Loss-cone Instability Research Articles

Kinetic instabilities in two-isotopic plasma in the gas-dynamic trap magnetic mirror

A fusion neutron source (FNS) based on the gas-dynamic trap (GDT, Budker Institute, Novosibirsk) is considered for confinement of two-species plasma heated by neutral beam injection in a regime where the fast ion distribution function is far from Maxwellian. Kinetic instabilities are expected to develop in this regime, and in this paper we investigate the ion-cyclotron instability evolving in moderate densities of pure hydrogen and mixed deuterium–hydrogen target plasmas. The properties of the studied unstable mode, such as its azimuthal wavenumbers, propagation direction and its being affected by changes in the bulk plasma density and composition, allow us to identify it as the drift cyclotron loss cone (DCLC) instability. This mode scatters fast ions and thereby leads to drops in diamagnetic flux signals and increases longitudinal energy and particle losses, with the average energy of the lost ions estimated to be far above the temperature of warm Maxwellian ions. Our interpretation is that the unstable wave grows due to interaction with the fast ions located near the loss cone in the velocity space and scatters them. Applying the method of suppressing the DCLC instability by filling the loss cone with warm plasma, we have determined the values of plasma density and deuterium percentage that allow us to suppress the DCLC instability in the GDT. These findings justify using mixed bulk plasmas in fusion neutron source operation.

Wave and Particle Analysis of Z‐Mode and O‐Mode Emission in the Jovian Inner Magnetosphere

AbstractWe report some of the most intense Z‐mode and O‐mode observations obtained by the Juno spacecraft while in orbit about Jupiter in a low to mid‐latitude region near the inner edge of the Io torus. We have been able to estimate the density of the plasma in this region based on the lower frequency cutoff of the observed Z‐mode emission. The results are compatible with the electron density measurements of the Jovian Auroral Distributions Experiment (JADE), on board the Juno spacecraft, if we account for unmeasured cold plasma. Direction‐finding measurements indicate that the Z‐ and O‐mode emission have distinct source regions. We have also used the measured phase space density of the JADE and the Jupiter energetic particle detector instruments to calculate estimated local growth rates of the observed O‐mode and Z‐mode emission assuming a loss cone instability and quasilinear analysis. The results suggest the emissions were observed near, but not within, a source region, and the free energy source is consistent with a loss cone. We have thus carried out the quasilinear wave analysis of the assumed remote Z‐ and O‐mode wave growths. It is shown that the remotely generated waves, propagated through an inhomogeneous medium to the satellite location, may account for the observed wave characteristics. The importance of Z‐mode in accelerating electrons in the inner Jovian magnetosphere makes these new wave mode confirmations at Jupiter of particular interest.

Simulation of the loss-cone instability in spherical systems – II. Dominating Keplerian potential

ABSTRACT According to our previous theoretical findings, physical processes in centres of galaxies, star clusters, and the Oort comet cloud can be significantly altered by a new so-called ‘gravitational loss-cone instability’. Using N-body simulations of a spherical stellar model in the dominating Keplerian potential, we confirm the possibility of the instability and go beyond the linear theory. Unlike most other instabilities, the new one shows no notable change in spherical geometry of the cluster, but it significantly accelerates the speed of diffusion of particles in phase space leading to a repopulation of the loss cone and early instability saturation.

Simulation of the loss-cone instability in spherical systems – I. Dominating harmonic potential

ABSTRACT A new so-called ‘gravitational loss-cone instability’ in stellar systems has recently been investigated theoretically in the framework of linear perturbation theory and proved to be potentially important in understanding the physical processes in centres of galaxies, star clusters, and the Oort Cloud. Using N-body simulations of a toy model, we confirm previous findings for the dominating harmonic potential and go beyond the linear theory. Unlike the well-known instabilities, the new one shows no notable change in the spherical geometry of the cluster, but it significantly accelerates the speed of diffusion of particles in phase space leading to an early instability saturation.

Loss-cone instability modulation due to a magnetohydrodynamic sausage mode oscillation in the solar corona

Solar flares often involve the acceleration of particles to relativistic energies and the generation of high-intensity bursts of radio emission. In some cases, the radio bursts can show periodic or quasiperiodic intensity pulsations. However, precisely how these pulsations are generated is still subject to debate. Prominent theories employ mechanisms such as periodic magnetic reconnection, magnetohydrodynamic (MHD) oscillations, or some combination of both. Here we report on high-cadence (0.25 s) radio imaging of a 228 MHz radio source pulsating with a period of 2.3 s during a solar flare on 2014-April-18. The pulsating source is due to an MHD sausage mode oscillation periodically triggering electron acceleration in the corona. The periodic electron acceleration results in the modulation of a loss-cone instability, ultimately resulting in pulsating plasma emission. The results show that a complex combination of MHD oscillations and plasma instability modulation can lead to pulsating radio emission in astrophysical environments.

Loss-cone instabilities for compact fusion reactor and field-reversed configuration

Loss-cone instabilities are studied for linear fusion devices. The gyro-kinetic equation for such a configuration is rigorously constructed in terms of action-angle variables by making use of canonical transformation. The dispersion relation, including for the first time, finite bounce frequency is obtained and numerically solved. The loss-cone modes are found near ion-cyclotron frequency. The growth rates are greatly reduced and approaching zero with increasing beta value. The results suggest that loss-cone instabilities are unlikely to be threatening to linear fusion devices since a new longitudinal invariant is found and gives a constraint which helps confinement.

High‐Frequency Thermal Fluctuations and Instabilities in the Radiation Belt Environment

AbstractThis paper overviews the electrostatic and electromagnetic theories of spontaneous emission in magnetized plasma as they relate to measured electric and magnetic field fluctuations in quiet time radiation belt and ring current region. The pervasively detected high‐frequency fluctuations in the upper‐hybrid frequency range as well as the background low‐frequency range spectral profile in the whistler mode range are explained within the context of the spontaneous emission theory. The quasilinear calculation of loss cone instability is also carried out in order to validate the assumption of spontaneous emission model. It is shown that the saturated wave amplitudes associated with the upper‐hybrid and multiple‐harmonic cyclotron instability are quite low, indicating that the theoretical explanation based upon the assumption of spontaneous emission theory may be adequate for understanding the observed background fluctuations during quiet times.

Observation of reflected electrons driven quasi- longitudinal (QL) whistlers in large laboratory plasma

This paper reports experimental and theoretical investigations on plasma turbulence in the source plasma of a Large Volume Plasma Device. It is shown that a highly asymmetrical localized thin rectangular slab of strong plasma turbulence is excited by loss cone instability. The position of the slab coincides with the injection line of the primary ionizing energetic electrons. Outside the slab, in the core, the turbulence is weaker by a factor of 30. The plasma turbulence consists of oblique [θ=tan−1(k⊥/k||)≈87°] Quasi-Longitudinal (QL) electromagnetic whistlers in a broad band of 40kHz<f≤80 kHz with k⊥∼1.2 cm−1 and k||∼0.06cm−1. Experimental observations suggest that the primary agent for the turbulence is not driven by primary ionizing energetic electrons but by the loss cone feature in the velocity distribution of reflected energetic electrons. A magnetic mirror is formed in the Electron Energy Filter when it is energized. It is shown that it is this mirror which is responsible for both reflection of the energetic electrons and imposing loss cone feature on it. Theoretical framework is based upon Oblique whistler approximation by Sharma and Vlahos [Astrophys. J. 280, 405 (1984)] and Verkhoglyadova et al. [J. Geophys. Res. 115, A00F19 (2010)] and Quasi Longitudinal (QL) whistlers by Booker and Dyce [Radio Sci. J. Res 69D (1965)] for excitation of the plasma turbulence in the magnetosphere.

Whistler Mode Waves Below Lower Hybrid Resonance Frequency: Generation and Spectral Features

AbstractEquatorial noise in the frequency range below the lower hybrid resonance frequency, whose structure is shaped by high proton cyclotron harmonics, has been observed by the Cluster spacecraft. We develop a model of this wave phenomenon which assumes (as, in general, has been suggested long ago) that the observed spectrum is excited due to loss cone instability of energetic ions in the equatorial region of the magnetosphere. The wavefield is represented as a sum of constant frequency wave packets which cross a number of cyclotron resonances while propagating in a highly oblique mode along quite specific trajectories. The growth (damping) rate of these wave packets varies both in sign and magnitude along the raypath, making the wave net amplification, but not the growth rate, the main characteristic of the wave generation process. The growth rates and the wave amplitudes along the ray paths, determined by the equations of geometrical optics, have been calculated for a 3‐D set of wave packets with various frequencies, initial L shells, and initial wave normal angles at the equator. It is shown that the dynamical spectrum resulting from the proposed model qualitatively matches observations.

Generation of lower and upper bands of electrostatic electron cyclotron harmonic waves in the Van Allen radiation belts

AbstractElectrostatic electron cyclotron harmonic (ECH) waves generated by the electron loss cone distribution can produce efficient scattering loss of plasma sheet electrons, which has a significant effect on the dynamics in the outer magnetosphere. Here we report two ECH emission events around the same location L≈ 5.7–5.8, MLT ≈ 12 from Van Allen Probes on 11 February (event A) and 9 January 2014 (event B), respectively. The spectrum of ECH waves was centered at the lower half of the harmonic bands during event A, but the upper half during event B. The observed electron phase space density in both events is fitted by the subtracted bi‐Maxwellian distribution, and the fitting functions are used to evaluate the local growth rates of ECH waves based on a linear theory for homogeneous plasmas. ECH waves are excited by the loss cone instability of 50 eV–1 keV electrons in the lower half of harmonic bands in the low‐density plasmasphere in event A, and 1–10 keV electrons in the upper half of harmonic bands in a relatively high‐density region in event B. The current results successfully explain observations and provide a first direct evidence on how ECH waves are generated in the lower and upper half of harmonic frequency bands.

Nonlinear dynamics of resonant interactions between wave packets and particle distributions with loss-cone-like structures

The paper studies the nonlinear mechanisms at work in magnetized plasmas when wave packets interact resonantly with particle distributions presenting loss-cone-like structures. Lower hybrid waves are considered in view of the great importance, in space and laboratory plasmas, of waves with frequencies below the electron cyclotron frequency. Owing to a three-dimensional Hamiltonian model and a numerical symplectic code, the authors study the nonlinear stage of the loss-cone instability for various particle distributions and wave spectra involving symmetric and asymmetric features. In particular, the wave-particle interaction process of dynamical resonance merging, which results from an instability of the trapped particles' motion and leads to complex stochastic phenomena, is discussed. Whereas interactions at normal cyclotron resonances are mostly considered, the role of the Landau and the anomalous cyclotron resonances is also studied to explain thoroughly the nonlinear wave-particle dynamics as well as the competition between loss-cone, fan, and beam instabilities. The relaxed particle distributions and the saturated wave spectra are analyzed. The time necessary for filling the loss-cone structures is determined as a function of the characteristics of the particle distributions. Whereas most of the previous works analyzed the asymptotic stage of the system's evolution in the frame of the well-known quasilinear theory, the paper considers the case when the energy carried by the wave packet is sufficiently large so that the description of the physical processes at work cannot be limited to the frame of weak turbulence theories.

A Special Radio Spectral Fine Structure Used for Plasma Diagnostics in Coronal Magnetic Traps

A specific combination of spectral fine structures in meter – decimeter dynamic spectra of solar radio burst emission is reported in observations carried out at the Astrophysical Institute Potsdam. We describe and interpret the occurrence of zebra patterns in fast drifting (type III burst-like) envelopes of absorbed continuum emission. A possible mechanism of the origin of such an involved spectral pattern is put forward, leading to a necessarily multinonequlibrium component coronal plasma. The suggested mechanism is based on the fact that during the passage of a fast electron beam through the corona the loss cone instability (which is caused by electrons captured in a magnetic trap generating the continuum) is quenched. As result, a fast drift burst appears in absorption, and the zebra pattern becomes visible on the low background emission. This zebra pattern is generated by a group of electrons with a nonequilibrium distribution over transverse velocities. In the absence of the beam the pattern is invisible against the background of the stronger continuum. It is shown that the mechanism is sensitive to the distribution parameters of the different electron ensembles. Therefore the effect in dynamic radio spectra is comparatively rare but its proper existence underlines that the simultaneous presence of different ensembles of electrons in the flaring corona can be quite a frequent situation. This can explain some problems in deconvolving X-ray photon spectra to electron energy spectra.

Properties of dayside outer zone chorus during HILDCAA events: Loss of energetic electrons

The dayside outer zone (DOZ) portion of the magnetosphere is a region where chorus intensities are statistically found to be the most intense. In this study, DOZ chorus have been examined using OGO‐5 plasma wave and GEOTAIL plasma wave, magnetic field and energetic particle data. Dayside chorus is noted to be composed of ∼0.1 to 0.5 s rising‐tone emissions called “elements.” The duration of the elements and their frequency‐time characteristics are repeatable throughout the chorus event (lasting from tens of minutes to hours), but may differ from event to event. Chorus is a right‐hand, circularly polarized electromagnetic plane wave. Waves are detected propagating from along the ambient magnetic field, Bo, to oblique angles near the Gendrin angle, θGendrin. All waves, independent of wave direction of propagation relative to Bo, are found to be circularly polarized, to first order. Chorus rising‐tone elements are composed of coherent “subelements” or “packets” with durations of ∼5 to 10 ms. Consecutive subelements/packets step in frequency with time to form the elements. The peak amplitudes within a packet can be ∼0.2 nT or greater. The subelement or packet amplitudes are at least an order of magnitude larger than previously estimated chorus amplitudes obtained by power spectral measurements. This discrepancy is due to the presence of interspacings between chorus elements, the interspacings between subelements/packets within an element, and the different frequencies of subelements/packets within a rising‐tone. DOZ chorus studied here were found to be consistent with generation via the loss cone instability of substorm‐injected temperature‐anisotropic (/ > 1) E = 5 to 40 keV electrons drifting from the midnight sector to the DOZ region. Using a large amplitude subelement/packet wave magnetic field amplitude of ∼0.2 nT, it is shown that the instantaneous Kennel‐Petschek pitch angle diffusion rate Dαα is ∼5 × 10−2 s−1. This latter quantity is based on incoherent waves. If energetic electrons stay in cyclotron resonance throughout their interaction with a coherent subelement of duration 10 ms, they may be “pitch angle transported” by ∼5°. Therefore electrons within 5° of the loss cone can be lost in a single wave‐particle interaction. Several such interactions as the electrons traverse the wave region can lead to much larger pitch angle transport angles. The similar time‐scales of chorus elements and bremsstrahlung X‐ray microbursts (∼0.5 s) can be explained by the “pitch angle transport” mechanism described above. Increasing and decreasing pitch angle transport via this mechanism will lead to much higher pitch angle diffusion or “super diffusion” rates. Isotropic unpolarized noise of ∼20 pT peak amplitude has also been detected. The noise is well above instrument noise levels and is speculated to be remnants of chorus or hiss.

Short‐Lived Absorptive Type III–like Microwave Bursts as a Signature of Fragmented Electron Injections

In this paper, we devote ourselves to interpreting the short-lived absorptive type III-like microwave bursts in the 2006 December 13 flare event observed with high temporal and spectral resolutions (8 ms and 10 MHz) by the Chinese Solar Broadband Radio Spectrometer (SBRS/Huairou) at 2.6-3.8 GHz. In the decimeter-centimeter wavelength range, we first present the observations of short-lived bursts represented as a number of absorptive "spikes" superposed on the type IV continuum that can be connected by fast-drifting lines. The mean drift rate, the instantaneous bandwidth, and the absorption depth of these absorptive spikes are about –12 GHz s−1, 70 MHz, and 40%, respectively. The duration at a single frequency band can be less than the instrument resolution of 8 ms. On the basis of numerical investigations of the loss-cone instability, we suggest that fragmented electron injections with durations of as short as several milliseconds into the loss cone could be the most appropriate mechanism with which to explain the bursts. The length of an electron beam is estimated to be about 400 km, on the basis of the observational results. These injections may be related to the fragmented energy release processes during the flare. We also observe some absorptive type III-like bursts accompanying ordinary type III bursts with reverse drifts. They start at the same frequency, and the starting frequency slowly drifts to the low-frequency region. This could be a signature of propagating bidirectional electron beams originating near the reconnection region.

Effect of angular momentum distribution on gravitational loss-cone instability in stellar clusters around a massive black hole

We study the small perturbations in spherical and thin disc stellar clusters surrounding a massive black hole. Because of the black hole, stars with sufficiently low angular momentum escape from the system through the loss cone. We show that the stability properties of spherical clusters crucially depend on whether the distribution of stars is monotonic or non-monotonic in angular momentum. It turns out that only non-monotonic distributions can be unstable. At the same time, instability in disc clusters is possible for both types of distribution.

Loss-cone instability: Wave saturation by particle trapping

The nonlinear mechanisms governing the interactions between whistler or lower hybrid waves and loss-cone type particles’ distributions in magnetized plasmas are of great importance if one considers the major role that waves of frequency below the electron cyclotron frequency play in space and thermonuclear fusion plasmas. Up to now, most of the numerical simulations have been devoted to study the nonlinear processes at work when the plasma is weakly relativistic and when the anisotropy of the particles’ distributions leads to the so-called maser instability. However, in many interesting cases, the particles’ energies are sufficiently weak to ensure the validity of the nonrelativistic approximation. In this framework, the paper studies the interaction at normal cyclotron resonances between lower hybrid waves and electron distributions presenting loss-cone like features. A theoretical Hamiltonian model and a corresponding numerical symplectic code are used to evidence and to explain the nonlinear mechanisms at work at the saturation stage of the loss-cone instability. Moreover, simple analytical expressions and scaling laws have been derived for the linear growth rates and the wave amplitude at saturation.

Gravitational loss-cone instability in stellar systems with retrograde orbit precession

We study spherical and disc clusters in a near-Keplerian potential of galactic centres or massive black holes. In such a potential orbit precession is commonly retrograde, that is, the direction of the orbit precession is opposite to the orbital motion. It is assumed that stellar systems consist of nearly-radial orbits. We show that if there is a loss-cone at low angular momentum (e.g. due to consumption of stars by a black hole), an instability similar to loss-cone instability in plasma may occur. The gravitational loss-cone instability is expected to enhance black hole feeding rates. For spherical systems, the instability is possible for the number of spherical harmonics l≥ 3. If there is some amount of counter-rotating stars in flattened systems, they generally exhibit the instability independent of azimuthal number m. The results are compared with those obtained recently by Tremaine for distribution functions monotonically increasing with angular momentum. The analysis is based on simple characteristic equations describing small perturbations in a disc or a sphere of stellar orbits highly elongated in radius. These characteristic equations are derived from the linearized Vlasov equations (combining the collisionless Boltzmann kinetic equation and the Poisson equation), using the action-angle variables. We use two techniques for analysing the characteristic equations: the first one is based on preliminary finding of neutral modes, and the second one employs a counterpart of the plasma Penrose–Nyquist criterion for disc and spherical gravitational systems.

Gravitational loss-cone instability in stellar clusters around massive black holes

AbstractStability of spherical and thin disk stellar clusters surrounding massive black holes are studied. Due to the black hole, stars with sufficiently low angular momenta escape from the system through the loss cone. We show that stability of spherical clusters crucially depend on whether the distribution of stars is monotonic or non-monotonic in angular momentum. It turns out that only non-monotonic distributions can be unstable. At the same time the instability in disk clusters is possible for both types of distributions.

Precipitation of trapped relativistic electrons by amplified whistler waves in the magnetosphere

Numerical study of a loss-cone negative mass instability to amplify whistler waves by energetic electrons in the radiation belts is presented. The results show that a very low intensity whistler wave can be amplified by 50keV electrons more than 25dB, consistent with the Siple experimental result [Helliwell et al., J. Geophys. Res. 85, 3360 (1980)]. The dependencies of the amplification factor on the energetic electron density and on the initial wave intensity are evaluated. It is shown that the amplification factor decreases as the initial wave intensity increases. However, this gain can still exceed 15dB for a 30dB increase of the initial wave intensity, which is needed for the purpose of precipitating MeV electrons in the radiation belts. We then show that there exists a double resonance situation, by which, as an example, a wave is simultaneously in cyclotron resonance with 50keV electrons as well as with 1.5MeV electrons; the wave is first amplified by 50keV electrons and then precipitates 1.5MeV electrons. With the aid of the cyclotron resonance, the threshold field for the commencement of chaos in the electron trajectories is reduced considerably from that for a general case. Pitch angle scattering of 1.5MeV electrons is demonstrated. The results show that a whistler wave with magnetic field amplitude of 0.08% of the background magnetic field can scatter electrons from an initial pitch angle of 86.5° to a pitch angle <50°.

Retrograde precession of stellar orbits and gravitational loss-cone instability in galactic centers

We consider disk and spherical subsystems of stars with nearly radial orbits under conditions when the well-known radial orbit instability is not possible. This requires that the precession of stellar orbits be retrograde, i.e., in the direction opposite to the orbital rotation of stars. We show that an instability that is an analogue of the loss-cone instability known in plasma physics can then develop in the presence of a “loss cone” in the angular momentum distribution of stars, which ensures a deficit or even absence of stars with low angular momenta. Examples of systems with a loss cone are the centers of galaxies or star clusters with massive black holes. The instability can produce a flux of stars onto the galactic center, i.e., it can serve as a mechanism of fueling the nuclear activity of galaxies. Mathematically, the problem is reduced to analyzing simple characteristic equations that describe small perturbations in a disk and a sphere of radially highly elongated stellar orbits. In turn, these characteristics equations are derived through a number of successive simplifications of the general linearized Vlasov equations (i.e., the system that includes the collisionless Boltzmann kinetic equation and the Poisson equation) in action—angle variables.