# Magnetospheric Multiscale Satellite Observations of Parallel Electron Acceleration in Magnetic Field Reconnection by Fermi Reflection from Time Domain Structures

F. s. Mozer, O. a. Agapitov, A. Artemyev, J. l. Burch, R. e. Ergun, B. l. Giles, D. Mourenas, R. b. Torbert, T. d. Phan, I. Vasko

► To cite this version:

F. s. Mozer, O. a. Agapitov, A. Artemyev, J. l. Burch, R. e. Ergun, et al., Magnetospheric Multi-scale Satellite Observations of Parallel Electron Acceleration in Magnetic Field Reconnection by Fermi Reflection from Time Domain Structures. Physical Review Letters, 2016, 116 (14), 10.1103/Phys-RevLett.116.145101. insu-03342784

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# Magnetospheric Multiscale Satellite Observations of Parallel Electron Acceleration in Magnetic Field Reconnection by Fermi Reflection from Time Domain Structures

F. S. Mozer,$^{1,*}$ O. A. Agapitov,$^{1,2}$ A. Artemyev,$^{3,9}$ J. L. Burch,$^{4}$ R. E. Ergun,$^{5}$ B. L. Giles,$^{6}$ D. Mourenas,$^{7}$ R. B. Torbert,$^{8}$ T. D. Phan,$^{1}$ and I. Vasko$^{9}$

$^{1}$Space Sciences Laboratory, University of California, Berkeley, California 94720, USA

$^{2}$Taras Shevchenko National University of Kyiv, Glushkova Avenue, 4, Kyiv 01601, Ukraine

$^{3}$Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90002, USA

$^{4}$Southwest Research Institute, San Antonio, Texas 78238, USA

$^{5}$LASP, University of Colorado, Boulder, Colorado 80303, USA

$^{6}$NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA

$^{7}$LPC2 E/CNRS-University of Orleans, Orleans 45100, France

$^{8}$University of New Hampshire, Durham, New Hampshire 03824, USA

$^{9}$Space Research Institute, Russian Academy of Science, Moscow, Russia 117342

(Received 27 January 2016; published 5 April 2016)

The same time domain structures (TDS) have been observed on two Magnetospheric Multiscale Satellites near Earth's dayside magnetopause. These TDS, traveling away from the X line along the magnetic field at 4000 km/s, accelerated field-aligned ~5 eV electrons to ~200 eV by a single Fermi reflection of the electrons by these overtaking barriers. Additionally, the TDS contained both positive and negative potentials, so they were a mixture of electron holes and double layers. They evolve in ~10 km of space or 7 ms of time and their spatial scale size is 10–20 km, which is much larger than the electron gyroradius (<1 km) or the electron inertial length (4 km at the observation point, less nearer the X line).

DOI: 10.1103/PhysRevLett.116.145101

Electron acceleration in space plasmas (Earth's auroral zone, magnetosphere, and magnetopause and at other planets, the Sun, and other stars, etc.) is a persistent feature that is not well understood and that has been poorly measured. The Magnetospheric Multiscale Satellites (MMS) were launched on March 12, 2015 [1] to measure, with unprecedented spatiotemporal detail, local acceleration processes as part of a broader study of magnetic field reconnection [2]. MMS consists of four closely spaced satellites (~10 km) equipped with high time resolution (~30 ms) measurements of electron distribution functions and higher time resolution (0.1 ms) measurements of electric and magnetic fields. MMS has flown through reconnection events at the dayside magnetopause to observe time domain structures (TDS) that are reported in this Letter to accelerate electrons from ~5 to ~200 eV by a single Fermi interaction of the charged particles reflected by the potential barrier of the overtaking TDS. Such a fast and strong acceleration process (corresponding to a factor of ~40 energy increase) may be one important new component in the chain of phenomena associated with reconnection and leading to global plasma heating [3,4]. Although the absolute energy of the accelerated particles in this event is not very large, the acceleration factor of 40 is impressive and it could lead to greater accelerated energies for different plasma parameters. TDS are millisecond duration pulses of parallel electric field that move along the magnetic field line at thousands of kilometers per second. They may be electrostatic or electromagnetic, and

they represent electron holes, double layers, or more complicated solitary waves. Because their potential structures are more complicated than the simple potential of an ideal electron hole or an ideal double layer, they are grouped into the generic category of TDS in this and earlier papers. TDS of one type or another have been theoretically studied in more than 250 articles dating back more than 50 years [5,6], and they have been found in the magnetosphere along auroral zone magnetic field lines on the S3-3 satellite [7,8]. They were more thoroughly studied on later auroral missions [9,10], and they have been seen in the magnetotail [11–13], the plasma sheet [14,15], and the plasma sheet boundary layer [16], at shocks [17], at magnetic field reconnection sites [18–22], in the solar wind [17,23,24], and at Saturn [25]. Interest in their properties and their ability to accelerate electrons to hundreds of keV has been enhanced by observations of huge fluxes of TDS on the Van Allen Probes in Earth's radiation belts [26,27].

*Observations*.—Figure 1 presents 150 ms of high-pass-filtered parallel electric field measurements made on the four MMS spacecraft. MMS4 and MMS1 saw seven correlated spiky parallel electric fields (the TDS), while MMS2 may have seen the last three of these spikes and MMS3 saw nothing. The parallel and perpendicular separations of the spacecraft are given in Table I. MMS1 and MMS4, separated by 9.3 km perpendicular to the magnetic field, saw the TDS pairs, while the other spacecraft, separated by 22–27 km perpendicular to the magnetic
<figure><img src="image_3.png" /><figcaption>FIG. 1. The electric field component parallel to the background magnetic field measured on the four MMS spacecraft during a 150 ms interval.</figcaption></figure>

field, may not have. This suggests that the perpendicular scale size of these TDS was 10–20 km, i.e., much larger than the thermal electron gyroradius (<1 km) or the electron inertial length (4 km at the observation site, less nearer the X line).

The electric fields of the second matching pair of TDS observed on the two spacecraft are illustrated with higher time resolution in the top panel in Fig. 2, with those observed on MMS4 delayed by 7.9 ms. Because their parallel separation was 29.2 km and their temporal separation was 7.9 ms, their speed along the magnetic field line was about 4000 km/s. It is noted that the MMS4 and MMS1 fields differed, with the positive electric field in the earlier measurement (on MMS4) being about 3 times larger than in the later measurement. This suggests that the structures varied spatially or temporally on scales of several electron gyroradii or gyroperiods. The bottom panel in Fig. 2 is the electric potential obtained by integrating the data in the top panel. The peak negative potential was about –20 V with an estimated uncertainty of 30% related to the variation of the response as a function of frequency of the on-axis electric field antenna (that observed most of the parallel electric field).

<table><caption>TABLE I. Parallel and perpendicular spacecraft separations.</caption><thead><tr><th colspan="3">Spacecraft separations (km)</th></tr><tr><th>SC pair</th><th>Parallel separation</th><th>Perpendicular separation</th></tr></thead><tbody><tr><td>1–2</td><td>–15.4</td><td>21.7</td></tr><tr><td>1–3</td><td>–9.9</td><td>26.9</td></tr><tr><td>1–4</td><td>–29.2</td><td>9.3</td></tr></tbody></table>

The TDS all had positive and negative potential parts. The positive potential parts of the TDS that overtake an electron have little net effect on the electron, because the fields in such potentials slightly decelerate and then reaccelerate the electron as the TDS passes by. However, the electric fields in the negative potential parts of a TDS that overtakes an electron will accelerate the electron away from the TDS in a process that looks like a moving wall (the parallel potential) reflecting the slower electrons by the electrostatic Fermi interaction [28,29]. This mechanism will be discussed following the presentation of the electron data. A similar acceleration mechanism has been suggested for the generation of field-aligned electron fluxes in Earth’s outer radiation belt [30].

The components of the magnetic field in geocentric solar ecliptic coordinates, measured at the time of the TDS (the vertical dashed line in the figure), are shown in Figs. 3(a)–3(c). The change of the z component of the field signified the magnetopause crossing, and the observations were located approximately in the magnetospheric sepa-ratrix, as illustrated in Fig. 3(d). Previous observations demonstrate that TDS often propagate away from the reconnection region along the magnetic separatrix [31], and such TDS have been discussed as being associated with electron acceleration during reconnection [3].

The upper panel in Fig. 4 presents 400 ms of 131 eV electron energy flux measured at three pitch angles during

<figure><img src="image_4.png" /><figcaption>FIG. 2. The electric field (top panel) and electric potential (bottom panel) associated with a single TDS that passed spacecraft MMS4 and, 7.9 ms later, passed MMS1. The electric potentials of the bottom panel were obtained by integrating the electric fields of the top panel and by assuming that the distance between successive data points was the TDS speed of 4000 km/s and the data rate was 8192 points/s.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>FIG. 3. (a)–(c) give the three components of the magnetic field on MMS 1 at the time of the TDS (the vertical dashed line), and (d) illustrates the relative positions of spacecraft MMS1 and MMS4 in the reconnection geometry.</figcaption></figure>

the time interval when the TDS passed over spacecraft 1. The TDS moved opposite to the magnetic field direction and the 174° electron flux (which was moving in that direction) decreased at the time of the TDS, suggesting that the 131 eV flux was influenced by the TDS. A possibility is that the TDS overtook low energy electrons and accelerated them via the Fermi mechanism associated with the electrons bouncing off a moving barrier only once. If this happened, the 174° electrons with velocities higher than the TDS speed observed before the TDS crossed the spacecraft

<figure><img src="image_6.png" /><figcaption>FIG. 4. The upper panel gives the flux of 131 eV electrons at three pitch angles as a function of time before and after the TDS passage shortly after 0.6 s. The bottom panel gives the ratio of the fluxes shortly before and after the TDS as a function of energy.</figcaption></figure>

were accelerated by the TDS, while the same energy electrons measured after the TDS crossing were not. Thus, the ratio of electron fluxes before and after the TDS crossing can provide information on the TDS interaction, as is illustrated in the bottom panel in Fig. 4. The vertical dashed line in this panel is the energy of an electron moving at a speed of 4000 km/s. The before-to-after electron flux ratio is about 0.8–1.0 for particle velocities around the TDS speed, but it becomes significantly larger than one (reaching ~1.6) for velocities higher than the TDS speed. Thus, it appears that electrons with field-aligned velocities less than that of the TDS were accelerated to 200 eV or greater by the overtaking TDS. This conclusion is supported by the before-and-after phase space densities presented in Fig. 5 in which, for 174° electrons (the upper panel), <100 eV electrons were apparently accelerated to >100 eV by the TDS passage.

After TDS passage in Fig. 5 (when the observed electrons have not encountered the TDS), the spectrum was flat. Before TDS passage, the accelerated electrons produced a positive slope in the phase space density. This unstable situation may result in further wave-particle interactions that remove the positive slope and affect the energies of the electrons that created it. The plateau, at energies comparable to the energy associated with the TDS speed, may correspond to the relaxed beam that generated the observed TDS.

*Discussion*.—A quantitative estimate of the Fermi acceleration is obtained by defining the parallel speeds in the satellite frame of reference of the TDS as $v_{\text{tds}}$ and the electron as $v_e$. In the TDS frame, the TDS speed is 0 and the electron speed is $(v_e - v_{\text{tds}})$. After elastic collision with the TDS, the electron velocity changes sign and becomes $(v_{\text{tds}} - v_e)$. Thus, in the satellite frame, the final electron

<figure><img src="image_7.png" /><figcaption>FIG. 5. Distribution functions of electrons before and after TDS passage for 174° pitch angle electrons (top panel) and 90° electrons (bottom panel).</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>FIG. 6. The top panel give the final electron energy versus its initial energy resulting from Fermi reflection of the electron by either a 4000 or 5000 km/s TDS. The bottom panel gives the minimum initial electron energy that can be scattered by the TDS as a function of the maximum negative potential in the TDS.</figcaption></figure>

speed is $(2v_{tds} - v_e)$ and its energy is $1/2m(2v_{tds} - v_e)^2$. A plot of the electron final energy as a function of its initial energy is given in Fig. 6(a) for a 4000 km/s barrier.

A limit that prevents low energy electrons from being accelerated to the ~180 eV maximum energy for a TDS speed of 4000 km/s [Fig. 6(a)] is that the potential barrier must be large enough to reflect an incident electron. Thus, $1/2m(2v_{tds} - v_e)^2$ must be less than the (negative) potential of the TDS. A plot of the minimum potential barrier as a function of the initial electron energy is given in Fig. 6(b). In the case of interest, the potential barrier was about 20 V, so incident electrons with energies less than about 5 eV were not reflected by the barrier. Thus, the most energetic Fermi accelerated electrons would have an energy of about 125 eV if the TDS speed were 4000 km/s.

There are two discrepancies between the analysis thus far and the data. The first is that the measured upper bound on the accelerated electron energy of ~250 eV (lower panel in Fig. 4) is much greater than the 125 eV maximum energy obtained for Fermi acceleration by a 4000 km/s TDS [Fig. 6(a)]. The second discrepancy is that the energetic electrons disappeared (upper panel in Fig. 4) about 150 ms before the TDS arrived at the spacecraft (Fig. 1). Both of these discrepancies are resolved if the TDS earlier had a greater speed, as the following estimate shows. Suppose that the TDS had a speed of 6000 km/s when it was a distance *d* from the spacecraft and that its speed decreased linearly to 4000 km/s during the time *T* that it moved the distance *d* to the spacecraft. Furthermore, suppose that the ~200 eV electrons were accelerated at the distance *d* and arrived at the spacecraft after traveling (*T* − 0.15) seconds. These two assumptions produce two equations

in two unknowns, *d* and *T*, whose values are
*d* = 1800 km and *T* = 0.37 s, respectively. Thus, the
~200 eV electron acceleration occurred a fraction of a
second before they crossed the spacecraft and at a
distance of 10–20 ion inertial lengths upstream. In this
way, the data provide additional evidence for the decay
of the TDS as they moved along the magnetic field
away from the *X* line.

It is interesting to consider what may happen to an
electron after undergoing the one-time Fermi acceleration.
As shown in Fig. 5(a), an incident 40 eV electron is
accelerated to 57 eV by this interaction. As this accelerated
electron moves into the converging magnetic field, its
parallel velocity is converted to perpendicular velocity
by conservation of the first adiabatic invariant. If the
magnetic field converges sufficiently and the TDS survives
over the convergence distance, the parallel speed of the
electron of interest will slow to the speed of the TDS and it
will undergo a further Fermi acceleration. In this way, the
electron can move into the converging magnetic field at a
roughly constant parallel velocity as its perpendicular
energy increases due to multiple Fermi interactions in
what amounts to a Landau resonance interaction between
the electron and the TDS. There is no evidence, yet,
whether a process like this is at work in reconnection
events. However, in the outer Van Allen radiation belts this
process has been shown to accelerate thermal (~100 eV)
electrons to tens of keV [32] and even hundreds of
keV [33].

The authors thank V. Krasnoselskikh for several useful
comments and suggestions. We are deeply indebted to the
entire MMS team that built such wonderful instruments and
an outstanding program. The work of F. S. M. and T. D. P.
was supported by NASA Grant No. NNX08AO83 J. L. B.,
R. B. T., and B. L. G. were supported by NASA Contract
No. NNG04EB99 C at SwRI. The work of O. A. A. and
F. S. M. was also supported under JHU/APL Contract
No. 922613 (RBSP-EFW). A. A. is grateful to the
Dmitry Zimin Dynasty Foundation for support. The work
of I. V. was supported by the Presidential Grant No. MK-
7757.2016.2.

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