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.     

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.     

Geodesic mode spectrum modified by the energetic particles in tokamak plasmas

Effect of a minor concentration of the energetic particles on GAM spectrum in a tokamak is analyzed by drift kinetic theory taking into the account the electron current and diamagnetic drift. A novel method of Jacobi functions is applied to solve the drift kinetic equation for the energetic bounce particles in the limit of high bounce frequency in comparison with the GAM frequency. Using the Q-asymptotic of Jacobi function, it is shown that the energetic minority ions can form the continuum minimum/maximum at the NB or ICR power deposition maximum where the geodesic eigenmode may be excited. In this case, the electron current modeled by shifted Maxwell distribution overcomes the ion Landau damping threshold thus resulting in the GAM instability.     

VLF emissions from ionospheric/magnetospheric plasma

VLF emissions such as hiss, chorus, oscillating tones, hiss-triggered chorus and whistler triggered emissions have been observed at low latitude Indian stations. In this paper we present dynamic spectra of these emissions and discuss their various observed features. It is argued that most of the emissions are generated during Doppler shifted cyclotron resonance interaction between the whistler mode wave and counter streaming energetic electrons. Resonance energy of the participating electron and interaction length are evaluated to explain the generation mechanism of some of these emissions observed at Indian stations.     

基于试验粒子模拟的电离层人工调制激发的极低频和甚低频波对磁层高能电子的散射效应

电离层调制加热能够有效激发极低频和甚低频(ELF/VLF)波,其中向上传播进入磁层的ELF/VLF波能够与高能电子发生共振相互作用,具有人工沉降高能电子、消除辐射带等潜在实际用途.本文综合运用射线追踪和试验粒子方法模拟电离层人工激发的单频ELF/VLF波在电离层和磁层的传播,以及在外辐射带层与高能电子的共振相互作用过程,通过投掷角和能量散射系数评估人工ELF/VLF波对磁层高能电子的共振散射效应.研究表明,电离层人工ELF/VLF波传播到磁层后呈现高倾斜性,传播所能跨域的空间范围主要取决于加热的纬度位置和调制频率.在内辐射带,与～100 keV到几个MeV高能电子发生一阶共振相互作用的为10 kHz的VLF波段;在外辐射带,为几百Hz到1 kHz的ELF波段.对于L=4.5的外辐射带,试验粒子模拟结果显示,单个粒子在人工ELF波作用下投掷角和能量(α,E)的改变具有随机性,而所有试验粒子平均化的?α2和?E2随时间呈现出近似线性的增大,说明波粒共振散射过程体现出整体性.基于试验粒子模拟得到的共振散射系数表明,幅度为10 pT的人工ELF波可在外辐射带的磁赤道局地对1 MeV电子产生较强的投掷角散射效应,进而影响高能电子的损失、沉降等动力学过程.当人工ELF/VLF波在传播过程中变得高度倾斜,不仅最基本的一阶共振十分重要,高阶共振散射也具有较大效应.这些定量分析结果表明,通过电离层加热激发人工ELF/VLF哨声波来沉降、消除辐射带高能电子具有可行性.     

Characteristics of nighttime VLF/ELF emissions with frequency drift and estimation of the large-scale electric field from the frequency drift observed at a low latitude Indian ground station, Jammu

Characteristics of nighttime VLF/ELF emissions are examined on the basis of the data obtained at our low latitude ground station Jammu (geomagnetic latitude, 22°26′ N; L = 1.17), India during our VLF/ELF campaign. From the detailed analysis of a huge amount of acquired VLF/ELF data at Jammu we have found three remarkable events which clearly exhibit a rise in their frequency in pre and past midnight sectors during magnetically quiet and substorm periods. Our analysis shows that the frequency drift in VLF/ELF emissions seems to be a rare phenomenon at low latitudes during magnetically quiet and substorm periods in pre and post midnight sectors. This property of temporal frequency drift (regular frequency increases with time) in VLF/ELF emissions observed at our station Jammu are interpreted in terms of a quasi-linear electron cyclotron instability model for wave excitation. The initial frequency increase is believed to be due to a combind effect of L-shell drift of energetic electrons. Further, the frequency drifts in VLF/ELF emissions observed at Jammu have been used to estimate the large scale electric field during quiet and substorm periods in pre and post midnight sectors. This investigation would be most useful for the study of the wave-particle interaction processes, magnetospheric plasma structure and particle dynamics, especially during quiet periods in premidnight sector at low latitudes.     

On the amplification mechanism of the ion-channel laser

The amplification mechanism of the ion-channel laser (ICL) in the low-gain regime is studied. In this concept, a relativistic electron beam is injected into a plasma whose density is comparable to or lower than the beam's density. The head of the electron beam pushes out the plasma electrons, leaving an ion channel. The ion-focusing force causes the electrons to oscillate (betatron oscillations) about the axis and plays a role similar to the magnetic field in a cyclotron autoresonance maser (CARM). Radiation can be produced with wave frequencies from microwaves to X-rays depending on the beam energy and plasma density: ω~2γ^3/2ω_pe, where γ is the Lorentz factor of the beam and ω_pe is the plasma frequency. Transverse (relativistic) bunching and axial (conventional) bunching are the amplification mechanisms in ICLs; only the latter effect operates in free-electron lasers. The competition of these two bunching mechanisms depends on beam velocity ν_0z; their dependences on ν_0z cancel for the cyclotron autoresonance masers. A linear theory is developed to study the physical mechanisms, and a PIC (particle-in-cell) simulation code is used to verify the theory. The mechanism is examined as a possible explanation for experimentally observed millimeter radiation from relativistic electron beams interacting with plasmas     

Thermal effects on parallel resonance energy of whistler mode wave

In this short communication, we have evaluated the effect of thermal velocity of the plasma particles on the energy of resonantly interacting energetic electrons with the propagating whistler mode waves as a function of wave frequency and L-value for the normal and disturbed magnetospheric conditions. During the disturbed conditions when the magnetosphere is depleted in electron density, the resonance energy of the electron enhances by an order of magnitude at higher latitudes, whereas the effect is small at low latitudes. An attempt is made to explain the enhanced wave activity observed during magnetic storm periods.     

Cyclotron Wave-Particle Interactions in the Whistler-Mode Waveguide

We study the cyclotron interaction of energetic electrons and whistler waves in plasma waveguides formed by inhomogeneous distribution of cold plasma. Such waveguides can be formed in the Earth's magnetosphere, e.g., by the plasmapause or by ducts with enhanced background-plasma density. In this paper, we consider a cylindrically symmetric model of a magnetospheric duct with enhanced cold-plasma density in a homogeneous magnetic field. The spatial structure of the eigenmodes of such a waveguide is found. We obtain a set of self-consistent quasilinear equations for cyclotron instability with eigenmode structure taken into account, thus generalizing the quasilinear theory of a magnetospheric cyclotron maser.     

The hard excitation regime for a relativistic backward-wave oscillator

We study theoretically the processes which take place in a relativistic backward-wave oscillator (BWO) in the parameter region corresponding to hard excitation of oscillations. The onset of both stationary oscillations near the boundary of the hard excitation regime and hard nonstationary oscillations realizing the self-modulation regimes of BWO operation are analyzed along with the dynamics of a BWO-based amplifier. In particular, it is shown that hard excitation of self-oscillation can restrict significantly the output characteristics of a relativistic BWO operated in the regenerative-amplification regime. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 8, pp. 675–681, August 2008.     

低纬电离层人工调制所激发的ELF波射线追踪

通过大功率极低频(ELF)/甚低频(VLF)高频调幅波能有效地扰动低电离层电流, 形成等效的ELF/VLF电离层虚拟天线,辐射ELF/VLF波, 所辐射出的低频信号能够传播进入到磁层,对其传播特性的研究对于理解辐射带高能电子沉降具有重要意义.本文基于磁层射线追踪理论,通过数值模拟得到在低纬地区所激发出的ELF波在磁层中的射线路径,并对其特征进行分析.数值模拟结果表明, 从低纬激发的ELF波在南北半球来回弹跳,并逐渐传播到更远处,对于不同频率的ELF波, 频率越高,传播距离越近,频率越低,传播距离越远,在传播过程中, ELF波会逐渐倾向于在一个固定的磁层区域附近来回反射,在此过程中波法向角也逐渐变为90°,射线方向倾向于沿着背景磁场方向传播.     

Magnetospheric substorms and discrete arcs of the polar aurora

A brief review of the results of the research in physics of the Earth’s magnetosphere leading to a substantial modification of the previously developed approaches is presented. The main emphasis is placed on physics of magnetospheric substorms and the nature of auroral arcs. It is shown that the formation of powerful electron beams that produce multiple arcs can be associated with the penetration of cold electrons of an ionospheric origin into the region of field-aligned acceleration of hot magnetospheric electrons.     

地基高频加热激励ELF/VLF波对辐射带高能电子的准线性散射

地球内、外辐射带电子通量的变化对于空间飞行器,尤其是中低轨卫星的防护有着非常重要的影响.基于回旋共振波粒相互作用的准线性理论,使用地基高频发射器发射电波调制低电离层背景电流可以人工激励ELF/VLF波,这些波能使辐射带相对论电子发生抛射角散射沉降进入大气层从而降低其生存期.为了定量地分析人工激励ELF/VLF波散射辐射带高能粒子的可行性,针对内、外辐射带,本文选取了两个典型区域：L=4.6和L=1.5.数值计算结果表明,在内、外辐射带由于ELF/VLF波的人工注入而造成的高能电子损失时间尺度很大程度上取决于冷等离子体参量α^*(∝B²/N₀,这里B是背景磁场,N₀是电子数密度)、电波频谱特性和功率,以及与波发生回旋共振的电子能量.一般来讲,在外辐射带人工ELF/VLF哨声波散射相对论电子使之沉降到大气层要容易得多;低能量的高能电子(200keV)要比高能量的相对论电子(500keV)更有效地通过抛射角散射进入大气层.考虑到高频电波加热电离层激励的ELF/VLF波可能会被捕获在磁层空腔中,来回反射从而得到增强,因此在适当的条件下,地基高频加热装置发射足够的电波功率进入电离层诱导大幅度ELF/VLF波注入到内磁层,能够在1至3天的时间尺度内快速散射外辐射带相对论电子使之沉降,也能够在10天量级的时间尺度里散射生存周期一般为100天甚至更长的内辐射带相对论电子. 关键词： 地基高频加热电离层 ELF/VLF波激励 高能电子散射和沉降 共振波粒相互作用     

Hot Electron Ring Formation in ECR Heated Plasma

Energetic particles can be .generated by electron cyclotron resonant heating (ECRH) in tokamak plasma, forming electron ring. The bounce frequency is taken into account in resonance condition. The electron energy is limited by detaching of the adjacent overlapped islands. An analytical criterion for transition is obtained. The critical potential obtained is in good agreement with numerical calculation. Experiment for observing the trapped energetic electrons is suggested.     

Theory of second-order cyclotron resonance as related to the origin of discrete VLF emissions in the magnetosphere

Recent analytical and numerical results concerning the role of the second-order cyclotron resonance effects in formation of discrete emissions in the magnetosphere are reviewed. Peculiarities of whistler cyclotron interactions with energetic particles having sharp (step-like or beam-like) distribution functions evolving in space and time are studied. Formation of such distributions is considered, and an analytical self-consistent theory of the second-order cyclotron resonance effects is developed. In particular, characteristics of electron beams produced by the interaction of a VLF wave packet from a ground-based transmitter are studied. It is shown that spatial and temporal gradients of the parallel velocity of the beams formed can be opposite to the case of a pure adiabatic motion of a single particle. Such a behavior can be significant for the generation of secondary emissions. It is proven that the optimal conditions for the instability occur for a nonstationary quasi-monochromatic wavelets whose frequency changes in time. The theory developed permits one to estimate the wave amplification and spatio-temporal characteristics of these wavelets. Numerical results on beam formation and generation of secondary emissions are presented. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 8, pp. 713–727, August 1999.     

Landau damping of electrons with bouncing motion in a radio-frequency plasma

One-dimensional particle simulations have been conducted to study the interaction between a radio-frequency electrostatic wave and electrons with bouncing motion. It is shown that bounce resonance heating can occur at the first few harmonics of the bounce frequency (nω_b,n=1,2,3,...). In the parameter regimes in which bounce resonance overlaps with Landau resonance, the higher harmonic bounce resonance may accelerate electrons at the velocity much lower than the wave phase velocity to Landau resonance region, enhancing Landau damping of the wave. Meanwhile, Landau resonance can increase the number of electrons in the lower harmonic bounce resonance region. Thus electrons can be efficiently heated. The result might be applicable for collisionless electron heating in low-temperature plasma discharges.     

Global synchronization of oscillations in the level of whistlers near Jupiter as a consequence of the spatial detection of the <Emphasis Type="Italic">Q</Emphasis> factor of a magnetosphere resonator

The formation of the space-time structure of the intensity distribution for whistlers, as well as the content of the energetic electrons in the radiation belts of Jupiter, has been considered. Parametric nonlinear processes in a plasma magnetospheric maser have been analyzed. It has been shown that, owing to the azimuthal inhomogeneity of a magnetic trap in combination with the fast rotation of the planet, a component that is characterized by the periodic modulation and is independent of the azimuth coordinate is formed in the Q factor of the magnetospheric resonator. This modulation is manifested as an external force that ensures the synchronization of oscillations in the level of whistlers in individual magnetic field tubes under the global-resonance conditions.     

A free-electron laser in a uniform magnetic field

The interaction of free electrons and free electromagnetic radiation, in the presence of a uniform magnetic field, can result in stimulated emission or absorption. We analyze the dynamics of single electrons by solving the classical, relativistic Lorentz force equations of motion in these combined fields. An electron may gain energy from, or lose energy to, the radiation field, depending crucially on the phase and oscillation frequency of the electron's helical motion within the superposed, circularly polarized light wave. To first order in the radiation field strength, electrons in a monoenergetic, uniformly distributed beam become spatially bunched, but there is no net energy change. To second order, however, the beam may experience a gain or loss of energy, corresponding to attenuation or amplification of radiation. We compare the bunching of this laser process to the bunching processes involved in 1) the Stanford free-electron laser and 2) the cyclotron maser, and find significant differences in each case. Our analytic results provide a clear, simple picture of the interaction process, and can be useful in exploring light amplification in astrophysical magnetic fields, the magnetosphere, or in laboratory devices. Supported in part by Army Contract No. DASG 60-77-C-0083 and NASA Grant NSG-7490.     

The effect of plasma drift on the electromagnetic cyclotron instability

It is shown that the drift of plasma across a homogeneous magnetic field causes the generation of a wave electric field which, for waves propagating along the magnetic field in the whistler mode, is in the direction of the magnetic field. This leads to Landau damping of the wave field by the background electron distribution, simultaneously with amplification via the electromagnetic cyclotron instability. The drift velocity of the plasma for zero net growth of a whistler mode signal is calculated. It is suggested that such a process occurs in the equatorial region of the magnetosphere during a geomagnetic storm and accounts for the missing band of emissions at half the equatorial gyrofrequency.     

Relativistic study of electromagnetic electron cyclotron instability based on trapped electrons in kappa-Maxwellian auroral plasmas

The presence of relativistic electrons in the Earth's magnetosphere may excite EMEC waves via resonant interaction. The understanding of EMEC waves induced by such electrons requires relativistic treatment. Therefore, we present here the investigation of EMEC waves based on relativistic trapped electrons represented by kappa-Maxwellian distribution in auroral plasmas. The analytical expressions of real frequency and relativistic growth rate are derived. Our numerical outcomes report that relativistic approximation increases the wave growth and causes reduction in the threshold value of drift velocity of trapped electrons for instability. The wave frequency that corresponds to the maximum growth decreases as we go from nonrelativistic limit to relativistic. The maximum growth increases with the increment in plasma frequency, perpendicular thermal velocity, drift velocity of trapped electrons, and Lorentz factor γ. Moreover, the relativistic effects on maximum growth are more pronounced for smaller values of drift velocity and perpendicular thermal velocity.