Download S. Savin

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|2/8p ~niMiVA2/2 Z
For IMF Bz<0
MP moves
inward:
Rs=11.3+0.25Вz
Rs –subsolar MP
distances in
Earth radii,
‘В’, in nT
X
Y
Reconnection
[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
Interball-1, May 26, 1996, 01-04 UT
Byz
|B|
Bx -spectra,
0.1 –10 Hz
SW
BS
MSH
TBL
MP
cusp
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
|B| on MHD model MP
Bin
Bout
|B|
small
large
MP from [Maynard, 2003] -last closed field lines for the northern axis of dipole,
deflected by 23 degrees anti-sunward (colored by - |B|)
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
Energy transformation in MSH
Magnetosheath (MSH)
niTi + niMi/2(<Vi>2+(<dVi2>) + |B|2/8p
{1} >
{2}
{3}
Low latitude boundary layer (LLBL)
niTi + niMi/2(<Vi>2+(<dVi2>) + |B|2/8p
{1} >
{2}
<< {3}
macro
RECONNECTION
niMiVA2/2
micro
RECONNECTION
Turbulent Boundary Layer (TBL) and outer cusp
niTi + niMi/2(<Vi>2+(<dVi2>)+|B|2/8p +|dB|2/8p
{1} ~
{2}
>>
{3} <
{4}
MSH
MP
BIMF
Bin
Fx ,
u
magnetosphere
Fz
Relation of viscous gyro-stress to that of Maxwell:
~ const
u/B 3
0
where ru- directed ion gyroradius, and L – the MP width. For b ~ 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)
Cluster OT crossing on 2002.02.13
theta
L ~ RE
En
magnetosphere
OT
MSH
dipole tilt~14 d
phi
energetic ions
|B|
ions
energetic electrons
Surface charge decelerates plasma flow along normal
electrons
and accelerates
it along magnetopause tailward
• Quicklook for OT
encounterMSH
(09:00-09:30
MP
cusp
Plasma jet interaction with MP
niMiVi2/2 < k (Bmax)2 /m0
[k ~ (0.5-1) – geometric factor]
niMiVi2/2 > k (Bmax)2 /m0
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/m0 in the absence of effective
dissipation (that is well known in laboratory plasma physics)
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.,
Part of the time, when ions are in resonance with the wave
- perpendicular ion energy
s that can provide the particle flow
across the southern and northern TBL, which is large
enough i.e. for populating of the dayside magnetosphere
Measurements of ioncyclotron 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
Plasma percolation via the
structured magnetospheric
boundary
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(dB/B0)ri2 Wi ~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~k^2ri2Te/Ti VA/k||(dB/B0)2~
~ const/B03 ~ 1010 m2/s
Interpretation of
the early data
from Prognoz-8
in terms of the
surface charge at
MP
Ion flux
magnetosphere
re ~
MSH
[Vaisberg, Galeev, Zelenyi, Zastenker, Omel’chenko, Klimov И.,
Savin et al., Cosmic Researches, 21, p. 57-63, (1983)]
Mass and momentum
transfer across MP of
finite-gyroradius ion
scale
~90 km  ri at 800 eV
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).
~ along MP
normal
dominant flow
along MP
Cluster 1, February 13, 2001
Thin 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
dF ~300 V
1
Mechanisms for acceleration of
plasma jets
Besides macroreconnection of anti-parallel magnetic
fields (where the magnetic stress can accelerate the
plasma till niMiViA2 ~ B2/8p), 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
.
Magneto
sonic jet
-Acceleration in the
perpendicular nonuniform electric field
by the inertial drift
-Fermi-type
acceleration by a
moving boundary;
Bi-coherence & the
energy source for
the magnetosonic
jet
Fl + Fk = F
mHz
Inertial drift
Vd(1) = 1/(M wH2) dF/dt = Ze/(M wH2) dE/dt
d Wkin ~ d(nM(Vd(0))2/2) ~ 30 keV/сm3 (28 measured)
Vd(0) = с[ExB] ; J ~ e2/(MpwHp2)dE/dt
Electric field
in the MSH
flow frame
Cherenkov nonlinear resonance
1.4 +3 mHz = fl + f k = (kV)/2p ~ 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
TBL
dipole
MSH tilt~19 deg.
cusp
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
reconnection bulges
GDCF model
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. 14251434,
(2000)]
Ms~2
magnetosphere
Ms~1.2
MSH
[ 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
Reconnection
X
Reconnection
X
Reconnection
X
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
B2/8p
nTi
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
=
Fs
vertical
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 ~
re or c/wpe
From both
inter-spacecraft
lag and
curl B=4p/c j
CLUSTER-1
2001.02.02,
16:00-17:30
UT. Panels:
a) Ex bispectrogram
b) wavelet Ex
spectrogram
(.3 – 20 mHz,
lines– inferred
cascades)
c)Ex waveform
d) |B|
e)Ex spectrum;
Insert 1 – a
cascade on Eyspectrogram,
1610-1625 UT
‘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 (dBx>8 nТ)
crossings by Interball-1 from the
dipole tilt (normalized by the SW
dynamic pressure)
GSM dependence of turbulent
boundary layer (dBx>13 nТ) crossings
by Polar from the dipole tilt
(normalized by the SW dynamic
pressure)
March 24, 2001, Cluster
• For collapse at ion
gyroradius scale we
estimate equilibrium from
DH B  curl u  B = 0
u^   DH  | B | / | B | VTi
We estimate DH from shift by
squared ion gyroradius ri2 at ion
gyroperiod for the gradient scale
~ ion gyroradius
a nonlinear wave
linear mirror
waves
decay, cascade, transformation
at MP/BL,…
(e.g. KAW=>AW+MS)
nonlinear
mirror waves
jets
Interaction with MP
Interaction
with MP/BL
current
sheet (CS)
Hall
dynamics
reconnection
CS residuals
‘diamagnetic bubbles' (DB)
or 'mirror structures' (MS)
-(purely) nonlinear eigen mode?
-phase state with minimum energy?
-topology (sizes!), equilibrium,
energy sources?
Possible relation to Alfvenic collapse :
-another eigen mode?
-possible mixed eigen mode with DB and Alfvenic collapsons?
jets
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:
??
D  c / w pe  r e  c / w pi  r i
Few 10’s m
UHW,
few km
30-500 km
LHW, isomagnetic shocks
DB/ Mirror structures
wpe-waves
distance
between
Electric probes
AC/ magnetic barriers
Jets
Inter-Cluster distance
Conclusions
- 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 finitegyroradius scale,
-filamentary penetrated plasma (including jets, accelerated by inertial drift in nonuniform 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.