Cyclotron Instability Research Articles

A linear parameters study of ion cyclotron emission using drift ring beam distribution

Ion Cyclotron Emission (ICE) holds great potential as a diagnostic tool for fast ions in fusion devices. The theory of Magnetoacoustic Cyclotron Instability (MCI), as an emission mechanism for ICE, states that MCI is driven by a velocity distribution of fast ions that approximates to a drift ring beam. In this study, the influence of key parameters (velocity spread of the fast ions, number density ratio, and instability propagation angle) on the linear MCI is systematically investigated using the linear kinetic dispersion relation solver BO (Xie 2019 Comput. Phys. Commun. 244 343). The computational spectra region considered extends up to 40 times the ion cyclotron frequency. By examining the influence of these key parameters on MCI, several novel results have been obtained. In the case of MCI excited by super-Alfvénic fast ions (where the unique perpendicular speed of fast ion is greater than the perpendicular phase velocity of the fast Alfvén waves), the parallel velocity spread significantly affects the bandwidth of harmonics and the continuous spectrum, while the perpendicular velocity spread has a decisive effect on the MCI growth rate. As the velocity spread increases, the linear relationship between the MCI growth rate and the square root of the number density ratio transitions to a linear relationship between the MCI growth rate and the number density ratio. This finding provides a linear perspective explanation for the observed linear relation between fast ion number density and ICE intensity in JET. Furthermore, high harmonics are more sensitive to changes in propagation angle than low harmonics because a decrease in the propagation angle alters the dispersion relation of the fast Alfvén wave. In the case of MCI excited by sub-Alfvénic fast ions (where the unique perpendicular speed of fast ion is less than the perpendicular phase velocity of the fast Alfvén waves), a significant growth rate increase occurs at high harmonics due to the transition of sub-Alfvénic fast ions to super-Alfvénic fast ions. Similarly, for MCI excited by greatly sub-Alfvénic fast ions (where the unique perpendicular speed of fast ion is far less than the perpendicular phase velocity of the fast Alfvén waves), the growth rate at high harmonics also experiences a drastic increase compared to the low harmonic, thereby expanding the parameter range of the velocity spread.

Stabilization of the Alfvén-ion cyclotron instability through short plasmas: Fully kinetic simulations in a high-beta regime

The Alfvén-ion cyclotron (AIC) mode is an instability that can be driven in magnetized plasmas with anisotropic pressure. Its chief deleterious effect is the driving of enhanced pitch-angle scattering of ions. Although the AIC mode has been observed in several mirror devices, it has not yet been observed in FRC devices developed by TAE Technologies [H. Gota et al., Nucl. Fusion 61, 106039 (2021)]. Previous theoretical work [T. Tajima et al., Phys. Rev. Lett. 39, 201 (1977)] has suggested that sufficient axial inhomogeneity, quantified by a critical axial plasma length, can stabilize this mode. This stabilization mechanism is examined in fully kinetic particle-in-cell simulations with one spatial dimension modeling a simplified magnetic mirror geometry for a plasma with β∼1. A fast-ion population provides the driving anisotropy for the AIC mode, and the resulting effect on the fast-ion pitch angle distribution is examined. The severity of mode activity is recorded for a scan of plasma lengths for multiple fast-ion injection angles. This scan yields critical lengths that show good qualitative agreement with those from the past theoretical work.

Identification of core ion cyclotron instabilities on HL-2A tokamak

Instabilities in multiplies of ion cyclotron frequency range are identified and termed as core ion cyclotron emission (ICE) in recent HL-2A neutral beam injection heated experiments. Characteristics of the core ICE are presented, including frequency dependence and harmonics features. The detected frequencies are found to agree well with the multiplies of the deuterium cyclotron frequency around the magnetic axis. Additionally, the core ICE exhibits a predominantly compressional property. Observations of distinct spectrum features and individual excitation of each harmonic have demonstrated that the core ICE harmonics are independent multiple modes. Notably, the variation of plasma current is a necessary condition for exciting the 4th harmonic ICE individually. The results suggest that the drive mechanism of core ICE varies between the different frequency ranges.

Velocity-space sensitivity and inversions of synthetic ion cyclotron emission

This paper introduces a new model to find the velocity-space location of energetic ions generating ion cyclotron emission (ICE) in plasmas. ICE is thought to be generated due to inverted gradients in the v⊥ direction of the velocity distribution function or due to anisotropies, i.e., strong gradients in the pitch direction. Here, we invert synthetic ICE spectra generated from first principles PIC-hybrid computations to find the locations of these ICE-generating ions in velocity space in terms of a probability distribution function. To this end, we compute 2D ICE weight functions based on the magnetoacoustic cyclotron instability, which reveals the velocity-space sensitivity of ICE measurements. As an example, we analyze the velocity-space sensitivity of synthetic ICE measurements near the first 15 harmonics for plasma parameters typical for the Large Helical Device. Furthermore, we investigate the applicability of a least-square subset search, Tikhonov regularization, and Lasso regularization to obtain the locations in velocity space of the ions generating the ICE.

Hybrid Simulation and Quasi-linear Theory of Bi-Kappa Proton Instabilities

The quasi-steady states of collisionless plasmas in space (e.g., in the solar wind and planetary environments) are governed by the interactions of charged particles with wave fluctuations. These interactions are responsible not only for the dissipation of plasma waves but also for their excitation. The present analysis focuses on two instabilities, mirror and electromagnetic ion cyclotron instabilities, associated with the same proton temperature anisotropy T ⊥ > T ∥ (where ⊥, ∥ are directions defined with respect to the local magnetic field vector). Theories relying on standard Maxwellian models fail to link these two instabilities (i.e., predicted thresholds) to the proton quasi-stable anisotropies measured in situ in a completely satisfactory manner. Here we revisit these instabilities by modeling protons with the generalized bi-Kappa (bi-κ power-law) distribution, and by a comparative analysis of a 2D hybrid simulation with the velocity-moment-based quasi-linear (QL) theory. It is shown that the two methods feature qualitative and, even to some extent, quantitative agreement. The reduced QL analysis based upon the assumption of a time-dependent bi-Kappa model thus becomes a valuable theoretical approach that can be incorporated into the present studies of solar wind dynamics.

Proton Temperature Anisotropy within the Interplanetary Coronal Mass Ejections Sheath at 1 au

The sheath plasma of interplanetary coronal mass ejections (ICMEs) is highly compressed, heated, turbulent, and magnetically intense relative to the ambient solar wind. In this Letter, we perform a detailed study of proton temperature anisotropy within the 333 ICME sheath regions observed on board the Wind spacecraft spanning the years 1995–2015. Our observations show that marginal stability thresholds of mirror mode and firehose instabilities predominantly constrain the proton temperature anisotropy within these sheath regions regardless of ICME sheath plasma speed. This is true even when the plasma beta values are less than 2, a parameter space that should have favored the prevalence of parallel firehose and proton cyclotron instabilities according to linear stability analysis. This investigation demonstrates the critical role played by distinct plasma instabilities in shaping the evolution of ICME sheath plasma compared to the broader solar wind environment.

Critical behavior near the instability threshold of an electron cyclotron maser formed in a mirror magnetic trap.

High-power electron cyclotron resonance discharge in a laboratory open trap is frequently accompanied by growth of electron cyclotron instabilities. We study a simple universal model that explains some of the stability conditions of such plasma observed experimentally, in particular, its crucial dependence on localization of the rf power deposition zone with respect to a minimum of B. An instability threshold seems to be sensitive to particular details of electron losses in a velocity space. Comparing theoretical predictions for the threshold condition with available measurements sheds light on a structure of fast-electron losses in ongoing experiments.

Bi-Kappa Proton Mirror and Cyclotron Instabilities in the Solar Wind

The charged particles in the solar wind are often observed to possess a nonthermal tail in the velocity distribution function, a feature that can be fitted with the Kappa model. The anisotropic, or bi-Kappa, model of protons, electrons, and other charged particles is thus adopted in the literature for interpreting the data as well as in the context of the analysis of wave–particle interactions. The present paper develops an approximate but efficient theory of the mirror and cyclotron instabilities excited by the bi-Kappa protons in the solar wind. A velocity moment-based quasi-linear theory of these instabilities is also formulated in order to investigate the saturation behavior. Applications of the formalism are made for instabilities close to the marginally unstable state, which is typical of the solar wind near 1 au.

Statistical Study of EMIC Waves and Related Proton Distributions Observed by the Arase Satellite

AbstractWe performed a statistical study of electromagnetic ion cyclotron (EMIC) wave distributions and their coupling with energetic protons in the inner magnetosphere using the Arase satellite data from May 2017 to December 2020. We investigated the energetic proton pitch‐angle distributions and partial thermal pressures associated with EMIC waves using inter‐calibrated proton data in the energy range of 30 eV/q–187 keV/q. With a cold plasma approximation, we computed the proton minimum resonance energies using the observed EMIC wave frequency and plasma density values. We found that the EMIC waves had left‐handed polarization near the magnetic equator close to the threshold of proton cyclotron instability, and propagated to higher latitudes along the field line with polarization reversal. H‐EMIC waves showed two peak occurrence regions in the morning and noon sectors at L = 7.5–9 outside the plasmasphere. The flux enhancements associated with morning side H‐EMIC waves appeared at E < 1 keV/q among all pitch angles, while H‐EMIC waves in the noon sector exhibited flux enhancement in field‐aligned directions at E = 1–100 keV/q. He‐EMIC waves showed a broad occurrence region from 12 to 20 magnetic local time at L = 5.5–8.5 inside the plasmasphere with strong flux enhancements at all pitch‐angle ranges at E = 1–100 keV/q. The proton minimum resonance energy using the obtained central frequency was consistent with the observed flux enhancements at different peak occurrence regions. We conclude that the free energy sources of EMIC waves in different geomagnetic environments drive various types of EMIC waves, and they interact with energetic protons at different energy ranges.

Does Turbulence along the Coronal Current Sheet Drive Ion Cyclotron Waves?

Evidence for the presence of ion cyclotron waves (ICWs), driven by turbulence, at the boundaries of the current sheet is reported in this paper. By exploiting the full potential of the joint observations performed by Parker Solar Probe and the Metis coronagraph on board Solar Orbiter, local measurements of the solar wind can be linked with the large-scale structures of the solar corona. The results suggest that the dynamics of the current sheet layers generates turbulence, which in turn creates a sufficiently strong temperature anisotropy to make the solar-wind plasma unstable to anisotropy-driven instabilities such as the Alfvén ion cyclotron, mirror-mode, and firehose instabilities. The study of the polarization state of high-frequency magnetic fluctuations reveals that ICWs are indeed present along the current sheet, thus linking the magnetic topology of the remotely imaged coronal source regions with the wave bursts observed in situ. The present results may allow improvement of state-of-the-art models based on the ion cyclotron mechanism, providing new insights into the processes involved in coronal heating.

Kinetic whistler instability in a mirror-confined plasma of a continuous ECR ion source

Kinetic instabilities in a dense plasma of a continuous electron cyclotron resonance (ECR) discharge in a mirror magnetic trap at the Gasdynamic Ion Source for Multipurpose Operation (GISMO) setup are studied. We experimentally define unstable regimes and corresponding plasma parameters, where the excitation of electromagnetic emission is observed, accompanied by the precipitation of energetic electrons from the magnetic trap. A comprehensive experimental study of the precipitating electron energy distribution and plasma electromagnetic emission spectra, together with theoretical estimates of the cyclotron instability increment proves that under the experimental conditions, the observed instability is related to the excitation of whistler-mode waves, which are a driver of losses of energetic electrons from the magnetic trap. The results of this study are important for the further development of the GISMO electron cyclotron resonance ion source facility and for the improvement of its parameters as an ion source. Also, this research on plasma kinetic instabilities is of fundamental interest and provides experimental tools to simultaneously study plasma electromagnetic activity and corresponding changes in a resonant electron energy distribution.

The Oblique Alfvén Ion Beam Instability in the Earth's Ion Foreshock

How ions evolve in the Earth’s ion foreshock is a basic problem in the heliosphere community, and the ion beam instability is usually proposed to be one major mechanism affecting the ion dynamics therein. This work will perform comprehensive analyses of the oblique ion beam instability in the Earth’s ion foreshock. We show that in addition to two well-known parallel instabilities (i.e., the parallel fast-magnetosonic whistler instability and the parallel Alfvén ion cyclotron instability), the oblique Alfvén ion beam (OA/IB) instability can also be triggered by free energy relating to the relative drift dV between the solar wind proton and reflected proton populations. For slow dV (e.g., dV ≲ 2.2V A , where V A denotes the Alfvén speed), it only triggers the OA/IB instability. When dV ≳ 2.2V A , the growth rate in the OA/IB instability can be about 0.6 times the maximum growth rate in parallel instabilities. Moreover, this work finds the existence of two types of OA/IB instabilities. The first one appears at slow dV and in the small wavenumber region at fast dV, and this instability can be described by the cold fluid model. The second one arises in large wavenumber regions at fast dV, and this instability only appears in warm plasmas. Furthermore, through the energy transfer rate method, we propose that the OA/IB instability is driven by the competition among the Landau and cyclotron wave-particle interactions of beam protons, the cyclotron wave-particle interaction of core protons, and the Landau wave-particle interaction of electrons. Because oblique waves can experience significant damping, the importance of the OA/IB instability may be the effective heating of ions in the Earth’s foreshock.

Alpha Particle Temperature Anisotropy in Earth’s Magnetosheath

In magnetized plasmas, temperature anisotropy manifests as distinct temperatures (T ⊥j , T ∥j ). Numerous prior studies have demonstrated that as plasma beta (β ∥j ) increases, the range of temperature anisotropy (R j = T ⊥j /T ∥j ) narrows. This limiting effect is conventionally taken as evidence that kinetic microinstabilities are active in the plasma, and has been previously observed for protons in the magnetosheath. This study is the first to use data from the Magnetic Multiscale Mission to investigate these instability-driven limits on alpha particle (ionized helium) anisotropy in Earth’s magnetosheath. The distribution of data over the (β ∥j , R j ) plane was plotted and shows the characteristic narrowing in the range of R j -values as β ∥j increases. The contours of the data distribution align well with the contours of the constant growth rate for the ion cyclotron, mirror, parallel firehose, and oblique firehose instabilities, which were calculated using linear Vlasov theory.

Study of Low-Frequency Electromagnetic Ion-Cyclotron Wave for Ring Distribution in Magnetosphere of Saturn

Magnetic cyclotron waves were discovered by the Cassini-Huygens spacecraft in Saturn's atmospheric torus’ magnetic layer. They are left-handed and propagate at a minor angle to the ambient magnetic field in most areas because their frequency is close to the frequency of the aqua ions. The ion cyclotron instability caused by Saturn's neutral cloud ions helps explain their formation. They can be classified as n = 2 mode fluctuations because of the ion-ring distribution. We planned the characteristics of these waves in advance of starting this project. Our dispersion growth rates are evaluated using kinetic method analysis as well. The results were calculated and explained for the exemplary values of the magnetosphere parameters suitable for Saturn. Another potential free energy source for ion cyclotrons is temperature anisotropy. Instead of the standard Maxwell distribution, a ring distribution is employed in this study. The focus of this research is EMIC waves’ oblique propagation in the magnetic field, which changes their temperature anisotropy, ion energy density, and propagation angle. The interaction of relativistic particles with ion cyclotron waves is also included in this extension. EMIC wave size decreases with the increasing density of particles, as shown by a numerical study. A comparison of planetary studies based on data from space plasma environments and magnetospheric systems produced these results. HIGHLIGHTS Temperature anisotropy - free energy source for Ion Cyclotron waves EMIC wave size decreases with the increasing density of particles Saturn's neutral cloud ions helps the formation of ion cyclotron instability GRAPHICAL ABSTRACT

Sub-grid modeling of pitch-angle diffusion for ion-scale waves in hybrid-Vlasov simulations with Cartesian velocity space

Numerical simulations have grown to play a central role in modern sciences over the years. The ever-improving technology of supercomputers has made large and precise models available. However, this accuracy is often limited by the cost of computational resources. Lowering the simulation's spatial resolution in order to conserve resources can lead to key processes being unresolved. We have shown in a previous study how insufficient spatial resolution of the proton cyclotron instability leads to a misrepresentation of ion dynamics in hybrid-Vlasov simulations. This leads to larger than expected temperature anisotropy and loss-cone shaped velocity distribution functions. In this study, we present a sub-grid numerical model to introduce pitch-angle diffusion in a 3D Cartesian velocity space, at a spatial resolution where the relevant wave–particle interactions were previously not correctly resolved. We show that the method is successfully able to isotropize loss-cone shaped velocity distribution functions, and that this method could be applied to simulations in order to save computational resources and still correctly model wave–particle interactions.

Doublet splitting of fusion alpha particle driven ion cyclotron emission

Ion cyclotron emission (ICE) originating from confined populations of fast ions in toroidal fusion plasmas is an important non-invasive, passive diagnostic for current and next-generation devices. The ability to model ICE signals accurately is an essential step towards inferring the characteristics of confined energetic alpha particles or fast neutral beam ions and background plasma. In this paper, the linear growth rates of the magnetoacoustic cyclotron instability, which is the leading explanation for ICE, are calculated in high-resolution 2D space for parameters corresponding to JET Pulse No. 26148. These calculations further highlight the origin of doublet splitting of the cyclotron harmonics and the perceived need to invoke nonlinear interactions with 1D3V particle-in-cell studies to account for lower harmonics with substantial amplitudes. The inclusion of signals of ICE from a well-resolved range of propagation angles can also account for these effects.

Electron Temperature Anisotropy Effects on Alpha/Proton Instability in the Solar Wind

In situ recordings by the solar Wind spacecraft reveal the ubiquitousness of alpha particles, whose drift velocities to the background proton vα are generally less than or equal to the local Alfvén velocity vA. The alpha beam instability plays a significant role in the alpha beam deceleration in the solar wind; nonetheless, the detailed mechanism of deceleration remains unclear. By using the linear Vlasov equation of the PDRK/B0 solver, the present work investigates the kinetic instability caused by both the alpha beam and the electron temperature anisotropy in the solar wind and assesses the effects of the electron temperature anisotropy on such instability. The results show that both anisotropic electrons and alpha beams lead to the excitation of several plasma waves, and the wave frequency, growth rate, and polarization properties are sensitive to the electron temperature anisotropy (Te⊥/Te‖), the parallel electron beta (βe‖), and the alpha beam drift velocity (vα/vA). With an excess parallel temperature Te⊥/Te‖<1, the parallel magnetosonic/whistler (PM/W), parallel Alfvén wave (PAW), and oblique Alfvén/ion cyclotron (OA/IC) instabilities could be generated, while for an excess perpendicular temperature Te⊥/Te‖>1, the PM/W, OA/IC, parallel whistler (PW), and kinetic Alfvén wave (KAW) instabilities could grow. In the region of Te⊥/Te‖<1, the thresholds of the PM/W, PAW, and OA/IC instabilities extend to lower drift velocity vα/vA. In the region of Te⊥/Te‖>1, the thresholds of the PM/W and OA/IC instabilities increase, while those of the PW and KAW instabilities are shifted to lower vα/vA. The current study presents a comprehensive overview for alpha beam instabilities that limit the alpha beam drift velocity in the solar wind.

Plasma Oscillations and Kinetic Instabilities at Ion Scales in the Expanding Magnetosheath

We investigate a relationship between a decaying spectrum of magnetic field perturbations and kinetic instabilities in a slowly expanding magnetosheath plasma using two-dimensional hybrid expanding simulations in (X, Y) space. We impose an initial ambient magnetic field B 0/B 0 = (1, 0, 0), and superimpose a flat spectrum of Alfvénic fluctuations with average amplitudes equal to δ B = ∣B − B 0∣ ∼ 0.2B 0. The expansion leads to the development of temperature anisotropy A p = T p⊥/T p∥ > 1 (T p⊥, T p∥ are plasma temperatures perpendicular and parallel with respect to B 0, respectively) and the system becomes unstable with respect to the ion cyclotron and mirror instabilities. The onset of mirror instability in the early stage of the simulation leads to the development of filaments that fill the simulation volume. The filaments represent pressure-balanced structures as they develop in the form of magnetic field (δ B) perturbations balanced with corresponding density perturbations. Further expansion of the system leads to the thinning of these filaments, which gradually become extremely narrow. The filamentation maintains the power spectral density in δ B ⊥ at (here d p0 is the proton inertial length) over the range 0.2 < kd p0 < 1.1. The filaments remain well developed in the form of density, magnetic field, and temperature anisotropy perturbations at t ∼ 10,000/Ω p0 (here Ω p0 is the initial proton gyrofrequency) and slowly dissipate when the expansion continues further.

Neutral beam driven ion cyclotron instability of lower hybrid wave in a tokamak plasma

The effect of dust grains on the parametric coupling of neutral beam driven ion–cyclotron wave instability with a lower hybrid pump wave is studied. A high amplitude lower hybrid pump, which is launched into a tokamak for heating purposes in the presence of neutral beam driven ion-cyclotron waves, can excite the parametric coupling involving two lower hybrid sidebands. In a tokamak, the lower hybrid waves result in parametric excitation of the ion-cyclotron mode and quasi-modes near the edge when the electron oscillatory velocity is greater than the sound velocity. This parametric coupling increases the growth rate of instability when the lower sideband wave is resonant. Moreover, the presence of dust grains in the tokamak plasma, their radius, and the number density significantly affect the growth rate of the instability, which in turn can affect the advanced stage operations of a tokamak. The growth rate of parametric instability scales with the amplitude of the pump wave. The growth rate is found to be linearly increased with the dust grain density, but it decreased with increasing size of dust grains, which means large sized dust grains stabilize the instability. The theoretical results explained in the present paper are very helpful in explaining the complexity in the plasma properties of a tokamak due to the dust–plasma interactions, which can diminish the performance of the International Thermonuclear Experimental Reactor due to potential safety issues.

Verification of a fully kinetic ion model for electromagnetic simulations of high-frequency waves in toroidal geometry

For the study of high-frequency electromagnetic waves in tokamaks, an electromagnetic simulation model, in which the ion dynamics is described by a six-dimensional Vlasov equation and the electron dynamics is described by a drift kinetic equation, is formulated and implemented in the global gyrokinetic toroidal code (GTC). Analytic dispersion relations are derived in reduced systems and compared with various theories to verify the model. Linear simulations of a generalized ion Bernstein wave and ion cyclotron emission are verified by comparing the GTC simulation results with analytic dispersion relation theory and magnetoacoustic cyclotron instability theory, respectively, in cylindrical geometry.