Simulation study on the nonlinear EMIC waves

Transcription

1 SH21B-2210 Simulation study on the nonlinear EMIC waves Kicheol Rha 1*, Chang-Mo Ryu 1 and Peter H Yoon 2 * lancelot@postech.ac.kr 1 Department of Physics, Pohang University of Science and Technology, Korea 2 IPST, University of Maryland, USA

2 2/40 Abstract Nonlinear evolution of EMIC waves accompanying particle heating and the electromagnetic fluctuation spectrum associated with the drift Alfv en-cyclotron (or EMIC) instability related to a current disruption event is investigated by means of PIC simulation. It is shown that parametric decay processes lead to an inverse cascade of EMIC waves and the generation of ion-acoustic waves by decay instability. It is found that the nonlinear decay processes accompany small perpendicular heating and parallel cooling of the protons, and a pronounced parallel heating of the electrons. The simulation shows that the drift Alfv encyclotron instabilities are excited in two frequency regimes, a relatively low frequency mode propagating in a quasi-perpendicular direction while the second high-frequency branch propagating in a predominantly parallel propagation direction, consistent with observations as well as with a recent theory.

3 Solar wind electron distribution Electron distribution [Yin et al. JGR (1998)] 1 a a a 1 + erf λ(v - v F (v) = e + 2 p1-2 p2 2 p1 n (1 + v ) (1 + v ) (1 + v ) 2 1D reduced Lorentzian distribution 3/40 cut)

4 4/40 Beam-plasma instability [Vedenov et al. NF (1961), Drummond et al. NFS (1962)]

5 Weak turbulence equations Wave (ω k,k) Particle Wave (ω k, ) 5/40 [Yoon et al. POP (2005, 2006), APJ (2012)]

6 Weak turbulence equations spontaneous thermal effects 3 ~ g = 1/( nλ D ) 6/40 [Yoon et al. POP (2005, 2006), APJ (2012)]

7 Simulation results As temperature ratio is increased, the tail formation in the backward and forward is slightly reduced over the same time period. 7/40 Electron velocity distribution functions for six different cases

8 Simulation results Langmuir turbulence in between condensate and primary Langmuir mode is generated. Condensation mode with high phase speed accelerates the suprathermal tail via Landau damping. 8/40 Time evolution of the Langmuir wave intensity for six different cases

9 9/40 Simulation results The small T i /T e is necessary for the existence of ion-sound turbulence; otherwise, the ion-sound mode suffers damping. The presence of an ion-sound wave is deemed important since it mediates the three-wave decay process, which involves two Langmuir waves and an ion-sound wave. Time evolution of the ion-sound wave intensity for six different cases

10 10/40 Substorm Disturbance of the Earth s magnetosphere release its energy into the charged particles so that intense and widespread aurora can be observed in the polar regions.

11 11/40 Observation Fourier spectrograms of magnetic field [Usanova et al. GRL (2011)] Wave properties as observed in the spacecraft frame of reference [Hoppe et al. JGR (1983)]

12 12/40 EMIC instabilities ci ω 1 Ω ci ω 0.1 < < 0.5 Ω B z component and its wavelet transform [Lui et al., JGR (2008)] u = 0.05, β = 1, β = 1 The instabilities in two distinct domains in the q-space. [Mok et al., JGR (2010)] EMIC instabilities are associated with substorm onset

13 13/40 Simulation results These waves are characterized by relatively high wave number kv A /Ω i ~ 1 and frequency ω/ω i ~ 0.6. However, as time progresses, the wave intensity associated with these waves show a gradual and steady decrease. Time evolution of EMIC waves for quasi-parallel propagation (θ = 5 )

14 14/40 Simulation results The wave spectra for quasiperpendicular propagation are initially characterized by a broad range of wave numbers, 0.7 < kv A /Ω i < 1.5, and frequency, ω/ω i ~ 0.1 to ω/ω i ~ Time evolution of EMIC waves for quasi-perpendicular propagation (θ = 80 ) As time progresses the wave power decreases, as in case of the quasiparallel mode. However, a careful examination reveals that the peak wave intensity has undergone a slight shift in frequency to lower band and that the wavelength also shifts toward longer bandwidth.

15 15/40 Simulation results ω 1 Ω ci ω 0.1 < < 0.5 Ω ci u = 0.05, β = 1, β = 1 The power spectrum of (a) δb (t, k) associated with quasi-parallel EMIC waves, and (b) δb (t, k) associated with quasiperpendicular EMIC waves The observational data & theoretical calculation

16 16/40 Wave launching The initial magnetic field fluctuation The initial electric field fluctuation associated with the above initial magnetic field fluctuation is also given by Faraday s law.

17 Simulation results The wave spectra for both polarizations, which are initially characterized by an average wave number k x v A /Ω i 0.8, have undergone decay processes. The ion density fluctuations were not initially imposed, but they are generated as a result 17/40 Time evolution of EMIC and fast-magnetosonic waves ((a) and (b)), and ion density fluctuation ((c) and (d)) of the parametric decay process.

18 18/40 Simulation results After 25Ω i 1, or so, the electromagnetic modes split off with the Alfv en-cyclotron wave mode shifting to lower k x mode while the fast-magnetosonic wave mode changes relatively little in wave numbers. The power spectrum of (a) δb (k x, t) associated with EMIC and fast-magnetosonic waves and (b) δn i (k x, t) associated with ion-acoustic wave. The density fluctuation δn i (k x, t) did not exist for early times, but is generated as a result of parametric decay processes.

19 19/40 Simulation results The change in β i corresponds to an increase, while a similar change in β i leads to a decrease by damping of the left-hand circularly polarized Alfv encyclotron waves. The electrons are continuously heated in the parallel direction, Evolutions of (a) ion betas and (b) electron betas. even beyond the initial increase, as a result of Landau damping of the ion-acoustic waves.

20 20/40 Conclusion 1. Langmuir turbulence generated by beam-plasma instability describes the formation of energetic tail distribution. 2. The ratios of proton to electron temperatures, T i /T e, play a crucial role in determining the shape of tail formation. 3. The EMIC instability can exist as a two frequency structure, namely, a high-frequency (ω ~ Ω i ) quasi-parallel mode and a low-frequency (ω < Ω i ) quasi-perpendicular mode. 4. Particle heating occurs via parametric decay process of EMIC waves. 5. Various instabilities can influence the particle acceleration and heating in the astronomy and space physics.

21 SM31B-2332 A study of solitary wave trains generated by injection of a blob into plasmas Cheongrim Choi 1, Kicheol Rha 2*, Chang-Mo Ryu 2, Eun Jin Choi 1, Kyoung W. Min 1, Ensang Lee 3 and George K. Parks 4 * lancelot@postech.ac.kr 1 Department of Physics, Korea Advanced Institute of Science and Technology, Korea 2 Department of Physics, Pohang University of Science and Technology, Korea 3 School of Space Research, Kyung Hee University, Korea 4 Space Sciences Laboratory, University of California, Berkeley, USA

22 22/40 Abstract In this study, using a one-dimensional electrostatic particle-in-cell (PIC) simulation we investigated the generation of consecutive electrostatic solitary waves (ESWs) due to injection of a plasma blob. For a given Gaussian perturbation, strong charge separation occurs at the leading edge of the blob due to the mass difference of ions and electrons, resulting in a large increase of the electrostatic potential. The electrons are then trapped in the potential with significant heating. Ions are reflected backward and forward at the boundaries of the initial perturbation, forming fast, cold ion beams. The forward propagating ion beam and hot electrons escaping from the potential produce successive ESWs. Furthermore, the backward reflected ion beam forms ion holes by ion two-stream instability. This suggests that a localized perturbation of plasmas can be a source of consecutive ESWs observed in space.

23 23/40 Solitary waves Observation Characteristic features Waveforms of parallel electric field E [Omura et al., JGR (1999)] Solitary wave structures [Schamel, PHYSICS REPORTS (1986)]

24 24/40 Double layers Observation Characteristic features Electron energy flux and E of an auroral DL [Ergun et al., PRL (2009)] Double layer structures [Schamel, PHYSICS REPORTS (1986)]

25 25/40 Pseudo-potential method n t i + x ( n v ) = 0 vi v ϕ t x x i + vi + = 2 ϕ = n + n n x 2 e nth i i i 0 ; Continuity Equation ; Momentum Equation ; Poisson Equation ( ) 0 0 n = εexp ϕ, ε n / n e e i

26 26/40 ϕ 0, v 0, and n 1 at ξ ± i ni M nv i i = ξ ξ vi v ϕ M ξ ξ ξ Pseudo-potential method Using the infinite boundary condition i vi = i ( ) 0 2 d ϕ 2 = ε e + δ exp( ϕ )( 1 βϕ + βϕ ) dξ LHS : RHS : ( ϕ ) 0 n i 1 = 1 v / M i 1 2 Mvi vi ϕ = 0 2 ϕ 2 2 dv dϕ 2 d d d 1 d 2 d d d 2 d d ϕ dξ 2 ϕ ϕ ϕ = ξ ξ ξ ξ dϕ dv dv = dξ dϕ dξ ϕ / M V ( ϕ ) 2 1 n i = 2 1 dϕ + = 0 2 dξ 1 2 ϕ / M ; The energy integral form

27 27/40 Pseudo-potential method 2 ϕ 2 ( ) ( ) ( ) ϕ V ϕ = δ 3β + 3βϕ βϕ e + M ϕ / M + 1 e + 3 δβ. Initial condition : ( ) d ( ) ϕ 0 = 0, ϕ 0 / dξ = d d 2ϕ 2 ξ = dv d ( ϕ ) ϕ M =1.579 M =1.57 Numerical solution

28 28/40 Simulation model The plasma chamber is separated at distance 64 by the grid potential g. Initially, the plasma is contained in the source Schematic of the injected ion-beam plasma device chamber; the opposite side is the target chamber.

29 29/40 Dispersion relations Continuity equation Momentum equation Poisson equation The dispersion relation for the ion density in the simulation

30 Simulation results (a) After time tω pi = 290, the grid bias is sufficiently reduced for the ions to overcome the potential barrier, and the ions are ejected into the target chamber as an ion-beam. (b) The velocities of S 1, S 2 and S 3 lie in the range of 1 < V < 1.59, which is the wellknown criterion for the ion-acoustic solitary wave velocity in a plasma. (a) Ion density profile and (b) ion density contour. The wavelets for (c) grid 180 and (d) /40 (c) (d) As the ion-acoustic waves disappear, a solitary wave appears with a higher central frequency.

31 31/40 Simulation results The ion phase velocity is shown to decrease sharply when a solitary wave occurs, which suggests that the ion acoustic solitary wave is generated via inverse Landau damping. It can be easily seen that the ion kinetic energy converts into Ion phase-space diagrams that of the ion-acoustic wave.

32 32/40 Simulation model The above velocity perturbation was added to the Maxwellian distributions, which were realized in the simulations by the acceptance-rejection sampling method. Simulation setup

33 33/40 Simulation results While the blob was introduced as a charge-neutral beam initially, charge separation soon occurs between the electrons and the ions due to the difference in their thermal velocities; this leads to the development of a bipolar electric field, which, in The initial evolution of the perturbations turn, accelerates the electrons in both directions.

34 34/40 Simulation results As this bipolar electric field becomes large, the electrons are more strongly accelerated and pushed into the center of the bipolar electric field. On the other hand, the ions are reflected or ejected outward, forming new beams propagating forward and backward from the original blob. The further development of the system

35 35/40 Simulation results The phase velocity of electron & the electric field The phase velocity of ion & the electric field

36 36/40 Simulation results The ion beam produces (a) The power spectrum of the electrostatic potential & (b) the imaginary part of the solution of the dispersion relation instability and modifies an ionacoustic wave mode slightly in the region k de > 0.

37 Simulation results 37/40 (a) The electron phase space distribution, (b) (c) the electron velocity distribution functions, (d) the wavelet analysis (a) The ion phase space distribution, (b) the electric field, (c) the ion velocity distribution function, and (d) the wavelet analysis.

38 38/40 Simulation model Nonthermal electron distribution function [Cairns et al., GRL (1995)]

39 39/40 Simulation results The number density, electric field & potential, electron / ion phase-space diagrams. The electric potential

40 40/40 Conclusion 1. The solitary waves can be excited by making use of various methods such as modulating the grid voltage in a double plasma model and injection of a blob into plasmas. 2. Decreasing grid modulation as the initial perturbation, a train of stable solitary waves is formed due to the inverse Landau damping process of ion beams. 3. The electron holes corresponding to solitary waves are formed by beam instabilities as trapped electrons are released from the initial Gaussian perturbation.