Electrostatic Ion Cyclotron Waves Research Articles

Detection of a low-frequency ion instability in a magnetic nozzle

Abstract A low-frequency ion instability, with frequency f I between the ion gyrofrequency and the lower hybrid frequency f c , i < f I ≪ f LH , is detected in an argon plasma expanding in a magnetic nozzle for magnetic fields between 240 < B z , max < 700 G. The frequency of the instability exhibits a linear dependence with magnetic field strength, and the wave amplitude has a radial maximum that would match the location of a conical density structure, i.e. high-density cones. For all of the magnetic field cases analysed, the high-frequency spectra showed upper and lower sidebands centred around the driving frequency and at a separation equal to the instability frequency, 27.12 MHz ± f I kHz. Measurements of the perpendicular wavenumber would satisfy, for certain magnetic field strengths, the dispersion relation of both an electrostatic ion cyclotron wave (ICW) and of an ion acoustic wave. It is hypothesised that the observed low-frequency wave could be an acoustic-like instability propagating perpendicular to the magnetic field, which develops as an ICW at some magnetic field strengths. From the data collected, it is suggested that the high-frequency sidebands may be caused by modulation of the low-frequency wave.

The collisional study of EIC waves in a magnetized dusty plasma with the inclusion of a DC electric field

This study investigates Electrostatic Ion Cyclotron (EIC) waves and their behaviour in weakly collisional plasmas, utilizing a proposed kinetic analytical model. The findings include alterations in EIC wave dispersion characteristics due to collisions, with parameters such as dust density, collision frequency, gyro-radius, magnetic field, density ratio, and electric field influencing wave growth rate and frequency. Temperature analysis reveals that higher electron-to-ion temperature ratios lead to increased frequency and critical drift velocity, while decreasing the growth rate. In addition, the critical drift velocity is studied for the unstable mode and it is observed that the relative density ratio increases with a reduction in critical drift velocity. Electron collisions destabilize EIC waves, while ion collisions stabilize them. Furthermore, the presence of dust particles decreases the growth rate of EIC waves as dust grain density increases. These results align with observations reported in previous literature.

Existence of Electrostatic Ion Cyclotron Waves in a Laboratory Created E Region Ionospheric‐Like Plasma

AbstractMolecular ions are relatively cold in the E region ionosphere; however, they can upwell to the magnetosphere during geomagnetically active times. Resonance between electrostatic ion cyclotron (EIC) waves is a potential pathway to energize molecular ions. In this work, the E region ionospheric plasma was modeled in the laboratory, and EIC waves were excited by a nonuniform field‐aligned current. The EIC wave was excited even when the ion neutral collision frequency is much higher than the ion cyclotron frequency, and the fundamental frequency was observed to be below the ion cyclotron frequency. In addition, the wave dispersion of the collisional EIC wave was calculated, which shows a consistent trend with experimental results as the collisions increasing. Therefore, this work suggests that EIC waves can be excited in the E region ionospheric‐like plasma, which can support the explanation of the energization of molecular ions in the E region ionosphere.

Electrostatic Ion Cyclotron Waves Observed by CSES in the Equatorial Plasma Bubble

AbstractBroadband ELF electrostatic emissions have been observed by the China Seismo‐Electromagnetic Satellite (CSES) inside the equatorial plasma bubbles (EPBs). Analyses reveal that the electric field fluctuates nearly perpendicular to the ambient magnetic field, with the transverse component gyrotropically distributed around the magnetic field line. The observed emissions, Doppler shifted and broadened, are found to be close to the local oxygen ion (O+) cyclotron frequency in the plasma reference frame. Accompanying ion heating and deceleration are consistent with the consequences of the ion cyclotron resonance. All these results indicate that the electrostatic emissions pervading a major part of the EPB are the O+ electrostatic ion cyclotron (EIC) waves. The inhomogeneous‐energy‐density‐driven instability triggered by the non‐uniform electric field and density gradient across the EPBs could be the source of the EIC waves. The CSES observation provides new evidence for the shear driven EIC wave in the equatorial ionosphere.

Nonlinear electrostatic ion cyclotron wave collapse and formation of wave packets in the presence of trapped electrons.

The weakly nonlinear and dispersive electrostatic ion cyclotron wave dynamics in the presence of Schamel distributed trapped electrons is studied in collisionless plasmas. The dynamics of the nonlinear wave is shown to be governed by a Schamel-Ostrovsky type equation. Analytical and numerical solutions of this equationreveal the collapse of a solitary (localized) pulse at a critical time that depends on the trapping parameter and the strength of the magnetic field. The time-dependent computational result is noteworthy, which predictstheformation of wave packets (wave group) beyond the critical time. The results are in good agreement with the astrophysical observations in auroral plasmas.

In the existence of a transverse dc electric field, the kinetic theory of current‐driven electrostatic ion cyclotron waves excitation in a magnetized dusty plasma

AbstractThe theoretical modelling for the electrostatic ion cyclotron (EIC) waves in the existence of a transverse direct current (dc) electric field in a collisionless magnetized dusty plasma has been investigated using the kinetic theory model. It is examined that after incorporation of dc electric field with the dust grains can alter the dispersion properties of EIC waves in a magnetized dusty plasma. Our model developed accounts for the critical drift velocity, electron‐to‐ion temperature ratio, magnetic field, the number density of dust grains, relative density of negatively charged dust grains, and finite gyroradius parameter. Our investigation found that normalized growth rate and frequency increase with the relative density ratio and electric field. Moreover, the critical drift velocity for the excitation of the mode with negatively charged dust grains and electron‐to‐ion temperature ratio has been studied, and it was found that critical drift velocity decreases with the increase in negatively charged dust grains. The impact of dust grains on the low‐frequency waves has also been studied, and it was found that an increase in dust grain number density results in the reduction of growth rate. Some of our theoretical findings are consistent with the experimental observations.

Nonlinear dynamical modelling of high frequency electrostatic drift waves using fluid theoretical approach in magnetized plasma

A novel third order nonlinear evolution equation governing the dynamics of the recently observed high frequency electrostatic drift waves has been derived in the framework of a plasma fluid model in an inhomogeneous magnetized plasma. The corresponding linear dispersion relation arising out of the fluid equations has been studied in detail for the conventional low frequency as well as the recently observed high frequency electrostatic drift waves along with the electrostatic ion cyclotron waves. The derived nonlinear evolution equation of third order is then decomposed into two second order equations as the order of the equation becomes reduced after this kind of decomposition under certain conditions, and one equation becomes linear whereas the other equation becomes nonlinear. The detailed analysis of fixed points leading to bifurcations has been performed using the qualitative theory of differential equations and the bifurcation theory of planar dynamical systems for the reduced second order nonlinear equation. The bifurcation curves for the individual fixed points are also shown for the variations of different parameters in the parameter space of this reduced nonlinear equation. Then some exact as well as approximate travelling wave solutions of this reduced nonlinear equation have been derived. As the other second order reduced equation is linear in nature, its exact oscillatory and exponential solutions are obtained. The intersection of the solutions of these two reduced second order equations provides the solutions of the original third order nonlinear evolution equation; it is verified that the solutions of the reduced nonlinear second order equation are subsets of the oscillatory solution of the reduced linear second order equation in most cases whereas the intersection is different if the exponential solution of the reduced linear second order equation is considered. This further implies that the solutions of the reduced second order nonlinear equation can directly represent the solutions of the original third order nonlinear evolution equation in most cases representing the dynamics of the nonlinear high frequency electrostatic drift waves. These solutions of the novel third order nonlinear evolution equation represent certain vortex-like structures as our work is restricted to (1 + 1) dimensions only. The possible applications of our novel results on the dynamics of the high frequency electrostatic drift waves are discussed along with future directions for research in this field.

Study of Electrostatic Ion-Cyclotron Waves in Magnetosphere of Uranus

In this manuscript, the method of characteristics particle trajectories details used and the dispersion relation for the ionosphere of Uranus were being used to investigate electrostatic ion-cyclotron waves with parallel flow velocity shear in the presence of perpendicular inhomogeneous DC electric field and density gradient. The growth rate has been calculated using the dispersion relation. Electric fields parallel to the magnetic field transmit energy, mass, and momentum in the auroral regions of the planetary magnetosphere by accelerating charged particles to extremely high energies. The rate of heating of plasma species along and perpendicular to the magnetic field is also said to be influenced by the occurrence of ion cyclotron waves and a parallel electric field in the acceleration area.

Plasma–neutral coupling allows electrostatic ion cyclotron waves to propagate below ion cyclotron frequency

The effect of ion–neutral collisions on the propagation characteristics of electrostatic ion cyclotron (EIC) waves in a partially ionized plasma is investigated. The dispersion relation of EIC waves is derived using a fluid model taking neutral dynamics into account. The propagation properties of EIC modes, including the damping factor, are examined for various ionization degrees and collision frequencies, which determine the momentum transferred from ions to neutral particles. It is found that the motion of neutral particles driven by plasma–neutral coupling leads to an increase in the effective ion mass, and consequently, EIC waves can propagate even below the ion cyclotron frequency. In a hot neutral gas, the gas-thermal mode can also propagate as well as the EIC mode. The possibility of observing in the laboratory and the Earth's ionosphere is discussed.

Fine-scale dynamics of fragmented aurora-like emissions

Abstract. Fragmented aurora-like emissions (FAEs) are small (few kilometres) optical structures which have been observed close to the poleward boundary of the aurora from the high-latitude location of Svalbard (magnetic latitude 75.3 ∘N). The FAEs are only visible in certain emissions, and their shape has no magnetic-field-aligned component, suggesting that they are not caused by energetic particle precipitation and are, therefore, not aurora in the normal sense of the word. The FAEs sometimes form wave-like structures parallel to an auroral arc, with regular spacing between each FAE. They drift at a constant speed and exhibit internal dynamics moving at a faster speed than the envelope structure. The formation mechanism of FAEs is currently unknown. We present an analysis of high-resolution optical observations of FAEs made during two separate events. Based on their appearance and dynamics, we make the assumption that the FAEs are a signature of a dispersive wave in the lower E-region ionosphere, co-located with enhanced electron and ion temperatures detected by incoherent scatter radar. Their drift speed (group speed) is found to be 580–700 m s−1, and the speed of their internal dynamics (phase speed) is found to be 2200–2500 m s−1, both for an assumed altitude of 100 km. The speeds are similar for both events which are observed during different auroral conditions. We consider two possible waves which could produce the FAEs, i.e. electrostatic ion cyclotron waves (EIC) and Farley–Buneman waves, and find that the observations could be consistent with either wave under certain assumptions. In the case of EIC waves, the FAEs must be located at an altitude above about 140 km, and our measured speeds scaled accordingly. In the case of Farley–Buneman waves a very strong electric field of about 365 mV m−1 is required to produce the observed speeds of the FAEs; such a strong electric field may be a requirement for FAEs to occur.

Electrostatic Ion-cyclotron Wave Excitation by a Gyrating Ion Beam in a Magnetized Plasma Containing Heavy Positive Ions

In the present paper, we have developed a theoretical model of cylindrical magnetized plasma column consisting of electrons, ions & heavy positive ion species. A gyrating ion beam of potassium having radius ~1.5 cm and energy 10eV is launched through one end of the cylinder parallel to the static magnetic field and the electrostatic ion cyclotron wave is assumed to propagate nearly perpendicular to the magnetic field. The presence of heavy positive ions in the collisionless magnetized plasma decreases the critical drift for the excitation of EIC waves and hence the injected beam drives the electrostatic ion cyclotron (EIC) waves to instability through Cerenkov interaction. Therefore, the plasma is observed to contains two excited EIC wave modes; a (light positive) ion mode and a (heavy positive) ion mode. The frequencies and growth rates for both the positive unstable modes are worked out using fluid theory for the typical existing experimental parameters which are found to increase with the increase in ion beam energy and beam density. It is also observed that the unstable wave frequency and growth rate for both the modes increases with the increase in relative ion concentration of and heavy positive ions respectively. Magnetic field is also one of the important factors which influence the plasma instabilities appreciably. As the magnetic field increases, the frequency of both the ion modes increases linearly.

Physically significant wave solutions to the Riemann wave equations and the Landau-Ginsburg-Higgs equation

The nonlinear Riemann wave equations (RWEs) and the Landau-Ginsburg-Higgs (LGH) equation are related to plasma electrostatic waves, ion-cyclotron wave electrostatic potential, superconductivity, and drift coherent ion-cyclotron waves in centrifugally inhomogeneous plasma. In this article, the interactions between the maximum order linear and nonlinear factors are balanced to compute realistic soliton solutions to the formerly stated equations in terms of hyperbolic functions. The linear and nonlinear effects rheostat the structure of the wave profiles, which vary in response to changes in the subjective parameters combined with the solutions. The established solutions to the aforementioned models using the extended tanh scheme are descriptive, typical, and consistent, and include standard soliton shapes such as bright soliton, dark soliton, compacton, peakon, periodic, and others that can be used to analyze in ion-acoustic and magneto-sound waves in plasma, homogeneous, and stationary media, particularly in the propagation of tidal and tsunami waves.

On O+ Ion Heating by BBELF Waves at Low Altitude: Test Particle Simulations

AbstractWe investigate mechanisms of wave particle heating of ionospheric O+ ions resulting from broadband extremely low frequency (BBELF) waves using numerical test particle simulations that take into account ion‐neutral collisions, in order to explain observations from the Enhanced Polar Outflow Probe (e‐POP) satellite at low altitudes (∼400 km) (Shen et al., 2018, https://doi.org/10.1002/2017JA024955). We argue that in order to reproduce ion temperatures observed at e‐POP altitudes, the most effective ion heating mechanism is through cyclotron acceleration by short‐scale electrostatic ion cyclotron (EIC) waves with perpendicular wavelengths λ⊥ ≤ 200 m. The interplay between finite perpendicular wavelengths, wave amplitudes, and ion‐neutral collision frequencies collectively determine the ionospheric ion heating limit, which begins to decrease sharply with decreasing altitude below approximately 500 km, where the ratio becomes larger than 10−3, νc and fci denoting the O+‐O collision frequency and ion cyclotron frequency. We derive, both numerically and analytically, the ion gyroradius limit from heating by an EIC wave at half the cyclotron frequency. The limit is 0.28λ⊥. The ion gyroradius limit from an EIC wave can be surpassed either through adding waves with different λ⊥ or through stochastic “breakout,” meaning ions diffuse in energy beyond the gyroradius limit due to stochastic heating from large‐amplitude waves. Our two‐dimensional simulations indicate that small‐scale (<1 km) Alfvén waves cannot account for the observed ion heating through trapping or stochastic heating.

Excitation and characteristics of electrostatic ion-cyclotron waves launched by a grid

Previous experimental studies on electrostatic ion-cyclotron waves (EICWs) and their instability were often performed in a narrow plasma column in Q-machines, in which the wave was conventionally generated via the instability driven by an electron current parallel to a magnetic field. The propagation characteristics of wave patterns have seldom been studied, especially the different characteristics in pulse and continuous wave patterns. In this paper, we present the experimental launching of the EICW via a grid applied with either a pulsed or a sinusoidal external excitation voltage in a magnetized plasma device. Either pulsed or continuous EICWs were excited, and the wave pattern trajectories were observed. Using the time-of-flight method, both phase and pulse (group) velocities of the wave signals were directly measured. It was shown that for the continuous EICW excitation, the measured dispersion relation is in agreement with the result from the kinetic theory in some range of parameters in the fundamental and harmonic frequency bands. The dependence of the measured pulse and phase velocities on the magnetic field shows agreement with the fluid theory only in the low field strength case but is closer to the result from the kinetic theory in the high field strength case.

Nonlinear electrostatic waves in the auroral plasma

Nonlinear electrostatic waves in a two-component magnetized plasma comprising of cold ions and suprathermal electrons following κ-distribution have been analyzed. The nonlinear electrostatic waves are considered to be propagating at an oblique direction to the ambient magnetic field. A parametric study of the effect of initial driving electric field amplitude (E0), wave Mach number (M), spectral index (κ), propagation angle (α) and ion drift velocity (δ) on the evolution and the existence domain of nonlinear electric field structures is carried out. The theoretical plasma model is able to generate electrostatic ion cyclotron and ion acoustic waves, with the variation in the initial driving electric field amplitude and Mach number. It is observed that with increase in the driving strength, the electric field structures evolve from sinusoidal to sawtooth to highly spiky bipolar waveforms. The presence of κ–electrons is perceived to reduce the initial driving strength required to generate spiky bipolar electric field structures as compared to Boltzmann-electrons. Further, the period of the waveforms were found to decrease with increase in κ. The electric field amplitude and the phase speed of the bipolar structures predicted by the theoretical model is found to be in the range of observed electric field and speed in auroral region by the FAST satellite.

Linear analysis of electrostatic waves in the lunar wake plasma

Propagation characteristics of electrostatic electron and ion cyclotron waves, ion- and electron- acoustic waves in a four-component magnetized plasma comprising of protons, doubly charged Helium ions, beam electrons and superthermal electrons following a kappa distribution are presented. The model supports 12 plasma modes: two electron cyclotron (modes 1 and 12), two electron acoustic (modes 2 and 11), two fast ion acoustic (modes 3 and 10), two slow ion acoustic (modes 4 and 9), two proton cyclotron (modes 5 and 8) and two Helium cyclotron (modes 6 and 7). At parallel propagation, with increase in electron beam speed, mode 11 first merges with slow ion acoustic mode 4 and then with fast ion acoustic mode 3 and drives them unstable. For oblique propagation and without the electron streaming, coupling of various plasma modes occurs and it weakens with increase in the angle of propagation. Further, for oblique propagation with finite electron beam velocity, merging as well as coupling of various plasma modes are observed. Growth rates as well as wave numbers of the excited slow and fast ion acoustic modes are much smaller in magnetized plasma than in an unmagnetized one. The results are relevant to observations of electrostatic waves in the lunar wake.

Effects of inhomogeneity on electrostatic ion cyclotron instability excited by a particle beam

Electrostatic ion cyclotron (EIC) waves excited by a particle beam are studied in a magnetized inhomogeneous collisionless plasma using linear Vlasov theory. The dispersion relation of the beam-plasma system is established based on some relevant assumptions and the numerical results are presented. The behavior of EIC waves with account of parameters such as plasma inhomogeneity, propagation angle and beam velocity is studied. In particular, mode frequencies, growth rate maxima and perpendicular wavevectors are investigated in terms of these parameters. It is shown that, for lower inhomogeneities, the growth maxima are highly affected by the value of relative beam velocity. However, for higher inhomogeneities, the system is more stable for all beam velocities. It is also shown that the beam velocity has a major effect on the growth maxima only before reaching a maximum value on the curves and after the maximum, there is a declining trend in the effect of beam velocity on the growth maxima. Furthermore, for larger propagation angles, there is a more sensitive dependency on the beam velocity. At large values of relative beam velocities, the dependency of growth maxima on beam velocity becomes very weak for all propagation angles. It is found that the perpendicular wavevector decreases with both inhomogeneity and beam velocity. The decrease is smoother at larger values of propagation angle or higher inhomogeneities. In other words, for faster beams and higher inhomogeneities, the system is unstable at larger perpendicular wavelengths. It is also found that the values of maximum instability in terms of propagation angles strictly depend on inhomogeneity. For a relatively high inhomogeneity, the maxima occur over a wide range of propagation angles at almost the same value of perpendicular wavevector. A direct relationship between the magnitudes of mode frequency and growth rate is observed, implying that a higher frequency is a prerequisite for a positive (and relatively steep) slope on the growth rate curve.

S.14.08 Epigenetic aging in major depressive disorder

The preferential heating of 3He by the electromagnetic ion-cyclotron waves, which propagate in the direction parallel to the magnetic fields in the solar corona, is investigated. The results obtained from this study indicate that the parallel propagating electromagnetic ion-cyclotron waves, if driven, can be efficient at heating 3He through the first harmonic resonance. This preferential heating of 3He can lead to a high temperature ratio THe3/THe4∼10–20 and thus largely increases the number of 3He to be further accelerated to high energies. Comparing to the electrostatic ion-cyclotron waves, we find that the electromagnetic ion-cyclotron waves can be even more efficient at heating 3He than the electrostatic ion-cyclotron waves if both types of waves are excited with comparable wave energy densities. Therefore, the electromagnetic ion-cyclotron waves, if generated in solar flares, should also play an important role in solar 3He-rich events along with the electrostatic ion-cyclotron waves.

Higher harmonics electrostatic ion cyclotron parallel flow velocity shear instability with inhomogeneous DC electric field in the magnetosphere of Saturn

In present paper higher harmonic electrostatic ion-cyclotron (EIC) parallel flow velocity shear instability in presence of perpendicular inhomogeneous DC electric field with the ambient magnetic field has been studied, in different regions of the magnetosphere of Saturn. Dimensionless growth rate variation of EIC waves has been observed with respect to $k_{ \bot } \rho _{i}$ for various plasma parameters. Effect of velocity shear scale length ( $A_{i}$ ), temperature anisotropy ( $T_{ \bot } /T_{\|}$ ), magnetic field ( $B$ ), electric field ( $E$ ), inhomogeneity ( $P/a$ ), angle of propagation ( $\theta $ ), ratio of electron to ion temperature ( $T_{e}/T_{i}$ ) and density gradient ( $\varepsilon _{n}\rho _{i}$ ) on the growth of EIC waves in the inner magnetosphere of Saturn has been studied and analyzed. The mathematical formulation for dispersion relation and growth rate has been done by using the method of characteristic solution and kinetic approach. This theoretical analysis has been done taking the data from the Cassini in the inner magnetosphere of Saturn in the extended region where ion cyclotron waves have been observed. The change in the growth of these waves due to the presence of Enceladus has been analyzed.

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