Pitch Angle Distribution Evolution of Energetic Electrons by Whistler-Mode Chorus

We develop a two-dimensional momentum and pitch angle code to solve the typical Fokker-Planck equation which governs wave-particle interaction in space plasmas. We carry out detailed calculations of momentum and pitch angle diffusion coefficients, and temporal evolution of pitch angle distribution for a band of chorus frequency distributed over a standard Gaussian spectrum particularly in the heart of the Earth＇s radiation belt L = 4.5, where peaks of the electron phase space density are observed. We find that the Whistler-mode chorus can produce significant acceleration of electrons at large pitch angles, and can enhance the phase space density for energies of 0.5 - 1 MeV by a factor of 10 or above after about 24h. This result can account for observation of significant enhancement in flux of energetic electrons during the recovery phase of a geomagnetic storm.     

Simulation of Resonant Interaction between Energetic Electrons and Whistler-Mode Chorus in the Outer Radiation Belt

We construct a realistic model to evaluate the chorus wave-particle interaction in the outer radiation belt L = 4.5. This model incorporates a plasmatrough number density model, a field-aligned density model and a realistic wave power and frequency model. We solve the 2D bounce-averaged momentum-pitch-angle Fokker-Planck equation and show that the Whistler-mode chorus can be effective in the acceleration of electrons, and enhance the phase space density for energies of -1 MeV by a factor from 10 to 10^3 in about two days, consistent with the observation. We also demonstrate that ignorance of the electron number density variation along field line and magnetic local time in the previous work yields an overestimate of energetic electron phase space density by a factor 5-10 at large pitch-angle after two days, suggesting that a realistic plasma density model is very important to evaluate the evolution of energetic electrons in the outer radiation belt.     

Bounce-Averaged Acceleration of Energetic Electrons by Whistler Mode Chorus in the Magnetosphere

We construct the bounce-averaged diffusion coefficients and study the bounce-averaged acceleration for energetic electrons in gyroresonance with whistler mode chorus. Numerical calculations have been performed for a band of chorus frequency distributed over a standard Gaussian spectrum specifically in the region near L = 4.5, where peaks of the electron phase space density occur. It is found that whistler mode chorus can efficiently accelerate electrons and can increase the phase space density at energies of about 1 MeV by more than one order of magnitude about one day, in agreement with the satellite observations during the recovery phase of magnetic storms.     

场向传播的内磁层哨声波对辐射带高能电子的共振扩散

基于高斯分布的哨声波谱密度分布、偶极子背景磁场模型以及建立在卫星观测数据基础上的半经验电子密度纬度分布模型,对于等离子体层顶以外区域(4≤L≤7),计算了准线性当地及弹跳平均电子共振扩散系数,并估算了与磁层哨声波回旋共振导致的辐射带电子损失及加速时间尺度.结果表明,波粒共振相互作用区域取决于电子能量、波谱分布、电子赤道抛射角以及当地电子密度及背景磁场.哨声波共振频率除了与以上5个参量有关外,还与地磁纬度有关.赤道哨声波主要影响较低能量辐射带电子的加速,中高纬度哨声波主要作用于较高能量辐射带电 关键词： 共振波粒相互作用 地球辐射带 哨声波 回旋共振加速及散射沉降     

Spatial Distribution of Energetic Electrons during Magnetic Reconnection

Electron acceleration by the inductive electric field near the X point in magnetic reconnection is an important generation mechanism for energetic electrons. Particle simulations have revealed that most of energetic electrons reside in the magnetic field line pileup region, and a depletion of energetic electrons can be found near the centre of the diffusion region [Phys. Plasmas, 13 (2006) 012309]. We report direct measurement of energetic electron in and around the ion diffusion region in near-Earth tail by the cluster, and our observations confirm the above predictions: a depletion of the high-energy electron fluxes is detected near the centre of the diffusion region. At the same time, the plasma temperature has a similar profile in the diffusion region. .     

基于AKEBONO哨声波参数的内辐射带高能电子扩散模拟

为能准确地模拟内辐射带中哨声波对高能电子扩散损失的影响,基于内辐射带AKEBONO哨声波参数统计模型,及随纬度分布的背景冷等离子体密度模型,对引起电子扩散损失的大气分子,空间等离子体嘶声、闪电激发的哨声、人工激发的甚低频三类哨声波,利用准线性扩散理论,计算1.4≤ L≤2.0区域的不同能量电子,受到库仑碰撞和波粒回旋共振相互作用的弹跳周期平均赤道投掷角扩散系数,分析不同作用机制、不同类哨声波、不同能量、不同磁壳参数等对辐射带高能电子扩散损失的影响.结果表明：在赤道面损失锥角附近,高能电子主要受到库仑碰撞作用而扩散;在赤道投掷角接近90°附近区域,等离子体嘶声和闪电激发的哨声是引起扩散的主要因素;内辐射带电子主要受到甚低频电磁波波粒回旋共振扩散影响;扩散系数对高能电子能量及其所处磁壳参数比较敏感,通常,高能电子的能量或所处磁壳参数越大,扩散系数越大.     

Generation of VLF emissions with the increasing and decreasing frequency in the magnetosperic cyclotron maser in the backward wave oscillator regime

We study the mechanisms of the formation of falling tones in the dynamic spectrum of whistler-mode waves generated by energetic electrons in the Earth’s magnetosphere when the backward-wave oscillator (BWO) regime is realized in the magnetospheric cyclotron maser. As was shown earlier, this regime allows one to explain many features of ELF/VLF chorus emissions in the magnetosphere, in particular, the generation of elements with discrete frequency spectrum, characterized by a large growth rate and a fast frequency drift. On the basis of numerical simulations of a simplified system of nonlinear equations describing the magnetospheric BWO dynamics under the assumption of small efficiency of wave-particle interactions we show that the falling tones are generated in the case where the generation region is shifted from the equatorial plane (geomagnetic-field minimum) upstream with respect to the motion of energetic electrons. In this case, the resonant electrons move towards the decreasing magnetic field in the process of generation; hence, their longitudinal velocity increases, which corresponds to a decrease in the cyclotron-resonance frequency. Two mechanisms of the shift of the generation region from the equator are considered, i.e., (i) an increase in the linear instability growth rate (e. g., due to an increase in the energetic-electron density), and (ii) persistence of the phase bunching of the particles coming back to the generation region due to the bounce oscillations. We show that both of these mechanisms can result in the formation of falling tones, but the properties of the generated emissions such as the frequency drift rate and characteristic time interval between the elements are different. The conditions of preserving the phase bunching due to the bounce oscillations are discussed. Probably, this mechanism can operate in the case where the length of the generation region along the magnetic field is close to the characteristic bounce-oscillation length of energetic electrons which is realized for a sufficiently high cold-plasma density in the generation region.     

Numerical simulation of chorus-driving acceleration of relativistic electrons at extremely low L-shell during geomagnetic storms

During 2018 major geomagnetic storm, relativistic electron enhancements in extremely low L-shell regions (reaching L～3) have been reported based on observations of ZH-1 and Van Allen probes satellites, and the storm is highly likely to be accelerated by strong whistler-mode waves occurring near very low L-shell regions where the plasmapause was suppressed. It is very interesting to observe the intense chorus-accelerated electrons locating in such low L-shells and filling into the slot region. In this paper, we further perform numerical simulation by solving the two-dimensional Fokker-Planck equation based on the bounce-averaged diffusion rates. Numerical results demonstrate the evolution processes of the chorus-driven electron flux and confirm the flux enhancement in low pitch angle ranges (20°-50°) after the wave-particle interaction for tens of hours. The simulation result is consistent with the observation of potential butterfly pitch angle distributions of relativistic electrons from both ZH-1 and Van Allen probes.     

典型甚低频电磁波对辐射带高能电子的散射损失效应

辐射带中高能电子与空间甚低频电磁波由于波粒共振相互作用发生投掷角散射, 进而沉降入稠密大气而损失. 为研究甚低频电磁波对辐射带中高能电子的散射作用机制, 本文基于准线性扩散理论, 利用库仑作用和波粒共振相互作用扩散系数的物理模型, 得到了两组典型甚低频电磁波与高能电子波粒共振相互作用的赤道投掷角弹跳周期平均扩散系数, 并分析了甚低频电磁波共振散射作用与大气库仑散射作用对不同磁壳及不同能量的辐射带电子扩散损失的影响规律. 以磁壳参数L=2.2, 能量E=0.5 MeV的辐射带电子作为算例, 采用有限差分方法数值求解扩散方程, 计算分析了电子单向通量和全向通量随时间的沉降损失演化规律. 研究结果表明: 当电子能量大于0.5 MeV, 磁壳参数大于1.6时, 甚低频电磁波的共振散射作用显著; 随着磁壳参数或电子能量的增大, 斜传播甚低频电磁波引起的高阶共振相互作用越来越大; 电子全向通量近似随时间呈指数函数形式衰减.     

Dynamics of the Magnetospheric Cyclotron ELF/VLF Maser in the Backward-Wave-Oscillator Regime. I. Basic Equations and Results in the Case of a Uniform Magnetic Field

We consider the nonlinear dynamics of absolute instability of whistler-mode waves in the Earth's magnetosphere in the presence of a step-like deformation in the distribution function of energetic electrons. Development of this instability, implying the transition of the magnetospheric cyclotron maser to the regime of a backward-wave oscillator (BWO), was proposed earlier as a generation mechanism of magnetospheric chorus emissions. We derive simplified nonlinear equations describing the dynamics of the magnetospheric BWO in the case of low efficiency of wave-particle interactions. Numerical simulations of these equations confirm qualitative similarity of the laboratory and magnetospheric BWOs and justify quantitative estimates of parameters of chorus emissions. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 9, pp. 719–729, September 2005.     

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结合HL-2A 装置的参数,在电子回旋共振加热(ECRH)离(在)轴加热的情况下,研究高能量捕获电子驱动的鱼骨模不稳定性。数值结果表明,高能量电子极向比压βh 大于某一个比压阈值βh,crit 时,鱼骨模会被高能量电子激发,其频率随高能量电子极向比压的增大而缓慢增加且与高能量电子的环向进动频率一致;比压阈值βh,crit 随着高能量电子密度剖面峰化程度的增加而减小,但当密度剖面增大到一定值时比压阈值βh,crit 趋近于一个常数。此外,还分析了箍缩角和扰动能对鱼骨模实频和增长率的影响。发现在箍缩角α0 =1附近增长率有一极小值,表明高能量勉强通行电子对鱼骨模具有稳定作用;而扰动能 δWˆc增大时,鱼骨模表现出实频变大而增长率变小的特征,这表明了本底等离子体对鱼骨模有一定的稳定效果。     

HL-2A 装置中高能量捕获电子鱼骨模不稳定性研究

结合HL-2A 装置的参数,在电子回旋共振加热(ECRH)离(在)轴加热的情况下,研究高能量捕获电子驱动的鱼骨模不稳定性。数值结果表明,高能量电子极向比压β_h 大于某一个比压阈值β_h,crit 时,鱼骨模会被高能量电子激发,其频率随高能量电子极向比压的增大而缓慢增加且与高能量电子的环向进动频率一致;比压阈值β_h,crit 随着高能量电子密度剖面峰化程度的增加而减小,但当密度剖面增大到一定值时比压阈值β_h,crit 趋近于一个常数。此外,还分析了箍缩角和扰动能对鱼骨模实频和增长率的影响。发现在箍缩角α₀ =1附近增长率有一极小值,表明高能量勉强通行电子对鱼骨模具有稳定作用;而扰动能 δWˆ_c增大时,鱼骨模表现出实频变大而增长率变小的特征,这表明了本底等离子体对鱼骨模有一定的稳定效果。     

Modelling Energetic Electrons by a Kappa-Loss-Cone Distribution at Geostationary Orbit

We adopt a recently developed relativistic kappa-loss-cone （KLC） distribution to model energetic electrons energy spectra observed at the geostatlonary orbit in the storm of 3-4 November 1993. The KLU distribution is found to fit well with the observed data from four satellites during different universal times. This suggests that the electron flux obeys the power-law not only at the lower energies but also at the relativistic energies, and the KLU distribution may provide a better understanding of environments in those space plasmas where relativistic electrons are present.     

Dynamics of the magnetospheric cyclotron ELF/VLF maser in the backward-wave-oscillator regime. II. The influence of the magnetic-field inhomogeneity

We study the influence of the magnetic-field inhomogeneity on the nonlinear dynamics of the absolute instability of whistler-mode waves in the Earth’s magnetosphere in the presence of a step-like deformation in the distribution function of energetic electrons. Development of this instability, implying the transition of the magnetospheric cyclotron maser to the regime of a backward-wave oscillator (BWO), was proposed earlier as a generation mechanism of magnetospheric chorus emissions. We analyze the results of numerical simulations of the simplified nonlinear equations describing the magnetospheric-BWO dynamics in the case of low efficiency of wave-particle interactions. We found that the case of an inhomogeneous magnetic field where the system length is much greater than the length characterizing the linear stage of the BWO regime has important specific features compared with the case of a homogeneous medium. The main feature of the nonlinear wave dynamics in the magnetospheric BWO in an inhomogeneous magnetic field consists in the fact that for a sufficiently large excess over the generation threshold, a sequence of separate wave packets, i.e., discrete elements, is formed. The frequency within each packet varies in time, and these discrete elements are close in their properties to the chorus elements observed in the magnetosphere. The results of calculations confirm the quantitative estimates of parameters of chorus emissions, which were performed earlier on the basis of the BWO model. ^†Deceased Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 11, pp. 977–987, November 2008.     

Storm-Time Strong Field-Aligned Ion Upflow in Region of the SED Plume

We report the observations from the GPS TEC and DMSP F-13 satellites showing that very strong upward field-aligned （FA） ion velocity and flux in the outer region of the storm-enhanced density （SED） occurred in the event of the geomagnetic storm on 29-31 May 2003. By a method of coordinate transformation, upward FA ion velocities in excess of 25Orals are obtained from the observations of the DMSP F-13 satellite. Further, an FA ion flux is estimated to be about 4.5 x 1013 ions/m2 s in the dusk sector. The estimated FA ion velocity and flux provide a powerful direct proof to support the scenario that there is a strong coupling of particles between the ionosphere and plasmasphere in the region of the SED plume. In the process, FA ion flux transports from the ionosphere to the plasmasphere in the region of the SED plume. Therefore, the plume of SED in the ionosphere provides an important source to the enhanced density of O^＋ in the storm-time plasmasphere.     

Observation and analysis of whistler-mode wave and electrostatic solitary waves within density depletion near magnetic reconnection X-line

The PWI/WFC data onboard Geotail during one burst time interval when Geotail is skimming a magnetic reconnection diffusion region in the near-Earth magnetotail is carefully analyzed.Both the whistler-mode wave and the electrostatic solitary wave are found within the region with density depletion on the boundary layer near the magnetic reconnection X-line.The whistler-mode wave is electromagnetic whistler wave propagating quasi-parallel to the ambient field with a small angle between the wave vector and the ambient magnetic field.The whistler-mode wave associated with ESWs suggests that enhanced electromagnetic whistler-mode fluctuations can also be generated after the decay of the ESWs,which is different from the 2-D PIC simulation results.     

Excitation of chorus-like waves by temperature anisotropy in dipole research experiment (DREX): A numerical study

Due to their significant roles in the radiation belts dynamics, chorus waves are widely investigated in observations,experiments, and simulations. In this paper, numerical studies for the generation of chorus-like waves in a launching device,dipole research experiment(DREX), are carried out by a hybrid code. The DREX plasma is generated by electron cyclotron resonance(ECR), which leads to an intrinsic temperature anisotropy of energetic electrons. Thus the whistler instability can be excited in the device. We then investigate the effects of three parameters, i.e., the cold plasma density nc, the hot plasma density nh, and the parallel thermal velocity of energetic electrons, on the generation of chorus-like waves under the DREX design parameters. It is obtained that a larger temperature anisotropy is needed to excite chorus-like waves with a high nc with other parameters fixed. Then we fix the plasma density and parallel thermal velocity, while varying the hot plasma density. It is found that with the increase of nh, the spectrum of the generated waves changes from no chorus elements, to that with several chorus elements, and then further to broad-band hiss-like waves. Besides, different structures of choruslike waves, such as rising-tone and/or falling-tone structures, can be generated at different parallel thermal velocities in the DREX parameter range.     

Second-Order Resonant Interaction of Ring Current Protons with Whistler-Mode Waves

We present a study on the second-order resonant interaction between the ring current protons with Whistler-mode waves propagating near the quasi electrostatic limit following the previous second-order resonant theory. The diffusion coefficients are proportional to the electric field amplitude E, much greater than those for the regular first-order resonance, which are proportional to the electric field amplitudes square E^2. Numerical calculations for the pitch angle scattering are performed for typical energies of protons Ek = 50 keV and 100 keV at locations L = 2 and L = 3.5. The timescale for the loss process of protons by the Whistler waves is found to approach one hour, comparable to that by the EMIC waves, suggesting that Whistler waves may also contribute significantly to the ring current decay under appropriate conditions.     

Calculation of Interaction Potentials between Spherical and Deformed Nuclei

The interaction potential for spherical-deformed reaction partners is calculated. The shape, separation and orientation dependence of the interaction potential and fusion cross section of the system ^32S＋^154Sm are investigated within the double-folding model of the deformed nuclei. The effective nucleon-nucleon interaction is taken to be the M3Y-Reid potential. The density is considered for three terms of the expansion using the truncated multipole expansion method, which is a deformed Fermi shape With quadrupole and hexadecapole for the density distribution of ^154Sm. It is found for the interaction potential that the height and the position of barrier strongly depend on the deformations, the orientation angle of the deformed nucleus, and hence produce great effects on fusion cross section. The integrated fusion cross section is in good agreement with the experimental data.