Session PO11: Basic: Waves, Instabilities, & Strongly Coupled Plasmas

Oscillatory kink instability of electron phase-space holes

Electron holes (soliton-like BGK modes of positive potential) are routinely formed as a nonlinear result of beam-plasma instabilities, and widely observed in space. In a sufficiently strong magnetic field in the electron trapping direction ($\Omega>\omega_p$) their purely growing ($\gamma\sim 200\omega_p$) transverse instability is suppressed and they can survive for thousands of plasma periods. PIC simulations show they sometimes break up on this longer timescale because of an oscillatory kink instability, which couples to external waves. This talk will explain the kinematic physical mechanisms of the two regimes of oscillatory kinks: one* at moderate field $\Omega\sim\omega_p$ and one extending to infinite field; and will present analytic calculations of their dispersion relations, which agree with simulations. A remarkable feature is that the positive slope of the trapped particle distribution at bounce resonance contributes (contradicting prior theoretical claims) to {\it stabilizing} the kink, because the hole has negative inertia. The growth rate decreases rapidly as the hole potential is reduced, $\propto\phi^{3/2}$. Thus shallow holes can last a very long time, and holes of limited transverse extent can be fully stable. *I H Hutchinson Phys. Rev. E, 99, 053209 (2019)   

Kinetic stability of Chapman-Enskog plasmas

In this talk we will discuss the kinetic stability of classical, collisional plasmas. Fluid equations are typically used to describe such plasmas, since their distribution functions are close to being Maxwellian. The small deviations from the Maxwellian distribution are calculated via the Chapman-Enskog (CE) expansion, and determine macroscopic momentum and heat fluxes in the plasma. Such a calculation is only valid if the underlying CE distribution function is stable at collisionless scales. We will demonstrate that at sufficiently high plasma $\beta$, the CE distribution function can be subject to numerous microinstabilities across a wide range of scales, the most significant of which we shall characterize. Of specific note is the discovery of the previously uncharacterized `whisper-wave instability', whose growth rate in certain parameter regimes is large compared to other instabilities. Our approach enables us to construct the kinetic stability maps of classical, two-species collisional plasma in terms of the mean free path, the electron skin depth and the plasma $\beta$. Our work highlights that collisional plasmas can be kinetically unstable; in this situation, the determination of transport coefficients with the standard CE expansion is not necessarily valid.   

Unified view of nonlinear wave structures associated with whistler-mode chorus waves

A range of nonlinear wave structures, including Langmuir waves, unipolar electric fields and bipolar electric fields, are often observed in association with whistler-mode chorus waves in the near-Earth space. We demonstrate that the three seemingly different nonlinear wave structures originate from the same nonlinear electron trapping process by whistler-mode chorus waves. Only a single quantity, the ratio of the Landau resonant velocity to the electron thermal velocity, controls the type of nonlinear wave structure that will be generated. When the tail of the electron distribution is trapped by chorus, the trapped electrons form a spatially modulated bump-on-tail distribution and excite Langmuir waves. When the thermal electrons are trapped by chorus, they form phase space holes and hence produce bipolar electric fields. Between these two regimes, trapped electrons generate nonlinear electron acoustic waves, which in turn disrupts the trapped electrons and accumulates them in a limited spatial region, leading to the unipolar electric field structures. This study connects a variety of seemingly unrelated nonlinear field structures and provides a simple, integrated picture of the microscopic interactions between whistler waves and electrons.   

Nonlinear evolution of the ion-ion streaming instability in single- and multi-ion species plasmas

When two streams of ions flow through one another, the relative flows may drive the growth of large-amplitude ion acoustic waves via the ion-ion streaming instability (IISI). We study the linear and nonlinear evolution of the IISI using a 2D+2V high-order continuum method novel to this problem. The electrostatic energy generated by the IISI is converted into ring-like velocity distributions of ions that are both heated and slowed. Due to variation in the ion trapping conditions for species of differing charge-to-mass ratio, we find that the plasma streaming velocity may be altered radically by the IISI. Here, this process causes the collisionless stopping of a lighter ion species by a heavier ion species. When the two streams each contain a mixture of species, the differing ion trapping conditions cause a velocity separation of the ion species. We observe that the heavier ion species emerges from the interaction significantly hotter than the lighter ion species, and can even be heated to a temperature significantly above that of the electrons.   

Cherenkov radiation of Alfv$\'e$n Waves by an Intense Proton Beam in a Large Magnetized Plasma

Cherenkov radiation of waves by charged particles has a bearing on a number of astrophysical and terrestrial problems [1, 2]. Spontaneous radiation of traveling Alfv$\'e$n waves by a short-burst of protons (5-20 keV, 2-12 A, pulse-width $\approx$ 8 $\mu$s, pitch-angle $\approx$ 0$^\circ}$) has been investigated on the Large Plasma Device [3]. In these experiments, the proton beam was injected into a magnetized plasma (n $\approx$ 10$^{12}$ cm$^{-3}$, Te = 0.1 - 5.0 eV, B = 0.25 - 1.50 kG, H$^+$ ions, 19 m long, 0.6 m diameter). The beam energy was varied to explore sub- and super-Alfv$\'e$nic regimes of the beam propagation (beam-speed/Alfv$\'e$n-speed = 0.5 - 4.0) for inertial and kinetic Alfv$\'e$n waves. The interaction of the beam with the plasma was diagnosed using a retarding-field energy analyzer, three-axis magnetic-loop, and Langmuir probes. Cherenkov radiation of Alfv$\'e$n waves is observed when the beam-speed exceeds the Alfv$\'e$n speed. In this regime, the wave forms a conical pattern and lags behind the super-Alfv$\'e$nic proton-burst. References: (1) Krechetov, Geomagnetism and Aeronomy, 35(5), 688 (1995); (2) Van Compernolle et. al., Phys. Plasmas 15, 082101 (2008); (3) Tripathi et. al., Phys. Rev. E 91, 013109 (2015)   

The nonmodal evolution of the instabilities of a Hall plasma driven by a sheared Hall current

A nonmodal kinetic approach to the analysis of the instabilities of a Hall plasma driven by a Hall current with a sheared current velocity is presented. The developed theory predicts that the static spatial structure of the perturbations in the plasma with the inhomogeneous electric field is determined in the frame convected with one of the plasma components. Because of the different shearing of the ion and electrons flows in the Hall plasma, this static mode is observed by the second component as the Doppler-shifted continuously sheared mode with time-dependent wave numbers. Due to this effect, the development of the instabilities driven by the sheared current is the nonmodal process, which is investigated as the initial value problem. The nonmodal solutions for the Hall plasma instabilities of the kinetic and hydrodynamic types are presented.   

Complex-Hamiltonian Paraxial Description of Damped Geodesic Acoustic Modes

Geodesic acoustic modes (GAMs) are a fundamental part of the dynamics of turbulence and zonal flows in tokamaks. They exhibit simple yet non-trivial dispersive and dissipative properties. In linear numerical simulations, they are often initialized in the form of (e.g. Gaussian) packets which evolve in time. Depending on the parameters, the damping rate can be comparable to the oscillation frequency. Wigner-function methods developed in the frame of non-Hermitian quantum mechanics are shown to be applicable to damped geodesic oscillations. In this approach, the standard approximation of ``weak damping'', often introduced for the treatment of plasma waves, is not needed. The method requires that the properties of the plasma do not vary significantly across the width of the packet, so that a paraxial expansion can be applied. The equations governing the packet in the paraxial limit are shown to be formally the same as the equations of paraxial WKB theory, employed e.g. for high-frequency wave beams in plasmas, with the real Hamiltonian replaced by the corresponding complex one. Analytic solutions can be derived in particular cases and compared to the results of global gyrokinetic simulations performed with the code ORB5.   

Observation of Toroidal Acoustic Mode in a Current-less Toroidal Plasma

Geodesic Acoustic Mode (GAM) is the pressure oscillations supported by plasma compressibility in a toroidal magnetic geometry where average geodesic curvature provides a restoring force. GAMs exhibit top bottom antisymmetry in the density fluctuations and the potential fluctuations are nearly independent of the poloidal angle. In the present work, we report a simple yet surprising experimental demonstration of the existence of a Toroidal Acoustic Mode (TAM) in a nearly collisionless, currentless toroidal device (CTD), BETA, for the first time. A CTD, unlike Tokamak, does not have a zeroth order toroidal current. The observed TAM mode in our experiments is a global, discrete frequency mode with n=0, m=1, for density fluctuation and n=0, m>=0, for potential fluctuations. The real frequency of the observed TAM mode is fTAM=3√2cs/(2ΠR), where cs=√(Te/Mi); Te is the local electron temperature and Mi is the ion mass. The mode is found to be driven by the non-linear interaction of a finite frequency interchange-like mode with itself. The observed frequency of both TAM mode and driver mode are found to scale linearly with 1/√(Mi), where Mi is the ion mass, but with their slopes different by a factor of 2. This mode is found to have characteristics similar to GAMs often found in Tokamak.   

Novel Mode-Particle Resonances for Ballooning Modes in Fusion Reacting Plasmas

The excitation of ballooning modes introduced originally in the mid-sixties [1,2] is important in the dynamics of magnetically confined plasmas. A significant class of these modes, that are localized along the magnetic field lines, is oscillatory in time [3,4] and can be viewed as a superposition of oppositely propagating waves with equal amplitudes. Each of these waves is assumed to involve a mode-particle resonance with a high energy particle population. The resulting superposition leads to a composite mode [4] that has a significantly different time dependence from that given by the well known Landau damping of single plasma waves. In fusion burning plasmas [3] thermal particles, that are the majority and can sustain ballooning mode structures, coexist with high energy particle populations. The considered composite modes are shown to be of relevance to this kind of plasmas.\\ $[1]$ B. Coppi, M.N. Rosenbluth and S. Yoshikawa, Phys. Rev. Lett. 20, 190 (1968).\\ $[2]$ B. Coppi, Phys. Rev. Lett. 39, 939 (1977).\\ $[3]$ B. Coppi, Phys. Letters A, 172, 439 (1993).\\ $[4]$ B. Coppi, Plasma Physics Reports, 45, 1 (2019).   

Internal resonances in dusty plasma

This talk will discuss the nonlinear mode coupling and 1:2 internal resonance recently observed experimentally for the first time in a dusty plasma with vertical dust pairs. Analysis of the power spectra density (PSD) and amplitude-frequency response shows the horizontal S2 mode is excited through vertical excitation when a commensurate relationship between the vertical B and the horizontal S2 mode is satisfied at low plasma pressures. A theoretical model describing the vertical dust particle pair under vertical excitation, considering interactions to quadratic terms, will also be provided. For this case, the equations of motions are solved in decoupled coordinates employing a multiple scale method in order to obtain the theoretical amplitude-frequency response at the onset of 1:2 internal resonance. The resulting response curve will be shown to match experimental data   

Effects of Coulomb Coupling and Plasma Magnetization on Stopping Power

Fusion fuel in recent experiments has the potential to exhibit both moderate-to-strong Coulomb coupling and magnetization (e.g. magnetized liner inertial fusion). Therefore, it is important to understand fusion product slowing and dynamics in fuel under such conditions. Here, molecular dynamics simulations are used to assess how Coulomb coupling and plasma magnetization influence the stopping power of the classical one component plasma. With respect to the weakly-coupled limit, strong coupling increases the magnitude of the stopping power, shifts the Bragg peak to higher speeds (with respect to the background plasma thermal speed), and causes the stopping power curve to broaden. Stopping power was split into two components; one associated with one-dimensional friction, and the other with a thermal energy exchange rate. From these two components, in the limit of a massive projectile, stopping power was used to calculate the self-diffusion coefficient and the thermal relaxation rate of the background plasma. The influence plasma magnetization has on projectile dynamics and stopping power was assessed, along with the related potential wake that forms about the projectile as it traverses through the plasma.   

Gravity Crystals

In the limit of very strong interparticle coupling, plasmas become spatially-correlated and can form long-range order known phenomenologically as Wigner crystallization. In principle, this phenomenon can exist at any energy scale ranging from the dense interiors of white dwarf stars to the coldest man-made objects in laser-cooled ion traps. Although several laboratory examples of Wigner crystallization exist, all efforts have been confined to the microscopic regime and require expensive cutting-edge technology for its study. This talk will present an experimental method for studying Wigner crystallization at macroscopic lengthscales by employing a gravity well as the confining potential. Plasma properties were measured throughout multiple phases of strongly coupled plasma, which included a first-order phase transition to a crystalline state. These ``gravity crystals'' expand the range of Wigner crystallization by a factor of a million and does so using a versatile and broadly accessible platform.   

The Effect of Self-Generated Magnetic Fields on Ablative Rayleigh--Taylor Instability Dynamics

Measurements of magnetic (B) field induced by the ablative Rayleigh--Taylor instability (ARTI) in laser-produced plasmas\footnote{ M. J.-E. Manuel \textit{et al.}, Phys. Rev. Lett. \textbf{108}, 255006 (2012).} indicate that it may play an important role in the dynamics of this instability. The B field modifies the thermal conduction, and the Righi--Leduc term can be destabilizing by moving heat away from the top of the spike toward the bubbles.$^{\mathrm{\thinspace }}$\footnote{ A. Nishiguchi, Jpn. J. Appl. Phys. \textbf{41}, 326 (2002).}$^{\mathrm{,}}$\footnote{ C. A. Walsh \textit{et al.}, Phys. Rev. Lett. \textbf{118}, 155001 (2017).} In this talk, we present an analysis of the linear stage of the ARTI with self-generated B fields. We identify an unstable mechanism arising from the interplay between the Biermann battery term that generates B field, which in turn affects the energy equation through the Righi--Leduc term. In essence, this mechanism is similar to the magnetothermal instability arising in the underdense corona.\footnote{ D. A. Tidman and R. A. Shanny, Phys. Fluids \textbf{17}, 1207 (1974).} At the ablation front, however, the coupling of this mechanism with the hydrodynamics needs to be self-consistently solved. We~discuss the new dispersion relation derived.