Cyclotron Resonance Interaction Research Articles

Parametric analysis of pitch angle scattering and losses of relativistic electrons by oblique EMIC waves

This study analyzes the effects of electromagnetic ion cyclotron (EMIC) waves on relativistic electron scattering and losses in the Earth’s outer radiation belt. EMIC emissions are commonly observed in the inner magnetosphere and are known to reach high amplitudes, causing significant pitch angle changes in primarily >1 MeV electrons via cyclotron resonance interactions. We run test-particle simulations of electrons streaming through helium band waves with different amplitudes and wave normal angles and assess the sensitivity of advective and diffusive scattering behaviors to these two parameters, including the possibility of very oblique propagation. The numerical analysis confirms the importance of harmonic resonances for oblique waves, and the very oblique waves are observed to efficiently scatter both co-streaming and counter-streaming electrons. However, strong finite Larmor radius effects limit the scattering efficiency at high pitch angles. Recently discussed force-bunching effects and associated strong positive advection at low pitch angles are, surprisingly, shown to cause no decrease in the phase space density of precipitating electrons, and it is demonstrated that the transport of electrons into the loss cone balances out the scattering out of the loss cone. In the case of high-amplitude obliquely propagating waves, weak but non-negligible losses are detected well below the minimum resonance energy, and we identify them as the result of non-linear fractional resonances. Simulations and theoretical analysis suggest that these resonances might contribute to subrelativistic electron precipitation but are likely to be overshadowed by non-resonant effects.

Study of character of modulation instability in cyclotron resonance interaction of an electromagnetic wave with a counterpropagating rectilinear electron beam

In this paper, the interaction of a monochromatic electromagnetic wave with a counterpropagating electron beam moving in an axial magnetic field is considered. The purpose of this study is to investigate the conditions for occurrence of modulation instability (MI) in such a system and to determine at which parameters of the incident wave the MI is absolute or convective. Methods. Theoretical analysis of the MI character is carried out by studying the asymptotic form of unstable perturbations using the saddle-point analysis. The analytical results are verified by numerical simulations. Results. Theoretically, the boundary of change in the character of MI on the plane of input signal parameters (amplitude and detuning of the frequency from the cyclotron resonance) is determined. Numerical simulations confirm that as the signal frequency increases, the regime of self-modulation, which corresponds to the absolute MI, is replaced by the stationary single-frequency transmission corresponding to the convective MI. The numerical results coincide with the analytical ones for the system, which is matched at the end. The matching is implemented by smooth increasing of the guiding magnetic field in the region of electron beam injection. Conclusion. Determining the analytical conditions for the implementation of the absolute MI is of practical interest, since the emerging self-modulation can lead to the generation of trains of pulses with the spectrum in the form of frequency combs.

Formation of microwave soliton combs under cyclotron resonance interaction of electron beam with counter-propagating waveguide mode

We theoretically study the formation of periodical trains of microwave self-induced-transparency solitons (M\W-SIT soliton combs), which arise under cyclotron resonant interaction of an initially rectilinear electron beam with a steady-state electromagnetic wave counter-propagating in a cylindrical waveguide. Depending on the contained energy, solitons can either propagate toward the electron beam (i.e., in the direction of the unperturbed group velocity) or be entrained by the beam in the direction of its translational motion. As a result, a kind of feedback arises, leading to the appearance of soliton combs emitted from both the left and right boundaries of the system. This process can be described by the non-stationary self-consistent model, which is based on the parabolic equation for the field evolution taking into account the waveguide dispersion. Within the framework of the developed model, it is shown that waveguide dispersion does not prevent the formation of ultrashort solitons with duration of about several dozens wave periods. Moreover, the peak power of the entrained solitons can anomalously increase as the frequency of the incident wave approaches the cutoff frequency of the operating mode.

Entrainment, stopping, and transmission of microwave solitons of self-induced transparency in counter-propagating magnetized electron beam.

Based on numerical simulations of a boundary problem, we study various scenarios of microwave soliton formation in the process of cyclotron resonance interaction of a short electromagnetic pulse with a counter-propagating initially rectilinear electron beam taking into account the relativistic dependence of the cyclotron frequency on the electrons' energy. When a certain threshold in the pulse energy is exceeded, the incident pulse can propagate without damping in the absorbing beam, similar to the effect of self-induced transparency in optics. However, mutual motion of the wave and electrons can lead to some novel effects. For relatively small energy of the incident pulse, the microwave soliton is entrained by the electron beam opposite to the direction of the wave's group velocity. With an increase in the pulse energy, soliton stopping occurs. This regime is characterized by the close-to-zero pulse velocity and can be interpreted as a variety of the "light stopping." High-energy microwave solitons propagate in the direction of the unperturbed group velocity. Their amplitude may exceed the amplitude of the incident pulse, i.e., nonlinear self-compression takes place. A further increase in the incident energy leads to the formation of additional high-order solitons whose behavior is similar to that of the first-order ones. The characteristics of each soliton (its amplitude and duration) correspond to analytical two-parametric soliton solutions that are to be found from consideration of the unbounded problem.

Effects of Hot Protons on the Pitch Angle Scattering of Ring Current Protons by EMIC Waves

AbstractVia cyclotron resonant interactions, electromagnetic ion cyclotron (EMIC) waves play an important role in the loss of ring current protons. In this study, by calculating the proton bounce‐averaged pitch angle diffusion coefficients using both the cold and hot plasma dispersion relations, we investigate the effects of hot protons on the EMIC wave‐induced scattering loss of ring current protons. Our results show that, for H+ band (He+ band) EMIC waves, inclusion of hot protons results in significant decrease of pitch angle diffusion coefficients of ∼10–60 keV (4–30 keV) protons, while the scattering efficiency of higher energy protons increases at low pitch angles and decreases at relatively high pitch angles. We also find that the cold plasma approximation seriously underestimates the loss timescales of protons at energies from a few keV to tens of keV but overestimate that of higher energy protons. The differences in proton loss timescales caused by hot protons are generally less than a factor of ∼5 for H+ band but can exceed an order of magnitude for He+ band, showing a strong dependence on the hot proton concentration and temperature anisotropy and L‐shell. This study confirms that effects of hot protons play a crucial role in the EMIC wave driven loss of ring current protons and should be included in future modeling of ring current dynamics.

Ka-Band 100-kW Subnanosecond Pulse Generator Mode-Locked by a Nonlinear Cyclotron Resonance Absorber

We present the results of experiments on the generation of periodical trains of subnanosecond ${K}_{a}$-band pulses in the electron generator, which is based on passive mode locking. This technique is broadly used in laser physics for the generation of ultrashort pulses (USPs) but has not been previously employed in high-power microwave electronics. The microwave USP generator comprises a helical-waveguide gyrotron traveling wave tube and a saturable absorber in the feedback loop. Saturable absorption is implemented in an auxiliary section using the cyclotron resonance interaction with an initially rectilinear electron beam, for which nonlinear saturation is caused by the effect of the relativistic dependence of the gyrofrequency on the particle's energy. In agreement with theoretical predictions, periodical trains of 0.4-ns pulses with a peak power of 100 kW and repetition of 2.5 ns are measured. Phase coherence of radiated pulses is demonstrated based on analysis of the autocorrelation function. The experiments performed open a wide range of possibilities for the generation of coherent broadband radiation, which is in high demand for numerous applications.

Formation of microwave frequency-chirped solitons of self-induced transparency under conditions of cyclotron resonance absorption.

We study the formation of solitons of microwave self-induced transparency (M/W-SIT) which occurs under cyclotron resonance interaction of an electromagnetic pulse with an initially rectilinear magnetized electron beam. Taking into account the relativistic dependence of the gyrofrequency on the particle energy for electromagnetic wave propagating with a phase velocity different from the speed of light (i.e., far from the autoresonance conditions), such a beam can be considered as a medium of nonisochronous unexcited oscillators. Thus, similar to passing light pulses in the two-level medium, for sufficiently large amplitude and duration the incident electromagnetic pulse decomposes into one or several solitons. We find analytically the generalized solution for the M/W-SIT soliton with amplitude and duration determined, besides the soliton velocity, by the frequency self-shift parameter. The feasibility and stability of the obtained solutions are confirmed in numerical simulations of a semibounded problem describing propagation and nonlinear interaction of an incident electromagnetic pulse.

On the wave-particle interaction and removal of energetic particles

There is always a risk of destruction of man-made satellites by the energetic electrons trapped in Van Allen radiation belts in space. These energetic electrons also pose a biological danger to astronauts. The cyclotron resonance interaction is studied between the whistler-mode waves in the frequency range of ELF (Extremely Low Frequency 300 – 3000 HZ) and VLF (Very Low Frequency 3 – 30 kHz) propagating along geomagnetic field line and counter streaming energetic electron. During this process the pitch angle of energetic electrons reduces. This results in the dumping of these electrons into the lower ionosphere. This makes electrons unable to strike the satellites orbiting in low Earth orbit, Geosynchronous, Sun-synchronous or polar orbit. It is shown that the lifetime values of energetic electrons vary from 2.03 to 227.68 hours at low latitudes. It is shown that these waves can remove these energetic electrons from their path and ensure the safety of satellites.

Data‐Driven Simulation of Rapid Flux Enhancement of Energetic Electrons With an Upper‐Band Whistler Burst

AbstractThe temporal variation of the energetic electron flux distribution caused by whistler mode chorus waves through the cyclotron resonant interaction provides crucial information on how electrons are accelerated in the Earth's inner magnetosphere. This study employs a data‐driven test‐particle simulation which demonstrates that the rapid change of energetic electron distribution observed by the Arase satellite cannot be simply explained by a quasi‐linear diffusion mechanism, but is essentially caused by nonlinear scattering: the phase trapping and the phase dislocation. In response to upper‐band whistler chorus bursts, multiple nonlinear interactions finally achieve an efficient flux enhancement of electrons on a time scale of the chorus burst. A quasi‐linear diffusion model tends to underestimate the flux enhancement of energetic electrons as compared with a model based on the realistic dynamic frequency spectrum of whistler waves. It is concluded that the nonlinear phase trapping plays an important role in the rapid flux enhancement of energetic electrons observed by Arase.

Linear and Nonlinear Plasma Processes in Ionospheric HF Heating

Featured observations of high frequency (HF) heating experiments are first introduced; the uniqueness of each observation is presented; the likely cause and physical process of each observed phenomenon instigated by the HF heating are discussed. A special point in the observations, revealed through the ionograms, is the competition between the Langmuir parametric instability and upper hybrid parametric instability excited in the heating experiments and the impact of the natural cusp at foE (the peak plasma frequency of the ionospheric E region) on the competition. The ionograms also infer the generation of Langmuir and upper hybrid cavitons. Ray tracing theory is formulated. With and without the appearance of large-scale field-aligned density irregularities in the background ionosphere, ray trajectories of the ordinary mode (O-mode) and extraordinary mode (X-mode) sounding pulses are calculated numerically. The results explain the artificial Spread-F recorded by the digisondes in the heating experiments. Parametric instabilities, which are the directly relevant processes to achieve effective heating of the ionospheric F region, are formulated and analyzed. The threshold fields and growth rates of Langmuir and upper hybrid parametric instabilities are derived as the theoretical basis of many radar observations and electron-plasma wave interactions. Harmonic cyclotron resonance interaction processes between electrons and upper hybrid waves are introduced. Formulation and analysis are presented. The numerical results show that ultra-energetic electrons are generated. These electrons enhance airglow at 777.4 nm as well as cause ionization. Physical processes leading to the generation of artificial ionization layers are discussed. The nonlinear Schrodinger equation governing the nonlinear evolution of Langmuir waves and upper hybrid waves are derived and solved. The nonlinear periodic and solitary solutions of the equations are obtained. The localized Langmuir and upper hybrid waves generated by the HF heater form cavitons near the HF reflection layer and near the upper hybrid resonance layer, which induce bumps in the virtual height spread of the ionogram trace similar to that induced by the density cusp at E-F1 transition layer; the down-going Langmuir waves and upper hybrid waves evolve into nonlinear periodic waves propagating along the magnetic field, which backscatter incoherently the sounding pulses to cause downward virtual height spread.

Erratum: “Perpendicular Ion Heating by Cyclotron Resonant Dissipation of Turbulently Generated Kinetic Alfvén Waves in the Solar Wind” (2019, ApJ, 887, 63)

Solar wind ions are observed to be heated in the directions perpendicular to the large-scale magnetic field, with preferential heating given to heavy ions. In the solar corona, this heating may be responsible for the generation of the wind itself. It is likely that this heating results from the dissipation of plasma turbulence, but the specific kinetic mechanism that produces these preferential effects is not known. Solar wind turbulence at proton scales is often characterized in terms of highly oblique kinetic Alfv\'en waves (KAWs), which have been thought to dissipate through the Landau resonance and yield parallel heating. We show that the quasilinear resonant cyclotron interaction between KAWs and solar wind ions can actually produce perpendicular ion heating. We present an illustrative calculation of a steady, critically balanced spectrum of KAWs acting on homogeneous ion distributions with a plasma \b{eta} = 0.1, representative of turbulent conditions in the fast solar wind near 20 Rs. The KAWs are described here by a two-fluid dispersion relation. We find that thermal protons are strongly heated in the perpendicular direction within a typical quasilinear time of several thousand gyroperiods, which corresponds to only a few minutes at 20 Rs. Alpha particles in the same fluctuation field are heated to similar perpendicular thermal speeds, equivalent to the greater than mass proportional perpendicular temperatures that are commonly observed. We discuss improvements to this simple model that may determine whether this mechanism can be responsible for the observed coronal and solar wind ion heating.

Nonlinear Cyclotron Resonance Absorber for a Microwave Subnanosecond Pulse Generator Powered by a Helical-Waveguide Gyrotron Traveling-Wave Tube

A well-known principle for periodical production of high-power ultrashort optical pulses is related to passive mode locking realized when a saturable absorber is incorporated into the laser resonator. A similar effect can be implemented in two-section electronic oscillators comprising an amplifier and a saturable absorber, which should be applicable in the microwave frequency band and suitable for high-power operation. In this paper, we analyze in detail the possibility of realizing a saturable absorber based on cyclotron resonance interaction in the regular waveguide with initially rectilinear electron beam, when saturation is caused by the relativistic dependence of the gyrofrequency on electron energy. Maximum contrast between the absorption of a high-power signal and of a weak signal is achieved in the group synchronism regime when the particle velocity is close to the wave's group velocity. Within the frame of a time-domain self-consistent model, we demonstrate that when such an absorber is installed in the feedback loop of an electron generator powered by existing Ka-band helical-waveguide gyrotron traveling-wave tube, periodical generation of subnanosecond pulses can be provided with peak power up to several hundred kW and sub-GHz repetition frequency. We discuss the influence of deviation from the group synchronism regime on the parameters of generated pulses. Experimental feasibility of the considered scheme is verified based on three-dimensional particle-in-cell simulations.

Nonlinear Scattering of 90° Pitch Angle Electrons in the Outer Radiation Belt by Large‐Amplitude EMIC Waves

AbstractElectromagnetic ion cyclotron (EMIC) waves can cause relativistic electron scattering and atmospheric precipitation, primarily via cyclotron resonant interactions in the Earth's radiation belts. However, the conventional quasilinear resonance theory suggests that the cyclotron resonance condition is not satisfied for 90° pitch angle (PA) electrons, which constitute the majority of electrons in the outer radiation belt, such that scattering mainly affects low‐PA electrons. In contrast to this theory, using test particle calculations, we demonstrate that even exactly 90° PA electrons can be significantly scattered by large‐amplitude EMIC waves. The finite wave force results in the parallel transport of 90° PA electrons away from the equator, corresponding to intrinsically nonresonant scattering. This can lead to parallel velocity that meets cyclotron resonance conditions as local PA deviates from 90°. Different types of resonance are identified depending on the wave normal angle, that is, first‐ and second‐order resonances for parallel and oblique waves, respectively.

Perpendicular Ion Heating by Cyclotron Resonant Dissipation of Turbulently Generated Kinetic Alfvén Waves in the Solar Wind

Abstract Solar wind ions are observed to be heated in the directions perpendicular to the large-scale magnetic field, with preferential heating given to heavy ions. In the solar corona, this heating may be responsible for the generation of the wind itself. It is likely that this heating results from the dissipation of plasma turbulence, but the specific kinetic mechanism that produces these preferential effects is not known. Solar wind turbulence at proton scales is often characterized in terms of highly oblique kinetic Alfvén waves (KAWs), which have been thought to dissipate through the Landau resonance and yield parallel heating. We show that the quasilinear resonant cyclotron interaction between KAWs and solar wind ions can actually produce perpendicular ion heating. We present an illustrative calculation of a steady, critically balanced spectrum of KAWs acting on homogeneous ion distributions with a plasma β = 0.1, representative of turbulent conditions in the fast solar wind near 20 R s . The KAWs are described here by a two-fluid dispersion relation. We find that thermal protons are strongly heated in the perpendicular direction within a typical quasilinear time of several thousand gyroperiods, which corresponds to only a few minutes at 20 R s . Alpha particles in the same fluctuation field are heated to similar perpendicular thermal speeds, equivalent to the greater than mass proportional perpendicular temperatures that are commonly observed. We discuss improvements to this simple model that may determine whether this mechanism can be responsible for the observed coronal and solar wind ion heating.

Review of Controlled Excitation of Non-linear Wave-Particle Interactions in the Magnetosphere

Controlled experiments involving injection of 0.5 Hz – 8 kHz electromagnetic waves into the Earth’s magnetosphere have played an important role in discovering and elucidating wave-particle interactions in near-Earth space. Due to the significant engineering challenges of efficiently radiating in the ELF/VLF: 300 Hz – 30 kHz band, few experiments have been able to provide sustained transmissions of sufficient power to excite observable effects for scientific studies. Two noteworthy facilities that were successful in generating a large database of pioneering and repeatable observations were the Siple Station Transmitter in Antarctica and the High Frequency Active Auroral Research Program (HAARP) facility in Alaska. Both facilities were able to excite Doppler shifted cyclotron resonance interactions leading to linear and nonlinear wave amplification, triggering of free running emissions, and pitch angle scattering of energetic electrons. Amplified and triggered waves were primarily observed on the ground in the geomagnetic conjugate region after traversal of the magnetosphere along geomagnetic field aligned propagation paths or in the vicinity of the transmitter following two traversals of the magnetosphere. In several cases, spacecraft observations of the amplified and triggered signals were also made. The observations show the amplifying wave particle interaction to be dynamically sensitive to specific frequency and also specific frequency-time format of the transmitted wave. Transmission of multiple coherent waves closely spaced in frequency showed that the wave particle interaction requires a minimum level of coherency to enter the nonlinear regime. Theory and numerical simulations point to cyclotron resonance with counter streaming particles in the 10-100 keV range as the dominant process. A key feature of the nonlinear interaction is the phase-trapping of resonant particles by the wave that is believed to drive non-linear wave amplification and the triggering of free-running emissions. Observations and modeling of controlled wave injections have important implications for naturally occurring whistler mode emissions of hiss and chorus and the broader phenomena of radiation belt dynamics. A review of observational, theoretical, and numerical results is presented and suggestions for future studies are made.

Quasilinear Consequences of Turbulent Ion Heating by Magnetic Moment Breaking

Abstract The fast solar wind emerging from coronal holes is likely heated and accelerated by the dissipation of magnetohydrodynamic turbulence, but the specific kinetic mechanism resulting in the perpendicular ion heating required by observations is not understood. A promising mechanism has been proposed by Chandran et al., which in this paper we call “magnetic moment breaking” (MMB). As currently formulated, MMB dissipation operates only on the ion perpendicular motion, and does not influence their parallel temperature. Thus, the MMB mechanism acting by itself produces coronal hole proton distributions that are unstable to the ion-cyclotron (IC) anisotropy instability. This quasilinear instability is expected to operate faster than the nonlinear turbulent cascade, scattering ions into the parallel direction and generating quasi-parallel-propagating IC waves. To investigate the consequences of this instability on the MMB-heated protons, we construct a homogeneous model for protons with coronal hole properties. Using a simplified version of the resonant cyclotron interaction, we heat the protons by the MMB process and instantaneously scatter them to lower anisotropy while self-consistently generating parallel-propagating IC waves. We present several illustrative cases, finding that the extreme anisotropies implied by the MMB mechanism are limited to reasonable values, but the distinctive shape of the proton distribution derived by Klein & Chandran is not maintained. We also find that these combined processes can result in somewhat higher particle energization than the MMB heating alone. These quasilinear consequences should follow from any kinetic mechanism that primarily increases the perpendicular ion temperature in a collisionless plasma.

Formation of electron radiation belts at Saturn by Z-mode wave acceleration

At Saturn electrons are trapped in the planet’s magnetic field and accelerated to relativistic energies to form the radiation belts, but how this dramatic increase in electron energy occurs is still unknown. Until now the mechanism of radial diffusion has been assumed but we show here that in-situ acceleration through wave particle interactions, which initial studies dismissed as ineffectual at Saturn, is in fact a vital part of the energetic particle dynamics there. We present evidence from numerical simulations based on Cassini spacecraft data that a particular plasma wave, known as Z-mode, accelerates electrons to MeV energies inside 4 RS (1 RS = 60,330 km) through a Doppler shifted cyclotron resonant interaction. Our results show that the Z-mode waves observed are not oblique as previously assumed and are much better accelerators than O-mode waves, resulting in an electron energy spectrum that closely approaches observed values without any transport effects included.

Development and Demonstration of a Ka-Band Gyrotron Traveling-Wave Tube

The design and experiment of a pulsed Ka-band TE01-mode gyrotron traveling-wave tube are presented. This tube was designed to use the fundamental cyclotron resonance interaction with TE01 cylinder waveguide mode. Backward-wave oscillations of various origins were suppressed by ceramic loading technology. With the electron beam voltage of 66 kV and a beam current of 11 A, a saturated peak power of 110 kW was measured at 33.9 GHz, corresponding to a saturated gain of 34.4 dB, with a −3-dB bandwidth of 1.75 GHz.

Bounce Resonance Scattering of Radiation Belt Electrons by Low‐Frequency Hiss: Comparison With Cyclotron and Landau Resonances

AbstractBounce resonant interactions with magnetospheric waves have been proposed as an important contributing mechanism for scattering near‐equatorially mirroring electrons by violating the second adiabatic invariant associated with the electron bounce motion along a geomagnetic field line. This study demonstrates that low‐frequency plasmaspheric hiss with significant wave power below 100 Hz can bounce resonate efficiently with radiation belt electrons. By performing quantitative calculations of pitch angle scattering rates, we show that low‐frequency hiss‐induced bounce resonant scattering of electrons has a strong dependence on equatorial pitch angle αeq. For electrons with αeq close to 90°, the timescale associated with bounce resonance scattering can be comparable to or even less than 1 h. Cyclotron and Landau resonant interactions between low‐frequency hiss and electrons are also investigated for comparisons. It is found that while the bounce and Landau resonances are responsible for the diffusive transport of near‐equatorially mirroring electrons to lower αeq, pitch angle scattering by cyclotron resonance could take over to further diffuse electrons into the atmosphere. Bounce resonance provides a more efficient pitch angle scattering mechanism of relativistic (≥1 MeV) electrons than Landau resonance due to the stronger scattering rates and broader resonance coverage of αeq, thereby demonstrating that bounce resonance scattering by low‐frequency hiss can contribute importantly to the evolution of the electron pitch angle distribution and the loss of radiation belt electrons.

Near‐relativistic electron acceleration by Landau trapping in time domain structures

AbstractData from the Van Allen Probes have provided the first extensive evidence of nonlinear (as opposed to quasi‐linear) wave‐particle interactions in space with the associated rapid (less than a bounce period) electron acceleration to hundreds of keV by Landau resonance in the parallel electric field of time domain structures (TDSs) traveling at high speeds (~20,000 km/s). This observational evidence is supported by simulations and discussion of the source and spatial extent of the fast TDS. This result indicates the possibility that the electrostatic fields in TDS may generate the electron seed population for cyclotron resonance interaction with chorus waves to make higher‐energy electrons.