Cyclotron Resonance Conditions Research Articles

On the Possibility of Multiplying the Frequency of a Gigawatt Ultrashort Microwave Pulse

It has been shown that the frequency of an ultrashort microwave pulse of a lowest axisymmetric electric mode at the interaction with a counterpropagating relativistic tubular electron beam under the cyclotron resonance conditions can be doubled due to re-emission into a mode having resonance at the second harmonic of the gyrofrequency. The conversion of the 3-cm 1-ns gigawatt microwave pulse in a circular waveguide from the TM01 mode to the TM02 mode with the doubling of the frequency, reduction of the duration to 0.22 ns, and the achievement of the peak power above the initial value has been demonstrated in a numerical experiment. The possibility of forming an intense ultrashort frontal splash of oscillations with the doubled frequency has been shown for longer initial pulses with a subnanosecond front.

The excitation of whistler waves and wave-particle interaction in magnetic reconnection

A 2.5D PIC kinetic code is executed to simulate the excitation of electron whistlers and ion cyclotron whistler (L wave) during magnetic reconnection. Our simulation results suggest that quasi-parallel and anti-parallel whistler waves can be excited in the separatrix region near X-Line and in the outflow region, respectively. Electron whistlers play a crucial role in energy release and transfer, as the small mass of electrons allows them to move rapidly under the perturbation of a magnetic field during magnetic reconnection. The L wave excited near the separatrix region far from X-Line, it propagate obliquely to the local magnetic field. Velocity distribution functions (VDFs) indicate that these waves are associated with temperature anisotropy instabilities of electron-beams (ion-beam). The electron whistler in the separatrix region is excited by cyclotron resonance due to the electron beam. The electron whistler observed in the outflow region is generated by Landau resonance owing to beam-mode, where the v∥ is close to the phase speed vph of the wave. Regarding L wave, their excitation mechanism is attributed to significant perpendicular temperature anisotropy instability (Ti⊥>Ti∥) of ion-beam, and satisfies cyclotron resonance condition. Meanwhile, our simulation results illustrate that the existence of energy conversion between particles and waves during the wave excitation by using the Wave-Particle Interaction Analyzer (WPIA).

Analysis of a cusped helicon plasma thruster discharge

Experiments and simulations are used to analyze a compact helicon plasma thruster with a cusp in its internal magnetic field. The former rely on a compensated Langmuir probe and a Faraday cup, while the latter employ a hybrid PIC/fluid transport model combined with a frequency-domain electromagnetic field model. Measurements serve to tune the anomalous transport parameters of the model and overall show the same trends as the numerical results, including a secondary peak of electron temperature downstream in the magnetic nozzle, where electron cyclotron resonance conditions for the 13.56 MHz excitation frequency are met. The cusp plays a central role in determining the plasma losses to the walls and the profile of electron temperature, which in turn defines the excitation and ionization losses. While losses to the rear wall are reduced, losses to the lateral wall are increased, which, together with the low production efficiency, limit the performance of the device.

Quasilinear theory of Brillouin resonances in rotating magnetized plasmas

Both spin and orbital angular momentum can be exchanged between a rotating wave and a rotating magnetized plasma. Through resonances the spin and orbital angular momentum of the wave can be coupled to both the cyclotron rotation and the drift rotation of the particles. It is, however, shown that the Landau and cyclotron resonance conditions which classically describe resonant energy–momentum exchange between waves and particles are no longer valid in a rotating magnetized plasma column. In this case a new resonance condition which involves a resonant matching between the wave frequency, the cyclotron frequency modified by inertial effects and the harmonics of the guiding centre rotation is identified. A new quasilinear equation describing orbital and spin angular momentum exchanges through these new Brillouin resonances is then derived, and used to expose the wave-driven radial current responsible for angular momentum absorption.

Enhanced electron heating in the magnetic nozzle of a radio-frequency plasma via electron cyclotron resonance

The effect of electron cyclotron resonance on the electron flow is experimentally examined in the magnetic nozzle of a radio-frequency plasma source powered at 13.56 MHz under a series of operating conditions. Measurements of the electron energy probability function show that the bulk of electrons is effectively heated when the external magnetic field meets the cyclotron resonance condition in the proximity of the antenna. A careful tuning of the magnetic field topology inside the plasma source leads to a gain in electron density and temperature up to about 20% and 40%, respectively.

Anomalous resonance between low-energy particles and electromagnetic plasma waves

Cyclotron resonance between plasma waves and charged particles is a fundamental and ubiquitous process in the plasma universe, during which the particle’s gyromotion has a constant phase in the wave field to enable a sustained energy exchange. In this classical picture, however, the particle’s angular velocity is determined only by the background magnetic field. Here, we show that the classical condition of cyclotron resonance fails to describe the observations of low-energy particles in resonance with large-amplitude waves, which highlights the roles of the wave field in nonlinearly modifying the resonant picture. The revised scenario of anomalous resonance is then validated by the agreement between test-particle simulations and ultrafast spacecraft measurements, which present in-phase and/or antiphase relationships between the wave magnetic field and ion flux oscillations at energy and pitch-angle ranges incompatible with the classical resonance condition. This revision could significantly affect the wave-particle energy exchange and wave evolution processes.

Inner Belt Wisp Precipitation Measured by ELFIN: Regimes of Energetic Electron Scattering by VLF Transmitter Waves

AbstractMan‐made very low frequency (VLF) transmitter waves play a critical role in energetic electron scattering and precipitation from the inner radiation belt, a type of which is called wisp precipitation. Wisps exhibit dispersive energy‐versus‐L spectra due to the evolution of electron cyclotron resonance conditions with near‐monochromatic VLF transmitter waves. Here, we report on such observations of inner belt wisp precipitation events with full pitch angle resolution in the energy range of 50 to ∼500 keV as measured by Electron Loss and Fields Investigation (ELFIN) at L < ∼2 between March 2021 and April 2022. Statistical observations (82 events) reveal occasional (18 events) wisp precipitation events with local bounce‐loss‐cone electron flux enhancements, which provide new information compared with flux enhancements measured in previous studies only in the drift loss cone. Based on magnetic field and plasmaspheric density models, quasilinear theory, and detailed pitch angle distributions of wisps from ELFIN, we have estimated the wisp electron bounce‐averaged pitch angle diffusion coefficients to be of the order of 10−4 to 10−2 s−1. These are several orders of magnitude larger than the diffusion rates calculated from models using global statistical averages of VLF transmitter wave power. When using our estimated diffusion coefficients to deduce the associated local transmitter wave amplitudes near the equator, based on quasilinear calculations from a transmitter‐induced electron diffusion model, we find these wave amplitudes to be >1 mV/m. Although probable overestimates, such inferred wave amplitudes exceed the theoretical threshold amplitude for nonlinear interactions, strongly suggesting that it is necessary to include nonlinear effects for an accurate evaluation of energetic electron scattering by transmitter waves.

Effect of Electron Beam Properties on a Second Harmonic Gyrotron

In harmonic gyrotrons, the narrow operating region of the harmonic mode is significantly restricted by the severe mode competition from the fundamental parasitic modes, which makes it important to study the nonlinear effects of beam-wave interaction in the case of a nonideal electron beam. In this article, the effect of the electron velocity spread and the beam radius spread on the mode excitation, interaction efficiency as well as mode competition are analyzed for the desired harmonic mode and the parasitic fundamental mode operating far from the cut-off frequency. The effect of velocity spread is interpreted via the electron cyclotron resonance condition as well as the electron beam susceptibility with respect to the resonator field. The results show that the velocity spread can greatly broaden the effective operating region of the harmonic mode and the efficiency degradation can be contained at a reasonable level by proper design consideration of the interaction circuit. Whereas, the beam radius spread is the main factor that accounts for the efficiency degradation and can aggregate the mode competition. The results are referential to the design and analysis of harmonic gyrotrons as well as continuously frequency tunable gyrotrons.

Development of ECR ion source with high-temperature superconducting REBCO coils

A new High-Temperature Superconducting ECR (HTS-ECR) ion source is under development in Research Center for Nuclear Physics (RCNP), Osaka University. This ion source will be used for production of high intensity proton, deuteron and He ion beams. The HTS-ECR magnets are composed of three solenoid coils and a set of sextupole coils made of REBCO tapes, a high-temperature superconductor. The HTS-ECR ion source is designed to operate at frequency of 2.45 GHz and 10 GHz. Performance test of the HTS coils had been carried out at 31 K and 77 K. This HTS coil technology will be applied to development of a meter-size HTS coil system of a high intensity compact AVF cyclotron. This paper introduces the basic design of the HTS-ECR ion source. The performance test results showed that REBCO solenoids remain superconducting state with a current up to 400 A. Simulation results of the magnetic field and electromagnetic field distributions in a plasma chamber fulfilled the requirements of electron cyclotron resonance conditions at 2.45 GHz and 10 GHz. Simulation result of mirror ratios and electromagnetic field amplitudes are also presented in this paper.

Whistler instability driven by the sunward electron deficit in the solar wind

Context. Solar wind electrons play an important role in the energy balance of the solar wind acceleration by carrying energy into interplanetary space in the form of electron heat flux. The heat flux is stored in the complex electron velocity distribution functions (VDFs) shaped by expansion, Coulomb collisions, and field-particle interactions. Aims. We investigate how the suprathermal electron deficit in the anti-strahl direction, which was recently discovered in the near-Sun solar wind, drives a kinetic instability and creates whistler waves with wave vectors that are quasi-parallel to the direction of the background magnetic field. Methods. We combined high-cadence measurements of electron pitch-angle distribution functions and electromagnetic waves provided by Solar Orbiter during its first orbit. Our case study is based on a burst-mode data interval from the Electrostatic Analyser System (SWA-EAS) at a distance of 112 RS (0.52 au) from the Sun, during which several whistler wave packets were detected by Solar Orbiter’s Radio and Plasma Waves (RPW) instrument. Results. The sunward deficit creates kinetic conditions under which the quasi-parallel whistler wave becomes unstable. We directly test our predictions for the existence of these waves through solar wind observations. We find whistler waves that are quasi-parallel and almost circularly polarised, propagating away from the Sun, coinciding with a pronounced sunward deficit in the electron VDF. The cyclotron-resonance condition is fulfilled for electrons moving in the direction opposite to the direction of wave propagation, with energies corresponding to those associated with the sunward deficit. Conclusions. We conclude that the sunward deficit acts as a source of quasi-parallel whistler waves in the solar wind. The quasilinear diffusion of the resonant electrons tends to fill the deficit, leading to a reduction in the total electron heat flux.

Effect of magnetic field on optical emission from cold atmospheric pressure micro-plasma jet

Application of magnetic field can affect the charge particle dynamics, plasma constituents, and optical emissions from a cold atmospheric pressure micro-plasma jet. The present study focuses on the effect of an externally applied transverse magnetic field (B) on optical emissions from the plasma jet and the resulting particle behavior inside the plasma. Detailed experiments are performed to look at Hα, Hβ, He, and other emission lines from which the electron density (ne) and electron excitation temperature (Texc) are determined as a function of B. Reactive O2 and N2 species (RONS) that are important for biomedical applications are identified and the effect of B on them is investigated. The discharge is modeled using fluid theory, which predicts the temporal evolution of plasma parameters both during nascent and time to saturation (ts) values. It is observed that ts of ne reduces as B is increased. Besides the Lorentz force, strong B invokes the Zeeman effect and also contributes to the broadening of emission lines, thereby altering ne and Texc. The observed phenomena can be explained from the cross field transport and the dependence of Larmor radius and cyclotron frequency upon B. It is found that finite Larmor radius effect and the satisfaction of collisionally broadened ion cyclotron resonance condition can alter the emission intensities of RONS. Furthermore, the incidence of charged RONS on a specified surface area could be controlled by B.

Modulation of Whistler Mode Waves by Ultra‐Low Frequency Wave in a Macroscale Magnetic Hole: MMS Observations

AbstractWe report the quasi‐periodic whistler‐mode waves corresponding to electron temperature anisotropy T⊥/T// < 1 at the center of a macroscale magnetic hole (MH) near the Earth's magnetopause observed by the Magnetospheric Multiscale mission. A significant ultra‐low frequency (ULF) wave of background magnetic field was observed in this MH. The ULF wave dramatically exacerbates the evolution of MH and the formation of the donut‐shaped electron pitch angle distribution (PAD) in the macroscale MH. When the whistler‐mode waves were generated, they are consistent with troughs of the ULF wave and density increases, which is also related to the butterfly type PAD at those moments. The analysis of dispersion relation and cyclotron resonance condition indicate that whistler‐mode waves were mainly generated by the butterfly type PAD of electrons. Our results provides new insights into one possible excitation mechanism of whistler‐mode wave.

Multipoint Analysis of Source Regions of EMIC Waves and Rapid Growth of Subpackets

AbstractElectromagnetic Ion Cyclotron (EMIC) rising tone emissions are important in understanding the nonlinear wave evolution and interaction with the energetic particles. We present observations of rising tone emissions of EMIC waves by THEMIS A, D, and E spacecraft in the outer magnetosphere. These emissions with subpacket structures in the proton band were observed during the time interval 14:20 UT to 14:30 UT on September 9, 2010. The observed waves are left‐handed polarized with wave normal angles less than . THEMIS A was closest to the equator and was in a higher L‐shell than THEMIS E and D. The smallest radial separation is 2,000 km between THEMIS E and D spacecraft. This configuration of THEMIS allows us to investigate the subpackets of rising tone EMIC waves observed simultaneously at 14:23 UT by three spacecraft. Hilbert Huang Transformation (HHT) is applied to show the variations of the instantaneous frequency and the observed wave amplitude. The direction of energy flow is determined from the analysis of the Poynting flux. There is a rapid nonlinear growth of the EMIC subpackets within one wavelength. Subpackets are dynamic in nature as their structure changes within one wave period, which is further supported by the nonlinear wave growth theory. Optimum and threshold amplitudes for the EMIC wave growth are calculated beside the nonlinear transition time (). Observed ion energies and pitch angle spectra of the ion fluxes are consistent with the energy associated with the Landau and cyclotron resonance conditions.

Autoresonance phenomenon in a long mirror

The paper describes an implementation of a long mirror-based variant of cyclotron autoresonance which permits a local temporary change in the mirror`s induction and provides a mode for filling the trap with primary plasma, and for the generation of plasma bunches with an energetic electron component and their accumulation within a single cavity. The approach does not require injection of external particles into the acceleration zone as particles can be generated directly within the mirror using specialized conditions of electron cyclotron resonance (ECR) as part of the operational mode. A detailed study of the spectral-angular distribution of Bremsstrahlung in various operational modes has been undertaken. The results of this study permit the optimal value of the time sequence between the leading edge of the pulsed magnetic field and the microwave pulse to be determined, which ensures the optimal mode of electron trapping in the cyclotron autoresonance mode. Bremsstrahlung radiation recorded in the transverse direction has a significantly higher intensity of photons and energy compared to the longitudinal direction during the acceleration and subsequent confinement mode of plasma bunches. The observed changes in the intensity and spectral distribution of the Bremsstrahlung, which depend on the values of the operating parameters for acceleration, afford the possibility to define the dependence of the number of initial plasma particles trapped by cyclotron autoresonance for the different operating modes. The results will improve our understanding of the processes taking place at various stages of the operational modes. In general, such studies are important for gaining an improved understanding of the mechanisms of generation and confinement of hot electron plasma bunches with an energetic electron component for autoresonant interaction in a long mirror.

Numerical analysis of the spectral broadening of the EC resonance for Gaussian beams propagating in inhomogeneous plasmas, with applications to EC H&CD in ITER

A model is proposed which accounts for the modification in the electron cyclotron (EC) resonance condition for Gaussian beams injected in inhomogeneous plasmas, due to the finite width of the transversal spectrum caused by the paraxial character of the beams, within the framework of the complex geometrical optics. The resonance modification due to the non-uniformity of the equilibrium magnetic field is taken into account as well. This model, which is suitable for electron cyclotron resonance heating and current drive applications, has been implemented as an option in the beam-tracing code GRAY. Numerical examples of the application of this new tool to International Thermonuclear Experimental Reactor scenarios are given, with results that indicate a minor effect of the EC resonance broadening on the EC power deposition profiles for the considered cases.

Zebra-like patterns in whistler wave emission spectra from nonequilibrium mirror-confined laboratory plasma

Zebra-like patterns have been observed in the electron cyclotron emission spectra from strongly nonequilibrium plasma confined in a table-top mirror magnetic trap. The analysis of the experimental data suggests that the formation of zebra-like patterns could eventually be related to the modulation of the whistler waves by the ion-acoustic waves excited during the abrupt ejection of electrons into a loss cone caused by the development of the whistler instability under the electron cyclotron resonance condition.

New kinetic cyclotron instability for electron beam in time-changing magnetic fields

This paper examines the velocity distribution function and cyclotron resonance conditions for a beam of electrons moving in a magnetic field which gradually changes with time. A spatial gradient of magnetic field is known to result in an unstable horseshoe distribution of electrons. The field gradient in time adds additional effects due to an induced electric field. The resultant anisotropic velocity distribution function, which we call a Luvdisk distribution, has some distinctive properties when compared to the horseshoe. Fitting the cyclotron resonance condition circle shows that the frequency of the resultant emission is under the local cyclotron frequency. While the spatial gradient results in the emission coming almost perpendicularly to the field, the direction of the radiation under a time-changing field has more variability. The Luvdisk distribution also arises when the magnetic field has a gradient both in space and time. The beam can be unstable if those gradients are added or subtracted from each other (if the gradients are of equal or different sign), which occurs even when the total change of magnetic field is negative. While the frequency of the emission is related to the final magnetic field value, its direction is indicative of the field’s history which produced the instability.

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.

About the cyclotron resonance conditions in magnetized current-carrying plasmas

The resonant cyclotron wave-particle interactions in a cylindrical current-carrying plasma and in two-dimensional axisymmetric toroidal plasma models for tokamaks with D-shaped, elliptic and circular magnetic surfaces are discussed. The corresponding phase resonance conditions are derived by solving the linearized Vlasov equations as a boundary-value problem for perturbed plasma particle distribution functions, accounting for the geometry of a confinement magnetic field in the zero-order over magnetization parameters. It is shown that the Doppler shifts under the cyclotron resonance conditions in the current-carrying plasmas differ from those for a plasma in a uniform magnetic field due to the rotational transformation (including the shear-effects) of the helical magnetic field lines. As for elongated tokamaks, the cyclotron wave-particle resonance conditions in the general case, along with helicity-corrections, involve the bounce-resonances of the untrapped (circulating, passing) and two groups of so-called t-trapped and d-trapped particles.

Computational study of the three dimensional autoresonance acceleration of electrons cloud in magnetic fields varying on time

There are many particle acceleration mechanisms using electromagnetic waves and external magnetic fields where the electron cyclotron resonance condition is preserved. Among these mechanisms, the gyroresonant acceleration proposed by K. Golovanivsky consists of the 2D acceleration of electrons by a circular polarized standing transversal electric wave and a homogeneous magnetic field, which changes on time to compensate the increase of relativistic factor as the electrons are accelerated. By using an analytical model, he obtained a set of differential equations describing both the evolution of the electron energy and the phase shift between the particle velocity and the the electric field component of the microwave field. The 3D simulation of the electrons bunch acceleration by the TE111 cylindrical mode of 2.45 GHz in frequency and the strength of 100 kV/m, said acceleration mechanism is numerically studied. In our numerical scheme, the inhomogeneous magnetic field is produced by a set of 4 current coils, wherein the currents in the central coils change linearly on time. In the transversal mid plane, the initial magnetic field is fitted to the classical resonance value. The concentration of the electron bunch is ne = 2.6 × 108 cm−3, so the simple particle approximation is used. The electron trajectories, its velocities, and energies are obtained from the numerical solution of the relativistic Newton-Lorentz equation. Finally, the number of accelerated electrons was determined, identifying the favorable regions for the acceleration regime. These results can be useful for the design of gyroresonant accelerator devices. It is worth mentioning that said accelerators can be used as X-ray sources when accelerated electrons hit a metallic target.