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  ~n i M i V A 2 /2 For IMF Bz<0 MP moves inward: R s = В z R s –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 BxBx B yz |B| B x -spectra, 0.1 –10 Hz SW BS MSH TBL MP Interball-1, May 26, 1996, 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 R E ) Re r i ~ cusp

Distribution of the high level turbulence (RMS>5 nT) for Interball-1 magnetic field in Different magnetic dipole tilt angles are color- coded

MP from [Maynard, 2003] -last closed field lines for the northern axis of dipole, deflected by 23 degrees anti-sunward (colored by - |B|) |B||B| B in B out |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 at UT by Interball-1 and Polar are shown

Magnetosheath (MSH) n i T i + n i M i /2( 2 +( ) + |B| 2 /8  {1} > {2} {3} Low latitude boundary layer (LLBL) n i T i + n i M i /2( 2 +( ) + |B| 2 /8  {1} > {2} << {3} n i M i V A 2 /2 Turbulent Boundary Layer (TBL) and outer cusp n i T i + n i M i /2( 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 / B 0 3 where r u - 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 B 0 - 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) F x, u FzFz B IMF B in MSH magnetosphere MP

Cluster OT crossing on 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 OTMSHmagnetosphere dipole tilt~14 d L ~ R E Surface charge decelerates plasma flow along normal and accelerates it along magnetopause tailward EnEn MP MSH cusp

n i M i V i 2 /2 < k (B max ) 2 /  0 [k ~ (0.5-1) – geometric factor] n i M i V i 2 /2 > k (B max ) 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 n i M i V i 2 < (B max ) 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., 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 enough i.e. for populating of the dayside magnetosphere 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] : D p ~0.66(  B/B 0 )  i   i ~const/ B 0 2 ~(5-10)10 9 m 2 /s One can get a similar estimate for the kinetic Alfven waves (KAW in [Hultquist et al., ISSI, 1999, p. 399]): D KAW ~k  2  i 2 T e /T i V A /k || (  B/B 0 ) 2 ~ ~ const / B 0 3 ~ m 2 /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 , (1983)] Interpretation of the early data from Prognoz-8 in terms of the surface charge at MP

Cluster 1, February 13, (a) ion flux ‘nV ix ’, blue lines – full CIS energy range), black – partial ion flux for > 300 eV, red – for > 1keV ions; (b) the same for ‘nV iy ’; (c) the same for ‘nV iz ’; (d): ion density n i (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

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  ~300 V

Mechanisms for acceleration of plasma jets Besides macroreconnection of anti-parallel magnetic fields (where the magnetic stress can accelerate the plasma till n i M i V iA 2 ~ B 2 /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

F l + F k = F mHz Bi-coherence & the energy source for the magnetosonic jet

Inertial drift V d (1) = 1/(M  H 2 ) dF/dt = Ze/(M  H 2 ) dE/dt  W kin ~  (nM(V d (0) ) 2 /2) ~ 30 keV/сm 3 (28 measured ) V d (0) = с[ExB] ; J ~ e 2 /(M p  Hp 2 )dE/dt Electric field in the MSH flow frame

Cherenkov nonlinear resonance mHz = f l + f k  (kV)/2  ~ 4.4 mHz L = |V| /(  f l + f k )   5 R E 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 UT to GDCF. - energetic He++ at UT energetic tails of the MSH ions reach ~200 keV, that infers local acceleration GDCF model reconnection bulges cusp TBL MSH dipole tilt~19 deg.

In the jets kinetic energy W kin rises from ~ 5.5 to 16.5 keV/cm 3 For a reconnection acceleration till Alfvenic speed V A it is foreseen W kA ~ n i V A 2 /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 , (2000)]

MSH magnetosphere M s ~2 M s ~1.2

[ Shevyrev and Zastenker, 2002 ]

23/ , 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 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 E kin of 5 keV/сm 3 requires magnetic field pressure (W b ) > 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, 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

nT i B 2 /8  MnV i 2 /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, 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, From bottom: Magnetic field magnitude; Magnetic vector hodograms in maximum/ intermediate (left) and maximum/ minimum (right) variance frames.

Bi-spectrogram of B x in TBL at UT on June 19, 1998 Fl + Fk = Fs vertical horizontal Bi-spectrogram of B z 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 c url B=4  /c j

, 16:00-17:30 UT. Panels: a) Ex bi- spectrogram b) wavelet Ex spectrogram (.3 – 20 mHz, lines– inferred cascades) c)Ex waveform d) |B| e)Ex spectrum; Insert 1 – a cascade on Ey- spectrogram, 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 We estimate D H 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 current 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: Few 10’s m few km km UHW, LHW, isomagnetic shocks DB/ Mirror structures  pe -waves AC/ magnetic barriers distanceJets 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) 10 9 m 2 /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