In this paper, we derive the dispersion equations for field-aligned cyclotron waves in an axisymmetric dipole magnetospheric plasmas with both the bi-Maxwellian and bi-Lorentzian distribution functions. To evaluate the contribution of trapped particles to the transverse current density components the Vlasov equation is solved using a standard method of switching to new variables associated with conservation integrals; new time-like variable is introduced (instead of the geomagnetic latitude angle) to describe the bounce-motion of trapped particles along the geomagnetic field; the perturbed electric field and current density components are Fourier-decomposed over the length of the geomagnetic field lines. As a result, the transverse permittivity elements are expressed by summation of bounce-resonant terms including the double integration in velocity space, the resonant denominators, and the corresponding phase coefficients. Due to geomagnetic field nonuniformity, the wave-particle resonance conditions in magnetospheric plasmas are entirely different from ones in the straight magnetic field; the all spectrum of the electric field is present in the given current density harmonic; the left- and right-hand polarized waves are coupled. To have some analogy with the linear theory of cyclotron waves in the straight magnetic field, we assume that the n-th harmonic of the electric field gives the main contribution to the n-th harmonic of the current density, and the connection of the left- and right-hand polarized waves is small. In this case, the dispersion equations for cyclotron waves have the simplest form and are suitable to analyze the instabilities of both the electron- and ion-cyclotron waves accounting for the bounce resonance effects.
Recently, S Patil et al. have reported the existence of an enhanced operating regime when a low-pressure (5 mTorr) capacitively coupled discharge (CCP) is driven by a very high radio-frequency (60 MHz) source in the presence of a weak external magnetic field applied parallel to its electrodes. Their Particle-in-Cell (PIC) simulations show, that a significantly higher bulk plasma density and ion flux can be achieved at the electrode when the electron cyclotron frequency equals half of the applied RF frequency for a given fixed voltage. In the present work we take a detailed look at this phenome…
We derive the expression for the ponderomotive force in the real multicomponent magnetospheric plasma containing heavy ions. The ponderomotive force considered includes the induced magnetic moment of all the species and arises due to inhomogeneity of the traveling low-frequency electromagnetic wave amplitude in the nonuniform medium. The nonlinear stationary force balance equation is obtained taking into account the gravitational and centrifugal forces for the plasma consisting of the electrons, protons and heavy ions (He$^{+}$). The background geomagnetic field is taken for the dayside of the…
An interesting characteristic of magnetospheric chorus is the presence of a frequency gap at $ω\simeq 0.5Ω_e$, where $Ω_e$ is the electron cyclotron angular frequency. Recent chorus observations sometimes show additional gaps near $0.3Ω_e$ and $0.6Ω_e$. Here we present a novel nonlinear mechanism for the formation of these gaps using Hamiltonian theory and test-particle simulations in a homogeneous, magnetized, collisionless plasma. We find that an oblique whistler wave with frequency at a fraction of the electron cyclotron frequency can resonate with electrons, leading to effective energy exc…
In the presence of electron cyclotron current drive (ECCD), the Ohm's law of single fluid magnetohydrodynamics (MHD) is modified as ${\bf E} + {\bf v} \times {\bf B} = η( {\bf J} - {\bf J}_{\rm EC} )$. This paper presents a new closure relation for the EC driven current density appearing in this modified Ohm's law. The new relation faithfully represents the nonlocal character of the EC driven current and its main origin in the Fisch-Boozer effect. The closure relation is validated on both an analytical solution of an approximated Fokker-Planck equation as well as on full bounce-averaged, quasi…
The local magnetic field in a Penning-Malmberg trap is found by measuring the temperatures that result when electron plasmas are illuminated by microwaves pulses. Multiple heating resonances are observed as the pulse frequencies are swept. The many resonances are due to electron bounce and plasma rotation sidebands. The heating peak corresponding to the cyclotron frequency resonance is identified to determine the magnetic field. A new method for quickly preparing low density electron plasmas for destructive temperature measurements enables a rapid and automated scan of microwave frequencies. T…
Auroral kilometric radiation (AKR) is the paradigm of intense radio emission from planetary magnetospheres. Being close to the electron gyro frequency and/or its lower harmonics, its observation indicates the non-thermal state of the source plasma. Emission is produced when the plasma enters a state of energetic excitation which results in deformation of the electron distribution function. Under certain conditions this leads to "quasi-coherent" emission. It is believed that the weakly-relativistic electron-cyclotron-maser instability is responsible for this kind of radiation. Since energetical…
Electron cyclotron harmonic (ECH) waves play a significant role in driving the diffuse aurora, which constitutes more than 75% of the particle energy input into the ionosphere. ECH waves in magnetospheric plasmas have long been thought to be excited predominantly by the loss cone anisotropy (velocity-space gradients) that arises naturally in a planetary dipole field. Recent THEMIS observations, however, indicate that an electron beam can also excite such waves in Earth's magnetotail. The ambient and beam plasma conditions under which electron beam excitation can take place are unknown. Knowled…
Due to the smallness of the volumes associated with the flux surfaces around the O-point of a magnetic island, the electron cyclotron power density applied inside the island for the stabilization of neoclassical tearing modes (NTMs) can exceed the threshold for non-linear effects as derived previously by Harvey et al, Phys. Rev. Lett. 62 (1989) 426. We study the non-linear electron cyclotron current drive (ECCD) efficiency through bounce-averaged, quasi-linear Fokker-Planck calculations in the magnetic geometry as created by the islands. The calculations are performed for the parameters of a t…
Through the process of inward diffusion, a strongly localized clump of plasma is created in a magnetosphere. The creation of the density gradient, instead of the usual flattening by a diffusion process, can be explained by the topological constraints given by the adiabatic invariants of magnetized particles. After developing a canonical formalism for the standard guiding center dynamics in a dipole magnetic field, we complete our attempt to build a statistical mechanics on a constrained phase space by discussing the construction principles of the associated diffusion operator. We then investig…
Ion cyclotron resonance is one of the fundamental energy conversion processes through field-particle interaction in collisionless plasmas. However, the key evidence for ion cyclotron resonance (i.e., the coherence between electromagnetic fields and the ion phase space density) and the resulting damping of ion cyclotron waves (ICWs) has not yet been directly observed. Investigating the high-quality measurements of space plasmas by the Magnetospheric Multiscale (MMS) satellites, we find that both the wave electromagnetic field vectors and the bulk velocity of the disturbed ion velocity distribut…
Secondary drift-driven instabilities in the presence of a parallel-propagating electromagnetic ion cyclotron wave and cold multi-component ions
University of California San Diego（加州大学圣地亚哥分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Space Science Institute（太空科学研究所）；University of Helsinki（赫尔辛基大学）
A theoretical model of the high-beta equilibrium of magnetospheric plasma was constructed by consistently connecting the (anisotropic pressure) Grad-Shafranov equation and the Vlasov equation. The Grad-Shafranov equation was used to determine the axisymmetric magnetic field for a given magnetization current corresponding to a pressure tensor. Given a magnetic field, we determine the distribution function as a specific equilibrium solution of the Vlasov equation, using which we obtain the pressure tensor. We need to find an appropriate class of distribution function for these two equations to b…
Simultaneous observation of characteristic 3-dimensional (3D) signatures in the electron velocity distribution function (VDF) and intense quasi-monochromatic waves by the Magnetospheric Multiscale (MMS) spacecraft in the terrestrial magnetosheath are investigated. The intense wave packets are characterised and modeled analytically as quasi-parallel circularly-polarized whistler waves and applied to a test-particle simulation in view of gaining insight into the signature of the wave-particle resonances in velocity space. Both the Landau and the cyclotron resonances were evidenced in the test-pa…
Turbulence properties and kinetic signatures of electron in Kelvin-Helmholtz waves during a geomagnetic storm
University of Maryland College Park（马里兰大学帕克分校）；NASA Goddard Space Flight Center（美国宇航局戈达德太空飞行中心）；University of New Hampshire（新罕布什尔大学）；Dartmouth College（达特茅斯学院）；University of Maryland Baltimore（马里兰大学巴尔的摩分校）
The high cadence plasma, electric, and magnetic field measurements by the Magnetospheric MultiScale spacecraft allow us to explore the near-Earth space plasma with an unprecedented time and spatial resolution, resolving electron-scale structures that naturally emerge from plasma complex dynamics. The formation of small-scale turbulent features is often associated to structured, non-Maxwellian particle velocity distribution functions that are not at thermodynamic equilibrium. Using measurements in the terrestrial magnetosheath, this study focuses on regions presenting bumps in the power spectra…
The analysis of the wave content inside a perpendicular bow shock indicates that heating of ions is related to the Lower-Hybrid-Drift (LHD) instability, and heating of electrons to the Electron-Cyclotron-Drift (ECD) instability. Both processes represent stochastic acceleration caused by the electric field gradients on the electron gyroradius scales, produced by the two instabilities. Stochastic heating is a single particle mechanism where large gradients break adiabatic invariants and expose particles to direct acceleration by the DC- and wave-fields. The acceleration is controlled by function…
Magnetic holes are plasma structures that trap a large number of particles in a magnetic field that is weaker than the field in its surroundings. The unprecedented high time-resolution observations by NASA's Magnetospheric Multi-Scale (MMS) mission enable us to study the particle dynamics in magnetic holes in the Earth's magnetosheath in great detail. We reveal the local generation mechanism of whistler waves by a combination of Landau-resonant and cyclotron-resonant wave-particle interactions of electrons in response to the large-scale evolution of a magnetic hole. As the magnetic hole conver…
The stability of an initially one-dimensional electron hole to perturbations varying sinusoidally transverse to its trapping direction is analysed in detail. It is shown that the expected low-frequency eigenmode of the linearized Vlasov-Poisson system consists of a shift-mode, proportional to the gradient of the equilibrium potential. The resulting dispersion relation is that the total jetting force exerted by a perturbed hole on the particles balances the electric restoring tension of the hole. The tension is quantitatively small and can often be ignored. The particle force is expressed as in…
One of the most striking properties of Kinetic Alfvén Waves (KAW) is that, unlike the also Alfvénic Electromagnetic Ion Cyclotron (EMIC) waves, these waves are right-hand polarized in the plasma frame. In particular, this signature property is key for the identification of KAW from in situ measurements of plasma waves. From the theoretical point of view, both the dispersion relation and the polarization of KAW has been mostly studied in proton-electron plasmas. However, most astrophysical and space plasmas are multi-species, and therefore in these systems the dispersion properties of the KAW m…
