Bale, SD

Eastwood, JP

Phan, TD

Tjulin, A

Physical Review Letters

Spiral - Imperial College Digital Repository

Observations of Turbulence Generated by Magnetic ReconnectionJ. P. Eastwood,1, ∗ T. D. Phan,1 S. D. Bale,1, † and A. Tjulin21Space Sciences Laboratory, University of California at Berkeley, Berkeley CA 94720, USA2The Blackett Laboratory, Imperial College London,London SW7 2BW, United Kingdom(Dated: December 15, 2008)AbstractSpacecraft observations of turbulence within a magnetic reconnection (guide field ∼ 0) ion diffu-sion region are presented. In the inertial subrange, electric and magnetic fluctuations both followeda -5/3 power law; at higher frequencies, the spectral indices were -1 and -8/3 respectively. Thedispersion relation was found to be consistent with fast mode/whistler waves rather than kineticAlfvén/ion cyclotron waves. Lower hybrid waves, which could be enhanced by whistler modeconversion, were observed but the associated anomalous resistivity was not found to significantlymodify the reconnection rate.PACS numbers: 94.30.cp, 52.35.Vd, 94.30.ct∗Electronic address: eastwood@ssl.berkeley.edu†Also at Department of Physics, UC Berkeley.1Magnetic reconnection is a fundamental plasma process that enables reconfiguration ofmagnetic field topology, resulting in the transfer of energy from the magnetic field to theplasma particles themselves [1]. Except for electron-positron plasmas, the diffusion regionexhibits a characteristic two scale structure due to differential ion and electron motion [2].For symmetric inflow conditions, a quadrupole out-of-plane Hall magnetic field pattern isobserved, together with a symmetric Hall electric field pointing into the current sheet onboth sides [3], and it is thought that this Hall field plays a key role in fast reconnection [4].However, such simulations typically show that magnetic fluctuations in the ion diffusionregion are small, because they cannot describe instabilities that propagate out of the recon-nection plane. Recent laboratory experiments appear to show a positive correlation betweenthe reconnection rate and the magnitude of electro-magnetic fluctuations up to the lowerhybrid frequency [5], which casts doubt on the role Hall effects play in controlling the rateof fast reconnection. Using small hybrid simulations, it has been concluded that although aturbulent configuration can arise in 3D, this does not significantly enhance the reconnectionrate [6].To establish the role such fluctuations might play relative to Hall physics in controllingreconnection, we present new observations of the fluctuations within a diffusion region in theEarth’s magnetotail current sheet made by the four Cluster spacecraft [7] and identified bythe presence of Hall electric and magnetic field signatures. The spectral properties of boththe electric and magnetic field fluctuations in the diffusion region are presented for the firsttime, and used to determine the nature of the waves in the dissipation range, a key questionbeing whether energy is deposited in the form of kinetic Alfvén waves [8] or whistler waves[9].Fig. 1 shows observations of the magnetic field (at 0.045 s resolution) from the FGMexperiment [10] together with ion plasma observations (at 4 s resolution) from the CISexperiment [11]. The spacecraft were located at [−15.6, 9.2, 3.1] Re (Geocentric Solar Mag-netospheric coordinates) when they crossed the neutral sheet at 02:25UT. The data areshown in a current sheet coordinate system: the L direction points Earthward and con-tains the main magnetic field reversal, the N direction is normal to the plane of the neutralsheet, and [L, M, N ] is a right handed triple. Relative to the GSM coordinate system, L =(0.895,−0.441, 0.068), M = (0.445, 0.892,−0.072), N = (−0.029, 0.094, 0.994).The positive to negative reversal in BL shows that the Cluster spacecraft made a north-202:10:00 02:20:00 02:30:00 02:40:00050100T, MKTime UT [HH:MM:SS]−3000300v N−3000300v M−3000300v L km s −110−210−1n, cm−3−25025EyGSE mV/m−808BN, nT−15015BM, nT−20020BL, nT01530|B|, nT  2345101102103104E, eVCluster 2003−10−09keV/(cm2str s keV)FIG. 1: Cluster observations of the Earth’s magnetotail current sheet on 9 October, 2003. Datafrom the FGM, EFW and CIS experiments are shown. Data from Cluster 1 - 4 are shown in black,red, green and blue respectively. The spectrogram in the top panel is from Cluster 3. Moments ofthe ion plasma are only available on Cluster 1 and 3.south crossing of the magnetotail current sheet (in the direction of their orbital motion; theencounter is shown in Fig. 2). At ∼02:19UT, the spacecraft began to move closer to theneutral sheet, and encountered tailward (-vL) ion plasma flow, indicating that the X-linewas Earthward of Cluster. During this interval, the density and temperature were relativelyconstant and had values characteristic of the plasma sheet (ni ∼ 0.05 cm−3, Ti ∼ 50 MK).The spacecraft separation was ∼ 300 km, less than the characteristic ion inertial length(c/ωpi ∼ 1000 km for ni = 0.05 cm−3). On the scale of Fig. 1 the observations of the fourspacecraft are essentially identical.3FIG. 2: Cartoon showing the Cluster diffusion region encounter. The magnetic field is shown inblack; red arrows show the Hall electric field.Although on average BM ∼ 0, indicating little or no guide field, a clear pattern is seenin the perturbations to BM across the current sheet. When BL > 0, BM is mainly negative,whereas when BL < 0, BM is mainly positive. This is seen more clearly in the top panelof Fig.3 which shows the correlation between vL, BL and BM , measured at 4s resolution byCluster 1 and Cluster 3 (the spacecraft for which plasma data is available). In the case ofthe Hall magnetic field, one expects a quadrupole pattern where BM is negative in the topleft and bottom right quadrants, and positive in the other quadrants. The pattern of Hallfields is clearly consistent with that expected, but since the spacecraft encountered only thetailward jet, only half of the quadrupole pattern is observed.The Hall magnetic field signature should be accompanied by a Hall electric field signature,specifically EN,Hall should point into the current sheet on both sides where EHall = (J ×B/ne) ∼ E+v×B. The electric field is measured by the EFW experiment (at a maximumrate of 25 vectors s−1) [12]. EFW uses 4 sensors at the end of wire booms to measure thecomponents of the d.c. electric field in the spacecraft spin plane (∼ the Geocentric SolarEcliptic (GSE) x-y plane). The third component of the electric field (along the spin axis)can be reconstructed using B (assuming that E·B = 0 i.e. E// = 0 which is expected tobe valid everywhere except within the much smaller electron diffusion region), provided Bis not too weak and does not lie in the spin plane. EN,Hall is negative above the currentsheet (BL > 0) and positive below the current sheet (BL < 0), such that EN,Hall pointsinto the current sheet on both sides. The bottom panel of Fig. 3 shows the correlationbetween BL and EN,Hall measured by Cluster 4 (which provides the cleanest measurementof E); the Hall electric field pattern is readily apparent. These observations indicate thatthe spacecraft were located within the ion diffusion region. We now examine the smallerscale fluctuations in the electric and magnetic field.4−1000 0 1000−30−20−100102030vL, kms−1BL, nT2003−10−09  2:23UT −  2:27UT (C1, C3)2nT10nT−20 0 20−30−20−100102030BL,nTEN,Hall,mVm−12003−10−09  2:23UT −  2:27UT (C4)FIG. 3: (top) scatterplot of vL and BL observations made by C1 and C3 between 02:23UT and02:27UT. The color of the circles shows the sign of BM (black = positive BM , red = negative BM ).The size of the circle shows the magnitude of BM , in comparison to the blue reference circles.(bottom) scatterplot of EN,Hall and BL as observed by C4.Fig. 4 shows the power spectral density (PSD) of the magnetic and electric field measuredby Cluster 4 between 02:20 and 02:30UT, calculated using the multi-taper method [13].The PSD of EyGSE is shown - due to solar illumination effects, this is the best measuredcomponent of the electric field [12]. This direction is approximately perpendicular to theoutflow. Correspondingly, the PSD of BzGSE is also shown. This is the component of themagnetic field perpendicular to EyGSE and the outflow. Outside the jet, in the reconnectioninflow region, no significant wave power is observed in either the magnetic or the electricfield.Between 0.02 Hz and 0.2 Hz, both the electric and magnetic PSD follow similar powerlaws. Linear regression [14] shows that the spectral index in this frequency range is -5/3.Above 0.2 Hz (which corresponds to the local ion cyclotron frequency), the PSDs diverge;510−310−210−110010110210−810−610−410−2100102104Cluster 4, 2:20 − 2:30 (solid), 2:05 − 2:15 (dotted), 2003−10−09PSD, (mV/m)2 /Hz, nT2 /HzFrequency, Hz  BzEyFIG. 4: Power Spectral Density of the EyGSE component of the electric field (red) and the BzGSEcomponent of the magnetic field (black), outside (dashed lines) and inside (solid lines) the jet. Theyellow lines show linear fits to the data.the electric field follows a -1 power law, and the magnetic field follows a -8/3 power law.We have computed these linear regressions up to a frequency of 3Hz. Above this frequency,the magnetic field data begins to be affected by ‘roll off’, where filtering that occurs in theprocess of measuring the data causes the power to be underestimated at high frequencies.The electric field however displays a distinct enhancement between 3Hz and 8Hz (not seenin the inflow).The data can be used to determine the frequency as a function of the wave k-vector, andthus model the dispersion relation of the fluctuations. Using the four spacecraft magneticfield data in combination with the k-filtering technique [15], it is found that the fluctuationsare propagating along the outflow direction in the frequency range where the PSDs diverge.This direction is approximately along the reconnecting magnetic field; assuming parallelpropagation and using Faraday’s law, we find that:kx =ωscvphsc,x= 2πfsc × δBz(f)δEy(f)(1)where vphsc,x = ωsc/kx is the spacecraft frame phase speed and ωsc is the spacecraft framefrequency. The phase speed in the jet frame, vphjet,x, can be estimated by subtracting theaverage jet speed (vjet ∼ 300 kms−1) i.e. vphjet,x = vphsc,x − vjet. Consequently, since k is frame610−310−210−110010110−310−210−1100101k × VA / Ωpiω / ΩpiDispersion relation in plasma rest frame; 2003−10−09 2:20 − 2:30Hot two fluid model β = 1.00θkB = 0.00°FIG. 5: Dispersion relation derived from the data and model dispersion relations calculated usingthe hot two fluid approximation.independent the wave frequency in the jet frame can also be determined as ωjet = vphjet,x×kx.Fig. 5 shows how ωjet varies as a function of kx. Note that both parameters have beennormalized. At low frequencies, there is a linear relationship between ω and k, with the phasespeed corresponding to the local Alfvén speed (VA,local = 900kms−1). As ω approaches Ωpi,the proton gyrofrequency, the dispersion curve bends up, corresponding to an increasedphase speed, related to the divergence of the PSDs in Fig. 4 at the frequency where theions are demagnetizing. For comparison, the hot two fluid plasma dispersion relationship isshown [16]. Free variables in this model are the plasma beta and the angle of propagation.A plasma beta of unity was chosen to compare with the data, and we assume parallelpropagation. The red, blue and green lines correspond to the fast (whistler), intermediate(alfvén-ion cyclotron) and slow modes respectively. The data most closely correspond tothe whistler mode, although the observed phase speed is higher than the theoretical curve.This may be because the waves are not exactly parallel propagating at some or all of thefrequencies under consideration, and the hot two fluid plasma dispersion relations are derivedfor small amplitude waves in homogenous plasmas.We now consider the role these fluctuations may play in enhancing resistivity. Applying7an analysis similar to that of [5] to the magnetic fluctuations, we find that the associatedelectric field is ∼ 0.3mV m−1, an order of magnitude smaller than the observed reconnectionelectric field.The enhancement of only the electric field in the 3 - 8 Hz frequency range (Fig. 4), evenaccounting for the magnetic field roll off, indicates that these fluctuations are electrostaticin nature. This also corresponds to the enhanced fluctuations at around 02:27UT towardsthe edge of the diffusion region in Fig 1. The lower hybrid frequency fLH =√ωciωce/2π =4 Hz for B = 6 nT, and 6.5 Hz for B = 10 nT. Thus this enhancement is consistent withlower hybrid wave activity and its expected spatial localization [17–19].Previous studies [17, 20] have concluded that although LH waves can generate anomalousresistivity, they make no significant contribution to the reconnection rate because the LHDIis stabilized in the high plasma beta conditions at the center of the current sheet. Here,although it is possible that whistler waves may be scattering off plasma density variationsand converting into lower hybrid fluctuations [21–23], the anomalous resistivity associatedwith the lower hybrid waves is still found to be small; η ∼ 10−3Ωm [24]. Given a cross tailcurrent density of ∼ 10−8Am−2, this corresponds to an electric field of ∼ 0.01mV m−1, (< 1%of the reconnection electric field) meaning that any modification to the overall reconnectionrate is negligible.We have presented observations of the fluctuations within a magnetic reconnection iondiffusion region (with little or no guide field) in the Earth’s magnetotail. Turbulent cascadesin both the electric and magnetic field fluctuations are inferred from the power law scaling,and energy injected by the reconnection exhaust propagates through the turbulent cascadealong the fast mode/whistler branch, providing a new opportunity to study turbulent pro-cesses. Lower hybrid waves, perhaps enhanced by the whistler mode conversion, were alsoobserved. The associated anomalous resistivity from both sources was calculated to be small,and so we conclude that whilst dispersive waves may prove to be important in, for example,particle acceleration processes [25], they do not significantly modify the reconnection rateor the Hall physics in magnetotail reconnection.8AcknowledgmentsThis work was supported by NASA grant NNX07AF32G at UC Berkeley. For theircomments and discussions about the work we thank T. S. Horbury, C. C. Chaston and F.S. Mozer[1] V. M. Vasyliunas, Rev. Geophys. 13, 303 (1975).[2] B. U. O. Sonnerup, Magnetic Field Reconnection (North-Holland, Amsterdam, 1979), pp.47–108.[3] F. S. Mozer, S. D. Bale, and T. D. Phan, Phys. Rev. Lett. 89, 015002 (2002).[4] J. Birn, J. F. Drake, M. A. Shay, B. N. Rogers, R. E. Denton, M. Hesse, M. Kuznetsova, Z. W.Ma, A. Bhattacharjee, and A. Otto, J. Geophys. Res. 106, 3715 (2001).[5] H. Ji, S. Terry, M. Yamada, R. Kulsrud, A. Kuritsyn, and Y. Ren, Phys. Rev. Lett. 92, 115001(2004).[6] B. N. Rogers, J. F. Drake, and M. A. Shay, Geophys. Res. Lett. 27, 3157 (2000).[7] C. P. Escoubet, M. Fehringer, and M. L. Goldstein, Ann. Geophys. 19, 1197 (2001).[8] R. J. Leamon, C. W. Smith, N. F. Ness, and H. K. Wong, J. Geophys. Res. 104, 22331 (1999).[9] O. Stawicki, S. P. Gary, and H. Li, J. Geophys. Res. 106, 8273 (2001).[10] A. Balogh, C. M. Carr, M. H. Acuña, M. W. Dunlop, T. J. Beek, P. Brown, K.-H. Fornacon,E. Georgescu, K.-H. Glassmeier, J. Harris, et al., Ann. Geophys. 19, 1207 (2001).[11] H. Rème, C. Aoustin, J. M. Bosqued, I. Dandouras, B. Lavraud, J. A. Sauvaud, A. Barthe,J. Bouyssou, T. Camus, O. Coeur-Joly, et al., Ann. Geophys. 19, 1303 (2001).[12] G. Gustafsson, M. André, T. Carozzi, A. I. Eriksson, C. G. Fälthammar, R. Grard, G. Holm-gren, J. A. Holtet, N. Ivchenko, T. Karlsson, et al., Ann. Geophys. 19, 1219 (2001).[13] D. B. Percival and A. T. Walden, Spectral Analysis for Physical Applications (CambridgeUniversity Press, Cambridge, 1993).[14] J. L. Devore, Probability and Statistics for Engineering and the Sciences (Duxbury, PacificGrove, CA, 2000).[15] J.-L. Pinçon and U. Motshmann, Analysis Methods for Multi-Spacecraft Data (InternationalSpace Science Institute, Bern, Ch, 1998), chap. 3, pp. 65–78.9[16] V. Formisano and C. F. Kennel, J. Plasma Phys. 3, 55 (1969).[17] S. D. Bale, F. S. Mozer, and T. D. Phan, Geophys. Res. Lett. 29(24), 2180,doi:10.1029/2002GL016113 (2002).[18] P. Petkaki, M. P. Freeman, and A. P. Walsh, Geophys. Res. Lett. 33, L16105,doi:10.1029/2006GL027066 (2006).[19] T. A. Carter, H. Ji, F. Trintchouk, M. Yamada, and R. M. Kulsrud, Phys. Rev. Lett. 88,015001 (2002).[20] R. C. Davidson, N. T. Gladd, C. S. Wu, and J. D. Huba, Phys. Plasmas 20, 301 (1977).[21] T. F. Bell and H. D. Ngo, J. Geophys. Res. 95, 149 (1990).[22] J. F. Bamber, W. Gekelman, and J. E. Maggs, Phys. Rev. Lett. 73, 2990 (1994).[23] T. F. Bell, U. S. Inan, M. Platino, J. S. Pickett, P. A. Kossey, and E. J. Kennedy, Geophys.Res. Lett. 31, L06811, doi:10.1029/2003GL018855 (2004).[24] F. V. Coroniti, Space Sci. Rev. 42, 399 (1985).[25] R. Selkowitz and E. G. Blackman, Month. Not. RAS 354, 870 (2004).10

Observations of Turbulence Generated by Magnetic Reconnection

http://spiral.imperial.ac.uk/bitstream/10044/1/19578/2/Physical%20Review%20Letters_102_3_2009.pdf

Observations of Turbulence Generated by Magnetic Reconnection

Abstract

Similar works

Full text

Available Versions

Spiral - Imperial College Digital Repository