New Features of Electron Phase Space Holes Observed by the THEMIS Mission

L. Andersson1, R. E. Ergun1,2, J. Tao1,2, A. Roux3, O. LeContel3, V. Angelopoulos4, J. Bonnell5, J. P. McFadden5, D. E. Larson5, S. Eriksson2, T. Johansson2, C. M. Cully6, D. N. Newman7, M. V. Goldman7, K.-H. Glassmeier8, and W. Baumjohann9 1Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado 80309, USA 2Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, Colorado 80309, USA 3Centre d’étude des Environnements Terrestre et Planétaires, Velizy, France 4Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90055, USA 5Space Sciences Laboratory, University of California, Berkeley, California, 94720, USA 6Swedish Institute of Space Physics, Uppsala, Sweden 7Center for Integrated Plasma Studies, University of Colorado, Boulder, Colorado 80309, USA 8TUBS, Braunschweig, D-38106, Germany 9Space Research Institute, Austrian Academy of Sciences, A-8042 Graz, Austria

The observational characteristics of EHs have been reported in a number of articles [e.g. 23,[7][8].They are detected as bipolar electric field signals (δE || ) parallel to B o [4][5][6].The parallel scale sizes (L || , defined here as the distance between peaks in δE || ) are most often several electron Debye lengths (λ D ) and the speeds (v EH ) are near to, but often less than, the electron thermal speed (v e ).
The perpendicular scale sizes (L ⊥ ) is comparable to L || in the low-altitude auroral region [23], whereas it has been reported that L ⊥ >> L || in most other space environments [7,8].EHs are most often weak (eΦ/k B T e << 1, where Φ is the center potential, e is the electron charge, and T e is the electron temperature).THEMIS observations largely support these earlier results.
Space-based measurements record a profile in time, so the derivation of Φ and L || depends on the speed of the EH.The statistical characteristics described above relate to "slow-moving" EHs.
By "slow-moving", we mean that the speeds of the EHs are derived from the time delay between the signals of two spatially separated electric field probes [e.g.7,23].Most instruments are limited to measuring v EH < ~1000 km/s with this technique.
In this article, we present the first 3-D observations of magnetic field perturbations caused by EHs including the detection of a δB || signal.We show that the perpendicular magnetic perturbation (δB ⊥ ) is primarily caused by the motion of a quasi-electrostatic EH.In other words, δB ⊥ is consistent with the Lorentz transformation of δE ⊥ [5,23].If EHs are quasi-electrostatic in their rest frame (see later discussion on the "rest" frame), δB ⊥ and δE ⊥ can be used to accurately determine their speed, particularly if they are "fast-moving" (>1000 km/s) and, subsequently, accurately derive Φ and L || .We also show that EHs with a detectable δB || have quite different characteristics than reported by earlier observations.They have large electric field amplitudes, δE ~ O(100 mV/m), high speeds (v EH > v e ), large parallel sizes (L || > 10 λ D ), moderate to strong center potentials (eΦ/k B T e ~ 0.5), and elongated shapes (L || > L ⊥ ).We suggest that δB || arises from the electron motion in the EH and that .These observations have a number of similarities to laboratory observations of elongated, high-speed holes associated with magnetic reconnection [22].
The observations are from the THEMIS mission [24], which has five identical satellites in highly eccentric orbits at low inclination with apogees that range from 10 R E to 30 R E .The satellites carry electron and ion analyzers [25], a three-axis electric field instrument (DC -8 kHz) [26], a DC magnetometer [27], and a search coil magnetometer [28].The δE || signal (Fig. 2a) shows a series of bipolar structures, a defining signature of EHs [4][5][6].
All of the EHs have a positive then negative polarity indicating that they are traveling in the same direction and, consequently, are likely to come from the same source.The perpendicular electric field signals (Fig. 2c-e  By modeling the hole as cylindrically symmetric with a Gaussian shape: δB || at the center of the EH can be derived by integrating the Biot-Savart equation: ------------------g where g(L || , L ⊥ ) < 1, is a dimensionless geometric factor.
Fig. 4  Since the δB || exists in all frames, the EHs cannot be entirely electrostatic.If an EH is cylindrically symmetric, then a radial magnetic field must be present, even in the "rest" frame ( since ).The rest frame is best defined as the frame in which the azimuthal magnetic field vanishes.δB r is due to J φ , so it should be detected by a spacecraft as bipolar signal (the radial magnetic field of a current ring has opposite signs for z>o and z<0).Careful examination of the measured magnetic field signals in Fig. 2 show that they are predominantly unipolar, so δB r << δB || .δB r is expected to be small if L || > L ⊥ .A small δB r is consistent with the elongated shape.
In conclusion, we have presented observations of the perturbation magnetic field and the first report of δB || associated electron phase-space holes.These EHs differ from earlier observations in that they have high speeds (v EH > v e ), large parallel sizes (L || > 10 λ D ), significant center potentials (eΦ/k B T e ~ 1), and elongated shapes (L || > L ⊥ ).In particular, these EHs have many characteristics that are similar to those generated by magnetic reconnection in a laboratory experiment [22].EHs also are known to be generated by double layers [18][19][20], so observations of EHs are an indicator of nonlinear, kinetic behavior in the active plasma sheet.

Fig. 1
Fig. 1 presents five minutes of observations from THEMIS Probe A at ~10 R E from Earth's center.The top panel (Fig. 1a) displays a spectrogram of the electron differential energy flux as a

Fig. 2
Fig. 2 presents 0.2 seconds of high time resolution δE and δB signals (filtered from ~1 Hz to δB′ lection].The mean velocity of the EHs is ~1x10 8 m/s.This high speed implies that these EHs are traveling faster than the thermal velocity (v e ~ 4x10 7 m/s).Using the derived velocity, the size of the EHs along B o is displayed in Fig.3b.L || is roughly 30 λ D , where λ D ~ 3.0 km (derived from a 3 s average electron distribution).The mean value of Φ (Fig.3c) is ~3 keV.Within uncertainties, T e ~ 8 keV (parallel to B o ).We cannot determine the radial offset of the measurements (distance perpendicular to B o from the center of the EH), so Φ represents a lower bound.These EH observations have moderate potentials (eΦ/k B T e ~ 0.5) and are unusual in that v EH > v e , and L || is tens of λ D .Similar results were reported from laboratory experiments on magnetic reconnection[22].The presence of the δB || signal supports the above conclusions.This signal can be explained from the electron currents generated by the perpendicular electric field signal.In the spacecraft frame, the duration of the EHs (~1.2 ms) is about two times the electron gyro-period (~0.66 ms), so an electron drift can be established whereas the ion motion is negligible.The resulting perpendicular current loop is around the center of the EH with J φ ≅ -en e δE r /|B o |.Here, δE r represents the radial perpendicular electric field perturbation, and n e is the ambient electron density.This current will generate a magnetic field in the same direction as B o in the center of the EH, hence δB || is always positive.The amplitude of δB || depends on δE r and the shape of the EH.

FIG. 1 .
FIG. 1.(a) Electron differential energy flux as a function of energy (vertical axis) and time (horizontal axis).The black trace is T e .(b) Ion differential energy flux.(c) Magnetic field in GSM coordinates at 128 samples/s.The black trace is |B o |.(d) E o in GSM coordinates at 128 samples/s.The black trace is E o|| .(e) E o xB o /|B o | 2 low-pass filtered to 1 Hz in GSM coordinates.The vertical dashed line marks the period of the EHs in Fig. 2. FIG. 2. (a) δE || (1 Hz -3.3 kHz) at 8192 samples/s during the period marked on Fig. 1.(b) δB || at (1 Hz -3.3 kHz) at 8192 samples/s.(c) δE X is from the long wire antennas and accurate to + 2 mV/m.(d) δB Y is orthogonal to δE X .One can see that δE X and δB Y signals of EHs are well correlated.(e)δE Y (+ 20 mV/m) is derived from a combination of all electric field dipole antennas including the short (7 m) dipole along the spacecraft spin axis[26].(f) δB X .

Figure 4 δB
Figure 4 ) have a corresponding unipolar perturbation, again, typical of EHs.Some of the EHs are such that δE X or δE Y are greater than δE || , a sufficient but not necessary condition for L || > L ⊥ (since the spacecraft may pass through the center of the EH rather than the edge, a small perpendicular signal does not, by itself, reveal the relation between L || and L ⊥ ).Almost all of the EHs have a corresponding positive unipolar perturbation in δB || (Fig.2b).The perpendicular δE and δB signals (Figs.2c-2f) are arranged in orthogonal pairs (δE X , Fig.2c, is orthogonal to δB Y , Fig.2d, etc.).δEX and δB Y are well correlated and δE Y and δB X have a nega-Most importantly, the data indicate that a quasi-electrostatic frame exists.In other words, there is a frame in which the perpendicular signals nearly vanish (are minimum).The velocity of this frame, and presumably that of the EH, can be derived from δE X and δB Y , the more accurate of the orthogonal pairs.Fig.3adisplays the derived velocity (c 2 δB Y /δE X ) of 67 EHs detected in a ~16 s "wave burst" tive correlation, albeit somewhat weaker.These δE and δB signals are consistent with a Lorentz transformation of a moving quasi-electrostatic structure [30, changed to SI units]: In their rest frame, the perpendicular signals nearly vanish.With v EH parallel to B o , the perpendicular components in Equation (1) reduce to: period (11:14:41 UT to 11:14:57 UT on March 28, 2008) of high-time resolution (8192 samples/s) waveform that includes the data in Fig. 2 [see refs 24 and 26 for discussion on wave burst data col- presents δB || versus eΦμ o n e /B o for the 67 EHs measured in the 16 s wave burst period.We do not correct for radial offset ( ), so both δB || and Φ represent lower bounds.δB || and Φ do not have the same behavior as a function of radial offset, so the data exhibit significant scatter.There are, however, two important properties.The values of δB || are nearly equal to but always less than that of eΦμ o n e /B o consistent with g(L || , L ⊥ ) < 1 and, furthermore, δB || increases with increasing Φ.These data, along with the observation that δB || > 0, support our supposition that δB || results from electron currents.Thus the δB || signal is in consort with the large amplitudes, high speeds, moderate to strong potentials, and elongated shape of the EHs.