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