An introductory guide to fluid models with anisotropic temperatures. Part 2. Kinetic theory, Padé approximants and Landau fluid closures
Year: 2019
Type: article
Abstract: In Part 2 of our guide to collisionless fluid models, we concentrate on Landau fluid closures. These closures were pioneered by Hammett and Perkins and allow for the rigorous incorporation of collisionless Landau damping into a fluid framework. It is Landau damping that sharply separates traditional fluid models and collisionless kinetic theory, and is the main reason why the usual fluid models do not converge to the kinetic description, even in the long-wavelength low-frequency limit. We start with a brief introduction to kinetic theory, where we discuss in detail the plasma dispersion function $Z(\unicode[STIX]{x1D701})$ , and the associated plasma response function $R(\unicode[STIX]{x1D701})=1+\unicode[STIX]{x1D701}Z(\unicode[STIX]{x1D701})=-Z^{\prime }(\unicode[STIX]{x1D701})/2$ . We then consider a one-dimensional (1-D) (electrostatic) geometry and make a significant effort to map all possible Landau fluid closures that can be constructed at the fourth-order moment level. These closures for parallel moments have general validity from the largest astrophysical scales down to the Debye length, and we verify their validity by considering examples of the (proton and electron) Landau damping of the ion-acoustic mode, and the electron Landau damping of the Langmuir mode. We proceed by considering 1-D closures at higher-order moments than the fourth order, and as was concluded in Part 1, this is not possible without Landau fluid closures. We show that it is possible to reproduce linear Landau damping in the fluid framework to any desired precision, thus showing the convergence of the fluid and collisionless kinetic descriptions. We then consider a 3-D (electromagnetic) geometry in the gyrotropic (long-wavelength low-frequency) limit and map all closures that are available at the fourth-order moment level. In appendix A, we provide comprehensive tables with Padé approximants of $R(\unicode[STIX]{x1D701})$ up to the eighth-pole order, with many given in an analytic form.
Source: Journal of Plasma Physics
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,980
Awards: G271070715, G2939914276, THE SOLAR WIND ESPECIALLY THE FAST STREAMS (SPEED GREATER THAN 600700 KM/S) IS PERMEATED BY A FLUX OF ALMOST INCOMPRESSIBLE LARGE AMPLITUDE FLUCTUATIONS OF PLASMA VELOCITY AND MAGNETIC FIELD KNOWN AS ALFV NIC TURBULENCE. THOUGH THE SPECTRUM IS TURBULENT THE VELOCITY-MAGNETIC FIELD CORRELATION CORRESPONDS TO THAT OF WAVES PROPAGATING AWAY FROM THE SUN. ANOTHER IMPORTANT AND AS YET UNEXPLAINED PROPERTY IS THAT THE TOTAL MAGNETIC FIELD MAGNITUDE REMAINS ALMOST CONSTANT IN THE SENSE THAT THE FLUCTUATIONS IN THE MAGNITUDE OF THE FIELD ARE MUCH SMALLER THAN THE MAGNITUDE OF THE FLUCTUATIONS IN THE MAGNETIC FIELD. DESPITE THE WEALTH OF OBSERVATIONAL EVIDENCE COVERING DISTANCES FROM 0.3 OUT TO MANY AU HOW THIS TURBULENT YET COHERENT ALFV NIC STATE IS ACHIEVED IN THE SOLAR WIND AS WELL AS ITS POTENTIAL DYNAMICAL ROLE IN SOLAR WIND HEATING AND ACCELERATION REMAIN FUNDAMENTAL OPEN QUESTIONS OF HELIOPHYSICS. WE PROPOSE TO INVESTIGATE THEORETICALLY THE ROLE OF NONLINEAR WAVE AND WAVE-PARTICLE INTERACTIONS IN MAINTAINING OR GENERATING THIS ALFV NIC STATE AND TO SEARCH FOR SPECIFIC SIGNATURES OF SUCH INTERACTIONS IN THE SOLAR WIND. A RECENT THEORETICAL RESULT HAS PREDICTED THAT LINEARLY POLARIZED ALFV N WAVES CAN GENERATE SUFFICIENT PRESSURE ANISOTROPY TO REMOVE THEIR OWN RESTORING FORCE WHEN PLASMA>1. THIS CAUSES SIGNIFICANT NONLINEAR MODIFICATIONS TO THE ALFV N WAVE AND EXCITES THE FIREHOSE INSTABILITY POSSIBLY LEADING TO CONSTANT MAGNETIC FIELD STEPS. THIS PLACES A STRINGENT LIMIT ON THE AMPLITUDE OF ALFV N WAVES IN TERMS OF THE PLASMA OR KINETIC TO MAGNETIC PRESSURE RATIO ABOVE WHICH THEY CAN NO LONGER OSCILLATE OR PROPAGATE IN COLLISIONLESS PLASMAS. AN ANALYSIS OF SOLAR WIND DATA FROM THE NASA WIND SPACECRAFT SHOWS CLEAR EVIDENCE OF THIS THRESHOLD AS WELL AS SECOND LOW THRESHOLD THAT APPEARS TO BE CONSISTENT WITH THEORETICAL EXPECTATIONS OF PARAMETRIC DECAY. INDEED THOUGH LARGE AMPLITUDE ALFV NIC FLUCTUATIONS WITH CONSTANT (TOTAL) MAGNETIC FIELD MAGNITUDE ARE AN EXACT SOLUTION IN MAGNETOHYDRODYNAMICS THEY ARE PARAMETRICALLY UNSTABLE AT LOW AND DECAY BY COUPLING WITH COMPRESSIBLE MODES AND SECONDARY ALFV N WAVES. PRELIMINARY STUDIES SUGGEST THAT THERE IS AN ABSOLUTE LIMIT TO ALFV NIC FLUCTUATION AMPLITUDES AS A FUNCTION OF PLASMA BETA RELATED TO THESE INSTABILITIES. SO FAR PARAMETRIC DECAY HAS BEEN STUDIED ASSUMING A MAXWELLIAN BACKGROUND PLASMA. HOWEVER THE WEAKLY COLLISIONAL SOLAR WIND DISPLAYS SEVERAL NON-THERMAL FEATURES E.G. TEMPERATURE ANISOTROPIES AND ION DIFFERENTIAL STREAMING ESPECIALLY IN THE FAST STREAMS. THIS PROPOSAL INVESTIGATES THE ROLE OF NON-LINEAR WAVE AND WAVE-PARTICLE INTERACTIONS IN MAINTAINING OR GENERATING THE ALFV NIC STATE WITH THE AIM OF UNDERSTANDING HOW THE SHAPE OF THE DISTRIBUTION FUNCTION CONTRIBUTES TO THE EXISTENCE OF SUCH TURBULENCE. THE OBJECTIVES ARE TO (1) CARRY OUT A THEORETICAL STUDY OF ALFV N WAVE STABILITY IN NON-MAXWELLIAN PLASMAS SUPPORTED BY HYBRID SIMULATIONS STARTING FROM ANISOTROPIC PROTON DISTRIBUTIONS OF THE TYPE FOUND IN THE SOLAR WIND. THIS WILL PROVIDE SCALINGS OF CRITICAL WAVE AMPLITUDES WITH ; (2) COMPLETE DATA ANALYSIS OF WIND AND ULYSSES MEASUREMENTS OF THE CORRELATION BETWEEN THE STATE OF SOLAR WIND TURBULENCE (ALFV NIC VS. NON-ALFV NIC WAVE-FORMS AMPLITUDES AND JOINT PROBABILITY DISTRIBUTIONS) AND THE PROTON DISTRIBUTION FUNCTIONS AT DIFFERENT VALUES. THE PROPOSAL FITS WITHIN THE HELIOPHYSICS DECADAL SURVEY GOAL DISCOVER AND CHARACTERIZE FUNDAMENTAL PROCESSES THAT OCCUR BOTH WITHIN THE HELIOSPHERE AND THROUGHOUT THE UNIVERSE AND FALLS UNDER HS-R SCIENCE AREA 5 HELIOSPHERIC PLASMA PROCESSES TURBULENCES WAVES COMPOSITION. THE PROPOSED STUDY WILL PROVIDE NEW INSIGHTS ON THE ROLE OF ALFV N WAVES IN SOLAR WIND DYNAMICS AS WELL AS PREDICTIONS THAT MAY BE VERIFIED BY THE UPCOMING PARKER SOLAR PROBE MISSION., RII Track-1: CPU2AL: Connecting the Plasma Universe to Plasma Technology in Alabama, G661977885
OpenAlex ID: W2911327207