Electromagneic Waves in a non- Maxwellian Dusty Plasma Nazish Rubab PhD student, KF University Graz IWF-OEAW Graz 26 January, 2011
Layout Dusty Plasma Non-Maxwellian Plasma Kinetic Alfven Waves Instability (KAWI) Cross-Field Instability Results 2
What is Dusty Plasma? plasma = electrons + ions small particle of solid matter + - - + Plasma + - absorbs electrons and ions + - + - + becomes negatively charged Debye shielding - + D - - + + - 3
Contd ion tail dust tail 4
Contd... 5
Dust in Fusion devices 6
Modes of Propagation 7
Contd... 8
Dust Acoustic Waves 9
DA wave Image Measurement of the dispersion relationship of the dust acoustic wave Original Experiments A. Barkan, N. D Angelo, and R. L. Merlino, Phys. Plasmas, 2, 3563 (1995). C. Thompson, A. Barkan, N. D Angelo, and R. L. Merlino, Phys. Plasmas, 4, 2331 (1997) 10
Electric Charge and Dust Charging Processes 11
Regular Variations 12
Contd... 13
Stochastic Variations (Charge Fluctuations) 14
Charging of a dust grain Charge on a dust grain surface: Charging cross-section: 15
Electron-Ion and dusty Plasmas The Difference 16
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Non-Maxwellian Velocity Distribution 18
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Kappa Distribution funnction 20
Relation between Maxwellian and kappa Debye lengths 21
Kinetic Alfven Waves Kinetic Alfvén waves (KAWs) are the extensions of their MHD counterparts in the range of short (kinetic) cross-field wavelengths comparable to ion gyroradius or electron inertial length ion gyroradius ρ i ( ions gyromotion and pressure effects) ion gyroradius at electron temperature ρ s (shows the electron pressure effects) ion inertial length δ i (effects due to ions inertia) electron inertial length δ e (effects due to electron inertia) (KAW) (IAW) 22
kinetic Alfven wave: short cross-field wavelength Bo Cross-field ion currents build up ion space charges and holes Field-aligned electron currents try to compensate ion charges but fail (electron inertia and/or electron pressure effects) Parallel electric field arise 23
Assumptions Low frequency waves (ω << << ω ci ci ) Two potential theory Charge neutrality 24
Basic set of equations Linearized Poisson equation is From Maxwell equation 25
Perturbed distribution for ion species Where Where and 26
Kinetic Alfven Wave Instability Assumptions Hot and magnetized electrons Thermal and un-magnetized Lorentzian ions Cold and un-magnetized Dust Geometry Distribution function for hot and magnetized electrons 27
Number densities purturbations Number densities for ion, electrons and dust are found to be respectively 28
Current density perturbations 29
Placing the value of number and current density perturbations in eq. (1) and (2), we get a set of coupled equations where 30
Dispersion Relation Dispersion relation of KAWI is obtained by solving Several modes of propagation can be derived from this equation by considering particular limits 31
Dispersion Relation Whistler Waves Mix Coupled Mode This equation shows that shear Alfven wave develops a longitudinal component making KAW a mixed electrostatic and electromagnetic mode. 32
Dispersion Relation where 33
Dust Acoustic Mode Zero ions flow 34
Results 35
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Conclusions Flow of Lorentzian ions have a significant effect on the wave characteristics Dust parameters have prominent effect on the growth rate of instability A high concentration of dust number density introduces upper instability which is small as compared to the lower instability Dust lower hybrid frequency (ω dlh ) arises due to the presence of hot and magnetized electrons and unmagnetized dust which provides a limit to the propagation of electromagnetic wave 40
Kappa has no concrete benefits for charging terms 41
Basic Assumptions Strongly magnetized electrons Cross field Instability Kappa distributed ions flowing perpendicular to the magnetic field (V 0 B 0 ) Cold and unmagnetized dust Geometry Distribution function 42
Current density of ions Number density of ions 43
Dispersion Relation Full dispersion equation is given by Which is the dispersion relation of electromagnetic streaming instabilities in a non-maxwellian dusty plasma Modified Two Stream Instability 44
In order to obtain an analytical solution w. r. t. ω, we need to approximate the Z-functions, so that the following relation is obtained 45
In the absence of electric current (V 0 =0 ) Which is the dispersion relation of Inertial Alfven waves with dust effects, in the limit 46
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Conclusions Instability is found to be insensitive to Lorentzian distribution for (V 0 B 0 ) in contrast to parallel propagation (V 0 B 0 ) where it has strong influence on the growth rates By considering cold electrons we get inertial Alfven waves in low beta plasma Mobile dust introduces a new cut-off frequency which limits the motion for the propagation of electromagnetic wave. For we arrive at the dispersion curves for MTSI, whose growth rates are larger as compared to Inertial Alfven wave instability Due to particular choice of equations which involve parallel background current density, the ions electromagnetic response can not not take part which limits the existence of ions Weibel instability 51
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