroscopy(Ly BES)diagnostic on the HL-2A tokamak

An edge Lyman-alpha-based beam emission spectroscopy(LyBES)diagnostic,using a heating NBI(neutral beam injection)system,is currently under development on the HL-2A tokamak.The 20-channel edge LyBES,which is intended to measure the density fluctuation in plasma edge(from R=1960 mm to R=2026 mm)with an improved spatial resolution of 3.3 mm,is a complement to the existing conventional beam emission spectroscopy(BES)diagnostic.In this article,we introduce the progress of LyBES diagnostic,including the collection optics,the monochromator,and the detector system.The reflectance of the collection mirrors is measured to be~82%at 122 nm,and the aberration geometrical radius of the collection optics is tested to be~150μm in the aimed area.The linear dispersion of the LyBES monochromator is designed to be~0.09 nm mm^(-1).The bandwidth of the detector system with the 5×10^(7)V A^(-1)preamplifier gain is measured to be~280 kHz,and the peak-to-peak noise of the detector system is tested to be~16 mV.The finalized design,components development and testing of the LyBES diagnostic have been completed at present,and an overall performance of the LyBES diagnostic is to be confirmed in the next HL-2A campaign.

Density enhancement mechanism of upwind schemes for low Mach number flows

Many all-speed Roe schemes have been proposed to improve performance in terms of low speeds. Among them, the F-Roe and T-D-Roe schemes have been found to get incorrect density fluctuation in low Mach flows, which is expected to be with the square of Mach number. Asymptotic analysis presents the mechanism of how the density fluctuation problem relates to the incorrect order of terms in the energy equation paU△U. It is known that changing the upwind scheme coefficients of the pressure-difference dissipation term DP and the velocity-difference dissipation term in the momentum equation DPU to the order of O （c- 1） and O（c0） can improve the level of pressure and velocity accuracy at low speeds. This paper shows that corresponding changes in energy equation can also improve the density accuracy in low speeds. We apply this modification to a recently proposed scheme, TV-MAS, to get a new scheme, TV-MAS2. Unsteady Gresho vortex flow, double shear-layer flow, low Mach number flows over the inviscid cylinder, and NACA0012 airfoil show that energy equation modification in these schemes can obtain the expected square Ma scaling of density fluctuations, which is in good agreement with corresponding asymptotic analysis. Therefore, this density correction is expected to be widely implemented into allspeed compressible flow solvers.

Experimental studies of cusp stabilization in Keda Mirror with AXisymmetricity(KMAX)

Stabilization of the axisymmetric magnetic mirror relies on the pressure-weighted magnetic field curvature.We report a new experiment by configuring a magnetic cusp structure to stabilize m=1 interchange mode in the KMAX tandem mirror.The cusp configuration is formed by reversing currents in the two side cell coils,and a stronger cusp can lead to a more stable plasma once the null point of the cusp is less than 35–40 cm away from the device axis.The density fluctuations measured by four axial Langmuir probes are mitigated by 70%–80%.The stabilization effect is consistent with the prediction of a theoretical calculation.

Recent Progress of the HL-2A Laser Interferometer

A new multi-channel far infrared （FIR） laser interferometer was built up and ap- plied to HL-2A. The unique feature of real-time heterodyne interferometer is the combination of high power radiation source （300 mW）, lower noise room temperature detector （noise tempera- ture below 6000 K） with good spatial resolution of 7 cm. Various parameters are optimized for maximum laser output power. Zero crossings of the signals are counted with field programmable gate array （FPGA） digital circuitry yielding the resolution of 1/1000 fringe. The newly measured results including density fluctuation are also presented.

CO_2 Laser Collective Thomson Scattering Diagnostics on the HT-7 Tokamak

A CW CO2 laser collective Thomson scattering diagnostics was developed to measure plasma density fluctuations on the HT-7 tokamak. The design and construction of CO2 laser scattering apparatus is described. The laser source is a continuous-wave CO2 laser with a cavity length of 1.9 m and a power output of about 10 W at 10.6 μm. The k-resolution of the system is △k ≈ 3.2 cm-1. The preliminary data from the diagnostic is presented.

Spontaneous current relaxation in NBI heated plasmas on EAST

We report on current profile evolution in EAST NBI driven plasmas where two neutral beams are injected,one during the current ramp phase and the second during flattop.At the end of the current ramp phase,it is found that a flat q profile with q0-1 is achieved with low magnetic shear in the core.It is observed that plasma current and density both relax much faster than resistive time,even in the absence of sawtooth activity when H-L transition occurs.Density fluctuations associated with magnetic perturbations（3/2） as a precursor to the H-L transition are observed.It is likely that these modes play a role in fast current transport.

Optical design of the Lyman alpha based beam emission spectroscopy (LAB) diagnostic on the HL-2A tokamak

In this article,we present the optical design of a novel diagnostic on the HL-2A tokamak,i.e.the 20-channel edge Lyman-alpha beam emission spectroscopy,which is a promising solution for edge density turbulence research on tokamaks,as it offers the possibility of density fluctuation measurement with a 3.3 mm spatial resolution while maintains a high temporal resolution of 1μs.The optical path,including the reflective collection optics,the high-dispersion spectrometer,and the linear detector array,is carefully optimized to obtain a good image quality and a high throughput.The maximum root mean square radius of the collection optics is 64μm.The detected photon flux is estimated to be about 1011 photons/s/channel.

Development of the HCN heterodyne collective scattering system on J-TEXT

A heterodyne collective scattering system has been designed and developed to investigate the turbulent transport of core plasma on J-TEXT.A dual-HCN laser which consists of two separately pumped HCN gas lasers at 337μm has been developed as the laser source of the scattering system.The intermediate frequency(IF)is~1 MHz when there is a 4μm cavity length difference and capable to maintain stability more than 5 h without manual operation.Detection channels at three different angles(2≤k_(⊥)≤12 cm^(-1))have been installed with Schottky barrier diode mixers of 893 GHz.The sampling frequency of the acquisition system is6 MHz to observe low-frequency density fluctuations.Initial experimental results have been detected and more results can be expected in future experiments.

Novel Implicit Lorentz Force-Type Magnetic Bearing for High-Precision Agile Maneuver of Magnetically Suspended Gyrowheel

The lorentz force-type magnetic bearing(LFTMB)with good linearity is suitable for the high-precision deflection control of the magnetically suspended gyrowheel(MSGW). Two kinds of novel implicit LFTMBs are proposed in allusion to the poor magnetic flux density uniformity of the existing explicit LFTMB. The improvement of uniformity is realized under the paramagnetic contribution of magnetic ring. Their structures are introduced,the mathematical models are established based on the equivalent magnetic circuit method and the magnetic fields are analyzed by the finite element method based on the design parameters. Simulation results indicate that the magnetic flux density uniformity of implicit LFTMBs is superior to the traditional explicit LFTMB. Furthermore,the implicit trapezoid LFTMB with double magnetic circuits is better than that of those with single magnetic circuit,in terms of the magnetic flux density uniformity and the magnetic flux density. The magnetic flux density of implicit trapezoid double magnetic circuits LFTMB is verified by the experiment. The error between the experimental results and the simulation results is within 5%,which shows that the implicit trapezoid double magnetic circuits LFTMB is promising to meet the high-precision agile maneuver requirement of the magnetically suspended gyrowheel.

From Allan Variance to Phase Noise:A New Conversion Approach

A new mathematical method is proposed to convert the oscillator instability parameters from Allan variance to Spectrum Density(SD)of random phase fluctuations,which is the inversion of the classic transformation formula from SD to Allan variance.Due to the fact that Allan variance does not always determine a unique SD function,power-law model of the SD of oscillator phase fluctuations is introduced to the translating algorithm and a constrained maximum likelihood solution is presented.Considering that the inversion is an ill-posed problem,a regularization method is brought forward in the process.Simulation results show that the converted SD of phase fluctuations from Allan variance parameters agrees well with the real SD function.Furthermore,the effects of the selected regularization factors and the input Allan variances are analyzed in detail.