Introduction
Magnetic reconnection is considered to drive global-scale dynamics in Earth's
magnetosphere , solar flares
, laboratory plasmas and astrophysical
systems. Magnetic reconnection changes the magnetic field topology and
releases magnetic energy into particle energy in plasmas. As reconnection
occurs, magnetic field lines appear to “break” and “reconnect” at the
X-line (Fig. 1a). Outside the diffusion region, plasma motions are frozen to magnetic
field lines that behaves like elastic strings. Within the diffusion region,
the violation of plasma that is frozen-in allows magnetic field lines to
disconnect and reconnect.
The name “diffusion region” originates from the early Sweet–Parker
reconnection model, in which oppositely directed magnetic field lines in the
current sheet diffuse into the plasma as plasmas are demagnetized by
inter-species collisions . The term diffusion
region has been extended to include any physical process that can violate the
frozen-in condition . The physics in the
limited diffusion region is of high importance in magnetic reconnection. The
global-scale evolution of the magnetic topology relies on the reconfiguration
of magnetic field lines in the diffusion region. The effects responsible for
breaking the frozen-in condition specify the reconnection electric field that
controls how quickly reconnection proceeds.
For reconnection to proceed, the frozen-in condition for both ion and
electron must be violated in the diffusion region. In the case of only one
species being unfrozen from the field line, one can trace the frozen magnetic
field lines tied to the other magnetized species. The exact condition for
unfreezing ion fluid is a non-zero curl of E+vi×B based on
the frozen-in theorem. According to the ion fluid momentum equation without
approximation,
E+vi×B=(1/niqi)∇⋅Pi+(mi/qi)dvi/dt+(mi/qi)νie(vi-ve),
where E is the electric field, Pi is the ion
pressure tensor, vi (ve) is the ion
(electron) flow velocity, and νie is the effective
ion–electron collision frequency. As evident from the ion momentum Eq. (1),
the ion frozen-in condition can be violated by three nonideal effects, i.e.,
an anisotropic ion pressure tensor, an ion inertial (acceleration) effect or
inter-species collisions manifested as friction. These nonideal effects are
the fluid manifestation of the kinetic effects leading to ion demagnetization
in reconnection. The expression (1) and arguments for ions apply equally to
electrons after a suitable change of charge, mass and subindexes.
The main nonideal effects for ion and electron fluid in reconnection are
still debated. Reconnection models are categorized according to which
nonideal process is thought to be dominant. In the resistive reconnection
model, inter-species collision is the dominant effect. The collisions can be
either binary or anomalous (induced by wave–particle interactions that are
not clearly understood). In collisionless reconnection models where effective
ion–electron collisions are infrequent, the nonideal effects have to be
anisotropic pressure effects and/or inertial effects. As plasmas are
convected toward the reconnection site, ions first become demagnetized at the
characteristic scale length of ion motions, while electrons are still
magnetized . Electrons are expected to be
demagnetized on a smaller spatial scale.
The reconnection electric field, defined in the co-moving frame of the
current layer, controls how quickly (by E⋅J)
magnetic energy is converted to particle energy in reconnection. The
reconnection electric field is the same in the ion momentum (Eq. 1) and the
electron momentum equation. From the perspective of the ions (electrons), the
reconnection electric field is the sum of the nonideal electric field
supported by ion (electron) nonideal effects and the simple ion (electron)
convection electric field. Although demagnetization is more difficult for
electrons, the reconnection electric field is equally explainable in terms of
ions or electrons near the X-line . In this sense,
ion demagnetization and electron demagnetization are two different but
equally fundamental aspects in specifying the reconnection electric field.
In collisionless reconnection, ion decoupling from the magnetic field lines
is considered to produce a Hall effect
, but what nonideal
effect is responsible for unfreezing ion fluid in the first place has not
been clear. Intuitively, it is tempting to attribute ion decoupling to the
Hall current term in the generalized Ohm's law,
E+vi×B=(1/nq)J×B,
but this relation is a trivial equivalence of the electron frozen-in
condition (E+ve×B=0). Ion
information is canceled out from this relation and nothing specific about
nonideal effects of ions can be inferred. Studies of ion-scale physics in
reconnection have been usually guided by the generalized Ohm's law, which is
essentially a combination of electron and ion momentum equations with some
approximations. Although appropriate for electrons to a certain extent, these
approximations neglect and hide important aspects of ion dynamics. The
correct approach to investigate ion-scale physics is the full momentum
equation without approximation .
Experimental clarification of the ion nonideal effects requires a comparison
between the nonideal electric field (E+vi×B) and ion pressure and/or inertial terms. Although attempts have
been made to compare the nonideal reconnection electric field with the
divergence of the electron pressure tensor, the electron diffusion region was
too small for the spacecraft to encounter . On the ion
skin depth scale, past spacecraft observations have reported ion kinetic
features such as non-gyrotropic ions and counterstreaming ions during
reconnection
, but
how these effects are linked to ion demagnetization and the violation of the
ion frozen-in condition has been elusive. Here we report observations from an
encounter of the THEMIS (Time History of Events and Macroscale Interactions
during Substorms) spacecraft with
the diffusion region near the reconnection X-line at the Earth's
magnetopause. The comprehensive field instrumentation and measurements of ion
velocity distribution on the THEMIS
spacecraft provide an ideal opportunity to address the question of ion
demagnetization in reconnection. By comparing the nonideal reconnection
electric field with ion pressure and/or inertial terms, we for the first time
identify the nonideal effects corresponding to ion demagnetization in the
diffusion region.
Schematics of magnetic reconnection in the Earth's magnetopause.
Panel (a): the magnetic field geometry at the dayside magnetopause
reconnection viewed in the noon–midnight plane. Magnetic field lines near
magnetopause reconnection can be divided into three classes according to
their topology: (1) interplanetary field lines (red) with no magnetic foot on
the Earth; (2) “open” field lines (green) with one magnetic foot connected
to the Earth and (3) “closed” field lines (blue) with both magnetic feet
connected to the Earth. Two branches of separatrix surface S1 and S2
intersect along a magnetic “X-line” directed out of the plane. Panel
(b): the expanded view of the region surrounding the X-line. A
portion of the plasma outflow came across the ion diffusion region identified
by a significant deviation of E from -Vi×B.
Data analysis
On 13 February 2013, THEMIS spacecraft E moved into the magnetopause and
detected a reconnection diffusion region (see Fig. 1b). THEMIS E was at (6.1, -6.9,
-0.6) in units of Re (Earth radii) in the geocentric solar magnetospheric
coordinate system (GSM). We adopted the boundary normal coordinate
NML to study the magnetopause current sheet. N, (-0.78,
0.59, 0.21) GSM, is the boundary normal direction (outward) as determined by
the minimal variance direction of the four samples per second magnetic fields
from 23:24:20 to 23:25:20 UT; L, (-0.07, -0.42, 0.90), GSM is
the direction of maximum variance of the magnetic field, and M
completes the right-hand orthogonal coordinate, directed out of plane. The
corresponding eigenvalues for the eigenvectors are 9.4, 18.7 and 3011.4.
There is some uncertainty in M and N since the ratio of
the two corresponding eigenvalues is less than 3, but the N from
minimal variance analysis (MVA) varies little if we shift the interval by
10 s. The determined N direction is
also very close to the N (-0.90, 0.42, 0.10) obtained from a
longer interval (23:23:00 to 23:33:00 UT). These facts suggest that the
N direction from MVA is reasonably good. Figure 2 shows
measurements of fields and particles during the magnetopause crossing. The
magnetopause current sheet, indicated by a change in BL from
-40 to 60 nT, was observed from 23:24:40 to 23:25:00 UT. Northward plasma
flow with velocities as large as 130 km s-1 was detected from 23:24:42
to 23:25:05 UT, immediately after the spacecraft crossed the separatrix S1
at 23:24:40 UT. The separatrix S1 is identified by a sudden increase of
1–10 keV electrons that originated in the magnetosphere. The electron
characteristics are a good indication of separatrix field lines because of
their small gyroradius and large mobility along the magnetic field. Around
23:25:10 UT, THEMIS E crossed the separatrix S2 and moved into the
magnetosphere. The separatrix S2 is identified by a boundary between a broad
spectrum of mixed electrons and a dominant magnetosphere electrons. Between
23:25:10 and 23:25:30 UT, the spacecraft was away from the current sheet and
the diffusion region, as evidenced by the large BL component.
After 23:25:30 UT, THEMIS E moved back into the magnetopause and observed
the southward plasma flow. BN shows a variation of a few
nanotesla on a 20 s timescale in addition to the direct current (DC) component near the current sheet. This variation in BN
may result from an eigenmode of the current sheet surface waves
. The DC BN is negative in the northward
plasma flow and positive in the southward flow, consistent with the
prediction that the bidirectional plasma flows are accelerated by a
J×BN slingshot effect resulting from reconnection.
The reversal of the ion flow is correlated with the reversal of
BN, suggesting that the determination of N is
reasonably good in this event. The observed bidirectional reconnection
outflows indicate that the spacecraft moved from the northward side to the
southward side of an active reconnection X-line. THEMIS E did not encounter
the X-line (BN=0,BL= 0) but its surrounding region.
Observations by THEMIS spacecraft E in the ion diffusion region. All
THEMIS data in Fig. 2 are of spin resolution and at the cadence of the
particle instrument. Panel (a): three components of the proton flow
velocity in the LMN coordinate system, showing a flow reversal in
the L (north–south direction). Panel (b): the plasmas
density. Panel (c): the electron differential energy flux. Panels
(d) and (e): three component of magnetic field in the
LMN coordinate. Panels (f) and (g): the comparison
of vi×B with the electric fields in
N and M, respectively. Three-dimensional electric
fields are obtained from the E⋅B= 0 assumption.
Panel (h): the ion non-gyrotropy index ,
characterizing the degree of non-gyrotropy in the distribution function. The
ion velocity distribution function in intervals marked by A, B, C and D are
show in Fig. 3. Panel (i): components of the ion pressure tensor in
the boundary normal coordinate. Panel (j): the non-gyrotropic part
of the ion pressure tensor.
Figure 2g exhibits a significant deviation in the measured electric field
EM from -vi×B from
23:24:44 UT to 23:24:58 UT during the current sheet crossing. This
deviation illustrates the violation of the ion frozen-in condition as a
support of the reconnection electric field EM,
experimentally defining the so-called ion diffusion region. The period from
23:25:20 to 23:25:44 UT is the edge of the diffusion region and far from the
current sheet center. The ion diffusion region in the current sheet is marked
by a pink rectangle. Within the diffusion region, a remarkable normal
electric field EN as large as 10 mV m-1 was observed. The
out-of-plane magnetic field BM displayed one bump around the
current sheet center (BL∼0); it was about 10 nT larger than
the average guide field outside the current sheet. The location and waveforms
of EN and BM are completely consistent with those of
the Hall magnetic fields and electric fields in the asymmetric reconnection
reported in early THEMIS observations .
Contrary to the situation of a quadrupole Hall BM and a bipolar
Hall EN in a symmetric reconnection, there is only one bump in
the Hall field in the asymmetric reconnection. The observed asymmetric Hall
electric fields and magnetic fields indicate the operation of collisionless
reconnection.
The length of the diffusion region along the normal direction is the crossing
time ΔT multiplied by the magnetopause velocity vn relative to the
spacecraft. We estimate vn by assuming that the magnetopause had a
constant tangential electric field as it moved in the normal direction at a
constant speed. The estimated vn is
(EM(1)–EM(2)) / (BL[1]–BL[2]) . Here the
fields EM(1), EM(2), BL[1] and BL[2] are measured at the
spacecraft frame at times 1 and 2 upstream and downstream of the current
sheet, respectively. As shown in Fig. 2d and g, EM(1) is
∼ 0.5 mV m-1 and BL[1] is∼-45 nT from 23:24:20 UT to
23:24:40 UT before the crossing. Immediately after the crossing EM(2) is
∼ 2.5 mV m-1 and BL[2] is ∼70 nT from 23:25:02 to
23:25:14 UT. The magnetopause velocity Vn is ∼ 17.4 km s-1.
The length of the diffusion region along the normal direction is 264.5 km,
about 7.3 magnetosheath ion skin depths or 1.2 magnetosphere ion skin depths
(c/ωpi). This scale size is consistent with the values of the
diffusion region in previously reported examples of collisionless
reconnection . The estimated
tangential reconnection electric field near the reversal of BL is
∼ 0.5–1.3 mV in the frame co-moving with the magnetopause current
sheet.
The departure of the pressure tensor from cylindrical symmetry about the
local magnetic field direction can be measured by a non-gyrotropy index
.The non-gyrotropy and similar agyrotropy indexes have been
successfully applied to characterize non-gyrotropic electrons in the electron
diffusion region . The comparison
between non-gyrotropy and nonideal electric field, however, has not been done
yet in these studies. In our event, Fig. 2h shows an intensified layer of ion
non-gyrotropy within the diffusion region, indicating strongly non-gyrotropic
ions when the ions are demagnetized. The ion non-gyrotropy is as large as 0.3
in the diffusion region, significantly larger than the average value
(∼ 0.05) outside the diffusion region. Both the off-diagonal pressure
component and the difference between the diagonal component can contribute to
the non-gyrotropy index . We find that the contribution from
the off-diagonal pressure component is dominant (> 90 %) in
the diffusion region.
Observations of ion velocity distributions near and within the ion
diffusion region. Panels (a–d): the cut of velocity distribution
functions perpendicular to the magnetic field measured from THEMIS ESA in the
intervals marked as A, B, C, and D in Fig. 2. The horizontal axis is the
direction of ion convection flow Vi⊥ and the vertical
axis is the direction of B×Vi⊥. The ion
bulk flow velocity has been subtracted from the distributions. The white
horizontal line in the distribution represents the flow convection velocity
in the spacecraft frame. Interval A is far from the diffusion region, B and C
are within the diffusion region and D is at the edge of the current layer and
away from the current sheet center.
The non-gyrotropic pressure can lead to the violation of the ion (or
electron) frozen-in condition via the off-diagonal terms in the pressure
tensor. Similar to the situation of non-gyrotropic electron pressure
, the gradient of the off-diagonal
ion pressure components can give rise to a nonideal reconnection electric
field in the diffusion region in 2-D reconnection,
(E+vi×B)M∼(∂PNM/∂N+∂PML/∂L)/niqi.
Figure 2i presents the ion pressure tensor components in the boundary normal
coordinate system. Spin-resolution ion moment data has been extensively used
in the Walen test (or tangential component test) . Ion
moments data are generally considered acceptable when the spacecraft takes
multiple samples in the reconnection current layer
.
From 23:24:46 to 23:24:54 UT, THEMIS observed a significant nonideal
reconnection electric field (E+vi×B)M of 3–4.5 mV m-1 (Fig. 2g) in the center of the
diffusion region associated with a gradient of the ion off-diagonal pressure
component (Fig. 2i). The density ni (Fig. 2b) was
∼ 6.2cm-3 at 23:24:50 UT, ΔN from 23:24:46 to
23:24:54 UT is ∼ -129 km, PNM (Fig. 2i) decreases from
2500 eV cm-3 to near 0, and ΔPNM
∼ -2500 eV cm-3. With all these numbers, our estimate of
ΔPNM/ΔNniqi is +3.2 mV m-1.
ΔPML is ∼ -1000 eV cm-3 in Fig. 2i. Assuming
ΔL∼ΔN, ΔPML/ΔLniqi
is ∼ 1.3 mV m-1. The assumption of ΔL∼ΔN
corresponds to an ion diffusion region extending 16 ion skin depth (roughly
from 23:24:46 to 23:25:20 UT) northward in the L direction. Such
an L-extent of the ion diffusion region is consistent with
reconnection models. The gradient of the off-diagonal ion pressure terms
agrees well with the nonideal reconnection electric field, indicating that
the non-gyrotropic pressure effect mainly contributed to breaking the ion
frozen-in condition. Ion inertial (acceleration) effects and, in principle,
the anomalous collision effect can also contribute to reconnection electric
fields. In the diffusion region, VN∼ -70 km s-1 and ΔVM∼ 130 km s-1 (Fig. 2a). The ion inertial term scales as
(mi/qi) VNΔVM/ΔN
(< 0.3 mV m-1), much less than the non-gyrotropic pressure
effect. The anomalous collision term is expected to be very small because the
observed reconnection should be collisionless, as implied by current sheet
thickness (ion skin depth) and the Hall fields. The ion pressure tensor can
be decomposed into a gyrotropic part and a non-gyrotropic part
. As shown in Fig. 2j, the non-gyrotropic part of the
pressure tensor mostly contributes to the off-diagonal components. Based on
the analysis of all possible effects in the ion momentum equation, we
demonstrate that the non-gyrotropic pressure effect is primarily responsible
for breaking the ion frozen-in condition in this event.
The ion momentum equation can be checked term by term in the normal direction
as well. (E+vi×B)N is about
7–10 mV m-1 near the reversal of BL. The ion inertial
term in the normal direction is on the order of 0.1 mV m-1. The
gradient of the pressure term in the normal direction is (∂PNN/∂N+∂PLN/∂L)/niqi.
The ΔPNN∼ -6000 eV cm-3 is the dominant term,
contributing
7.8 mV m-1 in the ion momentum equation. Within a difference of
20 %, the pressure gradient term is approximately consistent with the
(E+vi×B)N. This independent
verification of the ion momentum equation in the normal direction involves
the quantitative comparison between three independent data sets, indicating
that THEMIS measurements were reasonably reliable in the ion diffusion
region. Notice that a significant uncertainty in the ion moment data may
arise due to the time-aliasing effect, i.e., the mixing of different
populations during the one spacecraft spin, but the level of the verification
of the ion momentum equation in both N and M directions
is very difficult to explain by arbitrary time-aliasing effects.
As implied by the two-fluid momentum Eq. (1), electrons are expected to
exhibit similar dynamics to ions except that the nonideal electron terms
operate on the smaller electron scale in the diffusion region. Theoretical
studies show that non-gyrotropic pressure effects unfreeze electron fluid
near the reconnection X-line . Encompassing
the observation of ion non-gyrotropic pressure, an emerging scenario is that
the non-gyrotropic pressure effect applies universally to unfrozen ions on a
large spatial scale and to electrons on a small spatial scale. Near the
X-line, the reconnection electric field should be equally expressed in
terms of ion or electron non-gyrotropic pressure .
Figure 3 shows the ion velocity distributions perpendicular to the magnetic
field near and in the diffusion region. Panel (a) shows a typical gyrotropic
ion distribution in the magnetosheath outside the diffusion region. The
distributions in panels (b) and (c) are centered around
BL=-20 nT and BL=+40 nT, where the magnetic field
are found to deviate from the spin-averaged values by ∼ 30 and
∼ 20 % during one spin period. The velocity distributions in panels
(b) and (c) are in the clearly identified ion diffusion region and
characterized by non-gyrotropic bulges in the core component. According to
the definition of the pressure tensor, P=m∫dv3(v-u)(v-u)f(x,v,t),
where u is the bulk flow velocity, such non-gyrotropic bulges are
expected to contribute to non-zero integral of
(vM-uM)(vN-uN) and thus to large off-diagonal
pressure components. Two bulges are centered at (50, 15) and (-82,
-50) km s-1 in the interval C. The velocity spread of these bulges
is ∼ 100 km s-1, about half of the thermal speed in the
diffusion region. The observed non-gyrotropic distribution is particularly
important for magnetic field line reconfiguration in the diffusion region as
it can drive a current sheet instability that induces the normal magnetic
field component . In addition, the non-gyrotropic
distributions are expected to drive plasma waves that tend to stabilize the
plasma . The strongly non-Maxwellian distribution
observed in the diffusion region has two implications: (1) the effective
ion–electron collision is insufficient to lead to Maxwellian distributions
while ions are demagnetized, and (2) the ion demagnetization process is much
faster than ion thermalization and thus unlikely to be explained by effective
ion–electron collisions. The non-gyrotropic bulges in panels (b) and (c)
resemble those reported by GEOTAIL spacecraft in reconnection
. Numerical simulations suggest
that non-gyrotropic bulges are caused by the mixing of already accelerated
meandering ions with ions just convected into the vicinity of the X-line
geometry . Such a mixing process is
inferred to also occur in the asymmetric reconnection at the magnetopause
from observations from Cluster . Ions from distinct sources
form phase-bunched bulges in the distribution. This scenario of forming
non-gyrotropic bulges is supported by the difference between the energy of
the non-gyrotropic bulges shown in panels (b) and (c). The non-gyrotropy in
the warmer ion components in panel (d) resembles those in THEMIS observations
outside the current sheet center but near the reconnection site
. These non-gyrotropic warmer ions are formed by a
cucumber-type trajectory that has the neutral sheet-crossing and the
non-crossing segments near an X-line geometry .