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Stop Layer: A Flow Braking Mechanism in Space and Support from a Lab Experiment 1
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G. Haerendel1, L. Suttle2, S.V. Lebedev2, G.F. Swadling2, J.D. Hare2, G.C. Burdiak2, S.N. Bland2, 3
J.P. Chittenden2, N. Kalmoni2,#, A. Frank3, R.A. Smith2, F. Suzuki‐Vidal2 4
1 Max Planck Institute for Extraterrestrial Physics, Garching, Germany 5
2 Blackett Laboratory, Imperial College, London SW7 2BW, United Kingdom 6
3 Department of Physics and Astronomy, University of Rochester, Rochester, New York 7
14627, USA 8
# present address: Mullard Space Science Laboratory, University College London, United 9
Kingdom 10
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ABSTRACT. The paper presents short summaries and a synopsis of two completely 12
independent discoveries of a fast flow braking process, one realized by a laboratory 13
experiment (Lebedev et al. 2014), the other by theoretical reasoning stimulated by auroral 14
observation (Haerendel 2015a). The first has been described as a magnetically mediated sub‐15
shock forming when a supersonic plasma flow meets a wall. The second tried to describe 16
what happens when a high‐beta plasma flow from the central magnetic tail meets the strong 17
near‐dipolar field of the magnetosphere. The term stop layer signals that flow momentum 18
and energy are directly coupled to a magnetic perturbation field generated by a Hall current 19
within a layer of the width of c/ωpi and immediately propagated out of the layer by kinetic 20
Alfvén waves. As the laboratory situation is not completely collision‐free, energy transfer 21
from ions to electrons and subsequent radiative losses are likely to contribute. A synopsis of 22
the two situations identifies and discusses six points of commonality between the two 23
situations. It is pointed out that the stop layer mechanism can be regarded as a direct 24
reversal of the reconnection process. 25
1. INTRODUCTION. 26
It was at a conference in Scotland in August 2015 that one of the authors (G.H.) listened to 27
the presentation by one of the other authors (S.L.) and discovered to his surprise that the 28
situation just described in the laboratory appeared to resemble what he had recently 29
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postulated to happen in space during the breakup of a magnetospheric substorm. The 30
occasion was the 13th IPELS conference, the five letters standing for “Interrelationship 31
between Plasma Experiments in Laboratory and Space”. What is described in the following is 32
thus truly in the spirit of this biannual conference created in 1991. A new theoretical 33
concept, the “stop layer”, proposed to form at the interface between magnetotail and 34
dipolar magnetosphere, finds unexpected support from a magnetically mediated standing 35
shock layer formed in a lab experiment from a supersonic, magnetized plasma flow. In this 36
paper we will first describe separately the two physical situations and subsequently analyze 37
the commonalities and farther reaching consequences. 38
2. THE STOP LAYER POSTULATE 39
The concept of a stop layer has been introduced in (Haerendel 2015a) as a way to 40
understand the origin of auroral displays at the sudden onset of a substorm. It is a fast flow 41
braking mechanism allowing efficient energy conversion and momentum transfer at the 42
inner edge of the tail in a situation, when a highly stretched magnetic field suddenly starts to 43
contract earthward and a high‐beta plasma flow encounters the sharply increasing field of 44
the near‐dipolar magnetosphere. The situation is sketched in Figure 1. It is postulated that 45
such a stop layer has a thickness of the order of the ion inertial length or gyro radius. Thus 46
the ions can enter without paying attention to the magnetic field. Charge neutrality requires 47
an equally fast entry of the electrons. But since they are magnetized, they are being swept 48
into the layer with the agglomerating magnetic field. Like in the so‐called diffusion region in 49
a reconnection process, an electric polarization field, Ep, is set up slowing down the ions and 50
carrying a Hall current which balances the momentum inflow and couples the mechanical 51
energy extracted from the ion flow to the magnetic field. In addition, a longitudinal 52
structuring develops which gives rise to a divergence of the Hall current and connection to 53
field‐aligned currents (Figure 2). Thereby magnetic perturbations fields are generated which 54
propagate out of the layer parallel to B in the Alfvén mode and carry the deposited 55
momentum and energy earthward. It is the balance between the normal energy inflow by 56
the ions and the tangential structuring of the outflowing Poynting flux that determines the 57
divergence length of the Hall current. 58
Width and longitudinal structuring of the stop layer and connected propagating magnetic 59
perturbations have scales that, when mapped to the ionosphere, can account for the small‐60
scale structure of the aurora. Figure 3a shows an image of the so‐called breakup arc that 61
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marks the substorm onset. It has long since been known that the outflow from the 62
reconnection site at about 20 RE is pulsed. Haerendel (2015b) has argued that stop layers are 63
forming not only at the very onset of a substorm but always when the leading edge of a flow 64
burst as manifestation of the reconnection outflow encounters a strongly increasing 65
magnetic field and is suddenly slowed down. Observations of the THEMIS mission revealed 66
that the leading edge of a flow burst consists of a high‐beta plasma to be followed by a 67
strongly increasing normal field (e.g. (Runov et al. 2011)). Figure 3b shows an image from the 68
same substorm breakup about 29 min after onset. One can clearly distinguish two highly 69
structured fronts from two consecutively arriving flow bursts. According to the above 70
arguments these fronts are owed to the necessity to immediately remove the incoming flow 71
energy. Only this way can the stop layer and an efficient flow braking be maintained for 72
times much greater than the entry time of the ions. 73
Postulating the formation of a stop layer raised the question why the ions are not simply 74
reflected in the retarding potential, transferring momentum and little energy, similar to the 75
collision of a light with a heavy mass. The incoming flow of high‐beta plasma is not field‐free 76
but carries magnetic flux into the layer and compresses it to the level of the stopping 77
magnetospheric field. As a consequence, the ions when slowed down become magnetized 78
and trapped in the increasing magnetic field. The stop layer progresses at the same rate that 79
the entry of the ions requires. Contrary to the electrons in the compressed magnetic field, 80
the ions are not heated, since the flow energy is being readily removed from the layer by 81
Alfvén waves. . 82
So far there has been no observation of the existence of a stop layer of the order of c/ωpi. 83
However, as the observations presented in Figures 3 a&b show, inside the wider breakup arc 84
sheets of distinct, very short‐lived rays exist with thicknesses of the order of 10 km or less. 85
Mapped to the inner edge of the tail, this corresponds to several 100 km, i.e. comparable to86
pic / . Higher resolution images of the same event are also contained in (Dahlgren et al. 87
2013). These arcs are visible manifestations of what is called Alfvénic arcs and are often 88
found adjacent to the poleward expanding auroral bulge in satellite crossings of the auroral 89
oval and created by strongly field‐aligned electron beams with diffuse energy spectra mostly 90
below 1 keV (Haerendel and Frey 2014). Not explained in that paper was the origin of the 91
coarse rays. The longitudinal structuring of the stop layer offers a natural explanation. 92
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The paper in which the stop layer concept was proposed (Haerendel 2015a) and the 93
subsequent paper (Haerendel 2015b) analyze in detail the role of the stop layer in the 94
evolution of the substorm breakup and support this with quantitative evaluations based on a 95
set of simple conservation relations. Here we will briefly summarize some key properties. 96
The situation shown in Figure 4 is the interface of the near‐dipolar magnetospheric field to 97
the left and the adjacent part of the central current sheet of the strongly stretched tail to the 98
right. The flow velocity, v||, is the Alfvén speed formed with the radial magnetic field, Bx, 99
and the central density, ρ. The incoming energy flux is: 100
0
2
|| 2v
xB
F (1) 101
The characteristic time of the build‐up of a new stop layer is: 102
x
m
B
B
v
w (2) 103
Bm is the magnetosheric field, w the width of the stop layer, for which we set c/ωpi, and v 104
the flow speed normal to the central current or neutral sheet, with zx BB ||vv . τ is also 105
the lifetime of the stop layer in the sense that it will be shielded from the incoming flow by a 106
newly forming stop layer. The retarding electric field is: 107
wne2
v2||
pE , 108
(3) 109
and the Hall current, which is the generator of the currents associated with the energy 110
outflow: m
2||
2
v
BJGen
(4) 111
The Poynting flux out of the stop layer is: 112
Ff
dSP )1(
w
(5) 113
d is the half width of the central current sheet (Figure 4). It is defined by the extent, || , of 114
the high‐beta plasma along the neutral sheet and the equality of the lateral and transverse 115
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magnetic fluxes: ||/ xz BBd . f is the fraction of the inflowing energy that is consumed 116
locally in compressing B and heating the electrons (for details see [Haerendel 2015a]). A 117
decisive quantity is the divergence length of the Hall current: 118
f-
d
B
B
m
xdiv 1
w (6) 119
It follows from comparing the Poynting flux projected into the ionosphere with an 120
expression for the energy flux calculated from the magnetic perturbation caused by the 121
field‐aligned sheet current arriving in the ionosphere: 122
Gendivm
ionion J
d
B
BJ
||, (7) 123
The antisunward progression of the stop layer due to the agglomerating magnetic field is 124
given by: 125
/wvSL (8) 126
With the input parameters: Bm = 50 nT, Bx = 20 nT, n = 0.7 cm‐3, d = 500 km, f = 0.3 one 127
obtains: v|| = 522 km/s, F = 0.166 erg/cm2s, τ = 9.2 s, w = 192 km, vSL = 21 km/s, the retarding 128
potential Epw = 1.4 kV, the Hall current JGen = 3.2x10‐3 A/m, the divergence scale, 129
kmdiv 586 and a Poynting flux of SP = 8.3x10‐2 erg/cm2s. All of this can be projected into 130
the ionosphere and compared with the observed values. For this mapping one can 131
approximately use ionm BB / . This has been done in [Haerendel 2015a] with a choice of 132
input parameters and will not be repeated here. It suffices to confirm that spatial and 133
temporal scales as well as energy fluxes observed in the aurora are consistent with the 134
respective properties of the postulated stop layer. While the author derived some 135
confidence in the validity of this new concept from the agreement with the auroral 136
observations, his confidence is being strengthened by the lab experiment to be summarized 137
subsequently. 138
139
3. OBSERVATIONS FROM LAB EXPERIMENT 140
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In laboratory experiments we observe the formation of a magnetically mediated standing 141
shock layer, formed in a supersonic, magnetized plasma flow (fast magneto‐sonic Mach 142
number ~5), which has properties resembling those of the proposed stop‐layer. 143
In the space plasma scenario, the postulated stop layer is formed in the interaction of the 144
plasma flow with a stationary magnetic field of the Earth. In the experiment the magnetic 145
field which decelerates the flow is created due to pile‐up of the magnetic flux frozen into a 146
supersonic flow. The magnetized flow is stopped by a planar conducting obstacle, which 147
leads to accumulation of the magnetic flux ahead of the obstacle. Steepening of this 148
magnetic precursor leads to the development of a steady layer with enhanced plasma 149
density and B field ahead of the obstacle (Figure 5), extending to a distance of Δ~c/ωpi from 150
the obstacle at the time when it becomes observable. The magnetic field of the precursor is 151
stationary with respect to the obstacle, and acts differently on the electrons and the ions of 152
the incoming plasma flow, due to their different level of magnetization: the electrons are 153
well magnetized in the experiment ( ρLe << Δ ; 2π/Ωce<< texp), while the ions are not ( ρLi ~ 154
Δ; 2π/Ωci~ texp). As a result, the magnetized electrons are directly decelerated by the 155
magnetic field, while the un‐magnetized ions are decelerated by the cross‐shock electric 156
field, arising due to the decoupling of velocities of electrons and ions at the spatial scales 157
smaller than c/pi . 158
The pile‐up of magnetic field was directly measured using a combination of miniature 159
magnetic probes (Lebedev et al. 2014) and a Faraday rotation imaging diagnostic (Swadling 160
et al. 2014). The magnetic probe measurements show an increase of the B‐field in the 161
plasma accumulating in front of the obstacle to a level well above that in the unobstructed 162
flow, but this diagnostic does not provide a sufficient spatial resolution for a quantitative 163
analysis (the probe size is comparable with the stand‐off distance Δ). Measurements of 164
magnetic field distribution using the Faraday rotation diagnostic (Figure 6) do allow 165
excellent spatial resolution, but this diagnostic becomes sufficiently sensitive only at later 166
time, when both the magnetic field and the electron density are larger and the rotation 167
angle becomes detectable (θ ~ 10). Overall, the measurements show an increase of the 168
magnetic field in the layer by a factor of 2‐3 in comparison to the field in the upstream 169
plasma flow, and for the Faraday rotation measurements shown in Fig.6 the magnetic field 170
in the pile‐up region is ~5T. 171
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The most noticeable feature of the structure formed in the interaction is a shock‐like 172
transition (sub‐shock), developing at a distance of Δ ~0.15cm ~c/ωpi from the obstacle. 173
Measurements with Thomson scattering diagnostic show that at the early stages of the sub‐174
shock formation both the flow velocity and the plasma density experience jumps of only a 175
factor of ~2 at the sub‐shock [1]. After passing through the sub‐shock, the plasma continues 176
to flow towards the obstacle, where it accumulates in a thin and dense stagnation region 177
close to the obstacle surface. The formed magnetically supported layer persists for the 178
duration of the experiment, (texp ~150ns >> the characteristic flow time Δ/Vfl ~ 20ns), and 179
the boundary of it, the sub‐shock, slowly propagates away from the obstacle with velocity of 180
only ~10‐15% of the incoming flow velocity. The analysis of the experimental data [1] shows 181
that at the sub‐shock the ram pressure of the incoming flow is balanced primarily by the 182
magnetic pressure of the accumulated B‐field, while the thermal pressure in the 183
downstream region is an order of magnitude smaller than the ram pressure. 184
At the initial stages of the formation of the magnetic precursor we observe that a fraction of 185
ions is reflected from the sub‐shock. The reflected ions are only detected in the upstream 186
plasma and only as a transient effect at the early stages of the shock formation. This is 187
consistent with a relatively low collisionality of the plasma at the time when the layer starts 188
forming. Self‐emission images (Fig.7) of the layer obtained at time corresponding to these 189
early stages show a significant non‐uniformity of the sub‐shock. The perturbations are 190
oriented perpendicular to the B‐field and along the obstacle and look similar to those 191
expected in the stop‐layer, as sketched in Fig.2. The characteristic wavelength of the 192
perturbations is comparable to both the width of the layer (distance to the obstacle) and to 193
the ion inertial length (c/ωpi), again similar to shown in Fig.2. In the experiment it is seen 194
that later in time the sub‐shock becomes much more uniform (Fig.7), which is most 195
probably due to the gradual increase of the density of the incoming flow and the 196
corresponding increase of collisionality of the system. The decrease of the m.f.p. also leads 197
to the gradual steepening of the sub‐shock transition, and later to the increase in the 198
density and velocity jumps to ~3.5 [1]. 199
The experiments show that the width of the magnetically mediated layer, i.e. the position of 200
the sub‐shock in respect to the obstacle, only slowly increases with time at a speed of ~10‐201
15% of the incoming flow velocity. This indicates that there should be sufficiently fast 202
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energy losses from the post‐shock plasma, which is equivalent to a small value of the 203
effective adiabatic index γeff for the post‐shock plasma. The small measured temperatures 204
Te, Ti in the post‐shock plasma are consistent with a small adiabatic index in the 205
experiments ( γeff ~1.2), and this is due to the fast transfer of energy from the ions heated at 206
the shock to the electrons, with the subsequent energy losses via radiation through the 207
optically thin medium and additional ionisation of the Al ions. Indeed, the characteristic 208
electron‐ion energy exchange time Eei ~4ns and radiative cooling time τcool ~6ns are much 209
smaller than the experimental time. Thus the fast energy losses from the post‐shock plasma 210
are similar to what is required for the stop‐layer concept, though the physics responsible for 211
the cooling of the plasma in the experiment is somewhat different from that in the stop‐212
layer. It is also possible that excitation of Alfven waves does happen in the experiment, but 213
no attempts yet been made to observe this. 214
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3. SYNOPSIS 216
In both, the lab experiment and the situation in space, the plasma is accelerated by Bj 217
forces. Although the geometries of the plasma fronts differ considerably, being more 218
cylindrical in the lab case and cusp‐like in space, both have a plasma beta above unity. 219
Actually, the ion gyro radius based on the flow speed has to be comparable or exceed the 220
ion inertial length. The flow speeds are super‐Alfvénic, but in the space situation this applies 221
only to the central part of the cusp or with respect to the field component tangential to the 222
obstacle. The main commonality between the space and lab situations is that the flows are 223
completely stopped. There are six further commonalities: 224
1. The sub‐shock as well as the stop layer have widths of the order of pic / . 225
2. The ram pressure of the flows is balanced by the magnetic pressure. 226
3. While the electrons are magnetized, the ions penetrate directly into the layers and are 227
decelerated by an electric polarization field, which represents the inertial force of the 228
braking flow. 229
4. The two respective layers propagate upstream with speeds considerably lower than 230
the inflow speeds. 231
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5. The sub‐shock structure shows the presence of perturbations perpendicular to the B‐232
field with a wavelength comparable to the width of the layer. They are strongly 233
reminiscent of the structures postulated to form in the stop layer. 234
6. In both cases the ion temperature does not increase upon entering the layer, a 235
consequence of fast energy transfer. 236
These commonalities deserve some more detailed comments. 237
1. What is an observation in the lab experiment, is the fundamental postulate of the 238
stop‐layer theory. There is no direct observation in space, only a consistency with 239
the visible structure of the arcs at substorm breakup. 240
2. The momentum balance by the enhanced magnetic field is a physical necessity in 241
the theory of the stop layer. In the lab the resolution of the data from the Faraday 242
rotation measurements is currently insufficient to fully support this supposition (c.f. 243
item 4). 244
3. Deceleration by an upstream pointing electric field is in both cases the only logical 245
conclusion. However, theoretically it is consistent with the enhanced magnetic field 246
of the stop layer being created by a Hall current along the layer. 247
4. From equations 2 and 7 one derives an upstream propagation speed of the stop 248
layer of )/(vv || mzSL BB . The finding that upstream propagation of the sub‐shock 249
proceeds at 10‐15 % of the inflow speed, leads to the conclusion that the magnetic 250
field must have increased by about a factor of 6. This is substantially higher than 251
observed. There are two possible interpretations: Either the real field is stronger 252
than observed due to insufficient spatial resolution of the magnetic probe or the 253
transport of the magnetic field towards the sub‐shock is impeded by collisions of the 254
magnetized electrons. In the space situation, the poleward propagation speed of the 255
aurora is found to be consistent with the magnetic field agglomeration. 256
5. The theoretical reason for the existence of such substructure is the balance between 257
the inflow of energy into the stop layer and its removal by kinetic Alfvén waves. 258
Although the lab situation differs substantially, in that collisional coupling of ions 259
and electrons and subsequent radiative losses constitute another powerful energy 260
loss process, one may suspect that electromagnetic energy transport along the 261
magnetic field may be non‐negligible, at least initially. 262
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6. While the space situation may eventually find confirmation of this conclusion, the 263
lab situation needs further investigation of the respective roles of collisional and 264
electromagnetic energy transport out of the layer. 265
In conclusion we can only express our surprise about the temporal proximity of the 266
respective publications of lab experiment and stop layer concept. Unaware of the first the 267
publication of the latter followed by only ten months, and their commonalities were 268
discovered accidentally only five months later. What has been a conjecture in case of the 269
stop layer, derives strong support from the lab experiment. On the other hand, it provides 270
some theoretical underpinning of the findings in the lab. In both cases, further investigations 271
are needed. This applies in particular to the stop layer concept, which, apart from future 272
verifications by satellite data, should not be too difficult to be simulated numerically. As 273
pointed out already in (Haerendel 2015a), the stop layer concept represents the inverse to 274
the reconnection concept, in that the first is about a direct conversion of flow energy into 275
electromagnetic energy, whereas the latter is about conversion of electromagnetic energy 276
into flow energy. Both mechanisms play on scales of the ion inertia length, involve Hall 277
currents and electric polarization fields. More in‐depth research will eventually reveal the 278
existence of sub‐structures on the scale of the electron inertial length. 279
ADDENDUM: It is illuminating to pin down the inverse relation between stop layer and 280
reconnection at the example of the dipolarization fronts observed as part of the flow bursts 281
which structure the reconnection outflow. Runov et al. [2011] have shown that the leading 282
edge of a dipolarization front, the steep increase of the Bz‐component, has a scale of the 283
order of the thermal gyroradius. The measured normal electric field is consistent with the 284
estimated Hall field. It is this electric field which accelerates and injects ions in the upstream 285
direction. The recoil of the injected ion flux balances the magnetic stresses of the 286
dipolarization front in the frame of the overall flow. The situation is quite alike to the one 287
found to exist at the rear edge at the artificial comets [Haerendel et al. 1986]. The reactive 288
force of the accelerated ions corresponds to the braking force of the ions in the stop layer. 289
ACKNOWLEDGMENTS 290
We are indebted to Harald Frey for generating the two mosaic images of Figure 3 from the 291
01 March 2011 auroral event. We further thank S. Mende and E. Donovan for use of the all 292
sky data of the stations Gakona and Fort Yukon, Alaska, of the THEMIS GBO network. 293
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Figure 1: Sketch of a high‐beta plasma flow into the stop layer at the interface of magnetic 319
tail and near‐dipolar magnetosphere, including the Poynting flux, Sp, out of the layer 320
towards the ionosphere (Haerendel 2015a). 321
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Figure 2: Sketch of the stop layer modified by structure formation of order c/ωpi (Haerendel 324
2015a). Owing to divergence of the Hall current, each individual structure of size div is 325
framed by sinks and sources of field‐aligned currents. 326
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Figure 3 a & b: Two superposed projections of all‐sky images from Gakona and Ft. 330
Yukon/Alaska at 1 and 29 min after onset of the substorm of 01 March 2011. The structured 331
bright fronts are identified with stop layers. 332
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Figure 4: Sketch of current sheet avalanche and stop layer defining the geometry and the key 336
quantities (see text) (Haerendel 2015a). 337
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Figure 5. Interferometry image (a) and the corresponding map of electron line density (b) showing 352
structure of magnetically mediated standing shock formed in collision of supersonic magnetised 353
plasma flow with a planar conducting obstacle (Lebedev et al. 2014). 354
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Figure 6. Faraday rotation measurements of the structure of magnetic field in the magnetic precursor 371
layer formed ahead of the conducting obstacle: a) – rotation angle (degrees), b) – magnetic field (T). 372
The sub‐shock at the time of these measurements is positioned at ~2.5mm from the obstacle. 373
374
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Figure 7. Set of XUV images obtained in the same experiment. Plasma flows horizontally from the 375
wire at the left, the sub‐shock is formed at ~1.5mm from the obstacle, and the first two images show 376
modulation of emission at the shock front and in the post‐shock region. 377
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