Session BI03: Invited: Stix Award & Fundamental Plasma Physics I - Waves and Nonlinear Dynamics

Stix Award: Extreme Plasmas around Neutron Stars and Black Holes

In this talk, I will review recent advances in relativistic plasma physics. I will focus on the first-principles mechanisms of producing coherent radio emission from neutron stars and the dynamics of collisionless plasma accreting onto supermassive black holes in our galaxy and M87 (the primary targets of the Event Horizon Telescope).   

Physics of Dynamic Profile Staircases

Staircases are quasi-periodic layered states of inhomogeneous mixing zones interspersed by microbarriers, which impede transport and so locally steepen gradients. Staircases and layering are observed in many physical systems, including, but not limited to, magnetically confined plasmas. There, the microbarriers are thought to be due to E ✕ B shear layer feedback. However, we show that staircase formation is a much simpler and more general phenomenon. In fact, inhomogeneous mixing will occur when the turbulence field is organized in an array of nearly overlapping convective cells. Such a configuration is typical of systems near marginal stability, which occur frequently, including in confined plasmas. In such a cellular array, passive scalar staircases form due to the interplay of two disparate time scales, that of (fast) cell turn-over and (slow) diffusion across cell boundaries. To address the important features of cellular variability and jitter, we study staircase formation in a fluctuating cellular array. There we see that scalar staircases remain resilient over a broad range of excitations typical of the modest levels of turbulence in magnetic confinement experiments (i.e., Kubo number ≤ 1). Staircase curvature and cellular Peclet number are identified as figures-of-merit for the resiliency of dynamic staircases. We also observe that as long  as cell streamlines are maintained, effective diffusion across cell boundaries does not deviate significantly from that for the fixed cellular array [D*∝ √(D₀ D_cell)]. In addition, we examine the active scalar staircase. The dynamics of the active scalar are analogous to that of the magnetic potential in 2D MHD, where fields are expelled to cell boundaries and so stabilize the staircase cells. Here, turbulent resistivity measures cellular array elasticity. The active scalar system exhibits a novel feedback mechanism that reinforces the global staircase structure and promotes self-organization.   

First Laboratory Observations of Residual Energy Generation in Strong Alfvén Wave Interactions

In the MHD inertial range (scales larger than ion-kinetic scales) turbulent fluctuations in the solar wind are often Alfvénic in character, meaning that their magnetic and flow velocity fluctuations are proportional to each other and predominantly perpendicular to the background magnetic field. However, observations of the solar wind have shown that there is a significant difference in the energy in velocity fluctuations and normalized magnetic fluctuations. This difference, called the residual energy, should be zero for linear Alfvén waves, but is consistently observed to be negative in the solar wind, with magnetic fluctuations dominating. This work investigates the energy partition in strong three-wave interactions through an experimental campaign on the LArge Plasma Device (LAPD) in an MHD-like regime to better understand the physics underlying residual energy generation. Primary (driven) modes are launched from antennas, and secondary modes generated by the strong three-wave interaction are observed. The primary modes are shown to have no residual energy, while the secondary modes have significant residual energy - negative in the "sum" mode and positive in the "difference" mode. These results constitute the first laboratory demonstration that residual energy can indeed be generated by nonlinear mode coupling.   

First laboratory detection of anomalous resistivity and electron heating by lower hybrid drift waves inside reconnecting current sheets with a guide field

Magnetic reconnection plays an important role in explosive phenomena in magnetized plasmas such as solar flares and geomagnetic storms. Various waves and instabilities can be generated in the reconnecting current sheets due to abundantly available free energy and affect the reconnection dynamics. One frequently observed wave is lower hybrid drift waves (LHDW) which can be either quasi-electrostatic (ES-LHDW) or electromagnetic (EM-LHDW), depending on the plasma and field conditions. From the linear theory [1], we find that the characteristics of LHDW are determined by electron beta and the relative perpendicular drift velocity between electrons and ions normalized to the local sound speed. In the low electron beta regime with a guide field, strong ES-LHDW is observed inside the electron diffusion region in the Magnetic Reconnection Experiment (MRX). By using a specially developed probe [2], fluctuations in density and the out-of-plane component of the electric field are measured to correlate to generate a significant (~20% of the reconnection electric field) anomalous resistivity [4]. The observed small phase difference between the two fluctuations is consistent with our linear models [1,3], which suggests the important role played by the Lorentz force in generating the anomalous resistivity. We have performed quasilinear analysis and showed that ES-LHDW can generate anomalous electron heating exceeding the classical Ohmic heating in laboratory plasma [4]. We also found a positive correlation between the electron temperature and the amplitude of LHDW, and the correlation grows stronger with larger guide fields. Our work demonstrates the importance of wave-particle interaction during collisionless reconnection.

[1] J. Yoo et al., Geophys. Res. Lett. 47 (2020). DOI:10.1029/2020GL087192

[2] Y. Hu, J. Yoo, H. Ji, A. Goodman, and X. Wu, Rev. Sci. Instrum. 92, 033534 (2021).

[3] J. Yoo et al., Phys. Plasmas 29, 022109 (2022).

[4] J. Yoo et al., Phys. Rev. Lett. 132, 145101 (2024).   

Equilibrium and stability studies of non-neutral and pair plasmas in curved magnetic field geometries

Non-neutral plasmas (NNPs) are fascinating both for their application to research with antimatter (e.g., anti-hydrogen production, Ps chemistry, e-e+ “pair plasmas”, etc.) and for enabling precision experiments that can be compared to theory.  However, most of these have been done in uniform magnetic fields (Penning–Malmberg traps); we are now bringing these into the realm of non-uniform magnetic fields.  We have studied thermal equilibrium states of single-species plasmas confined in a dipole trap, numerically finding solutions for not only local thermal equilibria along magnetic field lines but also global thermal equilibria. These results agree with the analytic predictions. There is, in principle, no limit to the confinement time of a single-species plasma in a global thermal equilibrium state. In contrast to local thermal equilibrium states, global thermal equilibrium states are guaranteed to be stable since there is no free energy that could drive an instability. We have investigated the global stability properties of an e-e+ pair plasma at different positron to electron ratios in the linear regime, confined by the magnetic field of an infinitely long wire (i.e., the large-aspect-ratio limit of a levitated dipole coil). We expect that the most important instabilities are of low frequency and long wavelength compared to the cyclotron motion and are electrostatic in nature, since the plasma pressure is typically low compared to the magnetic pressure. In the non-neutral case, the plasma supports a diocotron mode; as the plasma approaches neutrality, the diocotron mode vanishes and is replaced by an interchange mode.  By extending NNP theories to non-uniform magnetic fields, we not only explore new territory in fundamental plasma physics but also build a predictive/interpretive framework for experiments, e.g.,  from the APEX (A Positron Electron eXperiment) Collaboration, that seek to combine e+ pulses with e- plasmas to create and study confined e+e- plasmas.

    

Quantum algorithms for simulating dissipative linear and nonlinear dynamics of plasmas

Quantum computing (QC) has the potential to speed up classical simulations of plasma dynamics, which requires dealing with large amounts of high-dimensional data, by leveraging quantum superposition and entanglement. Yet, due to the intrinsically linear and unitary nature of quantum mechanics, modeling dissipative nonlinear (NL) dynamics has required significant development. We have derived explicit QAs for modeling plasma physics including the linear dynamics of cold fluid waves in plasmas [1], electromagnetic waves [2], and diffusion, and have begun to develop QAs for nonlinear dynamics. In this talk, we discuss the new QAs, various techniques for encoding classical systems into quantum circuits [3], and their potential for quantum speedup. 

QAs for dissipative dynamics are usually based on the transformation of nonunitary initial-value problems into a system of linear equations which then can be solved by a quantum linear solver such as the quantum singular value transformation. Another recent method that we have explored, the Linear Combination of Hamiltonian Simulations algorithm, provides an explicit encoding in terms of multiple unitary evolution operators and thereby avoids matrix inversion.  

Nonlinear dynamics is especially challenging for quantum computers due to the no-cloning theorem which forbids copying unknown quantum states. This results in an exponential growth of resources when any iterative QA is applied to a NL problem. The Koopman—von Neumann (KvN) formulation [4] allows one to embed a NL system into a linear problem that describes the linear evolution of the wavefunction and, hence, the probability distribution function.  We present the first explicit KvN-based QA for simulating NL dynamics and the initial application of this method to representative test cases.