Plasma Dispersion Relation Research Articles

Response of a relativistically streaming pulsar plasma

The response tensor is derived for a relativistically streaming, strongly magnetized, one-dimensional Jüttner distribution of electrons and positrons, referred to as a pulsar plasma. This is used to produce a general treatment of wave dispersion in a pulsar plasma. Specifically, relativistic streaming, the spread in Lorentz factors in a pulsar rest frame and cyclotron resonances are taken into account. Approximations to the response tensor are derived by making approximations to relativistic plasma dispersion functions appearing in the general form of the response tensor. The cold-plasma limit, the highly relativistic limit and limits related to cyclotron resonances are considered. The theory developed in this paper has applications to generalized Faraday rotation in pulsars and magnetars.

Experimental and numerical investigation of the Doppler-shifted resonance condition for high frequency Alfvén eigenmodes on ASDEX Upgrade

Abstract The Doppler-shifted resonance condition for high frequency Alfvénic eigenmodes has been extensively studied on ASDEX Upgrade in the presence of one or a combination of two neutral beam injected (NBI) fast ion populations. In general, only centrally deposited NBI sources drive these modes, while off-axis sources globally stabilize the mode activity. For the case of a single central NBI source, the observed trend is: the highest frequency modes are driven by the lowest energy and lowest pitch angle NBI sources, in line with the expectation from the Doppler-shifted resonance condition. The expected mode frequencies are determined analytically from the two-fluid cold plasma dispersion relation and the most unstable frequency relation, while the mode growth rates are estimated using the fast ion slowing down distribution functions from the ASCOT code. The overall mode frequency trend in a source-to-source variation is tracked, although a systematic overestimate of ∼1 MHz is observed. Possible causes of this overestimate include the finite size of the resonant fast ion drift orbit and non-linear effects such as mode sideband formation. Alternatively, the expected mode frequencies are determined by tracking the growth rate maxima trajectories, this method improves the agreement with the experimentally measured values. A combination of two central mode-driving NBI sources results in the suppression of the mode driven by the lowest energy and the lowest pitch angle NBI source. Computing the analytically expected mode frequency following the method outlined above, again, generally tracks the experimentally observed trend. The mode’s Alfvénic nature allows for a practical application to track the core hydrogen fraction by following the mode frequency changes in response to a varying ion mass density. Such application is demonstrated in a discharge where the average ion mass is varied from ∼2m p to ∼1.5m p (where m p is the proton mass) via a hydrogen puff in a deuterium plasma, in the presence of a strong mode activity. The expected mode frequency changes are computed from the existence of the resonance condition, and the values track the measured results with an offset of ∼0.5 MHz. Overall, the results suggest an intriguing possibility to monitor and control the D-T ion fraction in the core of a fusion reactor in real time using a non-invasive diagnostic.

Effects of Superthermal Plasmas on Hiss Wave‐Driven Scattering Loss of Radiation Belt Electrons

AbstractPlasmaspheric hiss plays an important role in the loss of radiation belt electrons via cyclotron resonant interactions. The cold plasma approximation is widely used in the evaluation of hiss‐driven electron losses, which however can break down during disturbed periods of geomagnetic storms and substorms. The kappa particle velocity distribution, characterized by a pronounced high‐energy tail, is well‐established to model the profile of superthermal plasma under disturbed geomagnetic conditions. In the present study, by calculating the electron bounce‐averaged pitch angle diffusion coefficients with kappa plasma dispersion relations, we investigate the sensitivity of hiss‐induced cyclotron‐resonant electron scattering loss to the spectral index κ under a variety of superthermal plasma conditions. Our results demonstrate that, with increasing κ, the diffusion coefficients of ∼20–100 keV radiation belt electrons significantly decrease at lower pitch angles and increase at higher pitch angles. In contrast, for electrons at higher energies, the diffusion coefficients tend to increase at lower pitch angles and decrease at relatively higher pitch angles. We also find that decrease of L‐shell and increase of α* and temperature anisotropy tend to weaken the hiss‐driven pitch angle scattering efficiency of electrons at energies from tens to hundreds of keV with a dip at ∼30–50 keV, while the scattering of higher energy electrons can be enhanced. This study confirms the important role of superthermal plasmas in the hiss‐driven electron loss processes and should be carefully incorporated in future modeling of radiation belt electron dynamics.

Effects of nonthermality on dust-acoustic surface waves with dust rotation

Abstract Dust Acoustic Surface Waves (DASWs) real frequency and group velocity are investigated for semi-bounded dusty plasma whose electrons and ions are modeled by Cairn s Distribution Function (CDF) while massive particles i.e. dust are treated Maxwellian. Kinetic approach based on Vlasov-Poisson s set of equations is used for the derivation of plasma dispersion relation. It is observed that in the presence of rotational parameter r and the variation of nonthermal index α affect both real frequency and group velocity of the wave significantly. This study has wide astrophysical applications.

Statistical Analysis of Whistler Precursors Upstream of Foreshock Transient Shocks: MMS Observations

AbstractUsing the high‐time‐resolution data from the Magnetospheric Multiscale mission, precursor waves upstream of foreshock transient (FT) shocks are statistically investigated using the four‐spacecraft timing method. The wave frequencies and wave vectors determined in the plasma rest frame (PRF) are shown to follow the cold plasma dispersion relation for whistler waves. Combining with the feature of the right‐hand polarization in the PRF, the precursors are identified as whistler‐mode waves around the lower hybrid frequency. The occurrence of whistler precursors is independent of the Alfvén Mach number and the FT shock normal angle. More importantly, all the whistler precursors have group velocities pointing upstream in the shock frame, suggesting the dispersive radiation to be a possible generation mechanism. The study improves the understanding of not only the whistler precursors but also the overall FT shock dynamics.

Polarization and properties of low-frequency waves in warm magnetized two-fluid plasma

This paper presents the derivation of a general wave dispersion relation for warm magnetized plasma under the two-fluid formalism. The discussion is quite general except for the assumption of low frequency and slow phase speed, for which the displacement current is negligible, under the implicit assumption that the plasma is sufficiently dense to satisfy the condition ωpe>ωce, where ωpe and ωce denote the plasma oscillation frequency and electron gyro frequency, respectively. The present discussion does not invoke charge neutrality associated with the fluctuations although it is implicitly satisfied. The resulting dispersion relation that includes the fluid thermal effects shows that there are three eigen modes, which include those corresponding to ideal MHD, namely, fast, slow, and kinetic Alfvén waves, as well as higher-frequency modes including the ion and electron cyclotron and lower-hybrid resonances. The fluid effects in the ideal MHD wave branches are influenced by the finite Larmor radius scales, and when the wave number in the cross field direction is comparable to these values, the fluid effects become significant. It is found that the Larmor radius should be interpreted in the sense as ion-acoustic gyro-radius instead of ion thermal gyro radius only. That is, it is found that the electrons also contribute to the non-ideal effect associated with the kinetic Alfvén wave. A comprehensive explanation of the polarization of each mode is also presented. The present findings indicate that the polarity may change its sign only for the kinetic Alfvén mode branch and that such a transition is based on the propagation angle. When such a change does take place, it is found that the kinetic Alfvén wave transits to an ion-acoustic mode. For each branch, it is also found that the electric field along the ambient magnetic field is purely transverse.

Particle dynamics in a turbulent electric field

Charged particle velocity-space diffusion in a prescribed one-dimensional turbulent electric field is investigated through numerical trajectories in phase-space and compared against quasi-linear theory (QL), including resonance broadening (RB). A Gaussian spectrum electric field of variable amplitude E is studied in conjunction with two plasma dispersion relations, namely, the Langmuir and ion-acoustic dispersion. A first parameter scan shows that RB effects become significant for a Kubo number K of a few percent. A Kubo number scan shows that diffusion increases as a power law of D∝K3∝E3/2 for large Kubo numbers. Moreover, at large Kubo numbers, transport processes include significant diffusion measured at velocities much higher than the resonant region, where QL and RB predict negligible diffusion. For times much larger than the trapped particle flight time τb and the autocorrelation time τ0, the velocity distribution departs from a Gaussian. Nevertheless, measurements show that the variance increases linearly in time, with a Hurst parameter of H∼0.5, where the diffusion scales as K5/2∝E5/4 and K3/2∝E3/4 for small and large Kubo number, respectively.

Scattering of Radiation Belt Electrons by Fast Magnetosonic Waves: Considering the Kinetic Effects

AbstractWhen assessing the scattering of radiation belt electrons by fast magnetosonic (MS) waves, it is traditionally assumed that the waves follow the MS/whistler branch of the cold plasma dispersion relation (CPDR) in magnetohydrodynamics. However, MS waves are essentially ion Bernstein modes following a distinct kinetic dispersion relation. This study calculates the MS wave‐induced electron diffusion rates with the kinetic dispersion relation for the first time and compares the results with that obtained with the CPDR. It is found that the kinetic effects lead to a lower minimum resonant energy around 100 eV and a broader resonant pitch angle range. Kinetic effects also result in power spectral density attenuation when transforming wave frequency spectra into wavenumber spectra, so the diffusion rates are overall smaller than the ones obtained using the CPDR. Our results demonstrate that kinetic effects can significantly affect the role that MS waves play in the radiation belt dynamics.

Toward developing a comprehensive algorithm for solving kinetic plasma dispersion relations for parallel propagation with a kappa distribution

In general, it is challenging to numerically solve all the roots of plasma wave dispersion relations. The velocity distributions of multi-component particles in an anisotropic high-energy plasma can be better described by a drift loss-cone bi-Kappa distribution or a mixed drift loss-cone distribution containing bi-Kappa and bi-Maxwellian plasma in space and laboratories. In this work, we have developed a code with a new numerical algorithm to solve all roots of the kinetic dispersion relation for parallel propagation in hot magnetized plasmas with drift loss-cone bi-Kappa distribution. Solving all roots of the rational expansions of the kinetic dispersion relation is equivalent to a matrix eigenvalue problem of a linear system. We have performed detailed numerical solutions for three kinds of plasmas: bi-Maxwellian, bi-Kappa, and cold plasmas. We have also proposed a unified numerical method to solve the mixed dispersion relation based on the bi-Kappa and bi-Maxwellian distributions. The numerical results and benchmark studies demonstrate that the new algorithm is in agreement with the data from previous studies. This is a crucial step toward revealing a full picture of kinetic plasma waves and instabilities.

Simulation of ion cyclotron resonance heating by using particle-in-cell method in MPS-LD linear plasma device

The auxiliary heating of electrons and ions in linear plasma devices (LPDs) is necessary to achieve the boundary plasma relevant environment of tokamaks, to investigate the boundary physics and plasma—material interactions. In this work, the simulation of ion cyclotron resonance heating (ICRH) in the LPD multiple plasma simulation linear device (MPS-LD) is carried out by using a 3D particle-in-cell method, and the wave—ion interaction mechanism based on a ‘beach-heating’ technique in the ion heating region is investigated. A left-handed, circularly polarized wave along the magnetic field lines is used to represent the electromagnetic wave in the model, after the analysis of the cold plasma dispersion relation. The mechanism of ion heating by collisionless damping absorption is demonstrated and explained by using the plasma current as the plasma response. The dependencies of the heating efficiency on the plasma density, magnetic field strength and magnetic field configuration are studied. The correlation between plasma density and magnetic field strength, which satisfies the heating efficiency, is found and it is in perfect agreement with the theoretical derivation. Finally, by using the designed parameters of MPS-LD provided by SOLPS-ITER, the prediction of ICRH is performed. The simulation result shows that the ion temperature can be heated higher than 40 eV and it satisfies the requirement for scrape-off layer/divertor simulation experimentally in MPS-LD.

Oblique propagation and temperature effects on the resonant right-hand ion beam instability

The resonant right-hand instability (RHI) is often the dominant mode driven by reflected ions upstream of Earth’s quasi-parallel bow shock. In the tradition of Peter Gary, this paper further explores the right-hand instability using numerical solutions of the plasma dispersion relation and non-linear kinetic simulations, with parameters inspired by observations from NASA’s Magnetospheric Multiscale (MMS) mission. Agreement is found between the ion distributions in the particle-in-cell simulations and Magnetospheric Multiscale spacecraft data, which show the gyrophase bunching characteristic of the instability. The non-linear structures created by right-hand instability tend to be stronger when the plasma beta is lower. These structures have sizes of around 100 to 200 ion inertial lengths perpendicular to the magnetic field, presenting planet-sized disturbances to the magnetosphere. 2d and 3D hybrid particle-in-cell simulations show that modes with a range of propagation angles oblique to the magnetic field are excited, providing a ground to understand previous statistical studies of observed foreshock waves.

Steady states stability features of the electron–positron plasma diode

Stationary states stability features of a planar geometry diode with electron and positron counter flows are studied. Such a diode may be considered as a model to elucidate the nature of the pulsar radio emission. The equation for the electric field perturbation amplitude is derived. The exact solution of this equation for the homogeneous stationary field is found. On the basis of the plasma dispersion relation, the stability threshold in terms of the electron current density is found above which the stationary solutions become unstable. This threshold turned out to be 2 times higher than the known Pierce threshold. It can be expected that the development of the detected instability will lead to the electric field oscillations that induce electromagnetic radiation.

B-field induced mixing between Langmuir waves and axions

We present an analytic study of the dispersion relation for an isotropic magnetized plasma interacting with axions. We provide a quantitative picture of the electromagnetic plasma oscillations in both the ultrarelativistic and nonrelativistic regimes and considering both non-degenerate and degenerate media, accounting for the dispersion curves as a function of the plasma temperature and the ratio of the plasma phase velocity to the characteristic velocity of particles. We include the modifications on the Landau damping of plasma waves induced by the presence of the axion field, and we comment on the effects of damping on subluminal plasma oscillations.

BORAY: A ray tracing code for various magnetized plasma configurations

Ray tracing codes are useful to study the electromagnetic wave propagation and absorption in the geometrical optics approximation. In magnetized fusion plasma community, most ray tracing codes assume the plasma density and temperature be functions of the magnetic flux and study waves only inside the last closed flux surface, which are sufficient for the present day tokamak. However, they are difficult to be used for configurations with open magnetic field line plasmas, such as mirror machine and field-reversed-configuration (FRC). We develop a ray tracing code in cylindrical coordinates (r,ϕ,z) to support arbitrary axisymmetric configurations with both closed and open field lines plasmas. For wave propagation, the cold plasma dispersion relation is usually sufficient, and we require the magnetic field B(r,z) and species densities ns0(r,z) profiles as input. For wave absorption, we require a further temperature Ts0(r,z) profile to solve a hot kinetic plasma dispersion relation. In difference to other ray tracing codes which calculate the imaginary part of wave vector k⊥,i for wave absorption, we calculate the imaginary part of wave frequency ωi, which is shown to be equivalent with the former technique under weak damping approximation. The code can use either numerical or analytical equilibrium. Examples and benchmarks with electron cyclotron wave, lower hybrid wave and ion cyclotron wave for tokamak, spherical tokamak (ST), FRC and mirror machine are shown. Program summaryProgram Title: BORAYCPC Library link to program files:https://doi.org/10.17632/tnkrjdbcz8.1Code Ocean capsule:https://codeocean.com/capsule/6205646Licensing provisions: BSD 3-clauseProgramming language: MatlabNature of problem: Solve the plasmas electromagnetic wave propagation and absorption in the geometrical optics approximation for magnetized plasmas based on ray tracing of plasma dispersion relation. In axisymmetric (r,z) coordinates, the code can be used for both closed and open field lines plasmas of various configurations such as tokamak, spherical tokamak, FRC and mirror machine.Solution method: Runge-Kutta time integral to solve ray tracing equations for wave propagation, and integral the imaginary part of the wave frequency in hot kinetic dispersion relation for wave absorption.Additional comments including restrictions and unusual features: Kinetic relativistic effects and collisional damping are not included in the present version yet. Only axisymmetric two-dimensional (2D) profiles are support in present version.

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.

Assessment of applicability of cold plasma dispersion relation of slot region hiss based on Van Allen Probes observations

Electron scattering caused by plasmapheric hiss is the dominant mechanism that is responsible for the formation of slot region (1.8 ≤ <i>L</i> ≤ 3) between the Earth’s inner and outer radiation belts. The cold plasma dispersion relation of plasmaspheric hiss is widely used to quantify its scattering effect on energetic electrons. However, the existence of hot plasmas in the realistic magnetospheric environment will modify the dispersion properties of plasmaspheric hiss. According to Van Allen Probes observations, we select all hiss events in the slot region and compare the observed hiss wave amplitudes with the converted hiss wave amplitudes deduced from cold plasma dispersion relation and electric field observations, and then study the dependence of the applicability of cold plasma dispersion relation of slot region hiss on spatial position and geomagnetic activity. The results show that the cold plasma approximation tends to overestimate the amplitude of slot region hiss. The difference between the observed amplitude and the converted hiss wave amplitude has a strong day night asymmetry. However, it shows a slight dependence on the level of geomagnetic activities. In addition, we find that the converted wave magnetic field intensity is significantly lower (higher) than the observed magnetic field intensity at lower frequencies (higher frequencies), which indicates that the cold plasma approximation generally overestimates (underestimates) the scattering effects of hiss waves on the lower (higher) energy electrons in the slot region. Our study confirms that the application scope of the cold plasma dispersion relation of slot hiss has strong spatial and frequency limitations, which is of great importance in deepening our understanding of the dynamic evolution of electrons in the slot region.

Interaction of radio frequency waves with cylindrical density filaments: scattering and radiation pressure

The propagation of radio-frequency (RF) waves in tokamaks can be affected by filamentary structures, or blobs, that are present in the edge plasma and the scrape-off layer. The difference in the permittivity between the surrounding plasma and interior of a filament leads to reflection, refraction and diffraction of the waves. This, in turn, can affect the power flow into the core of the plasma and reduce the efficiency of heating and/or current generation. The scattering of RF waves, lower hybrid, helicon and ion cyclotron waves, by a single cylindrical filament, embedded in a background plasma, is studied using a full-wave analytical theory developed previously (Ram & Hizanidis, Phys. Plasmas, vol. 23, 2016, 022504). The theory assumes that the plasma in and around a filament is homogeneous and cold. A detailed scattering analysis reveals a variety of common features that exist among the three distinctly different RF waves. These common attributes can be inferred intuitively based on an examination of the cold plasma dispersion relation. The physical intuition is a useful step to understanding experimental observations on scattering, as well as results from simulations that include general forms of edge plasma turbulence. While a filament can affect the propagation of RF waves, the radiation force exerted by the waves can influence the filament. The force on a filament is determined using the Maxwell stress tensor. In 1905, Poynting was the first to evaluate and measure the radiation force on an interface separating two different dielectric media (Poynting, London Edinburgh Dublin Philos. Mag. J. Sci., vol. 9, 1905, pp. 393–406). For ordinary light propagating in vacuum and incident on a glass surface, Poynting noted that the surface is ‘pulled’ towards the vacuum. In a magnetized cold plasma, there are two independent wave modes. Even if only one of these modes is excited by an RF antenna, a filament will couple power to the other mode: a consequence of electromagnetic boundary conditions. This facet of scattering has consequences on the radiation force that go beyond Poynting's seminal contribution. The direction of the force depends on the polarization of the incident wave and on the mode structure of the waves inside and in the vicinity of a filament. It can either pull the filament toward the RF source or push it away. For slow lower hybrid waves, filaments with densities greater than the ambient density are pulled in, while filaments with lower densities are pushed out, thereby enhancing the density in front of the antenna. In the case of fast helicon and ion cyclotron waves, the direction of the force depends on the plasma and wave parameters; in particular, on the ambient density. The radiation force, in all three frequency ranges, is large enough to affect the motion of a filament and could be measured experimentally. This also suggests the possibility of modifying the edge turbulence using RF waves.

Effects of displacement current on wave dispersion relation and polarization properties in auroral plasmas

In-situ observations from the FREJA magnetospheric research satellite and the Fast Auroral SnapshoT satellite have shown that plasma waves are frequently observed in the auroral plasma, which are believed to be fundamentally important in wave energy dissipation and particle energization. However, the effects of a displacement current on these waves have not been examined. Based on the two-fluid theory, we investigate the dispersion relation and polarization properties of fast, Alfvén, and slow modes in the presence of a displacement current, and the effects of the displacement current on these waves are also considered. The results show that the wave frequency, polarization, magnetic helicity and other properties for the fast and Alfvén modes are highly sensitive to the normalized Alfvén velocity vA /c, plasma beta β, and propagation angle θ, while for the slow mode the dependence is minor. In particular, for both fast and Alfvén modes, the magnetic helicity is obviously different with and without the displacement current, especially for the Alfvén mode with the helicity reversals from right-handed to left-handed when vA /c increases from 0 to 0.3. The charge-neutral condition of both fast and Alfvén modes with frequencies larger than the proton cyclotron frequency is invalid in the presence of the displacement current. Moreover, the presence of the displacement current leads to relatively large magnetic compressibility for the Alfvén mode and relatively large electron compressibility for the fast mode. These results can be useful for a comprehensive understanding of the wave properties and the physics of particle energization phenomena in auroral plasmas.

Electromagnetic albedo of Quantum Black Holes

We compute the albedo (or reflectivity) of electromagnetic waves off the electron-positron Hawking plasma that surrounds the horizon of a Quantum Black Hole. We adopt the “modified firewall conjecture” for fuzzballs [1, 2], where we consider significant electromagnetic interaction around the horizon. While prior work has treated this problem as an electron-photon scattering process, we find that the incoming quanta interact collectively with the fermionic excitations of the Hawking plasma at low energies. We derive this via two different methods: one using relativistic plasma dispersion relation, and another using the one-loop correction to photon propagator. Both methods find that the reflectivity of long wavelength photons off the Hawking plasma is significant, contrary to previous claims. This leads to the enhancement of the electromagnetic albedo for frequencies comparable to the Hawking temperature of black hole horizons in vacuum. We comment on possible observable consequences of this effect.

Realistic Dispersion of Plasmaspheric Hiss in the Inner Magnetosphere and Its Effect on Wave-induced Electron Scattering Rates

Abstract The cold plasma approximation is a common treatment to study wave–particle interactions between plasmaspheric hiss and magnetospheric electrons, which, however, can become a challenge during periods of disturbed geomagnetic activity. To assess the validity of the cold plasma dispersion relation of plasmaspheric hiss, we adopt the cold plasma theory to calculate the wave magnetic field intensities from the electric field intensities observed by Van Allen Probe A from 2012 October 1 to 2018 February 28. Comparisons between the observed and converted hiss magnetic field intensities capture pronounced differences with the enhancement of substorm activity, and exhibit the largest discrepancies on the nightside MLT sector for low-frequency hiss waves. We also use both the hiss dispersion curves derived from the observations and the cold plasma dispersion relation to evaluate hiss-induced electron diffusion coefficients under different substorm activity conditions. The results indicate that the profiles of electron diffusion rates vary considerably for the two hiss dispersion relations and that the differences between them become increasingly distinct with substorm activity intensification. Our study therefore demonstrates that the cold plasma theory can become less reliable for plasmaspheric hiss waves under disturbed geomagnetic circumstances and that the realistic wave dispersion is essential to better quantify the electron scattering effect of hiss waves, which needs to be carefully incorporated into future global simulations of the generation and propagation of plasmaspheric hiss and associated dynamic variability of radiation belt electrons.