: The coordinate origin dependence of the phase distribution. Fig B(t) OBS OBS PRS PCS

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1 MHD, Abstract The earth s foreshoc is a region where particularly large amplitude MHD waves are commonly observed. They ehibit various waveforms, suggesting that nonlinear interaction between the waves is in progress. We introduce a method to quantitatively evaluate the strength of phase coherence among the waves from a given time series data. Besides we develop our method by applying wavelet filtering technique. From the analysis it was found that, although the turbulence is consisted of waves with a wide range of plasma rest frame frequnecies, only those frequencies lower than the ion gyrofrequency are responsible for generating the phase coherence. Shoclets SLAMS MHD MHD δb/b / shoclets SLAMS Short Large Amplitude Magnetic Structures [5][8] [4][9] MHD MHD IMF MHD MHD δb/b << [] [7] [] GEOTAIL Random Phase Approimation

2 . B - - Geotail 968 :44:5.-48:.8 Power. Observed data (OBS) Phase mush b 4 Phase Randomized Surrogate (PRS) B - Power Phase Phase Correlated Surrogate (PCS) B Power. Phase. φ() φ() : The coordinate origin dependence of the phase distribution. : Maing of the surrogate data. From the original time series (OBS, top row), the phase randomized surrogate (PRS, middle row) and the phase correlated surrogate (PCS, bottom row) are generated by shuffling and unifying the wave phase, respectively. Fig. OBS OBS PRS.. B(t) OBS L(τ) = B(t + τ) B(t) () τ OBS PRS PCS [6] Phase randomized surrogate PRS Phase correlated C φ (τ) = L P RS(τ) L OBS (τ) L P RS (τ) L P CS (τ) surrogate PCS Fig. Fig. GEOTAIL [] [7] [] ()

3 GEOTAIL GEOTAIL 6 [Hz] t=.65 [sec] Dirac : Magnetic field data observed by GEOTAIL satellite near the bow shoc region (top) and its wavelet amplitude (bottom). The magnetic field data was sampled every.65 [sec]. In bottom panel the vertical line represents the wavelet scale inde and the bottom line shows time translation. f(t) W f (a, b) = a f(t)ψ ( t b )dt () a a b * m m c a a = a m/4 m c m=,...,4 a = t m c [] ψ(t) Morlet ψ(t) = π /4 e iπft e t / (4) a ω = π/a Fig. 4 Fig. C φ C φ W f (a, b) a m C φ C φ τ = C φ Fig. GEOTAIL C φ m c = 9 shoclets t= Fig. m c = 9 GEOTAIL y C φ V SW = 5[m/s]

4 Cφ (τ=) Ωi 5 mc 5.Ωi 4: C φ evaluated for high-pass filterd ( ) and lowpass filterd data ( ). The vertical line represents the phase coherence inde estimated at τ = and the bottom line shows threshold wavelet scale inde. In the figure Ω i is the ion cyclotron frequency calcurated by using the observed data. 9 < m c < 7 n 4[/cc] B = 8[nT ] Alfven V A = 87.[m/s] shoclets Ω i =.8[rad/sec] ω W f (a, b) I(a, b) = W f (a, b) < W f (a, b) > b (7) I(a,b) W f (a, b) b I(a, b) > Fig. 5 Fig. LIM LIM shoclets Fig. 4 ω = ω + V SW (5) Alfven whistler ω = V A ω ω = ω + V SW V A ω 7ω (6) 5: The local intermittency measure evaluated for Ω i 7Ω i = 5.6[rad/sec] the data shown in Fig.. m c 4 C φ. C φ.ω i m c 7. B = (B, B y, B z ) 9[deg] θ 9[deg] local intermittency measure LIM [] LIM Farge[99] 8[deg] φ 8[deg] [] (φ θ) 4

5 p = (cos φ cos θ, sin φ cos θ, sin θ) T C φ shoclets 4 GEOTAIL. C φ.5..ω i < ω < Ω i. LIM C φ shoclets 6: Spatial distribution in ( φ - θ ) plane of some statistical properties observed upstream the bow shoc. From top to bottom, the average magnetic field < B (φ, θ) >, the fluctuation amplitude σ and the phase coherence inde C φ are represented. B = B p (8) B (φ, θ) Fig. 6 < B (φ, θ) > IMF / < B (φ, θ) >= B σ = < (B < B >) > / < B > (9) IMF 4. C φ MHD.Ω i < ω < Ω i ω > Ω i C φ C φ SLAMS shoclets shoclets Alfven Krashosel sih 5

6 [] Dudo de Wit T. and V. V. Krashosel sih, Non-Gaussian statistics in space plasma turbulence: fractal properties and pitfalls, Nonlinear Processes in Geophysics,, 6, 996. [] Farge M., Wavelet transforms and their application to turbulence, Ann. Rev. Fluid Mech., 4, 95, 99. [] Hada T., D. Koga and E. Yamamoto, Phase coherence of MHD waves in the solar wind, Space Sci. Rev., in press. [4] Hoppe M. M., C. T. Russell, L. A. Fran, T. E. Eastman and E. W. Greenstadt, Upstream hydromagnetic-waves and their association with bacstreaming ion populations - ISEE- and ISEE- observations, J. Geophys. Res., 86, 447, 98. [5] Kir J. G., P. Duffy and Y. A. Gallant, Stochastic particle acceleration at shocs in the presence of braided magnetic fields, Astron. Astrophys., 4,, 996. [6] Kantz H. and T. Schreiber, Nonlinear Time Series Analysis, Cambridge University Press, 997. [7] Koga D. and T. Hada, Phase coherence of foreshoc MHD waves: wavelet analysis, Space Sci. Rev., in press. [8] Kuramitsu Y. and T. Hada, Acceleration of charged particles by large amplitude MHD waves: effect of wave spatial correlation, Geophys. Res. Lett., 7, 69,. [9] Schwartz, S. J. and Burgess, D., Quasi-parallel shocs: a patchwor of three-dimensional structures, Geophys. Res. Lett., 8, 7, 99. [] Torrence C. and G. P. Compo, A Practical Guide to Wavelet Analysis, Bull. Amer. Meteor. Soc., 79, 6, 998. [], Geotail,,. 6