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We have obtained expressions for the moments of the quasi-linear integral of anisotropic plasma collisions. Resonant and adiabatic interactions of particles with an arbitrary wave mode are considered. Expressions for the moments describing the interactions of ion-cyclotron waves with ring current and magnetospheric helium ions have been derived as an example, using the obtained results.
Wave propagation in anisotropic plasma in presence of electron density irregularities, noting Faraday effect
In the scrape-off layer and the edge region of a tokamak, the plasma is strongly turbulent and scatters the radio frequency (RF) electromagnetic waves that propagate through this region. It is important to know, whether used for diagnostics or for heating and current drive, the spectral properties of these scattered RF waves. The spectral changes influences the interpretation of the diagnostic-data obtained and the current and heating profiles. A full-wave, 3D electromagnetic code ScaRF (see Papadopoulos et al. 2019) has been developed for studying the RF wave propagation through turbulent plasma. ScaRF is a finite-difference frequency-domain (FDFD) method for solving Maxwell's equations. The magnetized plasma is defined through the cold plasma, anisotropic permittivity tensor. As a result, ScaRF can be used to study the scattering of any cold plasma RF wave. It can be for the study of scattering of electron cyclotron waves in ITER-type and medium-sized tokamaks such as TCV, ASDEX-U, DIII-D. For the case of medium-sized tokamaks, there's experimental evidence that drift waves and rippling modes are present in the edge region (see Ritz et al. 1984). Hence, we study the scattering of RF waves by periodic density interfaces (plasma gratings) in the form of a superposition of spatial modes with varying periodicity and random amplitudes (see Papadopoulos et al. 2019). The power reflection coefficient (a random variable) is calculated for different realizations of the density interface. In this work, the uncertainty of the power reflection coefficient is rigorously quantified by use of the Polynomial Chaos Expansion (see Xiu & Karniadakis 2002) method in conjunction with the Smolyak sparse grid integration (see Papadopoulos et al. 2018) (PCE-SG). The PCE-SG method is proven accurate and much more efficient (roughly 2-orders of magnitude shorter execution time) compared to alternative methods such as the Monte Carlo (MC) approach.
Plasma waves and instabilities are integrally involved with the plasma "pickup" process and the mass loading of the solar wind (thus the formation of ion tails and the magnetic tails). Anisotropic plasmas generated by solar wind-comet interactions (the bow shock, magnetic field pileup) cause the generation of plasma waves which in turn "smooth out" these discontinuities. The plasma waves evolve and form plasma turbulence. Comets are perhaps the best "laboratories" to study waves and turbulence because over time (and distance) one can identify the waves and their evolution. We will argue that comets in some ways are better laboratories than magnetospheres, interplanetary space and fusion devices to study nonlinear waves and their evolution.
The plasma exit flow speed at the sheath entrance is constrained by the Bohm criterion. The so-called Bohm speed regulates the plasma particle and power exhaust fluxes to the wall, and it is commonly deployed as a boundary condition to exclude the sheath region in quasineutral plasma modeling. In this work, the Bohm criterion analysis is performed in the intermediate plasma regime away from the previously known limiting cases of adiabatic laws and the asymptotic limit of infinitesimal Debye length in a finite-size system, using the transport equations of an anisotropic plasma. The resulting Bohm speed has explicit dependence on local plasma heat flux, temperature isotropization, and thermal force. Comparison with kinetic simulations demonstrates its accuracy over the plasma-sheath transition region in which quasineutrality is weakly perturbed and the Bohm criterion applies.
Generation and amplification of magnetic fields in plasmas is a long-standing topic that is of great interest to both plasma and space physics. The electron Weibel instability is a well-known mechanism responsible for self-generating magnetic fields in plasmas with temperature anisotropy and has been extensively investigated in both theory and simulations, yet experimental verification of this instability has been challenging. Recently, we demonstrated a new experimental platform that enables controlled initialization of highly nonthermal and/or anisotropic plasma electron velocity distributions via optical-field ionization. Using an external electron probe bunch from a linear accelerator, the onset, saturation, and decay of the self-generated magnetic fields due to electron Weibel instability were measured for the first time to our knowledge. In this paper, we will first present experimental results on time-resolved measurements of the Weibel magnetic fields in non-relativistic plasmas produced by Ti:Sapphire laser pulses (0.8 μm) and then discuss the feasibility of extending the study to a quasi-relativistic regime by using intense CO 2 (e.g., 9.2 μm) lasers to produce much hotter plasmas.
The thermal and suprathermal ion populations present in the refilling regions after a magnetic storm are examined using retarding ion mass spectrometer (RIMS) data from the Dynamics Explorer 1 spacecraft. The RIMS instrument is described, and data are presented and discussed in detail for the outer plasmasphere, plasmapause, depleted dayside magnetosphere, and dayside cusp. Three distinct populations were observed: thermal ions, warm anisotropic plasma, and the polar wind. The characteristics of these populations are considered, including the densities, temperatures, and density ratios. Aspects of the ionospheric plasma outflow are discussed, including the field-aligned flow speed, the ionospheric plasma escape flux, plasmaspheric refilling, and wave-particle phenomena.
Results are reported for a statistical study of short-period fluctuations in the interplanetary plasma velocity and magnetic field. The data base used consists of measurements of the interplanetary plasma and magnetic field by Pioneer 6 with a time resolution of 72 sec and by Mariner 5 with a resolution of 5 min. The analysis is conducted to characterize the parent population from which all individual microscale events on these time scales are drawn. The microscale changes are grouped according to their energy densities relative to the energy density of the background magnetic field, and it is found that each grouping exhibits certain statistical properties within the limits of observational uncertainty. It is noted that these statistical properties are purely observational and independent of any physical model which may be used to interpret them. The results are discussed in the context of MHD discontinuity theory for a thermally anisotropic plasma.
Plasma and magnetic field data from the International Sun-Earth Explorer ISEE 2 spacecraft recorded during an outbound crossing of the dayside, northern hemisphere magnetopause in October 29, 1979, provide evidence for a slow shock (SS) in the observed reconnection layer. This layer is found to be bounded on the magnetosheath side by the SS; near the magnetospheric side of the layer, a second current sheet is found that may have been rotational discontinuity (RD). The direction of the accelerated plasma flow, the earthward sense of the normal magnetic filed across the SS and RD, and the relative orientation of the SS and the RD all indicate that the reconection site was located south of the spacecraft. Quantitative tests show that, allowing for experiemental uncertanties, data taken upstream and downstream of the SS are consistent with coplanarity and other Rankine-Hugoniot (RH) conditions. Examiniations of the flow parameters indicates two anomalous properties of the SS: the upstream flow, viewed in the deHoffmann-Teller frame, is superalfvenic and the downstream plasma is firehose unstable. In comparison to the long-wavelength slow-mode phase speed, however, the flow in the upstream region is super slow, while in the downstream region it is subslow, as requeired for a slow-mode shock. Further properties of the shock include a large decrease in total enthalpy across it, indicating the escape of a sizable heat flux from the shock structure, and the occurrence of a polarization reversal of the tangential magnetic field within the shock layer, a feature that is predicted by linear double-polytropic Hall-MHD and results from a large increase in pressure anistropy from the upstream region, where p(sub parallel) approximately equal to p(sub perp), to the downstream region, where p(sub parrallel) greater than p(sub perp). Quantitative tests of the RD-like discontinuity show that it satisfies the necessary RH conditions within experimental uncertainties and indicate that the flow across it is earthward, that is, it is the same as for the SS. Thus the RD is propagating behind the SS in the direction away from the Earth. The reversal in the order of the discontinuities is attributed to the reversal of the slow and intermediate phase speeds produced by the pressure anistropy in the region between the RD and the SS. The linear dispersion relation and polarization properties of dispersive MHD waves in an anisotropic plasma are examined in the appendix.
We report the ion exit flow speed at the sheath entrance is constrained by the Bohm criterion, which is used as a boundary condition for simulations that do not resolve the sheath region. Traditional Bohm criterion analysis invokes the equation of state and, thus, ignores transport physics in the sheath transition problem. An expression for the Bohm speed away from the asymptotic limit is derived from a set of anisotropic plasma transport equations. The thermal force, collisional temperature isotropization, and heat flux enter into the evaluation of the Bohm speed. By comparison with kinetic simulation results, this expression is shown to be accurate in the presheath–sheath transition region rather than a single point at the sheath entrance over a broad range of collisionality.
Inspection of broadband VLF records from OGO-4 shows that some whistlers exhibit a banded structure in which one or more bands of frequencies are missing from the whistler's spectrum. The phenomenon is commonly observed by satellites on midlatitude field lines at all local times and at various longitudes around the world. The dispersion of banded whistlers (BW) is of several tens of sec to the 1/2 power, indicating that they originated in the opposite hemisphere and are propagating downward at the satellite. BW are generally spread in time (tenths of seconds) rather than sharply defined and tend to occur at random. The frequency spacing of the bands may be either uniform or irregular, and may vary radically between successive events. Several possible explanations for BW are considered. In particular, an analysis of the interaction of plane electromagnetic waves traveling in an anisotropic plasma with a field aligned slab of enhanced ionization is presented with promising results.
A theoretical study is presented of the Alfven waves in the spiral interplanetary magnetic field. The Alfven waves under consideration are arbitrary, large amplitude, non-monochromatic, microscale waves of any polarization. They superpose on a mesoscale background flow of thermally anisotropic plasma. Using WKB approximation, an analytical solution for the amplitude vectors is obtained as a function of the background flow properties: density, velocity, Alfven speed, thermal anisotropy, and the spiral angel. The necessary condition for the validity of the WKB solution is discussed. The intensity of fluctuations is calculated as a function of heliocentric distance. Relative intensity of fluctuations as compared with the magnitude of the background field has its maximum in the region near l au. Thus outside of this region, the solar wind is less turbulent.
This paper presents a theoretical study of the Alfven waves in the spiral interplanetary magnetic field. The Alfven waves under consideration are arbitrary large-amplitude nonmonochromatic microscale waves of any polarization. They superpose on a mesoscale background flow of thermally anisotropic plasma. When the WKB approximation is used, an analytical solution for the amplitude vectors is obtained as a function of the background flow properties: density, velocity, Alfven speed, thermal anisotropy, and the spiral angle. The relative intensity of fluctuations compared with the magnitude of the background field has its maximum in the region near 1 AU. Thus outside of this region the solar wind is less turbulent. Owing to attenuation of microscale Alfven waves, fluctuation energy is converted into the kinetic energy of the solar wind.
On the basis of magnetohydrodynamic (MHD) theory we develop a scheme for distinguishing among the four low-frequency modes which may propagate in a high-beta anisotropic plasma such as the magnetosheath: the fast and slow magnetosonic, the Alfven, and mirror modes. We use four parameters: the ratio of transverse to compressional powers in the magnetic field, the ratio of the wave powers in the thermal pressure and in the magnetic field, the ratio of the perturbations in the thermal and magnetic pressures, and the ratio of the wave powers in the velocity and in the magnetic field. In the test case of an Active Magnetospheric Particle Tracer Explorers/Ion Release Module (AMPTE/IRM) magnetosheath pass near the Sun-Earth line downstream of a quasi-perpendicular shock, the four modes can be clearly distinguished both spatially and spectrally. Near the bow shock, the waves are Alfvenic in a large frequency range, 1 to 100 mHz. In the middle and inner magnetosheath, the waves below 10 mHz are Alfvenic. The fast mode waves occur in the higher-frequency end of the enhanced spectrum, 80 mHz for the middle magnetosheath and 55 mHz for the inner sheath. The wave enhancement in the intermediate frequencies is slow modes in the inner sheath and mirror modes in the middle sheath. This confirms the earlier report of the existence of the slow mode waves near the magnetopause. These slow waves provide evidence that the magnetopause is an active source of the waves in the sheath. We also show that the measured frequency of a wave is close to an invariant if the magnetosheath flow is in a steady state. Therefore changes in the frequencies of enhanced waves indicate emergence, or damping, or mode conversion of the waves.
The presence of anisotropic plasma distributions, trapped at the Earth's magnetic equator, has consequences for the electric field structure which must exist in equilibrium along the magnetic field line. Data from SCATHA and Dynamics Explorer 1 indicate that the core ion distributions at the magnetic equator can be well described as bi-Maxwellian distributions, with a perpendicular temperature an order of magnitude larger than the parallel temperature. A collisionless model is developed for the variation in plasma parameters, following the forms developed by Whipple (1977). If the core electron anisotropy is low, the resulting electric field of approximately 0.1 microV/m is pointed away from the equator. Under these conditions the self-consistent electric field will not overcome the effects of magnetic trapping. The resulting potential distribution results in a local maximum in total plasma density at the equator. Only when the electron distribution is primarily field-aligned can there be a density minimum at the equator. Comparisons are made between this model and the observed variations in DE 1 plasma parameters with latitude.
The dynamics and structure of the magnetosheath and the magnetopause, a new theory of MHD shock waves, evolution of intermediate shocks, and shock waves in an anisotropic plasma, are reported.
A theory was developed to explain the properties of the chorus magnetic and electric field components in the case of an arbitrary propagation angle. The new theory shows that a whistler wave has circularly polarized magnetic fields for oblique propagation. This theoretical result is verified by GEOTAIL observations. The wave electric field polarization plane is not orthogonal to the wave vector, and in general is highly elliptically polarized. A special case of the whistler wave called the Gendrin mode is also discussed. This will help to construct a detailed and realistic picture of wave interaction with magnetosphere electrons. It is the purpose of this innovation to study the magnetic and electric polarization properties of chorus at all frequencies, and at all angles of propagation. Even though general expressions for electromagnetic wave polarization in anisotropic plasma are derived in many textbooks, to the knowledge of the innovators, a detailed analysis for oblique whistler wave mode is lacking. Knowledge of the polarization properties is critical for theoretical calculations of resonant wave-particle interactions.
We generalize a complex heavy-quark potential model from an isotropic QCD plasma to an anisotropic one by replacing the Debye mass m> D with an anisotropic screening mass depending on the quark pair alignment with respect to the direction of anisotropy. Such an angle-dependent mass is determined by matching the perturbative contributions in the potential model to the exact result obtained in the Hard-Thermal-Loop resummed perturbation theory. An advantage of the resulting potential model is that its angular dependence can be effectively described by using a set of angle-averaged screening masses as proposed in our previous work. Consequently, one could solve a one-dimensional Schrödinger equation with a potential model built by changing the anisotropic screening masses into the corresponding angle-averaged ones, and reproduce the full three-dimensional results for the binding energies and decay widths of low-lying quarkonium bound states to very high accuracy. Finally, turning to dynamics, we demonstrate that the one-dimensional effective potential can accurately describe the time evolution of the vacuum overlaps obtained using the full three-dimensional anisotropic potential. This includes the splitting of different p-wave polarizations.