Simulation study of EM radiation f rom Langmuir waves in warm ma gnetized plasmas Iver H. Cairns Eun-Hwa Kim Peter A. Robinson School of Physics, University of Sydney, Australia < AIMS > Demonstrate that Langmuir/z-mode waves are converted into x-mode r adiation by linear mode conversion (parallel and oblique cases). Calculate the mode conversion efficiency for typical coronal and solar wind parameters (parallel and oblique cases). Apply results to solar radio bursts in the solar wind and corona
I. Linear Mode Conversion: Issues and Definition Inhomogeneous plasma: natural modes coupled 2 N // x-r o-l "! 0 Langmuir / z LMC Langmuir/z waves o mode waves in density gradients [e.g., Field, Budden, Jones ] Waves tunnel through evanescent gap between modes: Higher efficiency smaller separation Can we get x-mode too? X e = ( f / f p 2 ) x-mode?
Solar Radio Bursts : Type II and III frequency Type II - H MHz Type II - F Type III Hour Generation Process? Polarization Type II Very weak / linear [Nelson and Melrose, 1985] Type III 0 ~ 70 % (o-mode) NEVER 100% despite theory predicting this [Dulk and Suzuki, 1980] O LH RH X [Dulk and Suzuki, 1980]
Motivation : Generation of Type II / III Bursts Fast stream Langmuir wave EM radiation Solar wind? Bump-on-tail instability [e.g., Melrose, 1980] Issue Linear or Nonlinear Processes? 2 nd Harmonic Langmuir (2) Langmuir Fundamental Langmuir (1) Ion Sound Fundamental [e.g., Cairns, 1986] Classical theory : Outgoing EM wave Left-handed (o) circularly polarized mode Here: Can LMC yield both Right-hand (x) and Left-hand mode?
II. Aims and Model Demonstrate that Langmuir/z-mode waves are converted into x-mode radia tion by LMC (as well as o-mode radiation) Calculate the mode conversion efficiency for typical solar wind parameter s. Present applications to solar radio bursts in the solar wind and corona Answer the questions: Can Langmuir waves be converted into x-mode by LMC? How much energy is transferred to the o and x modes? Can x-mode be generated and propagate out from solar wind a nd coronal sources? HOW? Solve the full wave field equations using a numerical flui d simulation model.
Numerical Model Linearized Equations r A = A( z, t)exp( ik X X ) K Y = 0 K X = constant xˆ k! N 0 zˆ
Numerical Model v th! = 0. 1c Langmuir wave = & $ % f p f #! " 2!N 0 x cutoff Langmuir / z o x x o Langmuir / z o cutoff Mode Conversion z cutoff
A. 1. Can LMC convert Langmuir waves into the x mode? Spatial Dependence of the electric fields Polarization of outgoing EM waves Spatial Dependence : B 0 = 0 (K Y = 0) Mode conversion Point ES + EM E x EM E y Strong ES E z Z Inhomogeneous homogeneous EM + ES
III. :Can LMC of Langmuir waves yield x and o mode? Spatial Dependence superposition for weak B 0 : K Y = 0 Weak B 0 Strong B 0 ES + EM EM Strong ES homogeneous Z Inhomogeneous Z [Kim et al., PRL, 2007] TWO EM + ES EM + ES
Polarization : Hodograms B 0 increases R R L L Linear Elliptical Circular E y /E x b/a Ω (from dielectric tensor) polarization o x result 0.31 0.948 0.948 0.00177 Linear 0.76 0.948 0.948 0.104 Elliptical R 1.55 0.949 0.947 0.835 Elliptical L Mixture of o- and x-modes 2.60 0.951-0.951 Left o-mode only a and b are major and minor axes of the polarization vector
Conversion efficiency energy into o and x-modes? 1. 2. 2/3 2 q = ( k0l) K", k 0! = ( k 0 L) 1/3 [Willes and Cairns, 2001; Mjølhus, 1983] = # / c, Y = # /#, # = eb / m, v th! = 0. 1c c c Y 0 e
Mode conversion efficiency : N = N(z) N ) & B = B z total x o Ω & B 0 o!,! : decrease & oscillate! x :decrease Ω & B 0 0 o x x cutoff Langmuir / z x o Langmuir / z o cutoff Mode Conversion z cutoff Interference between two z-modes Phase difference B # = " +! K A L Z Z dz
IV. General Case: : N = N(z) N ) & B=( =(B x, 0, B z ) for! total!n 0 for Ω = 0.7 k B 0 Both x and o mode in general case! o mode x mode
General (oblique) case: Both x and o mode for all α for suitable θ and Ω. 2 radio windows (e.g., Budden)? No: 1, slowly varying with α. LMC favoured for situations with large range of α. for this Ω. Range of θ for radio window depends on. Magnetospheric continuum radiation: Both o and x plausible. Large range of α ~ 45 90 º near magnetic equator.
V. Application for typical solar and IP parameters r pc = < > Solar wind Corona Expect both x and o modes for typical solar and interplanetary parameters.
VI. Laboratory Tests Beam-plasma experiment with density gradient: o- and x-mode radiation near f p? Tune magnetic field strength and density scale lengths to change Ω and so switch x-mode on and off. Change magnetic field orientation to test α dependence. Inject o-mode into a plasma (tokamak?) and test for x-mode produced by LMC: LMC into Langmuir/z waves and second LMC into x/o. Vary injection angle and B so as to vary α and Ω. (Ionosphere has Ω too large to have x mode. Only o.)
VII. Conclusions Numerically simulated LMC between Langmuir/z and EM wa ves in warm magnetized plasmas. [Kim et al., PRL, 2007] First time: x-mode can be produced by linear mode conversio n from Langmuir waves (as can the o mode) for low enough Ω and both parallel and oblique density irregularities. Mode conversion efficiency is less than 8% (for v th! = 0. 1c ). In the solar wind and corona, LMC should produce the x-mod e, as well as the o mode. General case: 1 continuous radio window, not 2.
Conclusion Ours Previous x o o x Langmuir Langmuir Depolarization o Electron Density