## Vol. 66, No. 5 (2017)

##### 2017-03-05

###### GENERAL

## EDITOR'S SUGGESTION

2017, 66 (5): 050501.
doi: 10.7498/aps.66.050501

Abstract +

Random numbers are used to encrypt the information in the field of secure communications. According to one-time pad theory found by Shannon, the absolute security of the high-speed communication requires the ultrafast reliable random numbers to be generated in real-time.
Using complex algorithms can generate pseudorandom numbers, but they can be predicted due to their periodicity. Random numbers based on physical stochastic phenomena (such as electronic noise, frequency jitter of oscillator) can provide reliable random numbers. However, their generation rates are at a level of Mbit/s typically, limited by the bandwidth of traditional physical sources.
In recent years, high-speed physical random number generation based on chaotic laser has attracted much attention. Common methods of extracting random numbers are to sample and quantitate the chaotic signal in electronic domain with a 1-bit or multi-bit analog-to-digital converter (ADC) triggered by an RF clock and then post-process the original binary sequences into random numbers. However, the large jitter of the RF clock severely restricts the speed of ADC. Moreover, the existence of the subsequent post-processing process put a huge challenge to how the synchronization is kept among all the devices (e.g., XOR gates, memory buffers, parallel serial converters) by using an RF clock. Thus, to our knowledge, the fastest real-time speed of the reported physical random number generator is less than 5 Gbit/s.
In this paper, we propose a novel method of generating the real-time physical random numbers by utilizing chaotic laser pulses. Through sampling the chaotic laser in all-optical domain by using a mode-locked pulsed laser, chaotic laser pulse sequences can be obtained. Then, real-time physical random numbers are obtained directly by self-delay comparing the chaotic pulse sequences with no need of RF clock nor any post-processing.
Furthermore, a proof-of-principle experiment is carried out, in which an optical feedback chaotic semiconductor laser is employed as an entropy source. Experimental results show that the real-time random number sequences at rates of up to 7 Gbit/s can be achieved. The real-time speed is mainly limited by the bandwidth of the applied chaotic signal. If the chaotic laser with a higher bandwidth is adopted, the real-time generation rate can be further enhanced.

2017, 66 (5): 050201.
doi: 10.7498/aps.66.050201

Abstract +

In complex networks, the node importance evaluation is of great significance for studying the robustness of network. The existing methods of evaluating the node importance mainly focus on undirected and unweighted networks, which fail to reflect the real scenarios comprehensively and objectively. In this paper, according to the directed and weighted complex network model, by analyzing the local importance of the nodes and the dependencies among all the nodes in the whole network, a new method of evaluating the node importance based on a multiple influence matrix is proposed. Firstly, the method defines the concept of cross strength to characterize the local importance of the nodes. The index not only distinguishes between the in-strength and out-strength of the nodes, but also helps to discriminate the differences in importance among each with an in-degree of 0. In addition, to characterize the global importance of the nodes to be evaluated, we use the total important influence value of all the nodes exerted on the nodes, which makes up the deficiencies of the other evaluation methods which just depend on adjacent nodes. Emphatically, in the analysis of the influence ratio of source node on node to be evaluated, we not only take into account the distance factor between nodes, but also introduce the number of the shortest path factors. In order to make the evaluation algorithm more accurate, according to the number of the shortest paths, we present two perspectives to analyze how other factors affect the influence ratio. One is to evaluate how this source node exerts important influence on the other nodes to be evaluated. The other is to analyze how the other source nodes perform important influence on this node to be evaluated. In view of the above factors, three influence matrices are constructed, including the efficiency matrix, and the other two influence matrices from the perspectives of fixing source nodes and target nodes, respectively. Then, we use analytic hierarchy process to weight the three matrices, thereby obtaining the multiple influence matrix, which makes the global importance evaluation more comprehensive. Finally, the method is applied to typical directed weighted networks. It is found that compared with other methods, our method can effectively distinguish between nodes. Furthermore, we carry out simulation experiments of cascading failure on each method. The simulation results further verify the effectiveness of the proposed method.

2017, 66 (5): 050301.
doi: 10.7498/aps.66.050301

Abstract +

In the study of electromagnetic scattering of multi-target composite on and above the rough sea surface, the common algorithm such as the method of moment analyzes the relationship between the target and the rough sea surface point by point, so the common algorithm usually requires massive computation and a lot of time. In this paper, the rough sea surface is described by Pierson-Moscowitz (PM) spectrum and Monte Carlo method, and the composite electromagnetic scattering from multiple conductor flying targets above the rough sea surface is investigated by using the hybrid algorithm-the method of moment in the Kirchhoff approximation. The composite scattering region is divided into target region and rough sea surface region. The target region and the rough sea surface region are investigated by using the method of moment, and the Kirchhoff approximation, respectively. The formulas of the hybrid algorithm in different polarizations are derived in detail, and the scattering coefficients in different incident angles, target heights, target sizes, target distances and wind velocities are calculated in detail. The characteristics of the composite scattering coefficient from the multiple conductor flying target above the rough sea surface are also obtained. Results show that the hybrid algorithm, i. e., the combination of method of moment and the Kirchhoff approximation, can obtain higher accuracy, and reduce the computation time efficiently. The computation time used by the hybrid algorithm is 19% of that by using the method of moment. Moreover, the performance becomes more favorable with the increase of size of rough sea surface.

2017, 66 (5): 050502.
doi: 10.7498/aps.66.050502

Abstract +

Particle filer is apt to have particle impoverishment with unstable filtering precision, and a large number of granules are required to estimate the nonlinear system accurately, which reduces the comprehensive performance of the algorithm. To solve this problem, a new particle filter based on bat algorithm is presented in this paper, where particles are used to represent individual bat so as to imitate the search process of bats for preys. In traditional resampling process, particles are directly discarded, the improved algorithm adopts another approach and solves the problem of particle impoverishment. It combines the advantages of particle swarm optimization algorithm and harmonic algorithm perfectly. New particle filter has capacity of global and local search and is superior in computation accuracy and efficiency. By adjusting frequency, loudness, and impulse emissivity of particle swarm, the optimal particle at that time is followed by particle swarm to search in the solution space. The global search and local search can be switched dynamically to improve the overall quality of the particles swarm as well as the distribution rationality. In addition, the improved particle filter uses Lvy flight strategy to avoid being attracted by harmful local optimal solution, it expands the space of research and further promotes the optimization effect of particle distribution. Using the useful information about particle swarm, improved particle filter can make particles get rid of local optimum and reduce the waste of iterations in insignificant status change. Based on the number of valid particle samples, it can improve quality of particle samples by expanding their diversity. In information interaction mechanism of improved particle filter, the method in this paper sets scoreboard of particle target function to compare the value of particle target function at each iteration sub-moment with the value of target function on scoreboard to gain global optimum of all particles at current filtering moment. Taking information interaction between global optimum and particle swarm, the guiding function of global optimum is realized. The process of particle optimization is ended prematurely through setting a maximum iteration or termination threshold. There is a tendency for the whole particle swarm closing to high likehood area without global convergence so that the advantages of improved particle filter in accuracy and speed will not be damaged. In addition, convergence analysis and computational complexity analysis are given in this paper. Experiment indicates that this method can improve the particle diversity and prediction accuracy of particle filter, and meanwhile reduce the particle quantity obviously which is required by the state value prediction for nonlinear system.

###### ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

2017, 66 (5): 054102.
doi: 10.7498/aps.66.054102

Abstract +

Cirrus is an important regulator for the flow of radiant energy in the earth-atmosphere system through the processes of scattering and absorption of radiation. In order to satisfy the urgent requirement for accurate retrieval of cirrus microphysical properties, terahertz wave is expected to be the best waveband for inverting cirrus particle size and ice water path, with terahertz wavelengths on the order of the size of typical cirrus particles. There is an urgent need for establishing stable and accurate inversion method. A new retrieval method for particle size and ice water path is developed based on multiple lookup tables for spaceborne measurements of brightness temperature spectrum of 183 GHz, 325 GHz, 462 GHz, 664 GHz, and 874 GHz channels. Five parameters are derived to quantify the effects of particle size and ice water path on terahertz radiation spectrum due to the scattering of ice clouds, manifested by brightness temperature difference, brightness temperature difference slope, etc. To retrieve cirrus microphysical parameters, a weighted least square fit that matches the modeled parameters is used. The analysis of retrieval errors are conducted by a simulated data series and the results are compared with those retrieved by the other two methods, i. e., difference method and slope method. The results retrieved by the multiple lookup table method are much closer to the simulated data series than those from the other two methods. It is indicated that the method introduced here is a stable and valid method of inverting particles between 50 and 500 m and ice water path between 10 and 500 g/m2. Compared with the errors from the difference-featured method and slope-featured method, the retrieval errors are reduced by 68.78% and 60.28% for particle size, 78.17% and 49.01% for ice water path. The analyses of retrieval uncertainties show that, in general, uncertainties of particle size and ice water path vary with particle size and ice water path. The ice water path uncertainties mainly spread in a range of 0-15 g/m2. The particle size uncertainties fluctuate within a range of 0-20 m. In other words, for small particle size range, the uncertainties are 0-5 m for thick clouds and 5-20 m for thin clouds. However, for large particle size range, the uncertainties are 0-5 m for particles larger than 300 m and 5-15 m for those smaller than 300 m. The results will be helpful for further developing the terahertz wave remote sensing of cirrus microphysical parameter technology. Moreover, it is also an important reference to the improvement of cirrus retrieval accuracy.

2017, 66 (5): 054201.
doi: 10.7498/aps.66.054201

Abstract +

Traditional imaging spectropolarimetry generally requires slit, moving parts, electrically tunable devices, or the use of micropolarized arrays. Furthermore, the acquired raw data are a physical superposition of interferogram and image. Given their complicated structure, poor seismic capacity, low detection sensitivity, and heavy computations with approximation in spectral reconstruction, meeting the needs for applications in aviation, remote sensing, and field detection is difficult. To overcome these drawbacks, a new spectropolarimetric imaging technique based on static dual intensity-modulated Fourier transform is presented. The system consists of a front telescopic system, two phase retarders, a linear polarizer, a Wollaston prism, a Savart polariscope, a linear analyzer, a reimaging system, and a charge-coupled device (CCD) array detector. The incident light is modulated through a module of polarization spectrum modulation, which consists of the retarders and the polarizer. The Wollaston prism splits the modulated incident light into two equal intensities, orthogonally polarized components with a small divergent angle. After passing through the interference module, which is composed of the Savart polariscope and the analyzer, then the reimaging system, two full-polarization interferograms, which are the superposition of background images and interference fringes, are recorded simultaneously on a single CCD. The pure target image and the pure interference fringes can be simply achieved from the summation or the difference of the two interferograms. Spectral and complete polarization information can be acquired by using the Fourier transform of the pure interference fringes. The principle and the configuration of the system are described here in this paper. The reconstruction processes of the target image and the full Stokes polarization spectra are theoretically analyzed and mathematically simulated. The results show that the system can availably separate background image from interference fringes of the target, achieving high-precision spectral reconstruction and effective extraction of the complete polarization information. Compared with the features of existing instruments, one of the salient features of the described model is to use the dual-intensity modulation, which can avoid mutual interference between the image and the fringes from the hardware and is conducive to the extraction of pure interference fringes with high signal-tonoise ratio (SNR). With this feature, the inadequacies on traditional spectral reconstruction, such as large computation, heavy data processing, and low accuracy of acquired information, are overcome. Moreover, the entrance slit in the front telescopic system is removed, which greatly increases the transmittance and flux of the incident light and improves the SNR of the interferogram. The modified Savart polariscope is used in the interference module. Its transverse shearsplitting principle further enlarges the field of view and increases the spectral resolution of the straight fringes. Thus, this design has the advantages of good stability, high spectrum, high sensitivity, large SNR, high-precision information reconstruction, and low-complexity data processing, as well as simultaneous detection of image, spectrum, and complete polarization information. This work will provide an important theoretical basis and practical instruction for developing new spectropolarimetric imaging technique and its engineering applications.

2017, 66 (5): 054203.
doi: 10.7498/aps.66.054203

Abstract +

Zone plate coded imaging is an experimental technique for particle and strong X-ray imaging, which is widely applied to astronomy, nuclear medicine, and laser inertial confinement fusion researches. From conventional perspective, spatial resolution of zone plate depends on the encoding zone plate width of outermost ring r with a size greater than 1.22r. In X-ray region, however, the outermost ring width of Fresnel zone plate is limited by processing technology. Such a limitation makes it impossible to fabricate a sufficiently small zone plate, thus restricting the applications of Fresnel zone plate coded imaging. In this paper, we present a new reconstruction method of zone plate coded imaging by using a higher-order order Gabor zone plate. With the proposed method, higher spatial resolution can be achieved than with the regular methods, thus the spatial resolution is improved by 1/m times the width of outermost ring (where m is a positive integer). Consequently such a breakthrough goes beyond the limits of Rayleigh criterion in general.

2017, 66 (5): 054207.
doi: 10.7498/aps.66.054207

Abstract +

The target gas molecular absorption spectrum parameters especially line strengths are very important for measuring temperature and concentration with tunable diode laser absorption spectroscopy (TDLAS) technique. Usually, researchers use line strengths which come from spectrum database, like HITRAN and GEISA and HITEMP spectra database, but those database include values from the theoretical computation, as is well known, there is a big error between the theoretical value and the actual value. In order to modify the line strengths of the database, 20 ammonia spectrum absorption lines in a wavenumber range between 6611 and 6618 cm-1 are measured at different pressures by using direct tunable diode laser absorption spectroscopy (dTDLAS) technique. The measurement procedure is repeated at least 10 times at each pressure, and then average value is calculated. Voigt fitting is used to obtain all line integral area, and then the line integral area is obtained by linear fitting. The slope of the fitting straight line equals line strength. Uncertainty analysis is given for the measurements. The measured linestrength is a function of integrated area, temperature, pressure, species mole fraction and effective path length. So, the calculated linestrength uncertainties based on those parameters uncertainties, and the uncertainties of pressure, species mole fraction and effective path length are similar for all transitions with P =0.25%, =0.2%, and L =0.4%. The uncertainties of the integrated area and temperature are related to different lines, and their values come from the actual measurement. In the end, uncertainty propagation formula is used to calculate linestrength uncetainty. Uncertainties of our measured line strengths are in a 0.81%-3.33% range. Our measured line strength values are different from line strengths in the HITRAN 2012 database, and the deviations are in 0.51%-17.28% range.

2017, 66 (5): 054701.
doi: 10.7498/aps.66.054701

Abstract +

There has been a resurgence in the field of magnetohydrodynamic (MHD) flow control in the past 20 years. An increasing demand for sustained hypersonic flight and rapid access to space, along with numerous mechanical and material advances in flight-weight MHD technologies, has aroused renewed interest in this subject area. As a novel application of MHD flow control in the thermal protection field, MHD heat shield system has been proved to be of great intrinsic value by lots of researchers in recent years. Although its theoretical feasibility has been validated, there are many problems that remain to be further investigated. Among those problems, the Hall effect is a remarkable one that may affect the effectiveness of MHD flow control. Considering the fact that it is not sufficient to evaluate the Hall effect by merely using the chemical reaction model implemented in the nonequilibrium flow simulation to calculate the Hall parameter, a parametric study is conducted under the assumption of simplified uniform Hall parameter. First, coupling numerical methods are constructed and validated to solve the thermochemical nonequilibrium flow field and the electro-magnetic field. Second, a series of numerical simulations of the MHD head shield system is conducted with different magnitudes of Hall parameter under two magnetic induction intensities (B0=0.2 T, 0.5 T). Finally, the influence of Hall effect on the performance of MHD heat shield system is analyzed. Results indicate that Hall effect is closely related to the wall conductivity. If the vehicle surface is regarded as an insulating wall, the heat flux variation is co-determined by varying the Lorentz forces within the boundary layer and the shock-control effect. Compared with the one neglecting the Hall effect, the heat flux with Hall effect is slightly mitigated as the increase of Lorentz forces in the boundary layer dominates when the stagnation magnetic induction intensity B0 equals 0.2 T. However, the heat flux is increased when B0 equals 0.5 T, because the decrease of shock stand-off distance dominates which increases the gas temperature outside the boundary layer. Moreover, in this case the larger the Hall parameter, the higher the heat flux will be. As for the conductive wall, the performance of MHD heat shield system becomes worse with the increase of Hall parameter, and while it is equal to or higher than 5.0, this system loses its effectiveness.

2017, 66 (5): 054101.
doi: 10.7498/aps.66.054101

Abstract +

It is known that polarization as the third characteristic of electromagnetic waves plays substantial roles which are comparable with the wave amplitude and phase, in describing the tempo and spatial properties of electromagnetic waves. Various parameter groups for characterizing the polarization state of electromagnetic waves with different initial states and boundary conditions have been proposed. However, a full-scale set of conversion relationships between these parameter groups with specific initial phases is not yet available. In this work, the initial phases as additional parameters for the orthogonal linear polarization and the polarization ellipse parameter groups and the digitized elliptical angle ' as a complementary parameter to the polarization ellipse parameter group are taken into account respectively. Consequently, a full-scale set of conversion relationships between these parameter groups has been rigorously derived out. The validity of these conversion relationships are confirmed by the numerical calculations in terms of mathematical completeness and one-to-one correspondence. These conversion relationships make the tedious computation of the wave polarization much simpler and straightforward, benefiting practical implementation of the polarization theory of electromagnetic waves.

2017, 66 (5): 054204.
doi: 10.7498/aps.66.054204

Abstract +

In this paper, a new kind of quasi-boson method is used to eliminate the coordinates of the environment and redescribe the dissipative system by using an effective Hamiltonian; the localized mode and the interaction between cavities can be renormalized. Based on the quasi-boson approach, the single photon transport in one-dimensional coupled cavity array, with a driven cascade-type three-level atom embedded in one of the cavity, is investigated under the influence of the environment. The single-photon transmission and the reflection amplitudes are obtained analytically. And the additional effective potential induced by the interaction between the atom and the cavity is also derived. The effects of the controlling parameters on the reflection and transmission amplitudes are discussed with considering the dissipation. It is shown that the decay rates of the atoms and the cavity both reduce the reflection spectrum. But the dissipation of the atom has a significant influence on the reflection amplitude compared with the cavity decay under the same conditions. Due to the irreversible loss of energy, the photon number is non-conservative. Furthermore, the single-photon can be almost reflected by the three-level atom in the dissipative case when one adjusts the detuning and photon number of the quantized cavity field. The investigation will be of benefit to the realization of photon transport in a real experiment, which is also helpful for manipulating the photons in quantum information and quantum simulation.

2017, 66 (5): 054205.
doi: 10.7498/aps.66.054205

Abstract +

With the rapid development of space technology, human activities into space are increasing, thereby producing lots of space debris. And the space debris impact is the major cause for the mechanical damage to the space crafts and the main factor affecting the service life; it even endangers the life safety of the astronauts working outside the spacecraft and pose a threat to the astronomical observation and studies. Thus, the monitoring and early warning of space debris are gradually attracting wide attention. Obviously, laser detection as a good-directivity and strong anti-jamming active detecting means has a unique advantage in terms of a round-the-clock detection. Therefore, the developing of debris-detecting laser beam source becomes the most direct and effective means for increasing the space debris detection accuracy. The laser detecting ability is restricted by the laser beam quality, the pulse energy and the repetition frequency at the same time. The beam quality could affect the ability to detect and recognize space target. The bigger the laser pulse energy, the higher the repetition frequency and the smaller the detectable debris, the stronger the detecting ability will be. A good detection effect could be achieved at 80-100 Hz laser pulse repetition frequency. A further increase of the repetition frequency will greatly increase the difficulty and cost accordingly but the improvement of the detection performance is not obvious at all. Thus, repetition frequency around 100 Hz becomes the best choice for laser space debris detection. Based on the laser diode side-pumped rod-shaped amplifier, a high-repetition-frequency and high-beam-quality of joule level Nd:YAG nanosecond laser for space debris detection is developed in this work. The laser adopts MOPA structure, mainly including single longitudinal mode, pre-amplifier unit, SBS phase-conjugate beam control unit and energy extraction unit. In the energy extraction unit, beam splitting-amplifying-combining is adopted for reducing the thermal effect on beam quality by reducing the working current of the amplifier. Under the condition of 100 Hz high repetition frequency and 10.73 J single pulse energy injected by the single longitudinal mode seed, 3.31 J output energy is gained. The output laser beam has a 4.58 ns pulse width, far field beam spot of 2.12 times the value of the diffraction limit, and 0.87% energy stability (RMS).

2017, 66 (5): 054212.
doi: 10.7498/aps.66.054212

Abstract +

Until now, there have been many reports concerning the generation and propagation of partially coherent beams due to their less influencing ability in turbulent atmosphere and random media. Of particular interest, a Gaussian-Schell model beam has been widely chosen as a special example of partially coherent beam, since its spatial coherence degree is dependent on position only through the difference between the two position vectors. In the scalar domain, many coherent models have been well studied such as Gaussian and multi-Gaussian Schell-model sources, Bessel-Gaussian and Laguerre-Gaussian Schell-model sources and so on. Based on the theory for devising genuine cross-spectral density matrices for a stochastic electromagnetic beam, several scalar models have been also extended to the electromagnetic domain. In recent years, the propagation of partially coherent beams with spatially varying and non-uniform correlations has become a hot topic, because of their interesting characteristics such as locally sharpened and laterally shifted intensity maxima. In one of our previous studies, we have experimentally investigated the generation of non-uniformly correlated partially coherent beams. However, to the best of our knowledge, so far, there has been no investigation on the generation of non-uniformly correlated stochastic electromagnetic beams. In this paper, we theoretically and experimentally investigate the generation of non-uniformly correlated stochastic electromagnetic beams. Based on the relation between phase correlation and optical coherence, we investigate the 22 cross-spectral density matrix and the coherence distribution of the non-uniformly correlated stochastic electromagnetic beam we generated. It is shown that the coherence degree between two points in the generated beam depends not only on the distance between them, but also on the distances between the points and the center of the beam. In experiment, we use the Matlab rand function to generate a random phase pattern with uniform distribution. The modulation magnitudes of different positions are different and follow an inverse Gaussian distribution in position. Dynamic phase patterns are created from a series of random grey-scale images. Two phase-only liquid crystal spatial light modulators are employed to display computer-generated dynamic phase patterns and modulate the two orthogonally polarized components of the incident coherent light, respectively, and generate a stochastic electromagnetic beam. We measure the correlation distribution of the generated beam in Young's two-pinhole experiment. It is shown that the experimental observations are in agreement with our theoretical analyses. Other kinds of non-uniformly correlated stochastic electromagnetic beams can also be obtained by this approach. Non-uniformly correlated stochastic electromagnetic beams may have some applications in optical manipulation and free-space optical communication.

2017, 66 (5): 054702.
doi: 10.7498/aps.66.054702

Abstract +

The objective of this study is to investigate the flow structure of underwater supersonic gas jets in water flow. Supersonic gas jets submerged in a liquid flow field is experimentally studied in a water tunnel. In the experiments, a high speed camera system is used to observe the evolution of the gas jet bubble, and a dynamic pressure measurement system is used to measure the pressure fluctuation under different flow velocities simultaneously. We seek to study the mechanism of the vortex structure and the pressure fluctuation phenomenon during the gas jet evolution. The obtained results conclude that the main body formation and the pressure fluctuation of the gas jets depend heavily on the ambient flow speed. The instantaneous patterns of gas jets remarkably go upward due to the gravity effect in the still water. A shear vortex will be formed by jet-flow interaction when the ambient fluid flows. Larger vortexes are formed when the main body of the jet evolves downstream and mixes with the jet shear layer. The evolution pattern and pressure fluctuation characteristics of the gas-liquid interface are educed through a detailed analysis of the shear layer vortex structure. Backward reflection of pressure fluctuation is formed accompanying the jet bulging, necking, and back-attack. Consequently, the pressure fluctuation is transferred to the fluid at the nozzle surface and the test section. The pressure measurement system is used to confirm the pressure fluctuation phenomenon. Two measuring positions are set, i.e., pressure transducers are embedded at the nozzle surface and the test section. The pressure fluctuation with magnitude of 10 kPa is measured by the nozzle surface transducer in still water. The pressure fluctuation induced by the gas jets near the nozzle exit disappears simultaneously when the ambient fluid flows. However, the amplitude of pressure fluctuation decreases at the nozzle surface but increases at the test section with the increasing flow velocity. Power spectrum analysis is carried out and shows that the mechanical energy of the water tunnel gas jets is mainly distributed in the frequency band of 0-700 Hz. A jet induced large pressure fluctuation with a dominant frequency about 200 Hz can be captured near the nozzle surface in still water. With increasing water velocity, the dominant frequency of the unsteady pressure fluctuation decreases significantly at the nozzle surface. Conversely, the flow velocity leads to an increase in the spectral intensity of the pressure at the test section.

2017, 66 (5): 054202.
doi: 10.7498/aps.66.054202

Abstract +

Grating based X-ray imaging technology is a coherent imaging technique that bears tremendous potential in three-dimensional tomographic imaging of weak absorption contrast specimens. Three kinds of contrast information including absorption, phase and scattering can be retrieved separately based on a single set of raw projections. However, the grating based X-ray imaging with the conventional phase-retrieval method using the conventional phase-stepping approach and filtered back projection (FBP) reconstruction algorithm require large amounts of raw data, so that long exposure time and large amounts of radiation dose is accepted by the sample. According to the traditional grating based X-ray imaging system, we propose a low dose, fast, multi-contrast CT reconstruction approach based on the iterative reconstruction algorithm that optimizes dose efficiency but does not share the main limitations of other reported methods. Prior to reconstruction, firstly, the projections are acquired with the phase stepping approach and multi-contrast projections are retrieved from the raw data by conventional retrieval algorithm. Then the rotational variable differential phase projections are converted to rotational invariable projections by means of decomposing the differential phase projections into the rotational invariable projections in two mutually perpendicular derivative directions via the transformation of coordinates. Finally, the absorption, phase and scattering information are reconstructed with the iterative reconstruction algorithm and the phase is retrieved based on the fast Fourier transform (FFT). We validated and assessed the phase reconstruction approach with a numerical simulation on a phase Shepp-Logan phantom. The experiment was performed at the X-ray imaging and biomedical application beam line (BL-13W) in the Shanghai Synchrotron Radiation Facility (SSRF) where 20 keV X-ray from a Si(111) monochromator is emitted. The X-ray interferometer was positioned at 34 m from the Wiggler source. The images were recorded with a scintillator/lens-coupled CCD camera with 2048 pixel2048 pixel resolution and an effective pixel size of 9 m. The numerical tests and the experimental results demonstrate that, for the small radiation dose deposited in the sample, the iterative reconstruction algorithm provides phase reconstructions of better quality and higher signal to noise ratio than the conventional FBP reconstruction algorithm, and also provides the multi-contrast 3D images, including absorption image, phase image and scattering image. This development is of particular interest for applications where the samples need inspecting under low dose and high speed conditions, and will play an important role in the nondestructive and quantitative imaging in the industry, biomedical and medical diagnosis fields.

2017, 66 (5): 054206.
doi: 10.7498/aps.66.054206

Abstract +

The safety quality of vegetable oil is very important for human life. The objective of this research is to determine the content of heavy metal chromium (Cr) in each of three kinds of vegetable oils (soybean oil, peanut oil, and corn oil) quantitatively by collinear double pulse laser-induced breakdown spectroscopy (DP-LIBS). In this study, a total of 24 vegetable oil samples are prepared, and each kind of vegetable oil has 8 samples. Fortune paulownia wood chips with a diameter of 20 mm and thickness of 3 mm are placed into the vegetable oil samples to collect the Cr element. After that, the 24 samples (fortune paulownia wood chips that have enriched Cr element) are dried in the oven, and the LIBS spectra of samples are acquired in a wavelength range of 206.28-481.77 nm by a dual-channel high-precision spectrometer. The spectral line of Cr (Cr I 425.39 nm) is chosen as the quantitative analysis spectral line, while CN (CN 421.39 nm) molecular spectral line, Ca (Ca I 422.64 nm) atomic spectral line and the sum of their spectral line intensities are selected as the internal standard lines. Then the calibration curves of Cr are obtained by the basic calibration method, single-line internal standard method (CN 421.39 nm or Ca I 422.64 nm as the internal standard line) and dual-line internal standard method (CN 421.39 nm and Ca I 422.64 nm as the internal standard lines). Finally, the validation samples are used to verify the performances of the calibration curves of Cr element. The results show that the values of fitting degree (R2) of the basic calibration curves for three kinds of vegetable oils are all above 0.97, and the relative errors of validation samples with low concentration are bigger than those with high concentration. The values of (R2) of calibration curves obtained by single-line internal standard method are above 0.98, and the relative errors of validation samples are lower than those obtained using basic calibration method. And the values of (R2) of calibration curves for soybean oils, corn oils and peanut oils are 0.995, 0.992 and 0.996, respectively, with using dual-line internal standard method. The relative errors between the two validation samples are 12.8%, 1.73%, 9.19%, 6.05% and 6.23%, 6.69%, respectively. And the results obtained by the dual-line internal standard method are better than those obtained by the basic calibration method and single-line internal standard method. Thus it can be seen that the dual-line internal standard method can reduce the error of quantitative analysis effectively and improve the predicting ability of LIBS technique for Cr element detection in vegetable oil.

2017, 66 (5): 054208.
doi: 10.7498/aps.66.054208

Abstract +

We study the new spatial optical solitons and their propagating properties in the one-dimensional nonlocal cubic-quintic (C-Q) nonlinear model by the numerical method. We obtain multi-bright solitons and multipole soliton solutions in the one-dimensional nonlocal C-Q nonlinear model. The propagation of bright solitons is stable in the competing nonlocal cubic self-defocusing and quintic self-focusing nonlinear media when these nonlocal and nonlinear parameters are in the appropriate value domain. Considering the different nonlinear cubic effects, the interaction between two optical solitons with the same phase in the general nonlocal media displays the attraction or the repulsion for different nonlocal and nonlinear parameters. We find that the interval of two solitons affects the interaction between them. The refractive index is changed with the propagating constant when the nonlocal constant d3 is 10. Moreover, the triplepole, quadrupole and pentapole solitons can propagate steadily when the nonlocal parameters are appropriate, but hexa-pole (or above) solitons propagate unsteadily for any nonlocal parameter. Furthermore, we investigate the multi-pole solitons and their propagation stabilities by the Newton difference method and the Fourier split step method, obtain the stable propagation conditions for dipole, triplepole and quadrupole solitons, and find that the propagation of the pentapole and higher-order pole solitons is unstable. We also discuss the interactions of multi-pole solitons when they propagate along the axis z. The interactions are attraction or repulsion when the nonlocal and the nonlinear parameters are different. Meanwhile, we simulate the evolution of the refractive index along the axis z when the spatial optical solitons are multi-pole solitons. Finally, we study the relation between the power of soliton and the propagation constant under different degree of nonlocality. The power of the single bright soliton does not monotonically increase with the increasing propagation constant when the degree of nonlocality d3 is 10. We also derive the relation between the power of dipole bright solitons with the cubic nonlinearity parameter and the propagation constant under different degree of nonlocality. The power decreases monotonically with the increasing propagation constant when the cubic nonlinearity is a certain value or with the increasing cubic nonlinearity when the propagation constant is a certain value.

2017, 66 (5): 054209.
doi: 10.7498/aps.66.054209

Abstract +

Electronic diode plays an important role in electronic circuits owing to its capability of unidirectional movement of the current flux. An optical diode offers unidirectional propagation of light beams, which plays key roles in the all-optical integrated circuits. Unidirectional wave propagation requires either time-reversal or spatial inversion symmetry breaking. The former can be achieved with the help of nonlinear materials, magnetic-optical materials and so on. The realization of these schemes all needs the external conditions (electric field, magnetic field or light field), and thus their applications are limited. In contrast, spatial inversion symmetry breaking can make up for this shortcoming and has been widely studied.
Through breaking the structure's spatial inversion symmetry, much research demonstrated that the unidirectional light propagation could be achieved in a photonic crystal structure. Specially, the optical diode based on the photonic crystal heterojunction has been drawing much attention. Though relevant studies have been reported, how to find a more simple structure to realize high-efficiency optical diodes is always pursued by people. The previous design of optical diode is generally based on the orthogonal or non-orthogonal photonic crystal heterojunctions. However, the comparative analysis of the two types of heterojunctions has not been systematically carried out. The transmission characteristics of two-dimensional orthogonal and non-orthogonal silicon photonic crystal heterojunctions are obtained and compared. Firstly, the directional band gap mismatch of two-dimensional square-lattice silicon photonic crystals with the same lattice constant but different air hole radii is calculated by the plane wave expansion method. The band structure indicates that in a certain frequency range, one photonic crystal is the omni-directional pass band, while the other has directional band gap. This is just the necessary condition for the unidirectional light transmission through the photonic crystal heterojunctions. Therefore, the heterojunction constructed by the two photonic crystals is expected to achieve optical diode. Based on this, the orthogonal and the non-orthogonal heterojunctions are proposed. Their transmission spectra and field distributions are calculated by the finite-difference time-domain method. The results show that the unidirectional light transmission can be realized by the non-orthogonal heterojunction structure (unidirectional transmission efficiency reaches 45%) but not the orthogonal heterojunction structure. That is to say, the realization of unidirectional transmission is closely related to the orientation of the hetero-interface. Moreover, the non-orthogonal photonic crystal hetero-interface is optimized. It is found that the unidirectional transmission efficiency increases to 54% and the overall increases by 10%. More importantly, it greatly improves the performance of optical diode for its simple structure and small size, and provides another more effective design method.

2017, 66 (5): 054210.
doi: 10.7498/aps.66.054210

Abstract +

THz waves are very good candidates for high-capacity wireless links since they offer a much higher bandwidth than RF frequencies. Photonic crystal (PC) offers a new opportunity for integrated THz wave devices. It permits the integrated devices to be miniaturized to a scale comparable to the wavelength of the electromagnetic wave. Considering their governing properties such as photonic band gap (PBG) and photon localization effect to control electromagnetic wave propagations, PC-based THz modulator has attracted much attention. Tunability strategies include mechanical control, electrical control, magneto static control, temperature control and optical pumping. However, the development of high-speed THz wireless communication system is limited by the low modulation depth and rate of previously reported modulators. In this paper, we propose a novel magnetic-controlled THz modulator based on a magnetized plasma PC consisting of line defects and a point defect. InSb, a semiconductor with high electron mobility, is introduced into the point defect. According to the magneto-optical effect, the refractive index of InSb changes rapidly under the control of the applied magnetic field (MF) intensity. Then the mode frequency in the point defect changes dynamically. The structure is based on a two-dimensional PC constructed by triangular lattice of Si rods in air. Based on the magneto-optic effect, the magnetized plasma defect mode in the THz regime can be decomposed into the left- and right-handed circularly polarized light when the applied magnetic field is parallel to the direction of the THz wave. And the difference in effective refractive index between the left- and right-handed circularly polarized light increases with the applied uniform magnetic field increasing. Therefore the on/off modulation of left- and right-hand circularly polarized light can be realized. The steady-state field intensity distribution and the time domain steady state response of TE wave propagating parallelly to the external magnetic field are simulated by the finite-difference-time-domain and finite element method. The simulation results show that PC-based mode transfer modulator has the potential application to THz wireless broadband communication system with a good performance of high contrast ratio (25.4 dB), low insertion loss (0.3 dB) and high modulation rate (～4 GHz). It is convenient to load the modulation signals in an easy MF application way. The device designed is leading the way to extend the application of THz wireless communication filed with advantages of small size, low insertion loss, and high extinction ratio.

2017, 66 (5): 054211.
doi: 10.7498/aps.66.054211

Abstract +

SiO2 thin film is one of the most important low refractive index materials in the area of optical thin films. It is always used in the design and preparation of many kinds of multilayer films. The dielectric constant of the SiO2 thin film is a key characteristic for design of the multilayer thin film. The composite Gaussian oscillator model is one of the most important dispersion models for the dielectric constant of the amorphous SiO2 in the anomalous dispersion regime in the infrared range. More and more researchers have focused on the number and the physical meaning of the oscillators in the composite oscillator. A method to determine the SiO2 thin film oscillator quantity was proposed. In this method, the quantity of oscillator peaks was equivalent to the oscillator number of chemical composition, based on the factor analysis technology of chemometrics. Concretely, the composite oscillators of the dielectric constant were equivalent to the mixture, and the independent oscillators were equivalent to the compositions of the mixture. The absorbance of the mixture changed with the physical thickness of the thin film. Eight SiO2 film samples with different thickness were prepared on the Si substrate by the ion beam sputtering deposition. The infrared transmittances of the eight samples were used as elements in the spectral matrix. There were nine Gaussian oscillators in the range of 400-4000 cm-1, which was determined by the factor analysis technology. The dielectric constant of the SiO2 thin film in this range was obtained by the inverse calculation from the spectral transmittance. It provides the inverse calculation result for the dielectric constant of the SiO2 thin film with a specific physical meaning. By analyzing the dielectric constant in the range of 400-900 cm-1, the symmetric stretching vibrational frequency and the in-plane rocking frequency of the Si-O-Si bond of the SiO2 thin film can be obtained. Compared with fused silica, the symmetric stretching vibrational frequency increased while the rocking frequency was reduced. In fact, the frequency shifts are caused by the strain of the thin film. By analyzing the dielectric constant in the range of 900-1500 cm-1, four anti-symmetric stretching vibrational frequencies of the Si-O-Si bond in the SiO2 thin film were obtained. They have a certain corresponding relation with the anti-symmetric stretching vibrational frequency of the Si-O-Si bond in the fused silica. What's more, by analyzing the dielectric constant in the range of 3000-4000 cm-1, the water-cut (or hydroxyl) chemical defects in the films were confirmed. The chemical defects can influence the dielectric constant in the whole infrared range.

2017, 66 (5): 054501.
doi: 10.7498/aps.66.054501

Abstract +

The Hamilton-Jacobi equation is an important nonlinear partial differential equation. In particular, the classical Hamilton-Jacobi method is generally considered to be an important means to solve the holonomic conservative dynamics problems in classical dynamics. According to the classical Hamilton-Jacobi theory, the classical Hamilton-Jacobi equation corresponds to the canonical Hamilton equations of the holonomic conservative dynamics system. If the complete solution of the classical Hamilton-Jacobi equation can be found, the solution of the canonical Hamilton equations can be found by the algebraic method. From the point of geometry view, the essential of the Hamilton-Jacobi method is that the Hamilton-Jacobi equation promotes the vector field on the cotangent bundle T* M to a constraint submanifold of the manifold T* M R, and if the integral curve of the promoted vector field can be found, the projection of the integral curve in the cotangent bundle T* M is the solution of the Hamilton equations. According to the geometric theory of the first order partial differential equations, the Hamilton-Jacobi method may be regarded as the study of the characteristic curves which generate the integral manifolds of the Hamilton 2-form . This means that there is a duality relationship between the Hamilton-Jacobi equation and the canonical Hamilton equations. So if an action field, defined on UI (U is an open set of the configuration manifold M, IR), is a solution of the Hamilton-Jacobi equation, then there will exist a differentiable map from MR to T* MR which defines an integral submanifold for the Hamilton 2-form . Conversely, if * =0 and H1(UI)=0 (H1(UI) is the first de Rham group of U I), there will exist an action field S satisfying the Hamilton-Jacobi equation. Obviously, the above mentioned geometric theory can not only be applicable to the classical Hamilton-Jacobi equation, but also to the general Hamilton-Jacobi equation, in which some first order partial differential equations correspond to the non-conservative Hamiltonian systems. The geometry theory of the Hamilton-Jacobi method is applied to some special non-conservative Hamiltonian systems, and a new Hamilton-Jacobi method is established. The Hamilton canonical equations of the non-conservative Hamiltonian systems which are applied with non-conservative force Fi = (t)pi can be solved with the new method. If a complete solution of the corresponding Hamilton-Jacobi equation can be found, all the first integrals of the non-conservative Hamiltonian system will be found. The classical Hamilton-Jacobi method is a special case of the new Hamilton-Jacobi method. Some examples are constructed to illustrate the proposed method.

###### PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

2017, 66 (5): 055201.
doi: 10.7498/aps.66.055201

Abstract +

The electromagnetic surface waves which propagate along a non-magnetized cold plasma column have a great value in the application of plasma antenna. In this paper, the dispersion properties, the transmission power distributions, and the radiation patterns for these electromagnetic surface waves which have lower frequencies than the electron plasma frequency are analyzed numerically. Based on Helmholtz equation, the specific expression of dispersion equation is derivedby the field matching method, then the exact values of complex axial wave vector kz under different wave frequencies are obtained by solving the transcendental dispersion relation. Using the specific value of kz obtained above, the exact expressions of transmission power profile in the plasma column and field profiles in the three regions, i.e., plasma, dielectric, and free space are derived, respectively. Finally, based on the complex form of electric conductivity that is derived from the Boltzmann-Vlasov equation with Krook term and the complex axial wave vector kz obtained above, the influence of the parameter pea/c on phase property, and the dependence of radiation pattern and transmission power profile on wave frequency of the non-magnetized cold plasma column in a cylindrical dielectric tube system are analyzed. The results show that the electron plasma frequency has a significant influence on the phase property, which is evidently confirmed by the fact that the propagation velocities of the three modes m=0, m=1 and m=2 are all near to the light speed when the value of parameter pea/c gradually increases. Meanwhile, through the investigation of the radiation patterns for the three modes, an important conclusion is that the radiation pattern has evident dependence on wave frequency. While the radiation direction of the main lobe is in the axial direction for the m=1 mode, the m1 modes each have an angle between the radiation direction of the main lobe and the axial direction, this crucial conclusion is in good agreement with the theoretical calculation results obtained from other researcher. Further, we find that with the increase of wave frequency, the angle between the main lobe radiation direction and the axial direction turns smaller for each of m=0 and m=2 modes, and the width of main lobe gradually narrows for each of all modes, and the amplitude of the first side lobe becomes notable for each of m=0 and m=2 modes and ignorable for the m=1 mode. Also, the transmission power increases as the wave frequency increases for each of all modes. These theoretical calculation results provide a detailed theoretical reference for the designing of plasma stealth and high-precision requirements of plasma antenna design, and giving a comprehensive optimization guidance for the modulation of plasma antenna.

2017, 66 (5): 055101.
doi: 10.7498/aps.66.055101

Abstract +

Micro hollow cathode sustained discharge (MCSD) is simulated by using a fluid model, and the spatiotemoral characteristics of the electric potential, electron density, ion density and electric field are investigated. Results show that the MCSD acts in different modes at different times. The first stage is the Townsend discharge mode. The second is a transition mode from Townsend discharge mode to a hollow cathode effect mode, and the electron density, ion density and electric field near the cathode rise drastically, in which the MCSD is ignited initially. The third stage is the hollow cathode effect mode, and the MCSD forms generally. The last stage is stable discharge state. At the stable discharge stage, the electron density and the ion density each achieve 1015 cm-3 with a peak density located in the center of hollow cathode chamber. The value of electron density in the MCSD region is on the order of 1013 cm -3. The results also show that the micro-hollow cathode discharge (MHCD) contributes to the formation of MCSD, and the MCSD also facilitates the development of MHCD. In addition, the voltage on the second anode has important influence on the distributions of electric potential, electron density and electric field both inside the hollow cathode and outside the hollow cathode. Moreover, the influence on the MCSD is more apparent than the influence on the MHCD. With the increase of voltage on the second anode, the cathode sheath close to the first anode becomes more and more apparent. The second anode is necessary for the formation of micro-hollow cathode sustained discharge.

2017, 66 (5): 055203.
doi: 10.7498/aps.66.055203

Abstract +

Coaxial gun discharge plasma with high density and velocity has a number of potential applications in fusion energy, plasma refueling, disruption mitigation in tokamaks, plasma space propulsion, acceleration of dust particles to hypervelocity etc., and thus has become an important research topic in fields of nuclear physics and aerospace engineering. In this paper, we report the experimental investigation on electrical and transport characteristics of coaxial gun discharge plasma. Based on electrical and optical diagnoses, the discharge voltage, discharge current and axial velocity of plasma transport are measured. Meanwhile, the emission spectrum technology is employed to measure the Stark broadening of H spectral line and then plasma density is calculated. The experimental results show that the discharges in the coaxial gun present a feature of multiple discharges and blow-by instability phenomena are observed by photomultiplier acquired signals. In addition, the plasma velocity and density in the transport process are not constant. It is found that the axial plasma velocity in the transport process decreases due to mass gain caused by the snowplow model and the change tendency of plasma density in the transport process is dependent on various settings. A systematic study has been carried out for exploring plasma density change in transport process, and different experimental parameters are adopted in order to further analyze the physical mechanism of plasma density change in transport process. When the air pressure in the coaxial gun is changed from 4.0 Pa to 10 Pa, for 1.08 kJ applied power energy, an obvious difference appears in transport properties of plasma density, i.e., plasma density increases gradually in 4.0 Pa air while it increases first and then decreases in 10 Pa air. However, the plasma density increases continually in air pressure of 10 Pa when the power energy is increased to 7.68 kJ. Moreover, when the working gas is replaced with argon and discharge setting is 4.0 Pa pressure and 1.08 kJ applied power energy, the plasma density decreases continually in the transport process. The distinct behaviors, as analyzed, are mainly caused by plasma energy transformation difference in the transport process. As it is known, the plasma movement at high velocity in coaxial guns can ionize neutral particles and consume its energy, which results in the increasing plasma density and the decreasing electron and ion temperatures in the transport process. Then, a maximum density is present in the transport process when the electron and ion temperatures are lower than that at which gas ionization occurs. The axial location of maximum density changes with applied power energy, working gas pressure and species, which means that plasma energy transformation and density change properties in transport process strongly rely on different external parameters. The study provides some insight into how to better apply the coaxial gun discharge plasma to practical engineering field.

## EDITOR'S SUGGESTION

2017, 66 (5): 055202.
doi: 10.7498/aps.66.055202

Abstract +

Intense pulse ion beam (IPIB) has been extensively used in material surface modification. The ablation effect plays an important role in the interaction between IPIB and material. Therefore, the understanding of ablation mechanism is of great significance for IPIB application. Here, to investigate the ablation process and the characteristics of ablation products, pure zinc targets are bombarded by IPIB of 1.2-1.5 J/cm2 energy density at TEMP-4M accelerator. The ablation products are collected by monocrystalline silicon substrates in the IPIB irradiation process. By using the scanning electron microscopy, energy dispersive spectrometer and high precision balance, the surface morphology of the substrate and the characteristics of ablation products are obtained. The majority of observed ablation products are nearly circular particles with diameters of 0.03-2.00 m. There are a small number of zinc droplets and solid debris with large irregular shapes on the silicon substrate. Combining Monte Carlo method and infrared imaging diagnostic results, a heat conduction model is constructed by finite element method to describe the distribution and evolution of thermal field formed by IPIB on a zinc target. The results show that the zinc target can be melted and evaporated under a 1.2 J/cm2 IPIB irradiation. By comparing the experimental resuls with the simulation results, it is found that the gaseous, liquid and solid ablation products are generated collectively in the zinc ablation process. The causes of the different ablation products are also studied.

###### REVIEW

2017, 66 (5): 056601.
doi: 10.7498/aps.66.056601

Abstract +

One-atom-thick material such as graphene, graphene derivatives and graphene-like materials, usually has a dense network lattice structure and therefore dense distribution of electronic clouds in the atomic plane. This unique structure makes it have great significance in both basic research and practical applications. Studies have shown that molecules, atoms and ions are very difficult to permeate through these above-mentioned two-dimensional materials. Theoretical investigations demonstrate that even hydrogen, the smallest in atoms, is expected to take billions of years to penetrate through the dense electronic cloud of graphene. Therefore, it is generally considered that one-atom-thin materialis impermeable for hydrogen. However, recent experimental results have shown that the hydrogen atoms can tunnel through graphene and monolayer hexagonal boron nitride at room temperature. The existence of defects in one-atomthin material can also effectively reduce the barrier height of the hydrogen tunneling through graphene. Controversy exists about whether hydrogen particles such as atoms, ions or hydrogen molecules can tunnel through two-dimensional materials, and it has been one of the popular topics in the fields of two-dimensional materials. In this paper, the recent research progressof hydrogen tunneling through two-dimensional materials is reviewed. The characteristics of hydrogen isotopes tunneling through different two-dimensional materials are introduced. Barrier heights of hydrogen tunneling through different graphene and graphene-like materials are discussed and the difficulties in its transition are compared. Hydrogen cannot tunnel through the monolayer molybdenum disulfide, only a little small number of hydrogen atoms can tunnel hrough graphene and hexagonal boron nitride, while hydrogen is relatively easy to tunnel through silicene and phosphorene. The introduction of atomic defects or some oxygen-containing functional groups into the two-dimensional material is discussed, which can effectively reduce the barrier height of the hydrogen tunneling barrier. By adding the catalyst and adjusting the temperature and humidity of the tunneling environment, the hydrogen tunneling ability can be enhanced and the hydrogen particles tunneling through the two-dimensional material can be realized. Finally, the applications of hydrogen tunneling through two-dimensional materials in ion-separation membranes, fuel cells and hydrogen storage materials are summarized. The potential applications of hydrogen permeable functional thin film materials, lithium ion battery electrode materials and nano-channel ions in low energy transmission are prospected. The exact mechanism of hydrogen tunneling through two-dimensional material is yet to be unravelled. In order to promote these applications and to realize large-scale production and precision machining of these two-dimensional materials, an in-depth understanding of the fundamental questions of the hydrogen tunneling mechanism is needed. Further studies are needed to predict the tunneling process quantitatively and to understand the effects of catalyst and the influences of chemical environments.

###### CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

2017, 66 (5): 057102.
doi: 10.7498/aps.66.057102

Abstract +

A first-principles plane-wave pseudo potential method based on the density functional theory is used to investigate the phase structures, energies, electronic structures and elastic properties of Ti3AC2 (A=Si, Sn, Al, Ge) phases. In this paper, Ti3AC2 (A=Si, Sn, Al, Ge) crystal structures are first optimized, then the band structures, total and part density of states，charge density distributions and elastic properties of these compounds are analyzed, and the cohesive energies and formation energy of these phases are also calculated. The results show that the Ti3GeC2 is more stable than other compounds, the formation energy of Ti3AlC2 is the lowest in these compounds, which indicates that Ti3AlC2 is easier to generate; Ti3AC2 (A =Si, Sn, Al, Ge) each have a higher density of states at Fermi level, which shows the strong metallicity, meanwhile, the electrical conductivity of each phase is anisotropic. The DOS at the Fermi energy is mainly from the Ti-d electrons, which should be involved in the conduction properties although d electrons are considered to be inefficient conductors. The lowest valence bands are formed by the C-s states with a small mixture of Ti-p+d, and A-s+p states. The electrical properties are mainly decided by the p-d hybridizations between 3d electrons in Ti and the p electrons in A (A =Si, Sn, Al, Ge) and 2p electrons in C, and the strong hybridization of p-d states make the materials have stable structures. It should be noted that the calculated bond length of Ti-Ge is shorter than those of Ti-A (A=Si, Sn, Al) bonds. This implies that the Ti-Ge bond is stronger than Ti-A (A=Si, Sn, Al) bonds. Furthermore, the Fermi level of Ti3GeC2 is relatively low, which also indicates the relatively high stability of Ti3GeC2. The charge density provides a measure of the strength of the ionic bond, so that Ti3GeC2 and Ti3SiC2 have stronger ionic bonds than Ti3SnC2 and Ti3AlC2. The strong M-A bonds in Ti3GeC2 lead to a decreasing and c lattice parameter value increasing. The spherical shape of X represents more like an ionic bond. The z-directional localized shapes of A each is more like a covalent bond. The covalent bonds of A elements each are localized along the z direction so that they affect mostly the c lattice parameter; the calculated elastic properties of Ti3AC2 (A = Si, Sn, Al, Ge) phases show that the atomic binding force of Ti3AlC2 is weaker than those of other three phases, while the atomic binding force of Ti3GeC2 is relatively strong, which makes the strength of Ti3GeC2 quite high.

2017, 66 (5): 057301.
doi: 10.7498/aps.66.057301

Abstract +

As a stable single sheet of carbon atoms with a honeycomb lattice, graphene has become attractive for its potential applications in electrochemical storage devices, such as anodes for rechargeable Li batteries. Since both sides of it can hold adsorbents, a graphene sheet is expected to have extra storage sites and therefore it has a possibly higher capacity than graphite. However, certain shortcomings of Li battery, such as instability lead to battery failure under overcharging or overvoltage conditions. The limit to capacity results in a short time of discharge. Thus, more attention should be paid to the stabilities of electrode materials, such as Li cluster nucleation on graphene leading to dendrite formation and failure of the Li-ion battery. In this work, we build a supercell model of single layer graphene with hexagonal structure, and then change the size of Li cluster which is used to be adsorbed on graphene, with keeping m Li:C ratio at 1:6. Using the first principle based on density functional theory, we calculate the density of states, charge density difference and energy band structure. The interaction between Li and pristine graphene is studied in detail by analyzing the electronic properties and charge distribution of the isolated Li clusters and Li clusters adsorbed on graphene. It is found that the ionic bonding can be formed at the interface between Li clusters and graphene, and the charge transfer controls the interaction of the Li-carbon nanostructure. Combing thermodynamics method with the nucleation mechanism, the relationship between the cluster size and nucleation probability is analyzed, and the nucleation on graphene of Li with a certain concentration is also investigated. We estimate the nucleation barrier for Li on graphene and investigate the stability of Li adsorption on graphene by considering the effects of Li concentration and temperature. The Li concentration of 16.7% is considered for the formation of clusters with different sizes on graphene. With the size of Li cluster increasing, the cluster adsorbed on the graphene begins to be more stable than the single Li atom. The formation energy for the cluster is found to increase with the increase of temperature, and it is negative, meaning that Li cluster can be formed. It is expected that the corresponding calculation results from this atomistic simulation will shed some light on the in-depth understanding of Li-storage on graphene and the cycling stability and dendrite formation in Li-ion batteries with graphene-based materials serving as the anode.

2017, 66 (5): 057101.
doi: 10.7498/aps.66.057101

Abstract +

In the layered dichalcogenide 1T-TaS2, whether there is a disorder-driven transition from insulator to metal is still a matter in dispute. It is predicted that the commensurate charge density wave (CCDW) phase at low temperature behaves as a Mott insulator due to the strong correlation of electrons. Meanwhile, the stacking of TaS layers is found to be dislocated along the c axis, which will introduce considerable effect of disorder. Therefore, further theoretical study is needed to show the cooperative effect of correlation and disorder in 1T-TaS2.
The statistical dynamical mean-field theory, which treats interactions and disorder on an equal footing, is used to study the effect of disorder on the Mott insulating phase in 1T-TaS2. Two different kinds of disorder effects are considered in the one-dimensional extended Anderson-Hubbard model, where the stacking dislocation of TaS layers is described by the off-diagonal hopping disorder and the diagonal disorder term represents the effect of disorder introduced by impurities.
We find that the off-diagonal disorder by itself could not close the Mott gap at Fermi level, suggesting that Mott mechanism should be more dominant in the CCDW phase of 1T-TaS2 with the stacking dislocation of TaS layers. On the other hand, the diagonal disorder introduced by impurities will close the Mott gap when the strength of disorder (W) is larger than the correlation of electrons (U). Proved by the lattice-size scaling of the generalized inverse participation ratio, both the off-diagonal disorder and diagonal disorder can make all states Anderson-localized. As a result, there is no disorder-induced metal-insulator transition in a correlated system with either off-diagonal disorder or diagonal disorder.
In addition, an anomalistic state is introduced by the off-diagonal disorder at the center of the energy band of the non-interacting system, which is a special Anderson-localized state with a very larger localization length. In the correlated cases, the electron-electron interactions have strong effect on splitting the anomalistic state into two individual states, which are located symmetrically in both the upper and lower Hubbard subbands with an energy interval U.

2017, 66 (5): 057103.
doi: 10.7498/aps.66.057103

Abstract +

The rapid development of organic-inorganic hybrid perovskite solar cells has recently attracted the worldwide attention because their power conversion efficiency has risen from 4% to higher than 20% within just six years. It is well known that the perovskite materials with APbI3 crystal structure have a 3D framework of corner-sharing PbI6 octahedra, in which each Pb atom bonds with six I atoms, and the A cations fill in the octahedral interstices. At present, a lot of researches have focused on the synthesis and doping modification of perovskite materials. However, it is hard to detect directly the weak interactions between A cations and PbI6 skeleton in the APbI3 crystal structure through experiments, which have effect on the structural stability and electronic properties. To provide a full understanding of the interplay among size, structure, and organic/inorganic interactions, the stability, electronic structures and optical properties of APbI3 (A denotes Cs+, NH4+, MA+, FA+) were investigated by the plane-wave ultra soft pseudo potentials. Two dispersion corrections were taken into account in the weak interactions between A cations and PbI6 skeleton in the APbI3 crystal structure, respectively. The results show that the type and size of cations affect the distortion of PbI framework, indicating that the larger the radius of the A cation is, the stronger the interaction between the A cation and the PbI framework is. Further, it is identified that after geometry relaxation, the orientation of A cations (A denotes NH4+, MA+, FA+) is easy to change, and the PbI frameworks present structural distortion. CsPbI3 is more stable energetically than other three kinds of perovskite materials. For the PbI6 octahedra, the large dipole moments of 0.23D and 0.32D for the generalized-gradient approximation method or 0.28D and 0.29D for the local-density approximation method are also present in MAPbI3 and FAPbI3, respectively. In addition, the energy band structures, which affect the generation and migration of photon-generated carriers and optical properties, will alter with the structural distortion of PbI frameworks. By analyzing the energy band structures and corresponding density of states, we find that four systems have similar band structures near the Fermi energy, namely, the top of valance band is mainly contributed by I 5p orbitals, while the bottom of conduction band is dominated by Pb 6p orbitals and partly contributed by I 5p orbitals. A little difference of their electronic structures and optical absorption spectra originates from the distortion of PbI6 octahedra in APbI3 crystal structures. It is noted that the contribution of the ions Cs+ and FA+ on the top of valance band is slightly larger than that of the ions NH4+ and MA+. Compared with other three kinds of perovskite materials, CsPbI3 presents the narrowest direct band gap, the lowest effective carrier mass and excellent visible-light and infrared absorption. The results may provide some theoretical guidance for further research on perovskite materials in the application of solar cells.

2017, 66 (5): 057104.
doi: 10.7498/aps.66.057104

Abstract +

Aluminum and its alloy play an important role in nuclear industry, where irradiation damage continually occurs and significantly affects the structures and physical properties of materials: especially long-term irradiation can lead to the formation of helium bubbles and holes in the substrate. During the initial irradiation damage, point defects are the major defects.Studying the point defects is of great significance for understanding the irradiation damages and the mechanism of defect development. In this paper, three possible intrinsic point defects (Al vacancies, Al tetrahedral interstitials and Al octahedral interstitials) and three possible helium defects (substituted He, He tetrahedral interstitials and He octahedral interstitials) produced by initial irradiation damage in aluminum are studied by the first-principle plane wave pseudo-potential method within the framework of density functional theory. The formation of the defects and their effects on the stability of the system are compared through crystal structure, formation energy and binding energy. Besides, the electronic mechanism is analyzed from the point of view of density of states (DOS), partial density of states (PDOS), electron density difference and charge populations. It is shown that for the same type of defects, the greater the lattice distortions, the lower the stability of system is and the more difficult the formation of defects. For the formation of the same type of defects, the extent of difficulty in forming defects is in the following order: vacancies (substituted atoms), octahedral interstitials, and tetrahedral interstitials. However, for the same sites, although the intrinsic defects cause greater lattice distortions than the helium defects, they are in fact relatively easier to form, which indicates that the difference between the bonding performances of Al and He plays a leading role in determining the interaction between defects and the aluminum substrate. Besides, the results of binding energy and optimization show that interstitials readily combine with vacancies, and Al has stronger combining ability than He. On the whole, interstitials mainly exist in octahedral interstices, and both octahedral Al and He can cause some electrons to transfer to higher energy levels, lead to some weakening of the covalent interaction between atoms nearest to the interstitials, and eventually reduce the stability of the system. And further study shows that the bond between interstitial Al and its nearest atom features a strongly covalent state, while the interaction between He and its nearest atom is dominated by van der Walls force with weak ionic bond, which accounts for the lower stability of system doped with helium defects.

###### ATOMIC AND MOLECULAR PHYSICS

2017, 66 (5): 053601.
doi: 10.7498/aps.66.053601

Abstract +

Alloy nanoclusters have received extensive attention because they can achieve bifunctional properties by making good use of the cooperative effect of two metals. In this paper, an improved Basin-Hopping Monte Carlo (BHMC) algorithm is proposed to investigate the structural stabilities of Fe-Pt alloy nanoclusters. Different cluster sizes and chemical compositions are considered. Moreover, a similarity function is introduced to analyze the structural similarity between the stable structures of alloy clusters and those of their monometallic clusters. Meanwhile, the atomic distributions of Fe-Pt alloy clusters are considered for their stable structures. The results indicate that for Fe-Pt alloy clusters with the size N 24, there is no significant structural evolution with the increase of cluster size. Fe atoms prefer to segregate at the peripheral positions of the clusters, while Pt atoms tend to occupy the interior. The same distribution result can be obtained for the structures of clusters with different compositions. With Fe composition increasing, this distribution trend is more pronounced for the Fe-Pt alloy clusters.
In addition, by calculating the structural similarity function between alloy and monometallic clusters, we find that the stable structures of Fe-Pt alloy clusters gradually vary with composition ratio. Moreover, when the Fe atoms or Pt atoms are added into the Fe-Pt alloy system, they change the stable structures of Fe-Pt alloy clusters, resulting in a different structure from Fe and Pt monometallic ones. Also, the structural similarity is different when the Fe composition varies. Furthermore, the best stable structures of Fe-Pt clusters with different compositions and sizes are obtained by calculating the second-order finite difference in energy of Fe-Pt alloy clusters.

###### CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

2017, 66 (5): 056101.
doi: 10.7498/aps.66.056101

Abstract +

Compared with conventional semiconductors, the diluted magnetic semiconductors, in which the cations are substituted by transition metal ions, have attracted a great deal of attention due to their promising applications in spintronics. Recently, the unexpected room temperature ferromagnetism has been found in many undoped oxides. These findings challenge our understanding of magnetism in these systems, because neither cations nor anions have unpaired d or f electrons. Generally, the candidate defects responsible for the unexpected ferromagnetism must fulfill two conditions at the same time: (i) the defects should prefer a spin-polarized ground state with a nonzero local magnetic moments; (ii) the exchange interactions between local magnetic moments induced by defects should be ferromagnetic energetically. Among these oxides, TiO2 has recently attracted much attention because of its unique properties and potential applications in spintronics, laser diodes and biomaterials. In order to explore the origin of ferromagnetism in such an undoped TiO2 system, the electronic structures and magnetic properties of oxygen vacancy (VO) and Ti vacancy (VTi) in anatase TiO2 have been studied systematically by the first-principles calculation based on the density functional theory with the LDA+U method (UTi-3d = 5.8 eV). It is found that two electrons introduced by VO are captured by two neighbor Ti4+ ions, and thereby the Ti4+ ions are restored to Ti3+ ions with opposite spin orientation. Therefore, the single VO cannot induce local magnetic moment. The defect energy level locates near the Fermi level for VTi. Six oxygen atoms neighboring VTi constitute an octahedron, and the defect energy level is split into a single state A, a double state E and a triple state T in the octahedral crystal field. The occupation of four unpaired electrons introduced by six oxygen atoms is a+1t+3t-0e0 (subscripts + and - mean up-spin and down-spin, respectively), and the VTi can induce 4 B local moments. Furthermore, the magnetic coupling interaction between local magnetic moments induced by two VTi is ferromagnetic, and the magnetic coupling constant (JO) is 88.7 meV. It means the ferromagnetism can continue up to room-temperature. The VO cannot induce local magnetic moment, but it can enhance the coupling strength between two VTi, which can explain the origin of ferromagnetism observed experimentally in undoped anatase TiO2, i.e., the VTi induces local magnetic moment, while VO enhances the long range ferromagnetic coupling interaction between VTi. Especially, for the ferromagnetic coupling between local magnetic moments, we have proposed the second type direct exchange interaction model, which has been recommended in detail.

2017, 66 (5): 056401.
doi: 10.7498/aps.66.056401

Abstract +

Porous material contains a large number of pores, and once the pore space collapses, it changes into a dense material with the great increase of temperature because of the energy deposition by porosity collapsing. In the process of shock compression, the temperature is extremely increased, which influences the thermodynamic state of porous material significantly. Therefore, the calculation of temperature is important for the shock compression of porous material, yet it has not been solved well in the literature. In this paper, based on the study of Grneisen general function v(v), the Debye temperature function of solid material is extended to the region of porous material, and the equivalent Debye temperature function (v) of porous material is formulated, from which the isentropic temperature function Ts(v) of porous material is obtained. Furthermore, a computation model is established, in which the isentropic work of porous is assumed to be equal to that of compact material under the same pressure at 0 K. With this model, the isentropic pressure function ps(v) of the porous material is acquired. Hence, the reference equation for calculating temperature and pressure of porous material, i.e., Ts(v) and ps(v), is completed. To demonstrate this method, the p-v and T-v curves of the Hgoniot state of porous copperare computed, and the values of porosity are m 1.13, 1.22, 1.41, 1.56 and 1.98, respectively. The calculated results are in good agreement with the experimental data. A comparison with other calculation is also made, indicating a better reliability of the present method.

2017, 66 (5): 056501.
doi: 10.7498/aps.66.056501

Abstract +

Polyethylene (PE) is an important kind of plastic, which plays a significant role as the shell material of the fuel capsule, light weight structural element subjected to intense mechanical impact and explosion load. And it is well accepted that semi-empirical three-term equation of state (EOS) is one of the most widely used EOSs in practical work. Therefore, studies of semi-empirical three-term EOS of PE are significant for accurately predicting and analyzing the physical processes and experimental results under high pressure compression. A semi-empirical three-term complete EOS of PE based on the model of Helmholtz free energy is established in this work. According to the EOS model, the Helmholtz free energy is composed of cold energy, thermal contribution of atoms and thermal excitation of electrons. The cold energy is calculated by using the Mie potential. The optical frequency branch of atomic vibration and the thermal contribution of electrons are neglected in the calculation at temperatures below 104 K. The parameters of Helmholtz free energy are calculated by using the shock Hugoniot data and thermal parameters at ambient state. And then, the application pressure range and reliability of the semi-empirical three-term EOS of PE are evaluated. Shock Hugoniot, shock wave temperature and Grneisen coefficient of PE are deduced from the EOS. The results show that shock Hugoniot and shock wave temperature are consistent well with the experimental data and the first-principle calculation in a pressure range of 150 GPa. Because the specific volume of PE does not change obviously in the melting and chain dissociation process, the assumption of linear Hugoniot relation of PE is valid for calculating the cold energy parameters. The calculation results deviate from the experimental results at about 150 GPa while the compression lasts up to the chemical bond dissociation pressure of PE. In addition, the value of buck modulus and its derivative with respect to pressure at zero pressure and temperature depend strongly on Hugoniot parameters. Therefore, the parameter of Helmholtz free energy in this work is only valid for compression. In conclusion, the Helmholtz free energy model and parameters can well reproduce the experimental data and reasonably describe the thermodynamic state of PE at its dissociation pressure. Moreover, it should be pointed out that a more refined model of phase transition and thermal contribution of atoms and electrons should be considered when extrapolated to higher pressure.

###### INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

2017, 66 (5): 058101.
doi: 10.7498/aps.66.058101

Abstract +

Chemical vapor deposition is widely utilized to synthesize graphene with controlled properties for many applications. And it is one of the most important methods for the preparation of graphene with high quality in large area. Cu substrate is most commonly used for the preparation of graphene in chemical vapor deposition. As is well known, the properties of graphene are greatly affected by the number of layers. However, the syntheses and mechanisms of bi-layer and multi-layer graphene on Cu substrates are still under debate. And how to make a breakthrough in realizing the controllable syntheses of bi-layer and multi-layer graphene on Cu substrates has become a direction for many researchers.
In this work, we report bi-layer and multi-layer graphene on Cu substrates prepared by atmospheric pressure chemical vapor deposition. Firstly, the Cu foil is placed on the quartz slides of the tube furnace and heated to 1000℃ with a rate of 15℃/min. After reaching 1000℃, the Cu foilis annealed for 2 h in a gas mixture of hydrogen (20 sccm) and argon (380 sccm). After that, the graphene growth is carried out at 1000℃ under an 80 sccm gas mixture of argon and ethanol. Then, the samples are cooled down to the room temperature with a rate of 100℃/min in a protection gas of hydrogen and argon, and then taken out of the furnace. The graphene is prepared on the Cu foils and finally transferred onto the SiO2/Si substrates.
The quality and number of layers of the as-produced graphene are assessed by field emission scanning electron microscopy (SEM), transmission electron microscopy (TEM), Raman spectroscopy, and optical microscopy. By tuning the graphene growth, the monolayer, bi-layer and multi-layer graphene with higer quality and better continuity are obtained. And the growth times of monolayer, bi-layer, and four-layers graphene are respectively 25, 40, and 60 s. And wefind that the graphene layer will be increased in the process of insulation. The growth mechanisms of bi-layer and multi-layer graphene on copper substrates by atmospheric pressure chemical vapor deposition are also discussed. There will be some indiffusible carbon atoms or radicals near the copper foil surface due to the small molecular diffusion mean free path under normal pressure. We suggeste that the bi-layer and multi-layer graphene grown on copper substrates by atmospheric pressure chemical vapor deposition is dominated by van der Waals epitaxial mechanism. This work provides a reference for improving the quality of chemical vapor deposition monolayer, bi-layer and multi-layer graphene.

###### GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS

2017, 66 (5): 059201.
doi: 10.7498/aps.66.059201

Abstract +

Unlike the traditional models, a new stereo photographic model requiring no sea control points that are difficult to lay on a sea surface is developed in this paper. It is realized according to the order of camera intrinsic parameters calibration, relative orientation and absolute orientation based on average sea surface, and we give the governing equations and its algorithms. First of all, in the paper we present an imaging model that adopts non-measurement camera with considering only the radial distortion coefficients, and then give the method that calculates the camera intrinsic parameters by combining the co-planar equations and the distance equations to form a closed system of equations. For verifying the convergence of the governing equations, we lay four parallel sand ridges on a level ground in laboratory, measure seven lines of different heights and take a pair of the images by two cameras. The intrinsic parameters are successfully calculated by using the method, and further analysis shows that the results are highly precise. When observing the ocean waves in offshore sea, we need to recalculate the relative orientation parameters. At this time the governing equations are the co-planar equations, but the accuracy of the image matching is seriously related to the accuracy of the relative orientation parameters. However, as the mirror reflection of the sea surface, the matching accuracy of the sea image is often low, so we select 407 optimal matching points from among 1600 conjugate points and calculate the parameters. It needs a sequence of sea image pairs to obtain the absolute orientation parameters, 256 pairs in the paper. For each pair, we select firstly 300300 feature points on the left image approximately evenly, then find the conjugate points on the right image by image matching, calculate the coordinates of the corresponding sea surface points in the left camera coordinate system, and then fit the points into a plane; thus a plane sequence can be obtained. We establish a special object coordinate system on the average sea surface that is obtained by summing the plane sequence, and calculate the absolute orientation parameters by the geometric relationship between the two coordinate systems. And it is proved that the methods of relative orientation and absolute orientation proposed in this paper are feasible by reconstructing sea surface height field. The model greatly reduces the difficulty in calibrating the stereoscopic photography for ocean wave measurement, which is beneficial to its popularization and application.

2017, 66 (5): 059401.
doi: 10.7498/aps.66.059401

Abstract +

Ionospheric heating experiments have been conducted widely at high power heating stations, such as Arecibo, Platteville, HAARP, etc. It has been found that once high-power high-frequency (HF) radio wave is injected into the ionosphere, the electron temperature and density in the illuminated region of the ionosphere can be disturbed, and furthermore, a large number of nonlinear phenomena may be triggered because of the complicated instabilities. One of the most interesting heating effects is the generation of the artificial field-aligned irregularities (AFAI), which has profound influences on electromagnetic wave propagation. Many diagnostic methods have been used for studying the characteristics of AFAI, such as the HF vertical/oblique sounding, HF/VHF coherent radar, etc. During the heating experiments, traces spreading on frequency or height are observed from the HF vertical sounding ionograms, which suggests that the propagation of the sounding wave will be affected by AFAI.
In the ionosphere F region, the electron diffusion and thermal conductivity rate are greater along the geomagnetic field lines than across the field line, leading to a stretch of AFAI along the geomagnetic field line. For the special structure, the AFAI will scatter the incident wave in a cone with the axis parallel to the geomagnetic field direction, which is called artificial field-aligned scattering (AFAS). Because of the high sensitivity to the geomagnetic field of AFAS, we try to study different effects on the HF vertical sounding of AFAI generated at different latitudes, by constructing a propagation model and performing a simulation, in order to seek the potential applications in HF transmission.
Based on the special scattering feature of AFAI and the ray tracing technique, a propagation model for HF vertical sounding scattered by AFAI is proposed. With this model the ray paths of the sounding waves with AFAI are simulated in amid-latitude region, and a new kind of artificial spread trace is found to start from the heating frequency and spread to higher band. Taking account of the strong dependence of the AFAS on the geomagnetic field, the influences of AFAI on the HF vertical sounding at different latitudes are analyzed theoretically. It is indicated that the artificial spread traces will appear only when the following two conditions are satisfied: 1) the sounding wave can reach the AFAI height; 2) the sounding wave is incident perpendicularly to the AFAI. It is also shown that the spread trace becomes shorter with the latitude and the inclination increasing. Furthermore, the simulations from different heating stations suggest that artificial spread traces do not exist when HF vertical sounding is located just below the AFAI, which explains why such phenomena cannot be observed at high latitudes. Nevertheless, if the HF vertical sounding moves outside the heating station toward the south, the spread traces will be apparent for Arecibo, limited for Platteville and still unavailable for HAARP. Finally, if the AFAI is assumed to be present, apparent artificial spread traces of the mid-low latitude are predicted, and the important valuable applications of AFAI in HF transmission are proposed.

## EDITOR'S SUGGESTION

2017, 66 (5): 059701.
doi: 10.7498/aps.66.059701

Abstract +

X-ray pulsar navigation is a complete autonomous navigation system, which has broad application prospects. Because of the huge cost of the navigation system, the implementation of ground simulation system is essential to the application of X-ray pulsar navigation. At present, most of researches on the semi physical experiment system are static. The aim of this article is to develop the dynamic simulation experiment system as well as its performance test. Specifically, this system consists of the dynamic signal database, X-ray simulation source, vacuum system and detection system designed for different science purposes. The core component of the X-ray source is the gate controlled X-ray tube, which can simulate the pulse profile of arbitrary waveform. The detecting system is based on the silicon drift detector with high time response capability. It uses trapezoidal shape for signal processing, and the timing resolution of the detection system is better than 2 s. In addition, the dynamic signal generation method is given by analyzing the time transformation model while the SINC interpolation method is provided to generate the dynamic pulse profile. Finally, the spacecraft revolving around the earth for a circle and receiving a pulse signal of Crab is simulated. In the simulation, the orbital radius of satellite is 6578 km and the orbital period is 5400 s. The Crab pulsar is selected, and the pulse period is 33.4 ms, the number of photons received by the detector is 200 per second. As a contrast, a set of static experiments is also performed. The correlation coefficient between the cumulative pulse profile and the standard pulse profile is 0.9953. However, the correlation coefficient decreases gradually, from 0.9094 at 300 s to 0.4080 at 5400 s, in the dynamic experiment. Then, the pulse period is searched from the arrival time of photons. The periodicity of the pulse signal is sinusoidal when the search period is 60 s. The change rate of photon flux is less than 2\%, and the influence on the period search is negligible. The variation of pulse period is consistent with the motion law of spacecraft, which indicates that spacecraft motion is the dominant factor in time conversion. Finally, the arrival time of photons is transformed into the time at the solar system barycenter, indicating that the correlation coefficient between cumulative pulse profile and standard pulse profile is 0.9882. The result shows that the simulation system can simulate the X-ray pulse signal received by the spacecraft in orbit, which can provide the experimental basis for verifying the navigation algorithm and calibrating the detector performance.