Deep learning approaches to recover the plasma current density profile from the safety factor based on Grad–Shafranov solutions across multiple tokamaks

Many magnetohydrodynamic stability analyses require generation of a set of equilibria with a fixed safety factor q-profile while varying other plasma parameters.A neural network(NN)-based approach is investigated that facilitates such a process.Both multilayer perceptron(MLP)-based NN and convolutional neural network(CNN)models are trained to map the q-profile to the plasma current density J-profile,and vice versa,while satisfying the Grad–Shafranov radial force balance constraint.When the initial target models are trained,using a database of semianalytically constructed numerical equilibria,an initial CNN with one convolutional layer is found to perform better than an initial MLP model.In particular,a trained initial CNN model can also predict the q-or J-profile for experimental tokamak equilibria.The performance of both initial target models is further improved by fine-tuning the training database,i.e.by adding realistic experimental equilibria with Gaussian noise.The fine-tuned target models,referred to as fine-tuned MLP and fine-tuned CNN,well reproduce the target q-or J-profile across multiple tokamak devices.As an important application,these NN-based equilibrium profile convertors can be utilized to provide a good initial guess for iterative equilibrium solvers,where the desired input quantity is the safety factor instead of the plasma current density.

Reconstruction of the Density Profile for the EAST Tokamak Based on Polarimeter/Interferometer and Microwave Reflectometer Systems

A plasma density profile reconstruction procedure based on the Park matrix method has been developed for both circular and elongated plasma configuration on the Experimental Advanced Superconducting Tokamak（EAST）.This method incorporates the line integrated electron density measured by the HCN interferometer and polarimeter/interferometer（POINT） system,the equilibrium fit（EFIT） based on magnetic measurements and the edge electron density profile provided by the microwave reflectometer.It is shown that when the magnetic flux surfaces are slightly corrected,the fitting error is less than 5% in comparison with the measurement data.

Lunar Subsurface Mineralogy and Density Profile Modelling based on Moon Mineralogy Mapper Observation

The methods of deriving FeO and TiO_(2)contents from the Clementine spacecraft data were discussed,and an approach was developed to derive the content from the measurements using the Moon Mineralogy Mapper(M3)instrument on Chandrayaan-1.The density of lunar bedrock was then modeled on the basis of the derived FeO and TiO_(2)abundances.The FeO and TiO_(2)abundances derived from the M^(3)data were compared with the previous results of the Clementine data and were in good agreement.The FeO abundance data also agreed well with the Lunar Prospector data,which were used as an independent source.The previous Clementine and newly M3 derived abundances were compared with the laboratory measured FeO and TiO2 contents in the Apollo and Luna returned samples.The Clementine derived FeO content was systematically 1%–2%lower than the laboratory measurements in all the returned samples.The M^(3)derived content agreed well with the returned Apollo samples and was within±2.8%of the laboratory measurements.The Clementine derived TiO2 abundance was systematically 0.1%–4%higher than the laboratory measurements of the returned samples.The M3 derived TiO_(2)agreed well(±0.6%)with the laboratory measurements of the returned samples,except for samples with high TiO2 content.However,these results should be carefully interpreted because the error range requires verification.No error analysis was provided with the previous Clementine derived contents.

Preliminary Study of the Magnetic Perturbation Effects on the Edge Density Profiles and Fluctuations Using Reflectometers on EAST

The resonant magnetic perturbation （RMP） coils have been successfully designed and installed on the Experimental Advanced Superconducting Tokamak （EAST）. Using the reflectometer systems, the density profile and the density fluctuations during magnetic perturbations （MPs） phase have been investigated. During the experiments, two different cases are studied separately： steady MPs and rotating MPs. In both cases, a strongly density pump-out has been observed. In the steady MPs cases, an enhancement of the low frequency （〈60 kHz） density fluctuations in H-mode phase has been observed. The plasma density boundary out-shifts 5~ caused by the MPs. The pedestal density gradient is reduced by 50%, while the radial location nearly stays unchanged. In the rotating MPs, the line-averaged density, the D~ emission at the divertor region and the spectrum of the density fluctuations are modulated. The results suggest that the low frequency （〈60 kHz） density fluctuations may contribute to the strong density pump-out.

Microwave Reflectometry for Plasma Density Profile Measurements on HL-2A Tokamak

A modulated microwave reflectometry has been successfully developed on HL-2A, which can be used to measure the plasma density profile with time-delay method. This microwave reflectometry has two frequency ranges （26.5 to 40 GHz and 40 to 60 GHz） and it is suitable for measuring the plasma density ranging from 0.8×10^13 cm^-3 to 4.5×10^13 cm^-3. The temporal resolution is i ms and the spatial resolution is about 1 cm. This paper will present the basic principle of the microwave reflectometry, parameters calibration of the equipment and the experimental results on HL-2A tokamak.

Reconstruction of hollow areas in density profiles from frequency swept reflectometry

The standard density profile reconstruction techniques are based on the WKB approximation of the probing wave’s phase,making them unable to properly reconstruct blind areas in the cut-off frequency profile.The reconstruction suffers a significant immediate error that is not rapidly damped.It is demonstrated that even though no reflections occur inside the hollow region causing the blind area,the higher probing frequencies that propagate through it carry information that can be used to estimate its properties.The usually ignored full-wave effects were investigated with the use of full-wave simulations in 1 D,with special attention paid to the frequency band where they are dominant.A database of perturbation signals was simulated onfive-dimensions of parameters and an application of the database inversion was demonstrated for a magnetic island in a Tore Supra discharge.The new adapted reconstruction scheme improved the description of the density profile inside the hollow region and also along 10 cm after it.

Measurement of Density Profile with Step-Swept Microwave Reflectometry

A one-channel microwave reflectometer is used to measure the electron densityprofile in a low-density plasma experiment (n_e < 0.27 x 10^(19) m^(-3)) sustained by 2.45 GHzlower hybrid current drive (LHCD) on TRIAM-1M. In order to remove the effect of phase runawayphenomena, a step-like frequency-sweeping way is used and a special phase analysis technique isintroduced. The density profile is reconstructed in TRIAM-1M with the swept frequency ranged from 6GHz to 15 GHz. The corresponding cutoff density is from (0.045 ～ 0.28) x 10^(19) m^(-3) in theordinary polarization mode. The results are in good agreement with the measurements from amulti-channel 2 mm-wavelength interferometer.

SEGMENT DENSITY PROFILES OF COMPACT POLYMER CHAINS CONFINED BETWEEN TWO PARALLEL PLANE WALLS

We use the pruned-enriched Rosenbluth method to investigate systematically the segment density profiles of compact polymer chains confined between two parallel plane walls. The non-adsorption case of adsorption interaction energy ε = 0 and the weak adsorption case of ε= -1 are considered for the compact polymer chains with different chain lengths N and different separation distances between two walls D. Several special entropy effects on the confined compact polymer chains, such as a damped oscillation in the segment density profile for the large separation distance D, are observed and discussed for different separation distances D in the non-adsorption case. In the weak adsorption case, investigations on the segment density profiles indicate that the competition between the entropy and adsorption effects results in an obvious depletion layer. Moreover, the scaling laws of the damped oscillation period Td and the depletion layer width Ld are obtained for the confined compact chains. Most of these results are obtained for the first time so far as we know, which are expected to understand the properties of the confined compact polymer chains more completely.

Effects of Plasma Density Profile on Resistive Wall Mode Stability

Linear and nonlinear evolutions of the resistive wall mode(RWM) were numerically carried out with different plasma density profiles.Both stabilizing and destabilizing effects were observed.The plasma density shear had a stabilizing effect on the RWM,and the stabilizing effect was better as the plasma density shear rate increased.In the uniform density plasma,the effects of flowshear on the RWMstability were stronger than those for non-uniform density plasma.For lower flowshear,the effects of the plasma density shear rate on the RWMwere more obvious.In the nonlinear phase,the repulsive force associated with the piling up magnetic flux near the resistive wall prevented further growth of perturbed magnetic energy,and the RWMwas saturated.The saturation levels were almost independent of the density profiles.

Flexible pavement longitudinal joint quality evaluation using non-destructive testing

Longitudinal joint construction quality is critical to the life of flexible pavements.Maintaining deteriorated longitudinal joints has become a challenge for many highway agencies.Improving the joint's quality through better compaction during construction can help achieve flexible pavements with longer service lives and less maintenance.Current quality control(QC)and quality assurance(QA)plans provide limited coverage.Consequently,the risk of missing areas with poor joint compaction is significant.A density profiling system(DPS)is a non-destructive alternative to conventional destructive evaluation methods.It can provide quick and continuous real-time coverage of the compaction during construction in dielectrics.The paper presents several case studies comparing various types of longitudinal joints and demonstrating the use of DPS to evaluate the joint's compaction quality.The paper shows that dielectric measurements can provide valuable insight into the ability of various construction techniques to achieve adequate levels of compaction at the longitudinal joint.The paper proposes a dielectric-based longitudinal joint quality index(LJQI)to evaluate the relative compaction of the joint during construction.It also shows that adopting DPS for assessing the compaction of longitudinal joints can minimize the risk of agencies accepting poorly constructed joints,identify locations of poor quality during construction,and achieve better-performing flexible pavements.

Effects of donor density and temperature on electron systems in AlGaN/AlN/GaN and AlGaN/GaN structures

It was reported by Shen et al that the two-dimensional electron gas （2DEG） in an AlGaN/AlN/GaN structure showed high density and improved mobility compared with an AlGaN/GaN structure, but the potential of the AlGaN/AlN/GaN structure needs further exploration. By the self-consistent solving of one-dimensional Schroedinger- Poisson equations, theoretical investigation is carried out about the effects of donor density （0-1×10^19 cm^-3） and temperature （50-500 K） on the electron systems in the AlGaN/AlN/GaN and AlGaN/GaN structures. It is found that in the former structure, since the effective △Ec is larger, the efficiency with which the 2DEG absorbs the electrons originating from donor ionization is higher, the resistance to parallel conduction is stronger, and the deterioration of 2DEG mobility is slower as the donor density rises. When temperature rises, the three-dimensional properties of the whole electron system become prominent for both of the structures, but the stability of 2DEG is higher in the former structure, which is also ascribed to the larger effective △Ec. The Capacitance-Voltage （C - V） carrier density profiles at different temperatures are measured for two Schottky diodes on the considered heterostructure samples separately, showing obviously different 2DEG densities. And the temperature-dependent tendency of the experimental curves agrees well with our calculations.

Feasibility of applying the lower cut-off frequency for the density radial coverage extension in EAST reflectometry measurement

The extraordinary mode(X-mode)lower cut-off frequency is proposed for use in the reflectometry diagnostic on ITER for the electron density profile measurement,which is a trade-off between extreme plasma parameters and the accessible probing frequency.In contemporary experiments,the lower cutoff frequency can be identified at the probing frequency below the electron cyclotron frequency(f_(ce)) under certain plasma conditions.We provide here,for the first time,the experimental validation of the use of the lower cut-off frequency for the density profiles via the reflectometry measurement on EAST.The corresponding group delay of the lower cut-off frequency evolves continuously with the upper one,revealing a reasonable radial coverage extension of reflectometry measurement toward the plasma core.It is concluded that the lower cut-off frequency can be used as a supplement to the upper one in the density profile inversion process,which is of particular interest in the high magnetic field and/or density discharge to extend the radial coverage of reflectometry measurement.

Measurements of plasma density profile evolutions with a channel-guided laser

The discharged capillary plasma channel has been extensively studied as a high-gradient particle acceleration and transmission medium.A novel measurement method of plasma channel density profiles has been employed,where the role of plasma channels guiding the advantages of lasers has shown strong appeal.Here,we have studied the high-order transverse plasma density profile distribution using a channel-guided laser,and made detailed measurements of its evolution under various parameters.The paraxial wave equation in a plasma channel with high-order density profile components is analyzed,and the approximate propagation process based on the Gaussian profile laser is obtained on this basis,which agrees well with the simulation under phase conditions.In the experiments,by measuring the integrated transverse laser intensities at the outlet of the channels,the radial quartic density profiles of the plasma channels have been obtained.By precisely synchronizing the detection laser pulses and the plasma channels at various moments,the reconstructed density profile shows an evolution from the radial quartic profile to the quasi-parabolic profile,and the high-order component is indicated as an exponential decline tendency over time.Factors affecting the evolution rate were investigated by varying the incentive source and capillary parameters.It can be found that the discharge voltages and currents are positive factors quickening the evolution,while the electron-ion heating,capillary radii and pressures are negative ones.One plausible explanation is that quartic profile contributions may be linked to plasma heating.This work helps one to understand the mechanisms of the formation,the evolutions of the guiding channel electron-density profiles and their dependences on the external controllable parameters.It provides support and reflection for physical research on discharged capillary plasma and optimizing plasma channels in various applications.

Numerical simulation of ultrashort-pulse reflectometry(USPR)on EAST

The microwave reflectometer is a popular non-intrusive plasma density diagnostic instrument on tokamaks that provides centimeter and millisecond level resolution.The ultrashort-pulse reflectometer(USPR)achieves plasma density measurement by emitting a chirped wave containing a broadband signal and measuring the time of flight from different frequency components.A USPR system is currently being built on EAST(Experimental Advanced Superconducting Tokamak)to meet the needs of diagnostic of the pedestal density evolution,such as high-frequency small edge-localized modes.In order to predict the density reconstruction of the EAST USPR system,this work presents a numerical simulation study of the beam propagation of the chirped wave of extraordinary waves(X-mode)in the plasma based on Python.The electron density profile has been successfully reconstructed by the reflection signal interpretation.The small gap between the right-hand cut-off layer and the electron cyclotron resonance layer,due to the low plasma density on the plasma edge,causes unexpected leakage from the transmitting microwave beam to the pedestal and the core region.This kind of‘tunneling’effect will cause the reflected signal to have energy loss in the low-frequency band.The study also discusses the influence of the poloidal magnetic field on the reflected signal.The spatial variation of the poloidal magnetic field will lead to the conversion between extraordinary(X)waves and ordinary(O)waves,which leads to energy loss in the reflected signals.The simulation results show that the‘tunneling’effect and the O-X mode conversion effect have little effect on the EAST USPR system.Therefore,the currently designed transmit power meets the working requirements.

Directional power absorption in helicon plasma sources excited by a half-helix antenna

This paper deals with the investigation of the power absorption in helicon plasma excited through a half-helix antenna driven at 13.56 MHz. The simulations were carried out by means of a code,HELIC. They were carried out by taking into account different inhomogeneous radial density profiles and for a wide range of plasma densities, from 10^（11） cm^（-3） to 10^（13） cm^（-3）. The magnetic field was 200, 400, 600 and 1000 G. A three-parameter function was used for generating various density profiles with different volume gradients, edge gradients and density widths. The density profile had a large effect on the efficient Trivelpiece–Gould（TG） and helicon mode excitation and antenna coupling to the plasma. The fraction of power deposition via the TG mode was extremely dependent on the plasma density near the plasma boundary. Interestingly, the obtained efficient parallel helicon wavelength was close to the anticipated value for Gaussian radial density profile.Power deposition was considerably asymmetric when the n/B_0 ratio was more than a specific value for a determined density width. The longitudinal power absorption was symmetric at approximately n_0 =10^（11） cm^（-3）, irrespective of the magnetic field supposed. The asymmetry became more pronounced when the plasma density was 10^（12） cm^（-3）. The ratio of density width to the magnetic field was an important parameter in the power coupling. At high magnetic fields, the maximum of the power absorption was reached at higher plasma density widths. There was at least one combination of the plasma density, magnetic field and density width for which the RF power deposition at both side of the tube reached its maximum value.

Impact of utility-scale solar photovoltaic array on the aeolian sediment transport in Hobq Desert, China

Deserts are ideal places to develop ground-mounted large-scale solar photovoltaic (PV) powerstation. Unfortunately, solar energy production, operation, and maintenance are affected bygeomorphological changes caused by surface erosion that may occur after the construction of the solar PVpower station. In order to avoid damage to a solar PV power station in sandy areas, it is necessary toinvestigate the characteristics of wind-sand movement under the interference of solar PV array. The studywas undertaken by measuring sediment transport of different wind directions above shifting dunes andthree observation sites around the PV panels in the Hobq Desert, China. The results showed that the twoparameterexponential function provides better fit for the measured flux density profiles to the near-surfaceof solar PV array. However, the saltation height of sand particles changes with the intersection anglebetween the solar PV array and wind direction exceed 45°. The sediment transport rate above shifting duneswas always the greatest, while that around the test PV panels varied accordingly to the wind direction.Moreover, the aeolian sediment transport on the solar PV array was significantly affected by wind direction.The value of sand inhibition rate ranged from 35.46% to 88.51% at different wind directions. When theintersection angle exceeds 45°, the mean value of sediment transport rate above the solar PV array reducesto 82.58% compared with the shifting dunes. The results of our study expand our understanding of theformation and evolution of aeolian geomorphology at the solar PV footprint. This will facilitate the designand control engineering plans for solar PV array in sandy areas that operate according to the wind regime.

Recent progress on the J-TEXT three-wave polarimeter-interferometer

The J-TEXT three-wave polarimeter-interferometer system(POLARIS),which measures timespace distribution of electron density and current density,has been optimized with both the optical system and the equilibrium reconstruction method.The phase resolution of a Faraday rotation angle has been improved from 0.1 to 0.06 degree in chords from–0.18 to 0.18 m(plasma minor radius),and the sawtooth oscillation behavior has been detected by Faraday rotation angle measurement.By combining the POLARIS measured data and the equilibrium and fitting code(EFIT),an upgraded equilibrium reconstruction method has been developed,which provides a more accurate temporal and spatial distribution of current density and electron density.By means of the optimized POLARIS and improved equilibrium reconstruction,variations of profiles with increasing density have been carried out,under both Ohmic and electron cyclotron resonance heating discharges.

Experimental Results of IBW Heating on the HT-7 Tokmak

Ion Bernstein waves （IBWs） have been proposed to be useful for heating and improving transport in tokamak plasmas. An Ion Bernstein wave heating experiment using different frequency （27 MHz and 30 MHz） was carried out on HT-7 superconducting tokamak in recent experiments. At a frequency of 30 MHz, ne peaked and Ha dropped have been pervasively observed, Tp was improved by a factor of 2 - 4, and Te increased by a factor of 1 - 1.5. An obvious confinement of particle was observed during the IBW pulse. At 27MHz, both global and localized electron heating were observed depending on the location of the ion resonant layer by changing Bt. Central electron heating effect was obtained in the global heating mode and electron temperature strongly increased near the 2 ΩD resonant layer for localized heating mode.

Application of the Magnetic Surface Based PARK-Matrix Method in the HCOOH Laser Interferometry System on HL-2A

A new electron density profile reconstruction procedure based on the PARK-matrix method has been firstly exploited for the multi-chord formic acid（HCOOH, λ=432.5 μm） laser interferometry system on the HL-2A tokamak. According to the geometric coordinates of the magnetic surfaces reconstructed by the CF（current fitting） code and the assumption that the electron density between two adjacent magnetic surfaces is a constant, the local electron density is calculated layer by layer, and the electron density profile n_e（Z） can be determined, as well as the density profile n_e（R）. The simulation result indicates that the error of the PARK-matrix method is acceptable for the four-chord HCOOH laser interferometer. In the applications, it shows that the reconstructed electron density profile agrees well with the microwave reflectometry measurement,and the sawtooth reversion radius is consistent with that deduced from the soft X-ray signals.Meanwhile, the electron density profiles with electron cyclotron resonance heating（ECRH） and supersonic molecular beam injection（SMBI） are also reconstructed and analyzed.

Searching the Parameters of Dark Matter Halos on the Basis of Dwarf Galaxies’ Dynamics

Article devoted to searching the parameters of dark matter halos on the base of dwarf galaxies’ dynamics (Messier 32 and Leo I). For doing this, we propose the new approach founded on construction the coupled elliptical trajectory for a probe body in the gravitational fields of Newtonian potential and potential of dark matter’s halo. This allows more accuracy estimate its central density for the Navarro-Frenk-White profile and free parameter for the Einasto profile . Our result is in good correlation with results of other authors that are got by different numerical methods.