Suppression of low-frequency ultrasound broadband vibration using star-shaped single-phase metamaterials

In order to suppress the low-frequency ultrasound vibration in the broadband range of 20 k Hz—100 k Hz,this paper proposes and discusses an acoustic metamaterial with low-frequency ultrasound vibration attenuation properties,which is configured by hybrid arc and sharp-angle convergent star-shaped lattices.The effect of the dispersion relation and the bandgap characteristic for the scatterers in star-shaped are simulated and analyzed.The target bandgap width is extended by optimizing the geometry parameters of arc and sharp-angle convergent lattices.The proposed metamaterial configured by optimized hybrid lattices exhibits remarkable broad bandgap characteristics by bandgap complementarity,and the simulation results verify a 99%vibration attenuation amplitude can be obtained in the frequency of20 k Hz—100 k Hz.After the fabrication of the proposed hybrid configurational star-shaped metamaterial by 3D printing technique,the transmission loss experiments are performed,and the experimental results indicate that the fabricated metamaterial has the characteristics of broadband vibration attenuation and an amplitude greater than 85%attenuation for the target frequency.These results demonstrate that the hybrid configurational star-shaped metamaterials can effectively widen the bandgap and realize high efficiency attenuation,which has capability for the vibration attenuation in the application of highprecise equipment.

Current optimization-based control of dual three-phase PMSM for low-frequency temperature swing reduction

In this paper,a control scheme based on current optimization is proposed for dual three-phase permanent-magnet synchronous motor(DTP-PMSM)drive to reduce the low-frequency temperature swing.The reduction of temperature swing can be equivalent to reducing maximum instantaneous phase copper loss in this paper.First,a two-level optimization aiming at minimizing maximum instantaneous phase copper loss at each electrical angle is proposed.Then,the optimization is transformed to a singlelevel optimization by introducing the auxiliary variable for easy solving.Considering that singleobjective optimization trades a great total copper loss for a small reduction of maximum phase copper loss,the optimization considering both instantaneous total copper loss and maximum phase copper loss is proposed,which has the same performance of temperature swing reduction but with lower total loss.In this way,the proposed control scheme can reduce maximum junction temperature by 11%.Both simulation and experimental results are presented to prove the effectiveness and superiority of the proposed control scheme for low-frequency temperature swing reduction.

Low-frequency oscillation of train-network system considering traction power supply mode

The low-frequency oscillation(LFO)has occurred in the train-network system due to the introduction of the power electronics of the trains.The modeling and analyzing method in current researches based on electrified railway unilateral power supply system are not suitable for the LFO analysis in a bilateral power supply system,where the trains are supplied by two traction substations.In this work,based on the single-input and single-output impedance model of China CRH5 trains,the node admittance matrices of the train-network system both in unilateral and bilateral power supply modes are established,including three-phase power grid,traction transformers and traction network.Then the modal analysis is used to study the oscillation modes and propagation characteristics of the unilateral and bilateral power supply systems.Moreover,the influence of the equivalent inductance of the power grid,the length of the transmission line,and the length of the traction network are analyzed on the critical oscillation mode of the bilateral power supply system.Finally,the theoretical analysis results are verified by the time-domain simulation model in MATLAB/Simulink.

High-order Bragg forward scattering and frequency shift of low-frequency underwater acoustic field by moving rough sea surface

Acoustic scattering modulation caused by an undulating sea surface on the space-time dimension seriously affects underwater detection and target recognition.Herein,underwater acoustic scattering modulation from a moving rough sea surface is studied based on integral equation and parabolic equation.And with the principles of grating and constructive interference,the mechanism of this acoustic scattering modulation is explained.The periodicity of the interference of moving rough sea surface will lead to the interference of the scattering field at a series of discrete angles,which will form comb-like and frequency-shift characteristics on the intensity and the frequency spectrum of the acoustic scattering field,respectively,which is a high-order Bragg scattering phenomenon.Unlike the conventional Doppler effect,the frequency shifts of the Bragg scattering phenomenon are multiples of the undulating sea surface frequency and are independent of the incident sound wave frequency.Therefore,even if a low-frequency underwater acoustic field is incident,it will produce obvious frequency shifts.Moreover,under the action of ideal sinusoidal waves,swells,fully grown wind waves,unsteady wind waves,or mixed waves,different moving rough sea surfaces create different acoustic scattering processes and possess different frequency shift characteristics.For the swell wave,which tends to be a single harmonic wave,the moving rough sea surface produces more obvious high-order scattering and frequency shifts.The same phenomena are observed on the sea surface under fully grown wind waves,however,the frequency shift slightly offsets the multiple peak frequencies of the wind wave spectrum.Comparing with the swell and fully-grown wind waves,the acoustic scattering and frequency shift are not obvious for the sea surface under unsteady wind waves.

A bio-inspired spider-like structure isolator for low-frequency vibration

This paper proposes a quasi-zero stiffness(QZS)isolator composed of a curved beam(as spider foot)and a linear spring(as spider muscle)inspired by the precise capturing ability of spiders in vibrating environments.The curved beam is simplified as an inclined horizontal spring,and a static analysis is carried out to explore the effects of different structural parameters on the stiffness performance of the QZS isolator.The finite element simulation analysis verifies that the QZS isolator can significantly reduce the first-order natural frequency under the load in the QZS region.The harmonic balance method(HBM)is used to explore the effects of the excitation amplitude,damping ratio,and stiffness coefficient on the system’s amplitude-frequency response and transmissibility performance,and the accuracy of the analytical results is verified by the fourth-order Runge-Kutta integral method(RK-4).The experimental data of the QZS isolator prototype are fitted to a ninth-degree polynomial,and the RK-4 can theoretically predict the experimental results.The experimental results show that the QZS isolator has a lower initial isolation frequency and a wider isolation frequency bandwidth than the equivalent linear isolator.The frequency sweep test of prototypes with different harmonic excitation amplitudes shows that the initial isolation frequency of the QZS isolator is 3 Hz,and it can isolate 90%of the excitation signal at 7 Hz.The proposed biomimetic spider-like QZS isolator has high application prospects and can provide a reference for optimizing low-frequency or ultra-low-frequency isolators.

Permeability evolution mechanism and the optimum permeability determination of uranium leaching from low-permeability sandstone treated with low-frequency vibration

Low-frequency vibrations can effectively improve natural sandstone permeability,and higher vibration frequency is associated with larger permeability.However,the optimum permeability and permeability evolution mechanism for uranium leaching and the relationship between permeability and the change of chemical reactive rate affecting uranium leaching have not been determined.To solve the above problems,in this study,identical homogeneous sandstone samples were selected to simulate lowpermeability sandstone;a permeability evolution model considering the combined action of vibration stress,pore water pressure,water flow impact force,and chemical erosion was established;and vibration leaching experiments were performed to test the model accuracy.Both the permeability and chemical reactions were found to simultaneously restrict U6þleaching,and the vibration treatment increased the permeability,causing the U6þleaching reaction to no longer be diffusion-constrained but to be primarily controlled by the reaction rate.Changes of the model calculation parameters were further analyzed to determine the permeability evolution mechanism under the influence of vibration and chemical erosion,to prove the correctness of the mechanism according to the experimental results,and to develop a new method for determining the optimum permeability in uranium leaching.The uranium leaching was found to primarily follow a process consisting of(1)a permeability control stage,(2)achieving the optimum permeability,(3)a chemical reactive rate control stage,and(4)a channel flow stage.The resolution of these problems is of great significance for facilitating the application and promotion of lowfrequency vibration in the CO_(2)+O_(2) leaching process.

Observation of low-frequency oscillation in argon helicon discharge

We present here a kind of low-frequency oscillation in argon helicon discharge with a half helical antenna.This time-dependent instability shows a global quasi-periodic oscillation of plasma density and electron temperature,with a typical frequency of a few tens of Hz which increases with external magnetic field as well as radiofrequency(RF)power.The relative oscillation amplitude decreases with magnetic field and RF power,but the rising time and pulse width do not change significantly under different discharge conditions.The oscillation can only be observed in some specific conditions of low magnetic fields and low RF power when the gas flows in from one end of the discharge area and out from another end.This global instability is suggested to be attributed to the pressure instability of neutral depletion,which is the result of compound action of gas depletion by heating expansion and gas replenishment from upstream.There are two kinds of oscillations,large and small amplitude oscillations,occurring in different discharge modes.This study could be a good verification of and complement to earlier experiments.This kind of spontaneous pulse phenomenon is also helpful in realizing a pulsing plasma source without a pulsed power supply.

Method for measuring the low-frequency sound power from a complex sound source based on sound-field correction in a non-anechoic tank

Similar to air reverberation chambers, non-anechoic water tanks are important acoustic measurement devices that can be used to measure the sound power radiated from complex underwater sound sources using diffusion field theory. However,the problem of the poor applicability of low-frequency measurements in these tanks has not yet been solved. Therefore,we propose a low-frequency acoustic measurement method based on sound-field correction(SFC) in an enclosed space that effectively solves the problem of measuring the sound power from complex sound sources below the Schroeder cutoff frequency in a non-anechoic tank. Using normal mode theory, the transfer relationship between the mean-square sound pressure in an underwater enclosed space and the free-field sound power of the sound source is established, and this is regarded as a correction term for the sound field between this enclosed space and the free field. This correction term can be obtained based on previous measurements of a known sound source. This term can then be used to correct the mean-square sound pressure excited by any sound source to be tested in this enclosed space and equivalently obtain its free-field sound power. Experiments were carried out in a non-anechoic water tank(9.0 m × 3.1 m × 1.7 m) to confirm the validity of the SFC method. Through measurements with a spherical sound source(whose free-field radiation characteristics are known),the correction term of the sound field between this water tank and the free field was obtained. On this basis, the sound power radiated from a cylindrical shell model under the action of mechanical excitation was measured. The measurement results were found to have a maximum deviation of 2.9 d B from the free-field results. These results show that the SFC method has good applicability in the frequency band above the first-order resonant frequency in a non-anechoic tank. This greatly expands the potential low-frequency applications of non-anechoic tanks.

A drift-kinetic perturbed Lagrangian for low-frequency nonideal MHD applications

We find that the perturbed Lagrangian derived from the drift-kinetic equation in[Porcelli F et al 1994 Phys.Plasmas 1470]is inconsistent with the ordering for the low-frequency large-scale magnetohydrodynamic(MHD).Here,we rederive the expression for the perturbed Lagrangian within the framework of nonideal MHD using the ordering system for the low-frequency largescale MHD in a low-beta plasma.The obtained perturbed Lagrangian is consistent with Chen's gyrokinetic theory[Chen L and Zonca F 2016 Rev.Mod.Phys.88015008],where the terms related to the field curvature and gradient are small quantities of higher order and thus negligible.As the perturbed Lagrangian has been widely used in the literature to calculate the plasma nonadiabatic response in low-frequency MHD applications,this finding may have a significant impact on the understanding of the kinetic driving and dissipative mechanisms of MHD instabilities and the plasma response to electromagnetic perturbations in fusion plasmas.

Low-Frequency Oscillation Analysis of Grid-Connected VSG System Considering Multi-Parameter Coupling

With the increasing integration of new energy generation into the power system and the massive withdrawal of traditional fossil fuel generation,the power system is faced with a large number of stability problems.The phenomenon of low-frequency oscillation caused by lack of damping and moment of inertia is worth studying.In recent years,virtual synchronous generator(VSG)technique has been developed rapidly because it can provide considerable damping and moment of inertia.While improving the stability of the system,it also inevitably causes the problem of active power oscillation,especially the low mutual damping between the VSG and the power grid will make the oscillation more severe.The traditional time-domain state-space method cannot reflect the interaction among state variables and study the interaction between different nodes and branches of the power grid.In this paper,a frequency-domain method for analyzing low-frequency oscillations considering VSG parameter coupling is proposed.First,based on the rotor motion equation of the synchronous generator(SG),a secondorder VSG model and linearized power-frequency control loop model are established.Then,the differences and connections between the coupling of key VSG parameters and low-frequency oscillation characteristics are studied through frequency domain analysis.The path and influencemechanism of a VSG during low-frequency power grid oscillations are illustrated.Finally,the correctness of the theoretical analysis model is verified by simulation.

Development of a low-frequency magnetic lightning mapping system(LFM-LMS)in North China:validation and preliminary results

A low-frequency magnetic lightning mapping system(LFM-LMS)was built during the SHAndong Triggered Lightning Experiment(SHATLE),based on continuous measurements of magnetic field radiation from lightning.The hardware and source-mapping techniques used by the LFM-LMS were introduced;both Monte Carlo simulations and the observation of rocket-triggered lightning examples were employed to examine the location accuracy and detection effectiveness of the LFM-LMS.We estimated that the system’s location accuracy about 100−200 m horizontally and~200 m vertically.A natural intra-cloud lightning flash and a rocket-triggered lightning flash,both with intricate structures and discharging processes,were examined using the three-dimensional mapping results.The progressing path of negative lightning leaders is usually well-defined,and its propagation speed is estimated to be(0.5−1.4)×10^(6)m/s.In summary,the LFM-LMS can reconstruct the three-dimensional morphology of lightning flashes;this technology provides a efficient method for investigating the characteristics of lightning development,as well as the overall electrical strucuture of thunderstorms.

Understanding Lithium-ion Transport in Sulfolane- and Tetraglyme-Based Electrolytes Using Very Low-Frequency Impedance Spectroscopy

With the increasing interest in highly concentrated electrolyte systems,correct determination of the cation transference number is important.Pulsed-field gradient NMR technique,which measures self-diffusion coefficients,is often applied on liquid electrolytes because of the wide accessibility and simple sample preparation.However,since the assumptions of this technique,that is,complete salt dissociation,all ions participating in motion,and all of them moving independently,no longer hold true in concentrated solutions,the transference numbers,thus obtained are often over-estimated.In the present work,impedance spectroscopy at a frequency range of 1 MHz to 0.1 mHz was used to examine the concentration effect on lithium-ion transference number under anion-blocking conditions T abc Liþfor two electrolytes:lithium bis(fluorosulfonyl)imide(LiFSI)in sulfolane(SL)and lithium bis(trifluorosulfonyl)imide(LiTFSI)in tetraglyme(G4).The T abc Liþof the former was almost an order of magnitude higher than that of the latter.It also appeared to increase with increasing concentration while the latter followed an opposite trend.The faster Li^(+)transport in the SL system is attributed to the formation of a liquid structure consisting of extended chains/bridges of SL molecules and the anions,which facilitate a cation-hopping/ligand-exchanged-typed diffusion mechanism by partially decoupling the cations from the anions and solvent molecules.The G4 system,in contrast,is dominated by the formation of long-lived,stable[Li(G4)]+solvation cages that results in a sluggish Li+transport.The difference between the two transport mechanisms is discussed via comparison of the bulk ionic conductivity,viscosity,ion self-diffusion coefficients,and the Onsager transport coefficients.

Effect of low-frequency electromagnetic field on the as-cast microstructure of a new super high strength aluminum alloy by horizontal continuous casting

The super high strength aluminum alloy ingots with 100 mm in diameter were cast by the process of low-frequency electromagnetic horizontal continuous casting (LFEHC) and the effect of electromagnetic field on the as-cast microstructure was studied. Results show that microstructure of the sample prepared by the LFEHC process was greatly refined. Microstructures at the border and the center of the ingots were fine, uniform and rosette-shaped. Electromagnetic frequency plays a key role in microstructure refining. Fine and uniform microstructures can be obtained with optimal electromagnetic frequency. In this experiment, under a frequency of 30 Hz the microstructure was the finest and the most uniform.

Low-frequency pulsed electromagnetic field pretreated bone marrow-derived mesenchymal stem cells promote the regeneration of crush-injured rat mental nerve

Bone marrow-derived mesenchymal stem cells(BMSCs) have been shown to promote the regeneration of injured peripheral nerves. Pulsed electromagnetic field(PEMF) reportedly promotes the proliferation and neuronal differentiation of BMSCs. Low-frequency PEMF can induce the neuronal differentiation of BMSCs in the absence of nerve growth factors. This study was designed to investigate the effects of low-frequency PEMF pretreatment on the proliferation and function of BMSCs and the effects of low-frequency PEMF pre-treated BMSCs on the regeneration of injured peripheral nerve using in vitro and in vivo experiments. In in vitro experiments, quantitative DNA analysis was performed to determine the proliferation of BMSCs, and reverse transcription-polymerase chain reaction was performed to detect S100(Schwann cell marker), glial fibrillary acidic protein(astrocyte marker), and brain-derived neurotrophic factor and nerve growth factor(neurotrophic factors) m RNA expression. In the in vivo experiments, rat models of crush-injured mental nerve established using clamp method were randomly injected with low-frequency PEMF pretreated BMSCs, unpretreated BMSCs or PBS at the injury site(1 × 106 cells). Di I-labeled BMSCs injected at the injury site were counted under the fluorescence microscope to determine cell survival. One or two weeks after cell injection, functional recovery of the injured nerve was assessed using the sensory test with von Frey filaments. Two weeks after cell injection, axonal regeneration was evaluated using histomorphometric analysis and retrograde labeling of trigeminal ganglion neurons. In vitro experiment results revealed that low-frequency PEMF pretreated BMSCs proliferated faster and had greater m RNA expression of growth factors than unpretreated BMSCs. In vivo experiment results revealed that compared with injection of unpretreated BMSCs, injection of low-frequency PEMF pretreated BMSCs led to higher myelinated axon count and axon density and more Di I-labeled neurons in the trigeminal ganglia, contributing to rapider functional recovery of injured mental nerve. These findings suggest that low-frequency PEMF pretreatment is a promising approach to enhance the efficacy of cell therapy for peripheral nerve injury repair.

A state-of-the-art review on low-frequency nonlinear vibration isolation with electromagnetic mechanisms

Vibration isolation is one of the most efficient approaches to protecting host structures from harmful vibrations,especially in aerospace,mechanical,and architectural engineering,etc.Traditional linear vibration isolation is hard to meet the requirements of the loading capacity and isolation band simultaneously,which limits further engineering application,especially in the low-frequency range.In recent twenty years,the nonlinear vibration isolation technology has been widely investigated to broaden the vibration isolation band by exploiting beneficial nonlinearities.One of the most widely studied objects is the"three-spring"configured quasi-zero-stiffness(QZS)vibration isolator,which can realize the negative stiffness and high-static-low-dynamic stiffness(HSLDS)characteristics.The nonlinear vibration isolation with QZS can overcome the drawbacks of the linear one to achieve a better broadband vibration isolation performance.Due to the characteristics of fast response,strong stroke,nonlinearities,easy control,and low-cost,the nonlinear vibration with electromagnetic mechanisms has attracted attention.In this review,we focus on the basic theory,design methodology,nonlinear damping mechanism,and active control of electromagnetic QZS vibration isolators.Furthermore,we provide perspectives for further studies with electromagnetic devices to realize high-efficiency vibration isolation.

Low-frequency HIFU induced cancer immunotherapy:tempting challenges and potential opportunities

Immunotherapy is playing an increasingly important role in the treatment of tumors.Different from the traditional direct killing or excision therapies,immunotherapy depends on autologous immunity to kill tumor cells and tissues by activating or enhancing the body's immune system.Large numbers of recent studies suggest that low-frequency HIFU can not only enhance the intensity of the body's anti-cancer immune response,but also improve the efficiency of immunotherapy drug delivery to strengthen the effects of tumor immunotherapy.The focused ultrasound(FUS)destructs the tumor and simultaneously generates tumor debris and tumor-associated antigens,which enhances the immunogenicity of the tumor and stimulates the immune cells,inducing the body's immune response.Microbubbles are clinically used as a contrast.As a matter of fact,the addition of microbubbles can reinforce the destructive effect of FUS on the tumor and activate a stronger immune response.The combined application of ultrasound and microbubbles can more effectively open the blood brain barrier(BBB),which is beneficial to improving the intake of immune cells or immunotherapy drugs and exerting a positive influence in the lesion area.Currently,microbubbles and nanoparticles are commonly used as gene and drug carriers.Using ultrasound,the immune-related gene or antigen delivery itself can enhance the immune response and improve the efficacy of the immunotherapy.

Altered spontaneous brain activity patterns in patients with diabetic retinopathy using amplitude of low-frequency fluctuation

BACKGROUND Diabetes mellitus is a metabolic disorder characterized by prolonged elevation of blood glucose due to various causes.Currently,the relationship between diabetic retinopathy(DR)and altered connectivity of brain function is unclear.AIM To investigate the relationship between this brain activity and clinical manifestations and behaviors of DR patients by using the amplitude of low-frequency fluctuation(ALFF)technique.METHODS Twenty-four DR patients and 24 healthy controls(HCs)matched for age and gender were enrolled.We measured and recorded average ALFF values of DR patients and HCs and then classified them using receiver operating characteristic(ROC)curves.RESULTS ALFF values of both left and right posterior cerebellar lobe and right anterior cingulate gyrus were remarkably higher in the DR patients than in the HCs;however,DR patients had lower values in the bilateral calcarine area.ROC curve analysis of different brain regions demonstrated high accuracy in the area under the curve analysis.There was no significant relationship between mean ALFF values for different regions and clinical presentations in DR patients.Neuronal synchronization abnormalities in some brain regions of DR patients were associated with cognitive and visual disorders.CONCLUSION Abnormal spontaneous brain activity was observed in many areas of DR patients’brains,which may suggest a possible link between clinical manifestations and behaviors in DR patients.

Improved uranium leaching efficiency from low-permeability sandstone using low-frequency vibration in the CO_(2)+O_(2) leaching process

Extraction of uranium from low-permeability sandstone is a long-standing challenge in mining.The improvement of sandstone permeability has therefore become a key research focus to improve the uranium leaching effect.To address the low-permeability problem and corresponding leaching limits,leaching experiments are performed using newly developed equipment that could apply low-frequency vibration to the sandstone samples.The test results indicate that low-frequency vibration significantly improves the uranium leaching performance and permeability of the sandstone samples.The leaching effect of low-frequency vibration treatment is approximately nine times more effective than ultrasonic vibration treatment,whereas the concentration of uranium ions generated without vibration treatment is not detectable.Mathematical model that considers the combined action of physico-mechanical vibration and chemical erosion is established to describe the effect of low-frequency vibration on the permeability.The calculated results are in good agreement with the tested permeability values.This study thus offers a new method to effectively leach more uranium from low-permeability sandstone using CO_(2)+O_(2)and provides an insight into the impact of low-frequency vibration on the uranium leaching process.

A STUDY ON THE CHARACTERISTICS AND EFFECT OF THE LOW-FREQUENCY OSCILLATION OF THE ATMOSPHERIC HEAT SOURCE OVER THE EASTERN TIBETAN PLATEAU

There has been a lot of discussion about the atmospheric heat source over the Tibetan Plateau(TP)and the low-frequency oscillation of atmospheric circulation.However,the research on low-frequency oscillation of heat source over TP and its impact on atmospheric circulation are not fully carried out.By using the vertically integrated apparent heat source which is calculated by the derivation method,main oscillation periods and propagation features of the summer apparent heat source over the eastern TP(Q1ETP)are diagnosed and analyzed from 1981 to 2000.The results are as follows:(1)Summer Q1ETP has two significant oscillation periods:one is 10-20d(BWO,Quasi-Biweekly Oscillation)and the other is 30-60d(LFO,Low-frequency Oscillation).(2)A significant correlation is found between Q1ETP and rainfall over the eastern TP in 1985 and 1992,showing that the low-frequency oscillation of heat source is likely to be stimulated by oscillation of latent heat.(3)The oscillation of heat source on the plateau mainly generates locally but sometimes originates from elsewhere.The BWO of Q1ETP mainly exhibits stationary wave,sometimes moves out(mainly eastward),and has a close relationship with the BWO from the Bay of Bengal.Showing the same characteristics as BWO,the LFO mainly shows local oscillation,occasionally propagates(mainly westward),and connects with the LFO from East China.In summary,more attention should be paid to the study on BWO of Q1ETP.

Excitation of extremely low-frequency chorus emissions: The role of background plasma density

Low-frequency chorus emissions have recently attracted much attention due to the suggestion that they may play important roles in the dynamics of the Van Allen Belts.However, the mechanism(s) generating these low-frequency chorus emissions have not been well understood..In this letter, we report an interesting case in which background plasma density lowered the lower cutoff frequency of chorus emissions from above 0.1 f_(ce)(typical ordinary chorus) to 0.02 f_(ce)(extremely low-frequency chorus).Those extremely low-frequency chorus waves were observed in a rather dense plasma, where the number density N_e was found to be several times larger than has been associated with observations of ordinary chorus waves.For suprathermal electrons whose free energy is supplied by anisotropic temperatures, linear growth rates(calculated using in-situ plasma parameters measured by the Van Allen Probes) show that whistler mode instability can occur at frequencies below 0.1 f_(ce) when the background plasma density N_e increases.Especially when N_e reaches 90 cm–3 or more, the lowest unstable frequency can extend to 0.02 f_(ce) or even less, which is consistent with satellite observations.Therefore, our results demonstrate that a dense background plasma could play an essential role in the excitation of extremely lowfrequency chorus waves by controlling the wave growth rates.