Microwave Bursts Research Articles

Intermittent microwave bursts of a semiconductor laser with an ultra-long loop for generating timing-based random bits.

Chaotic dynamics of semiconductor lasers under optical feedback are useful for random bit generation (RBG). By exploring on an ultra-long feedback loop, a single-mode laser in a route-to-chaos unveils an emission intensity with intermittent microwave bursts, for which a fast form of timing-based RBG is demonstrated. Each microwave burst corresponds to a packet of periodic intensity oscillations at the relaxation resonance. Numerous bursts are found intermittently within a round trip. Repetitions of these intermittent microwave bursts are observed across consecutive round trips. Randomness is extracted from the timing of the bursts as far as the feedback is reinitialized. With a 5-km fiber for feedback to the laser, over 104 intermittent bursts of microwave at 7 GHz are obtained per round trip, where the irregular timing in the envelope leads to RBG at 9.6 Gbps. Such experimental results feature the form of timing-based RBG that is very fast by comparison, carried by the microwave, and stored in the feedback nonlinear dynamics.

Observations of the 2024 May 14 X8.7 Solar Flare with the Goldstone-Apple Valley Radio Telescope (GAVRT)

The Goldstone-Apple Valley Radio Telescope (GAVRT) project conducts a regular monitoring program of the Sun. The GAVRT Solar Patrol project uses a 34 m diameter antenna to produce raster-scan maps of the Sun simultaneously at 4 frequencies ranging from approximately 3 to 14 GHz. On 2024 May 14, as part of regular GAVRT Solar Patrol observations, raster maps were produced when an X8.7 solar flare occurred in active region AR13664. Here we present the GAVRT maps of the May 14 flare along with microwave flux density spectra showing the non-thermal microwave burst emission from mildly relativistic electrons produced in this largest flare of Solar Cycle 25 to date. AR13664 reappeared as AR13697 and continued to be very active, producing X flares while GAVRT monitored its activity. GAVRT microwave data provide a powerful complement to the energetic electrons tracked by X-ray, millimeter-wave and γ-ray emissions.

Episodic Energy Release during the Main and Post-impulsive Phases of a Solar Flare

When and where the magnetic field energy is released and converted in eruptive solar flares remains an outstanding topic in solar physics. To shed light on this question, here we report multiwavelength observations of a C9.4-class eruptive limb flare that occurred on 2017 August 20. The flare, accompanied by a magnetic flux rope eruption and a white light coronal mass ejection, features three post-impulsive X-ray and microwave bursts immediately following its main impulsive phase. For each burst, both microwave and X-ray imaging suggest that the nonthermal electrons are located in the above-the-loop-top region. Interestingly, contrary to many other flares, the peak flux of the three post-impulsive microwave and X-ray bursts shows an increase for later bursts. Spectral analysis reveals that the sources have a hardening spectral index, suggesting a more efficient electron acceleration into the later post-impulsive bursts. We observe a positive correlation between the acceleration of the magnetic flux rope and the nonthermal energy release during the post-impulsive bursts in the same event. Intriguingly, different from some other eruptive events, this correlation does not hold for the main impulse phase of this event, which we interpret as energy release due to the tether-cutting reconnection before the primary flux rope acceleration occurs. In addition, using footpoint brightenings at conjugate flare ribbons, a weakening reconnection guide field is inferred, which may also contribute to the hardening of the nonthermal electrons during the post-impulsive phase.

Bichromatic Rabi Control of Semiconductor Qubits.

Electrically driven spin resonance is a powerful technique for controlling semiconductor spin qubits. However, it faces challenges in qubit addressability and off-resonance driving in larger systems. We demonstrate coherent bichromatic Rabi control of quantum dot hole spin qubits, offering a spatially selective approach for large qubit arrays. By applying simultaneous microwave bursts to different gate electrodes, we observe multichromatic resonance lines and resonance anticrossings that are caused by the ac Stark shift. Our theoretical framework aligns with experimental data, highlighting interdot motion as the dominant mechanism for bichromatic driving.

The Non-Thermal Radio Emissions of the Solar Transition Region and the Proposal of an Observational Regime

The transition region is a very thin but most peculiar layer in the solar atmosphere located between the solar chromosphere and the corona. It is a key region for understanding coronal heating, solar eruption triggers, and the origin of solar winds. Here, almost all physical parameters (density, temperature, and magnetic fields) have the maximum gradient. Therefore, this region should be highly dynamic, including fast energy releasing and transporting, plasma heating, and particle accelerating. The physical processes can be categorized into two classes: thermal and non-thermal processes. Thermal processes can be observed at ultraviolet (UV) and extreme ultraviolet (EUV) wavelengths via multi-wavelength images. Non-thermal processes accelerate non-thermal electrons and produce radio emissions via the gyrosynchrotron mechanism resulting from the interaction between the non-thermal electrons and magnetic fields. The frequency range spans from several GHz to beyond 100 GHz, in great number of bursts with narrowband, millisecond lifetime, rapid frequency drifting rates, and being referred to as transition region small-scale microwave bursts (TR-SMBs). This work proposes a new type of Solar Ultra-wide Broadband Millimeter-wave Spectrometer (SUBMS) that can be used to observe TR-SMBs. From SUBMS observations, we can derive rich dynamic information about the transition region, such as information about non-thermal energy release and propagation, the flows of plasma and energetic particles, the magnetic fields and their variations, the generation and transportation of various waves, and the formation and evolution of the source regions of solar eruptions. Such an instrument can actually detect the non-thermal signals in the transition region during no flare as well as the eruptive high-energy processes during solar flares.

The Solar Origin of an In Situ Type III Radio Burst Event

Solar type III radio bursts are generated by beams of energetic electrons that travel along open magnetic field lines through the corona and into interplanetary space. However, understanding the source of these electrons and how they escape into interplanetary space remains an outstanding topic. Here we report multi-instrument, multiperspective observations of an interplanetary type III radio burst event shortly after the second perihelion of the Parker Solar Probe (PSP). This event was associated with a solar jet that produced an impulsive microwave burst event recorded by the Expanded Owens Valley Solar Array. The type III burst event also coincided with the detection of enhanced in situ energetic electrons recorded by both PSP at 0.37 au and WIND at 1 au, which were located very closely on the Parker spiral longitudinally. The close timing association and magnetic connectivity suggest that the in situ energetic electrons originated from the jet’s magnetic reconnection region. Intriguingly, microwave imaging spectroscopy results suggest that the escaping energetic electrons were injected into a large opening angle of about 90°, which is at least nine times broader than the apparent width of the jet spire. Our findings provide an interpretation for the previously reported, longitudinally broad spatial distribution of flare locations associated with prompt energetic electron events and have important implications for understanding the origin and distribution of energetic electrons in interplanetary space.

Coherence Characteristics of a GaAs Single Heavy-Hole Spin Qubit Using a Modified Single-Shot Latching Readout Technique.

We present an experimental study of the coherence properties of a single heavy-hole spin qubit formed in one quantum dot of a gated GaAs/AlGaAs double quantum dot device. We use a modified spin-readout latching technique in which the second quantum dot serves both as an auxiliary element for a fast spin-dependent readout within a 200 ns time window and as a register for storing the spin-state information. To manipulate the single-spin qubit, we apply sequences of microwave bursts of various amplitudes and durations to make Rabi, Ramsey, Hahn-echo, and CPMG measurements. As a result of the qubit manipulation protocols combined with the latching spin readout, we determine and discuss the achieved qubit coherence times: T1, TRabi, T2*, and T2CPMG vs. microwave excitation amplitude, detuning, and additional relevant parameters.

Correction to: Common Origin of Quasi-Periodic Pulsations in Microwave and Decimetric Solar Radio Bursts

Correction to: Common Origin of Quasi-Periodic Pulsations in Microwave and Decimetric Solar Radio Bursts

A Broadband Solar Radio Dynamic Spectrometer Working in the Millimeter-wave Band

Abstract Most solar radio telescopes operate below ∼18 GHz and cannot realize a complete frequency coverage of the microwave spectrum, especially in the optically thin regime during solar bursts, which can provide unique information about the magnetic field in the burst area in the solar corona. Therefore, the development of high-frequency microwave observation equipment is demanded by the solar radio community. In this paper, we present a microwave spectrum observation system operating at 35–40 GHz. In this system, the solar radio signal is acquired by an 80 cm Cassegrain circularly polarized antenna, which is then downconverted and channelized by a 35–40 GHz analog front end. The processed signal is finally sent to the digital receiver to generate the microwave dynamic spectrum, which is transmitted by gigabit Ethernet transmission to a host computer. The system performance has been tested and obtained as follows: a noise figure of ∼300 K, system linearity of >0.9999, time resolution of about 134 ms (default), and frequency resolution of 153 kHz. We further conduct calibration for this system and find that the observed Sun–Moon ratio is about 43.1–53.3 @ 35.25 GHz during the new Moon, and is quite close to the theoretical value. The coefficient of variation of the system is ∼0.61% in a 9 hr test. The system has been designed, developed, and tested for over 1 yr in Chashan Solar Observatory and is expected to play an important role in the microwave burst study in the 25th solar cycle.

Common Origin of Quasi-Periodic Pulsations in Microwave and Decimetric Solar Radio Bursts

We analyse quasi-periodic pulsations (QPP) detected in the microwave and decimeter radio emission of the SOL2017-09-05T07:04 solar flare, using simultaneous observations by the Siberian Radioheliograph 48 (SRH-48, 4-8 GHz) and Mingantu Spectral Radioheliograph (MUSER-I, 0.4-2 GHz). The microwave emission was broadband with a typical gyrosynchrotron spectrum, while a quasi-periodic enhancement of the decimetric emission appeared in a narrow spectral band (500-700 MHz), consistent with the coherent plasma emission mechanism. The periodicity that we found in microwaves is about 30 s, coming from a compact loop-like source with a typical height of about 31 Mm. The decimetric emission demonstrated a periodicity about 6 s. We suggested a qualitative scenario linking the QPPs observed in both incoherent and coherent spectral bands and their generation mechanisms. The properties of the QPPs found in the microwave signal are typical for perturbations of the flare loop by the standing sausage mode of a fast magnetohydrodynamic (MHD) wave. Our analysis indicated that this sausage-oscillating flare loop was the primary source of oscillations in the discussed event. The suggested scenario is that a fundamental sausage harmonic is the dominant cause for the observed QPPs in the microwave emission. The initiation of oscillations in the decimetric emission is caused by the third sausage harmonic via periodic and nonlinear triggering of the acceleration processes in the current sheets, formed at the interface between the sausage-oscillating flare loop and the external coronal loop that extended to higher altitudes. Our results demonstrate the possible role of MHD wave processes in the release and transport of energy during solar flares, linking coherent and incoherent radio emission mechanisms.

Energy and spectral analysis of confined solar flares from radio and X-ray observations

The energy and spectral shape of radio bursts may help us understand the generation mechanism of solar eruptions, including solar flares, coronal mass ejections, eruptive filaments, and various scales of jets. The different kinds of flares may have different characteristics of energy and spectral distribution. In this work, we selected 10 mostly confined flare events during October 2014 to investigate their overall spectral behaviour and the energy emitted in microwaves by using radio observations from microwaves to interplanetary radio waves, and X-ray observations of GOES, RHESSI, and Fermi/GBM. We found that: all the confined flare events were associated with a microwave continuum burst extending to frequencies of 9.4 ∼ 15.4 GHz, and the peak frequencies of all confined flare events are higher than 4.995 GHz and lower than or equal to 17 GHz. The median value is around 9 GHz. The microwave burst energy (or fluence) and the peak frequency are found to provide useful criteria to estimate the power of solar flares. The observations imply that the magnetic field in confined flares tends to be stronger than that in 412 flares studied by Nita et al. (2004). All 10 events studied did not produce detectable hard X-rays with energies above ∼300 keV indicating the lack of efficient acceleration of electrons to high energies in the confined flares.

Quiet-Filament Eruptions and Coronal Jets as Causes of Depressions in Microwave Radio Emission

Several solar events with different types of negative microwave bursts have been studied using data from different spectral ranges. The total radio flux data obtained at the Ussuriysk Observatory, the Nobeyama Observatory, the US Air Force Radio Solar Telescope Network (RSTN), and the spectropolarimeter of the Institute of Solar–Terrestrial Physics, Siberian Branch of the Russian Academy of Sciences (ISTP SB RAS) were used. The images were analyzed using data from the SDO/AIA space observatory in the 304 Å channel and the Nobeyama radio heliograph at a frequency of 17 GHz. It was shown that the “isolated” depressions of radio emission were caused by the absorption of radiation from radio sources and/or vast regions of the quiet Sun by low-temperature material of a large eruptive filament in the absence of flares. This confirmed the conclusions of the previous studies. It was revealed that the cause of negative bursts of the “pre-burst depression” type was the screening of a near-limb radio source by the material of coronal jets. In the case of a weak flare accompanying the jet, the negative burst could also be of the “isolated” type. A case of a previously unreported occurrence of a deeper depression of radio emission at high frequencies as compared to low frequencies was considered. It was shown that negative bursts are not as rare phenomena as previously thought.

Connecting solar flare hard X-ray spectra to in situ electron spectra

Aims. We aim to constrain the acceleration, injection, and transport processes of flare-accelerated energetic electrons by comparing their characteristics at the Sun with those injected into interplanetary space. Methods. We have identified 17 energetic electron events well-observed with the SEPT instrument aboard STEREO which show a clear association with a hard X-ray (HXR) flare observed with the RHESSI spacecraft. We compare the spectral indices of the RHESSI HXR spectra with those of the interplanetary electrons. Because of the frequent double-power-law shape of the in situ electron spectra, we paid special attention to the choice of the spectral index used for comparison. Results. The time difference between the electron onsets and the associated type III and microwave bursts suggests that the electron events are detected at 1 AU with apparent delays ranging from 9 to 41 min. While the parent solar activity is clearly impulsive, also showing a high correlation with extreme ultraviolet jets, most of the studied events occur in temporal coincidence with coronal mass ejections (CMEs). In spite of the observed onset delays and presence of CMEs in the low corona, we find a significant correlation of about 0.8 between the spectral indices of the HXR flare and the in situ electrons. The correlations increase if only events with significant anisotropy are considered. This suggests that transport effects can alter the injected spectra leading to a strongly reduced imprint of the flare acceleration. Conclusions. We conclude that interplanetary transport effects must be taken into account when inferring the initial acceleration of solar energetic electron events. Although our results suggest a clear imprint of flare acceleration for the analyzed event sample, a secondary acceleration might be present which could account for the observed delays. However, the limited and variable pitch-angle coverage of SEPT could also be the reason for the observed delays.

Implications of Flat Optically Thick Microwave Spectra in Solar Flares for Source Size and Morphology

Abstract The study aims to examine the spectral dynamics of the low-frequency, optically thick gyrosynchrotron microwave emission in solar flares to determine the characteristics of the emitting source. We present the high-resolution spectra of a set of microwave bursts observed by the Expanded Owens Valley Solar Array (EOVSA) during its commissioning phase in the 2.5–18 GHz frequency range with 1 second time resolution. Out of the 12 events analyzed in this study, nine bursts exhibit a direct decrease with time in the optically thick spectral index α l , an indicator of source morphology. Particularly, five bursts display a “flat” spectrum (α l ≤ 1.0) compared to that expected for a homogeneous/uniform source (α l ≈ 2.9). These flat spectra at low frequencies (<10 GHz) can be defined as the emission from a spatially inhomogeneous source with a large area and/or with multiple emission components. In a subset of six events with partial cross-correlation data, both the events with flat spectra show a source size of ∼120″ at 2.6–3 GHz. Modeling based on inhomogeneity supports the conclusion that multiple discrete sources can only reproduce a flat spectrum. We report that these flat spectra appear predominantly in the decay phase and typically grow flatter over the duration in most of the bursts, which indicates an increasing inhomogeneity and complexity of the emitting volume as the flare progresses. This large volume of flare emission filled with the trapped energetic particles is often invisible in other wavelengths, like hard X-rays, presumably due to the collisionless conditions in these regions of low ambient density and magnetic field strength.

Statistical analysis of solar radio fiber bursts and relations with flares

Fiber bursts are a type of fine structure that frequently occurs in solar flares. Although observations and theory of fiber bursts have been studied for decades, their microphysical process, emission mechanism, and especially the physical links with the flaring process still remain unclear. We performed a detailed statistical study of fiber bursts observed by the Chinese Solar Broadband Radio Spectrometers in Huairou with high spectral-temporal resolutions in the frequency ranges of 1.10−2.06 GHz and 2.60−3.80 GHz during 2000−2006. We identify more than 900 individual fiber bursts in 82 fiber events associated with 48 solar flares. From the soft X-ray observations of the Geostationary Operational Environmental Satellite, we found that more than 40% of fiber events occurred in the preflare and rising phases of the associated solar flares. Most fiber events are temporally associated with hard X-ray bursts observed by RHESSI or microwave bursts observed by the Nobeyama Radio Polarimaters, which implies that they are closely related to the nonthermal energetic electrons. The results indicate that most fiber bursts have a close temporal relation with energetic electrons. Most fiber bursts are strongly polarized, and their average duration, relative bandwidth, and relative frequency-drift rate are about 1.22 s, 6.31%, and −0.069 s−1. The average duration and relative bandwidth of fiber bursts increase with solar flare class. The fiber bursts associated with X-class flares have a significantly lower mean relative frequency-drift rate. The average durations in the postflare phase are clearly longer than the duration in the preflare and rising phases. The relative drift rate in the rising phase is clearly higher than that in preflare and postflare phases. The hyperbola correlation of the average duration and the relative drift rate of the fiber bursts is very interesting. These characteristics are very important for understanding the formation of solar radio fiber bursts and for revealing the nonthermal processes of the related solar flares.

CMOS-based cryogenic control of silicon quantum circuits.

The most promising quantum algorithms require quantum processors that host millions of quantum bits when targeting practical applications1. A key challenge towards large-scale quantum computation is the interconnect complexity. In current solid-state qubit implementations, an important interconnect bottleneck appears between the quantum chip in a dilution refrigerator and the room-temperature electronics. Advanced lithography supports the fabrication of both control electronics and qubits in silicon using technology compatible with complementary metal oxide semiconductors (CMOS)2. When the electronics are designed to operate at cryogenic temperatures, they can ultimately be integrated with the qubits on the same die or package, overcoming the 'wiring bottleneck'3-6. Here we report a cryogenic CMOS control chip operating at 3 kelvin, which outputs tailored microwave bursts to drive silicon quantum bits cooled to 20 millikelvin. We first benchmark the control chip and find an electrical performance consistent with qubit operations of 99.99 per cent fidelity, assuming ideal qubits. Next, we use it to coherently control actual qubits encoded in the spin of single electrons confined in silicon quantum dots7-9 and find that the cryogenic control chip achieves the same fidelity as commercial instruments at room temperature. Furthermore, we demonstrate the capabilities of the control chip by programming a number of benchmarking protocols, as well as the Deutsch-Josza algorithm10, on a two-qubit quantum processor. These results open up the way towards a fully integrated, scalable silicon-based quantum computer.

Spectroscopic observations of a flare-related coronal jet

Context. Coronal jets are ubiquitous in active regions and coronal holes. Aims. In this paper, we study a coronal jet related to a C3.4 circular-ribbon flare in the active region 12434 on 2015 October 16. Methods. The flare and jet were observed in ultraviolet and extreme ultraviolet wavelengths by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory (SDO). The line-of-sight magnetograms of the photosphere were observed by the Helioseismic and Magnetic Imager on board SDO. The whole event was covered by the Interface Region Imaging Spectrograph during its imaging and spectroscopic observations. Soft X-ray fluxes of the flare were recorded by the GOES spacecraft. Hard X-ray (HXR) fluxes at 4−50 keV were obtained from observations of RHESSI and Fermi. Radio dynamic spectra of the flare were recorded by the ground-based stations belonging to the e-Callisto network. Results. Two minifilaments were located under a 3D fan-spine structure before flare. The flare was generated by the eruption of one filament. The kinetic evolution of the jet was divided into two phases: a slow rise phase at a speed of ∼131 km s−1 and a fast rise phase at a speed of ∼363 km s−1 in the plane-of-sky. The slow rise phase may correspond to the impulsive reconnection at the breakout current sheet. The fast rise phase may correspond to magnetic reconnection at the flare current sheet. The transition between the two phases occurred at ∼09:00:40 UT. The blueshifted Doppler velocities of the jet in the Si IV 1402.80 Å line range from −34 to −120 km s−1. The accelerated high-energy electrons are composed of three groups. Those propagating upward along the open field generate type III radio bursts, while those propagating downward produce HXR emissions and drive chromospheric condensation observed in the Si IV line. The electrons trapped in the rising filament generate a microwave burst lasting for ≤40 s. Bidirectional outflows at the base of jet are manifested by significant line broadenings of the Si IV line. The blueshifted Doppler velocities of outflows range from −13 to −101 km s−1. The redshifted Doppler velocities of outflows range from ∼17 to ∼170 km s−1. Conclusions. Our multiwavelength observations of the flare-related jet are in favor of the breakout jet model and are important for understanding the acceleration and transport of nonthermal electrons.

Radio Astronomical Tools for the Study of Solar Energetic Particles I. Correlations and Diagnostics of Impulsive Acceleration and Particle Propagation

Solar energetic particles (SEPs) are sporadically ejected from the Sun during flares and coronal mass ejections. They are of major astrophysical interest, because the proximity of the Sun allows for detailed multi-messenger studies. They affect space weather due to interactions with electronics, with the Earth’s atmosphere, and with humans if they leave the protective shield of the magnetosphere of the Earth. Since early studies in the 1950s, starting with particle detectors on the ground, SEP events have been related to radio bursts. Two subjects are addressed in this chapter: attempts to establish quantitative correlations between SEPs and microwave bursts produced by gyro synchrotron radiation of mildly relativistic electrons, and the information derived from type III radio bursts on impulsive processes of particle acceleration and the coronal and interplanetary propagation. Type III radio bursts produced by electron beams on open magnetic field lines have a wide range of applications, including the identification of acceleration regions, the identification of confined particle acceleration with coronal signatures, but no SEPs, and the paths that the electrons, and energetic charged particles in general, take to travel from the low corona to the Heliosphere in case they escape. Simple scenarios of coronal particle acceleration are confirmed in relatively simple and short events. But the comparison with particle transport models shows that longer and delayed acceleration episodes exist especially in large SEP events. They will be discussed in a companion chapter.

Statistical Studies on Modified Neupert Effect

The qualitative description of the Neupert effect is that there is a causal relationship between the pulse component (hard X-ray, microwave burst) and the gradual component (soft X-ray emission) in a flare. The initial energy of the flare is released in the form of accelerating particles. The energetic particles produce HXR (hard X-ray) via nonthermal electron-ion bremsstrahlung as they lose their energies in the chromosphere. The SXR (soft X-ray) emission of the flare is the response of energetic particles injected into the chromosphere. According to the quantitative description of the classic Neupert effect, SXR should reach maximum instantly at the end of HXR emission (sign of nonthermal electron injection). However, previous observations have found that for quite a number of flares the SXR peak time (t2) is significantly later than the end time of HXR (t1) (τ=t2−t1,τ>0), deviating from the classic Neupert effect. In order to study the events deviating from the classic Neupert effect or not, we checked the RHESSI (Reuven Ramaty High Energy Solar Spectroscopic Imager) and GOES (Geostationary Operational Environmental Satellites) events list from 2002 to 2015, and found out flare samples that have simple lightcurves at 25–50 keV together with other criteria. A total of 276 flare samples were finally selected. We have analysed the τ distribution of these flares, as well as the relationship between the loop length (represented by the distance between two footpoint sources d) and τ. We found that: (1) 227 sample flares present τ>0, which means that about 82% of total samples deviate from the classical Neupert effect; (2) there is a roughly linear correlation between τ and d, that is, the longer the loop is, the later the maximum time of SXR with respect to the end of HXR; (3) there seems to have a critical distance, within which the classic Neupert effect works. These results confirm the necessity of modifying Neupert effect, and expound its physical significance.

Research on CuxSy/CoSz/graphene supercapacitor electrode materials

Multilayer graphene was prepared in this study by microwave burst method. Cu9S5/CoS/graphene and CuS/CoS2/graphene composites were obtained by hydrothermal method to regulate the molecular structure and combination of Cu and Co metal sulfides on graphene substrate. Graphite oxide was doped by hydrothermal method, and then Cu9S5/CoS/graphene composite was prepared by microwave explosion method. Raman, SEM and TEM were used to characterize the self-made graphene. Results showed that the multilayer graphene had a bag-like structure which was beneficial to anchor sulfide. Three graphene-based composites were characterized by scanning electron microscopy, X-ray diffraction, energy spectrum analysis and electrochemical properties. Moreover, results showed that CuS/CoS2/graphene had the best electrochemical performance, and its specific capacity reached 324 F/g when the current density was 1 A · g–1, which was much higher than that of the other two samples. Capacity retention rate, interfacial charge transfer resistance and electrolyte diffusion resistance also have advantages.