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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 p ~n i M i V A 2 /2. Re-connection

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The flow dynamic pressure compress the magnetic fieldat magnetopause (MP), which while reconnected, in turn, accelerates plasmaacross the flowtill Alfven speedby the magnetic stress, then:|B|2/8p ~niMiVA2/2


[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 ]


For IMFBz<0 MPmovesinward:

Rs=11.3+0.25ВzRs–subsolar MP distances in Earth radii,‘В’,innT




[Chapman & Ferraro, JGR, 36, 77, 1931]

[Axfordet 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

Interball-1, May 26, 1996, 01-04 UT




Bx -spectra, 0.1 –10 Hz




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






MP from[Maynard, 2003] -last closed field linesfor the northern axis of dipole, deflected by 23 degrees anti-sunward(colored by - |B|)

interball 1 ot summary
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 winterOT 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}niMiVA2/2

Turbulent Boundary Layer (TBL) and outer cusp

niTi +niMi/2(<Vi>2+(<dVi2>)+|B|2/8p+|dB|2/8p

{1} ~{2} >> {3} <{4}








Fx ,u



Relation ofviscous gyro-stressto that of Maxwell:

~ const u/ B03

where ru- directed ion gyroradius, and L – the MP width. Forb ~ 1-10 near MPthe viscous gyro-stressis of the order of that of Maxwell.Velocityu, rises downstream of the subsolar point, magnetic field B0 - has the minimun over cusp, i.e.the gyroviscousinteractionis most significantat 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
Cluster OT crossing on 2002.02.13


L ~ RE


  • 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.




dipole tilt~14 d


energetic ions



energetic electrons

Surface charge decelerates plasma flow along normal and accelerates it along magnetopause tailward






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 asproof for a macroreconnection; while every jet, accelerated in MSH should be reflected bya magnetic barrier forniMiVi2< (Bmax)2/m0in the absence of effective dissipation(that is well known in laboratory plasma physics)

resonance interaction of ions with electrostatic cyclotron waves
Resonance interaction of ions withelectrostaticcyclotron waves

Diffusion across the magnetic field can be due to resonance interaction of ions

withelectrostaticcyclotron 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


Measurements of ion-cyclotron waves onPrognoz-8, 10, Interball-1in the turbulent boundary layer (TBL) over polar cusps. Maximums are at the proton-cyclotron frequency.

Shown also are the data fromHEOS-2 (E=1/c[VxB]),and from the low-latitude MPAMPTE/IRMandISEE-1.

Estimation of the diffusion coefficient due toelectrostatic ion-cyclotron wavesdemonstrates thatthe dayside magnetosphere can be populated by the solar plasmathrough the turbulent boundary layer


Plasma percolation via the structured magnetospheric boundary

Percolationis 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)109m2/s


One can get a similar estimate for thekinetic Alfven waves (KAWin[Hultquist et al., ISSI, 1999, p. 399]):

DKAW~k^2ri2Te/Ti VA/k||(dB/B0)2~~const/B03 ~1010m2/s


Interpretation of the early data from Prognoz-8in terms of the surface charge at MP

Ion flux


re ~


[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

~ along MP normal

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).

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 currentat theTCS

dF ~300 V

mechanisms for acceleration of plasma jets
Mechanisms for acceleration of plasma jets
  • Besidesmacroreconnectionof 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 boundariesby inertial (polarization) drift.

Magneto sonic jet

  • Acceleration in the perpendicular non-uniform electric field by the inertial drift
  • Fermi-type acceleration by a moving boundary;

Inertial driftVd(1) = 1/(M wH2) dF/dt = Ze/(M wH2) dE/dtd 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 f l f k kv 2 p 4 4 mhz l v f l f k 5 r e
Cherenkov nonlinear resonance1.4 +3 mHz = fl + f k = (kV)/2p ~ 4.4 mHzL =|V| /( fl + fk )~ 5 RE

Maser-like ?

simultaneous polar data in northern ot


dipole tilt~19 deg.


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

reconnection bulges

GDCF model


In the jets kinetic energyWkin rises from ~ 5.5 to 16.5 keV/cm3For a reconnection acceleration till Alfvenic speed VA it is foreseen WkA ~ ni VA2/2 ~ const |B|2that 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)]







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-1G- Geotail; P- Polar










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 regioninto 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
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


May 29, 1996, 10:00-10:45 UT






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 b x in tbl at 0916 0950 ut on june 19 1998 fl fk fs vertical horizontal
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

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

Split probe

Search coil



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 waveform

d) |B|

e)Ex spectrum; Insert 1 – a cascade on Ey-spectrogram, 1610-1625 UT


Transverse (blue) and compressible (red) magnetic fluctuations from Polar data near MP normalized by SW dynamic pressure.

Transverse (blue) and compressible (red) magnetic fluctuations from Interball-1 data near MP normalized by 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)

GSM dependence of turbulent boundary layer (Bx>13nТ) crossings by Polar from the dipole tilt (normalized by the SW dynamic pressure)


For collapse at ion gyroradius scale we estimate equilibrium from

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
‘Cavitation' as a fundamental feature of turbulent plasma:


Interaction with MP

re- con- nec- tion

a nonlinear wave

current sheet (CS) Hall dynamics

linear mirror waves


with MP/BL

nonlinear mirror waves

decay, cascade, transformation at MP/BL,…

(e.g. KAW=>AW+MS)

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 & DB relation toAlfvenic collapse (AC):

  • AC - another eigen mode (along with DB)? Possible mixed eigen modewith 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 DBon the background of the larger external field and smaller plasma pressure.
  • - The latterDB 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
Collapse of magnetosound waves and shocks



Few 10’s mfew km30-500 km

UHW, LHW, isomagnetic shocksDB/ Mirror structures

wpe-wavesAC/ magnetic barriers


betweenInter-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 wavesprovide 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.