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Alfven waves are of fundamental importance in magnetized plasmas. This project aims to advance our understanding of the basic physics of the parametric instabilities of Alfven waves using advanced computer simulations. The results will have implications for important processes in the heliosphere involving Alfven waves, such as coronal heating and solar wind heating.
Alfven waves are of fundamental importance in magnetized plasmas, such as the solar wind and Earth’s magnetosphere. When the wave amplitude is large, nonlinear interactions among waves, such as three wave resonance, dominate the dynamics. The nonlinear process can be used as a diagnosis of the plasma composition because the composition affects the dispersion relation of Alfven waves, especially when the wave frequency is close to ion cyclotron frequencies. Previous experiments on the Large Plasma Device (LAPD) had demonstrated that the relative density of two ion species can be determined by examining nonlinear interaction of two counter-propagating Alfven waves. In this project we extended the study to a plasma with three ion species, where multiple wave bands exist, and more nonlinear interactions are possible. We also investigated the feasibility of launching two co-propagating waves to measure the ion composition. The findings of this study have implication in developing new technology to measure cold ion populations in space plasmas.
In this study, a 2-D self-consistent hybrid gyrofluid-kinetic electron model is used to investigate Alfven wave propagation along dipolar magnetic field lines for a range of ion to electron temperature ratios. The focus of the investigation is on understanding the role of these effects on electron trapping in kinetic Alfven waves sourced in the plasma sheet and the role of this trapping in contributing to the overall electron energization at the ionosphere. This work also builds on our previous effort by considering a similar system in the limit of fixed initial parallel current, rather than fixed initial perpendicular electric field. It is found that the effects of particle trapping are strongest in the cold ion limit and the kinetic Alfven wave is able to carry trapped electrons a large distance along the field line yielding a relatively large net energization of the trapped electron population as the phase speed of the wave is increased. However, as the ion temperature is increased, the ability of the kinetic Alfven wave to carry and energize trapped electrons is reduced by more significant wave energy dispersion perpendicular to the ambient magnetic field which reduces the amplitude of the wave. This reduction of wave amplitude in turn reduces both the parallel current and the extent of the high-energy tails evident in the energized electron populations at the ionospheric boundary (which may serve to explain the limited extent of the broadband electron energization seen in observations). Here, even in the cold ion limit, trapping effects in kinetic Alfven waves lead to only modest electron energization for the parameters considered (on the order of tens of eV) and the primary energization of electrons to keV levels coincides with the arrival of the wave at the ionospheric boundary.
The physics of the aurora is one of the foremost unsolved problems of space physics. The mechanisms responsible for accelerating electrons that precipitate onto the ionosphere are not fully understood. For more than three decades, particle interactions with Alfven waves have been proposed as a possible means for accelerating electrons and generating auroras. Due to the limitations of spacecraft conjunction studies and other multi-spacecraft approaches, it is unlikely that it will ever be possible, through spacecraft observations alone, to confirm definitively the proposed electron acceleration mechanism by making simultaneous measurements of both the accelerated electrons and the inertial Alfven wave responsible for the acceleration. Here, we show laboratory measurements of the resonant transfer of energy from Alfven waves to electrons under conditions relevant to the auroral zone. Experiments are performed by launching Alfven waves and simultaneously recording the electron velocity distribution. Numerical simulations and analytical theory support that the measured energy transfer process produces accelerated electrons capable of reaching auroral energies. The experiments, theory, and simulations demonstrate a clear causal relationship between Alfven waves and accelerated electrons that directly cause auroras.
We propose a method for studying absorption of Alfven wave propagation in a homogeneous non-isothermal plasma along a constant magnetic field, and relaxation of electron and ion temperatures in the A-wave. The absorption of a A-wave by the plasma arises due to dissipative effects - magnetic and hydrodynamic viscosities of electrons and ions and their elastic interaction. The method is based on the exact solution of two-fluid electromagnetic hydrodynamics of the plasma, which for A-wave, as shown in the work, are reduced to a nonlinear system of ordinary differential equations.
The Kelvin-Helmholtz (KH) instability of magnetohydrodynamic surface waves at the low latitude boundary layer is examined using both an eigenfrequency analysis and a time-dependent wave simulation. The analysis includes the effects of sheared flow and Alfven velocity gradient. When the magnetosheath flows are perpendicular to the ambient magnetic field direction, unstable KH waves that propagate obliquely to the sheared flow direction occur at the sheared flow surface when the Alfv\'en Mach number is higher than an instability threshold. Including a shear transition layer between the magnetosphere and magnetosheath leads to secondary KH waves (driven by the sheared flow) that are coupled to the resonant surface Alfven wave. There are remarkable differences between the primary and the secondary KH waves including wave frequency, the growth rate, and the ratio between transverse and the compressional component. The secondary KH wave energy is concentrated near the shear Alfven wave frequency at the magnetosheath with a lower frequency than the primary KH waves. Although the growth rate of the secondary KH waves is lower than the primary KH waves, the threshold condition is lower, so it is expected that these types of waves will dominate at lower Mach number. Because the transverse component of the secondary KH waves is stronger than the primary KH waves, more efficient wave energy transfer from the boundary layer to the inner magnetosphere is also predicted.
The objective of this project is to understand the damping, reflection, transmission, and phase mixing of Alfven waves in inhomogeneous plasmas by performing experiments on the Large Plasma Device (LAPD).
The growth rates for dust kinetic Alfvén wave (DKAW) based on semi-relativistic Maxwellian distribution function are investigated in a hot and magnetized plasma. The dispersion relation of DKAW is obtained on a dust acoustic velocity branch, and the kinetic instability due to cross-field semi-relativistic ion flow is examined by the effect of dust parameters. Analytical expressions are derived for various modes as a natural consequence of the form of the solution, and is shown through graphical representation that the presence of dust particles and the cross-field semi-relativistic ions sensibly modify the dispersion characteristics of low-frequency DKAW. The results are valid for a frequency regime well below the dust cyclotron frequency. We suggest that semi-relativistic particles are an important factor in the growth/damping of DKAWs. It is also found that relativistic effects appear with the dust lower hybrid frequency are more effective for dust kinetic Alfvén waves in the perpendicular component as compared to the parallel one. In particular, the relativistic effects associated with electrons suppress the instability while ions enhance the growth rates. The growth rates are significantly modified with dust parameters and streaming velocity of cross-field ions.
This report summarizes major theoretical findings in the linear as well as nonlinear physics of Alfvén waves and energetic particles in magnetically confined fusion plasmas. On the linear physics, a variational formulation, based on the separation of singular and regular spatial scales, for drift-Alfvén instabilities excited by energetic particles is established. This variational formulation is then applied to derive the general fishbone-like dispersion relations corresponding to the various Alfvén eigenmodes and energetic-particle modes. It is further employed to explore in depth the low-frequency Alfvén eigenmodes and demonstrate the non-perturbative nature of the energetic particles. On the nonlinear physics, new novel findings are obtained on both the nonlinear wave-wave interactions and nonlinear wave-energetic particle interactions. It is demonstrated that both the energetic particles and the fine radial mode structures could qualitatively affect the nonlinear evolution of Alfvén eigenmodes. Meanwhile, a theoretical approach based on the Dyson equation is developed to treat self-consistently the nonlinear interactions between Alfvén waves and energetic particles, and is then applied to explain simulation results of energetic-particle modes. Relevant list of journal publications on the above findings is also included.
Motivated by recent observations suggesting that the solar corona is heated by Alfvén wave damping at unexpectedly low heights, we performed experiments to study the basic plasma physics of Alfvén wave dissipation. Proposed coronal damping mechanisms rely on inhomogeneities in the plasma, but these theories have not been systematically studied in the laboratory. We performed experiments using the Large Plasma Device (LAPD) to test these theories.
Connect DIII-D physics with space plasma phenomena. In this case of using the toroidal Alfvén eigenmodes and frequency-chirping Reversed-Shear Alfvén eignmodes in DIII-D, we will document how the nonlinear interactions among dipolar Kinetic Alfvén Wave eigenmodes in space plasmas may determine saturation levels of these fluctuations. We seek evidence of nonlinear energy transfer and wave-wave coupling during 3-wave interactions mediated by a much lower-frequency mode. In FY2019, we found evidence of nonlinear “wave-wave” interactions in 175 relevant shots of archival DIII-D data. Toroidal mode number was identified and spectrograms were produced from each shot’s Mirnov coil data. Bispectral analysis was performed using a preliminary version of a new user friendly code derived from a 1995 M.S. thesis at WVU. These results formed a part of a May 2019 M.S. thesis at WVU.
A study of the ion Larmor radius effects on the solitary kinetic Alfven waves (SKAWs) in a magnetized plasma with superthermal electrons is presented by employing the kinetic theory. The linear dispersion relation of SKAW is shown to depend on the superthermal parameter κ, ion to electron temperature ratio, and the angle of wave propagation. Using the Sagdeev potential approach, the energy balance equation has been derived to study the dynamics of SKAWs. The effects of various plasma parameters are investigated for the propagation of SKAWs. It is shown that only compressive solitons can exist and in the Maxwellian limit our results are in good agreement with previous studies. Further, the characteristics of small amplitude SKAWs are investigated. Present study could be useful for the understanding of SKAWs in a low β plasma in astrophysical environment, where particle distributions are superthermal in nature.
Alfven wave is the single most important physical phenomenon of magneto-hydrodynamic turbulence and has far-reaching impact to almost all studies related to astrophysical magnetic field. Yet the restoration of the Alfven wave fluctuations from a given magnetic field, aka the local Alfven wave problem, is never properly addressed in literature albeit its importance. Previous works model the Alfven wave fluctuation as the perturbation along a straight-line, constant magnetic field. However, Lazarian & Pogosyan (2012) suggested that the decomposition of Alfven wave along a straight line, aka. the global frame decomposition, has a factor of discrepancy to the true local Alfven wave fluctuation. Here, in this paper, we provide a geometric interpretation on how the local Alfven wave is related to the global frame through the use of vector frame formulation. We prove both analytically and numerically that the local frame Alfven wave is an orthogonal transformation of that of the global frame and related by the local Alfvenic Mach number. In other words, when we observe Alfven wave in the global frame of reference, some of the Alfven wave will be mistaken as compressible waves. The importance of frame choices have a far-reaching impact to the analytical studies of MHD turbulence. Combining the frame formalism and the new techniques we can have accurate measurement to some of the fundamental turbulence properties like the inclination angle of mean magnetic field relative to the line of sight.
This paper discusses a novel parametric instability mechanism caused by particles that are weakly trapped in the potential wells of a nonlinear “pump” wave. The pump wave is unstable to the growth of daughter waves with longer wavelength and nearly the same phase velocity as the pump. This induces adjacent potential peaks in the wave to slowly approach one-another, receding from other pairs of peaks. Particles that are weakly trapped between approaching peaks, with kinetic energies just below the potential maxima, are heated by compression and escape the well, and then become retrapped on the other side of the approaching peaks, where they amplify the compression by pushing the peaks together. The mechanism applies to low-collisionality plasmas supporting waves with near-acoustic dispersion relations such as ion sound waves, magnetized Langmuir waves, or Alfven waves. The theory is compared to particle in cell simulations of TrivelpieceGould (TG) traveling waves, as well as to experiments on pure ion plasmas that observe parametric instability in TG standing waves.
Nonlinear circularly polarized Alfvén waves are studied in magnetized nonrelativistic, relativistic, and ultrarelativistic degenerate Fermi plasmas. Using the quantum hydrodynamic model, Zakharov equations are derived and the Sagdeev potential approach is used to investigate the properties of the electromagnetic solitary structures. It is seen that the amplitude increases with the increase of electron density in the relativistic and ultrarelativistic cases but decreases in the nonrelativistic case. Both right and left handed waves are considered, and it is seen that supersonic, subsonic, and super- and sub-Alfvénic solitary structures are obtained for different polarizations and under different relativistic regimes.
Here, plasma densification through magnetic compression has been suggested for time-resolved control of the wave properties in plasma-based accelerators [P. F. Schmit and N. J. Fisch, Phys. Rev. Lett. 109, 255003 (2012)]. Using particle in cell simulations with real mass ratio, the practicality of large magnetic compression on timescales shorter than the ion gyro-period is investigated. For compression times shorter than the transit time of a compressional Alfven wave across the plasma slab, results show the formation of two counter-propagating shock waves, leading to a highly non-uniform plasma density profile. Furthermore, the plasma slab displays large hydromagnetic like oscillations after the driving field has reached steady state. Peak compression is obtained when the two shocks collide in the mid-plane. At this instant, very large plasma heating is observed, and the plasmaβ is estimated to be about 1. Although these results point out a densification mechanism quite different and more complex than initially envisioned, these features still might be advantageous in particle accelerators.
Linear properties of high and low frequency waves are studied in an electron-positron-ion (e-p-i) dense plasma with spin and relativity effects. In a low frequency regime, the magnetohydrodynamic (MHD) waves, namely, the magnetoacoustic and Alfven waves are presented in a magnetized plasma, in which the inertial ions are taken as spinless and non-degenerate, whereas the electrons and positrons are treated quantum mechanically due to their smaller mass. Quantum corrections associated with the spin magnetization and density correlations for electrons and positrons are re-considered and a generalized dispersion relation for the low frequency MHD waves is derived to account for relativistic degeneracy effects. On the basis of angles of propagation, the dispersion relations of different modes are discussed analytically in a degenerate relativistic plasma. Numerical results reveal that electron and positron relativistic degeneracy effects significantly modify the dispersive properties of MHD waves. Our present analysis should be useful for understanding the collective interactions in dense astrophysical compact objects, like, the white dwarfs and in atmosphere of neutron stars.
Objectives: To establish, for lab & space conditions, EM-IEDDI’s (electromagnetic shear-driven instability's) dispersion relation, unstable range, instability threshold, and mode characteristics, we need LAPD’s Alfven-wave-favorable electromagnetic-style conditions, including higher "beta" (0.001 < beta ≤ 0.3) and low-collisionality. Also, we attempted to intentionally launch or spontaneously destabilize compressional and shear Alfven waves in the strong, localized, perpendicular-velocity-shear region at the interface between coaxial plasmas (one plasma cylinder inside an outer, otherwise hollow, tube, each having a different, controllable, value of plasma electrostatic potential, i.e., “space” potential (not to be confused with the temperature-dependent “floating” potential of an object immersed in the plasma). Nonlinear wave-wave interactions between same-family (EM-IEDD or Alfven) and cross-family (EM-IEDD-with-Alfven) fluctuations were targeted for documentation over a range of spectral overlap. Although laboratory experiments were conducted, the following theoretical work was left unfinished: Analytical non-modal prediction Computational non-modal prediction Check to see if Mikhailenko’s theory formulation leads to his published graphs