the flow dynamic pressure compress the magnetic field at magnetopause (mp), which while reconnected,...
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The flow dynamic pressure compress the magnetic field at magnetopause (MP), which while reconnected, in turn, accelerates plasma across the flow till Alfven speed by the magnetic stress, then:
|B|2/8~niMiVA
2/2For IMF Bz<0 MP moves inward:
Rs=11.3+0.25Вz Rs –subsolar MP distances in Earth radii,
‘В’, in nT
X
Y
Z
Re-connection
[Sweet, P. А. (1958), in
Lehnert, В. (ed.) Electromagnetic
Phenomena и Cosmic Physics, 123, Cambridge Univ. Press, New York]
[Parker, E. N., (1963), Phys. Rev.,
107, 924 ]
[Chapman & Ferraro, JGR, 36, 77, 1931] [Axford et al., JGR, 70, 1231, 1965]
[Stern, JGR, 90, 10,851,1985]
[V. Pletnev, G. Skuridin, V. Shalimov, I. Shvachunov, "Исследования космического
пространства" М.: Наука,
1965]
Distribution of surface currents
A question since 1978: Does TBL
exist?
There are 2 characteristic
examples from
Interball-1
Bx
Byz
|B|
Bx -spectra, 0.1 –10 Hz
SW BS MSH TBL MP
Interball-1, May 26, 1996, 01-04 UT
Generation of turbulent boundary layer in the process of interaction of hydrodynamic flow with obstacle (from [Haerendel, 1978]). “1” – marks open cusp throat, “2” – stands for high latitude boundary layer downstream the cusp.
Reynolds number (for the cusp scale of 2-3 RE) Reri ~ 100-500
cuspcusp
MP from [Maynard, 2003] -last closed field lines for the northern axis of dipole, deflected by 23 degrees anti-sunward (colored by - |B|)
|B|
Bin
Bout
|B| on MHD model MP
small
large
Interball-1 OT summary
• In summer outer cusp throat (OT) is open for the MSH flow.TBL (turbulent boundary layer) is mostly in MSH.
• In winter OT is closed by smooth MP at larger distance. Inside MP ‘plasma balls’ (~few Re) contain reduced field, heated plasma & weaker TBL.
• OT encounters on 98.06.19 at 10-11 UT by Interball-1 and Polar are shown
Magnetosheath (MSH)
niTi + niMi/2(<Vi>2+(<Vi
2>) + |B|2/8
{1} > {2} {3}
Low latitude boundary layer (LLBL)
niTi + niMi/2(<Vi>2+(<Vi
2>) + |B|2/8
{1} > {2} << {3} niMiVA2/2
Turbulent Boundary Layer (TBL) and outer cusp
niTi + niMi/2(<Vi>2+(<Vi
2>)+|B|2/8+|B|2/8
{1} ~ {2} >> {3} < {4}
macro RECONNECTION
Energy transformation in MSH
micro RECONNECTION
Relation of viscous gyro-stress to that of Maxwell:
~ const u / B03
where ru- directed ion gyroradius, and L – the MP width. For ~ 1-10 near MP the viscous gyro-stress is of the order of that of Maxwell. Velocity
u, rises downstream of the subsolar point, magnetic field B0 - has the
minimun over cusp, i.e. the gyroviscous interaction is most significant at the outer border of the cusp, that results in the magnetic flux diffusion
(being equivalent to the microreconnection)
Fx , uFz
BIMF Bin
MSH
magnetosphere
MP
Cluster OT crossing on 2002.02.13
• Quicklook for OT encounter (09:00-09:30 UT) Energetic electrons & ions are seen generally in OT, not in magtosphere, they look to be continuous relative to the lower energy particles. Note also the maximum in energetic electrons at the OT outer border at ~09:35 UT. The upstream energetic particles are seen to 10:30 UT.
|B|
theta
phi
energetic electrons
electrons
energetic ions
ions
OT MSHmagnetospheredipole tilt~14 d
L ~ RE
Surface charge decelerates plasma flow along normal and accelerates it along magnetopause tailward
En
MPMSH cusp
niMiVi2/2 < k (Bmax)2 /0
[k ~ (0.5-1) – geometric factor]
niMiVi2/2 > k (Bmax)2 /0
The plasma jets, accelerated sunward, often are regarded as proof for a macroreconnection; while every jet, accelerated in MSH should be reflected by a
magnetic barrier for niMiVi2 < (Bmax)2/0 in the absence of effective
dissipation (that is well known in laboratory plasma physics)
Plasma jet interaction with MP
Resonance interaction of ions with electrostatic cyclotron waves
Diffusion across the magnetic field can be due to resonance interaction of ions
with electrostatic cyclotron waves
et al.,et al.,
Part of the time, when ions are in resonance with the wave- perpendicular ion energy
that can provide the particle flow
across the southern and northern TBL, which is large across the southern and northern TBL, which is large enough i.e. for populating of the dayside enough i.e. for populating of the dayside magnetospheremagnetosphere
s
Measurements of ion-cyclotron waves on Prognoz-8, 10, Interball-1 in the turbulent boundary layer (TBL) over polar cusps. Maximums are at the proton-cyclotron frequency.
Shown also are the data from HEOS-2 (E=1/c[VxB]), and from the low-latitude MP AMPTE/IRM and ISEE-1.
Estimation of the diffusion coefficient due to electrostatic ion-cyclotron waves demonstrates that the dayside magnetosphere can be populated by the solar plasma through the turbulent boundary layer
Percolation is able to provide the plasma inflow comparable with that due to electrostatic ion cyclotron waves [Galeev et al.,
1985, Kuznetsova & Zelenyi, 1990] : Dp~0.66(B/B0)i
i ~const/B02 ~(5-
10)109 m2/s-----------------------------------------------------------------------------------------------------------------
One can get a similar estimate for the kinetic Alfven waves (KAW in [Hultquist et al., ISSI, 1999, p. 399]):
DKAW~k2i
2Te/Ti VA/k||(B/B0)2~ ~
const/B03 ~ 1010 m2/s
Plasma percolation via the structured magnetospheric
boundary
MSH
magnetosphere
Ion flux
e ~
[Vaisberg, Galeev, Zelenyi, Zastenker, Omel’chenko, Klimov И., Savin et al., Cosmic Researches, 21, p. 57-63, (1983)]
Interpretation of the early data
from Prognoz-8 in terms of the
surface charge at MP
Cluster 1, February 13, 2001. (a) ion flux ‘nVix’, blue
lines – full CIS energy range), black – partial ion flux for > 300 eV, red – for > 1keV ions; (b) the same for ‘nViy’; (c)
the same for ‘nViz’; (d):
ion density ni (blue),
partial ion density for energies > 300 eV (black) and that of > 1 keV (red).
Mass and momentum transfer across MP of finite-gyroradius ion scale ~90 km i at 800 eV
~ along MP normal
dominant flow along MP
1
Cluster 1, February 13, 2001Thin current (TCS) sheet at MP (~ 90 km) is transparent for ions with larger gyroradius, which transfer both parallel and perpendicular momentum and acquire the cross-current potential. The TCS is driven by the Hall current, generated by a part of the surface charge current at the TCS
~300 V
Mechanisms for acceleration of plasma jets
Besides macroreconnection of anti-parallel magnetic fields (where the magnetic stress can accelerate the plasma till niMiViA
2 ~ B2/8), there are experimental evidences for:
-Fermi-type acceleration by moving (relative the incident flow) boundary of outer boundary layer;
- acceleration at similar boundaries by inertial (polarization) drift.
-Acceleration in the perpendicular non-uniform electric field by the inertial drift
-Fermi-type acceleration by a moving boundary;
Magneto sonic jet
Fl + Fk = FmHz
Bi-coherence & the energy source for the magnetosonic
jet
Inertial drift
Vd(1) = 1/(M H
2) dF/dt = Ze/(M H2) dE/dt
Wkin ~ (nM(Vd(0))2/2) ~ 30 keV/сm3 (28 measured)
Vd(0) = с[ExB] ; J ~ e2/(MpHp
2)dE/dt Electric field in the MSH flow frame
Cherenkov nonlinear resonance
1.4 +3 mHz = fl + f k (kV)/2 ~ 4.4 mHz
L = |V| /( fl + fk )5 RE
Maser-like ?
Comparison of the TBL dynamics and model Lorentz system in the state of intermitten
chaos
Simultaneous Polar data in Northern OT
• From top: -Magnetic field
• Red lines- GDCF model, difference with data is green shadowed
• -energy densities of magnetic field, ion thermal & kinetic,
• note deceleration in OT in average relative to GDCF model (red) & ~fitting of kinetic energy in reconnection bulges at 10-11 UT to GDCF.
• -energetic He++• at 10-11 UT energetic
tails of the MSH ions reach ~200 keV, that infers local acceleration
GDCF model
reconnection bulges
cusp
TBL MSHdipole
tilt~19 deg.
In the jets kinetic energy Wkin rises from ~ 5.5 to 16.5 keV/cm3
For a reconnection acceleration till Alfvenic speed VA it is foreseen
WkA ~ ni VA2 /2 ~ const |B|2
that requires magnetic field of 66 nT (120 nT inside MP if averaged with MSH)
[Merka, Safrankova, Nemecek, Fedorov,
Borodkova, Savin,
Adv. Space Res., 25, No. 7/8, pp. 1425-
1434, (2000)]
MSH
magnetosphere
Ms~2
Ms~1.2
[ Shevyrev and Zastenker, 2002 ]
23/04-1998, MHD model, magnetic field at 22:30 UT; blue – Earth field; red - SW; yellow - reconnected; right bottom slide – plasma density;
I- Interball-1 G- Geotail; P- Polar
X
X
ReconnectionX
Reconnection
Reconnection
The jet is also seen by POLAR (~ 4 Re apart in TBL closer to MP)
BS
MP
• Interball-1 outbound from cusp to TBL, stagnation region and MSH (April 2, 1996)
• The jet with extra kinetic energy Ekin of 5 keV/сm3 requires magnetic field pressure (Wb) > than inside MP
(which should be averaged with that in MSH!)
Fine structure of transition from stagnation region into streaming magnetosheath: magnetic barrier with the
trapped ions• Energy per
charge spectrogram for tailward ions (upper), and magnetic field magnitude |B|
INTERBALL-1, April 2, 1996
Vortex street on April 2, 1996 in ion velocity (to the left) and in magnetic field (to the right)
• Interball-1 MSH/stagnation region border encounter on April 21, 1996.
• Comparison with switch-off slow shock [Karimabadi et al., 1995] displays strong magnetic barrier with pressure of the order of the MSH dynamic pressure. Inside ‘diamagnetic bubble’ ion temperature balances the external pressure
Polar,
May 29, 1996, 10:00-10:45 UT
nTi
B2/8
MnVi2/2
POLAR encounter of ‘diamagnetic bubbles’ on May 29, 1996 with general dominance of parallel ion temperature
• Interball-1 encounter of a double current sheet in TBL on June 19, 1998. From bottom: Magnetic field magnitude |B| (variation matrix eigenvalues are printed at the right side); Normal component and its unit vector in GSE; The same for intermediate component; The same for maximum variance component; Magnetic vector hodograms in maximum/ intermediate (left) and maximum/ minimum (right) variance frames.
• Polar encounter of a current sheet in TBL on June 19, 1998. From bottom: Magnetic field magnitude; Magnetic vector hodograms in maximum/ intermediate (left) and maximum/ minimum (right) variance frames.
Bi-spectrogram of Bx in TBL at
0916- 0950 UT on June 19, 1998 Fl + Fk = Fsvertical horizontal
Bi-spectrogram of Bz for the
virtual spacecraft crossing of the model current sheet
Faraday cups in electron mode
Split probe
Search coil
First direct detection of electron current sheet in TBL with scale ~ e or c/pe
From both inter-spacecraft lag and curl B=4/c j
2001.02.02, 16:00-17:30 UT. Panels: a) Ex bi-spectrogram b) wavelet Ex spectrogram (.3 – 20 mHz, lines– inferred cascades)c)Ex waveformd) |B| e)Ex spectrum; Insert 1 – a cascade on Ey-spectrogram, 1610-1625 UT
CLUSTER-1
‘Plasma ball’ crossings by Interball-1 versus dipole tilt angle
Transverse (blue) and compressible (red) magnetic fluctuations from Interball-1 data near MP normalized by SW dynamic pressure
Transverse (blue) and compressible (red) magnetic fluctuations from Polar data near MP normalized by SW dynamic pressure.
GSM dependence of turbulent boundary layer (Bx>13 nТ) crossings by Polar from the dipole tilt (normalized by the SW dynamic pressure)
.
GSM dependence of turbulent boundary layer (Bx>8 nТ) crossings by Interball-1 from the dipole tilt (normalized by the SW dynamic pressure)
March 24, 2001, Cluster
• For collapse at ion gyroradius scale we estimate equilibrium from
TiH
H
VBBDu
BuBD
||/||
0curl
We estimate DH from shift by squared ion gyroradius ri2 at ion gyroperiod for the gradient scale ~ ion gyroradius
‘Cavitation' as a fundamental feature of turbulent plasma:
‘diamagnetic bubbles' (DB) or 'mirror structures' (MS)
-(purely) nonlinear eigen mode? -phase state with minimum energy? -topology (sizes!), equilibrium, energy sources?
linear mirror waves
nonlinear mirror waves
re- con- nec- tion
jets
jetscurrent
sheet (CS) Hall
dynamics
Interaction with MP
Interaction with MP/BL
a nonlinear wave
decay, cascade, transformation at MP/BL,…
(e.g. KAW=>AW+MS)
CS residuals
Possible relation to Alfvenic collapse :
-another eigen mode? -possible mixed eigen mode with DB and Alfvenic collapsons?
Jets & DB relation to Alfvenic collapse (AC):
- AC - another eigen mode (along with DB)? Possible mixed eigen mode with co-existing DB and AC?
- Rising of |B| in AC (pinch?) should accelerate plasma first of all along magnetic field;
- Then this parallel 'jet' could deform further streamlines and magnetic field (which are curved in a flow around an obstacle), thus in the leading 'piston' the jet might become almost perpendicular (cf. the Interball case on June 19, 1998);
- Jet heating during interaction with the 'piston' should results in |B| dim (a DB?);
- In case of interaction (including the jet heating and decelerating), with MP/BL, having larger |B|, a jet (or its heated residual) will represent a DB on the background of the larger external field and smaller plasma pressure.
- The latter DB production mechanism is operative for a jet of any origin - either accelerated by a post-BS/ BL electrostatic structure, or produced in a (bursty) reconnection.
Collapse of magnetosound waves and shocks
SCALES in BS/ MSH/ MP:
ipiepeD cc //
Few 10’s m few km 30-500 km
UHW, LHW, isomagnetic shocks DB/ Mirror structures
pe-waves AC/ magnetic barriers
distance Jets
between Inter-Cluster distance
Electric probes
??
- Penetration of solar plasma into magnetosphere correlate with the low magnitude of magnetic field (|B|) (e.g. with outer cusp and antiparallel magnetic fields at MP).
-A mechanism for the transport in this situation is the ‘primary’ reconnection, which releases the energy stored in the magnetic field, but it depends on the IMF and can hardly account for the permanent presence of cusp and low latitude boundary layer. Instead, we outline the ‘secondary’ small-scale time-dependent reconnection.
Other mechanisms, which maximize the transport with falling |B|:- finite-gyroradius effects (including gyro-viscosity and charged current sheets of finite-gyroradius scale, -filamentary penetrated plasma (including jets, accelerated by inertial drift in non-uniform electric fields), -diffusion and percolation, In minimum |B| over cusps and ‘sash’ both percolation and diffusion due to kinetic Alfven waves provide diffusion coefficients ~ (5-10) 109 m2/s, that is enough for populating of dayside boundary layers. Another mechanism with comparable effectiveness is electrostatic ion-cyclotron resonance. While the cyclotron waves measured in the minimum |B| over cusps on Prognoz-8, 10 and Interball-1 have characteristic amplitude of several mV/m, the sharp dependence of the diffusion on |B| provides the diffusion ~ that of the percolation.
Conclusions
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