Forced kinetic current sheet formation as related to magnetic reconnection in the magnetosphere A. P. Kropotkin and V. I. Domrin Skobeltsyn Institute of Nuclear Physics, Moscow State University

Slow magnetic energy accumulation in the tail: loading phase Fast energy release: unloading phase Role of the current sheet in that fast process: energy transformation, jE>0, over a large portion of the CS What are the specific mechanisms?

Asymptotic solution,  Ion trajectories: -meander or centrifugal drift in the central region  Momentum balance over x: magnetic tension is balanced by the pressure gradient - drift in - outside No energy transformation Birn – Schindler equilibrium current sheet

CS with arise as a result of dynamical reconfiguration. This can begin with a fast loss of initial equilibrium starting with a weak violation of existing force balance. A small initial disbalance: quasi-1D if processes on an intermediate time scale are considered: MHD wave transit time in CS MHD wave transit time in the tail

2 alternatives A. “Internal” initial disturbance in CS: balance violated : No wave from outside. B. “External” initial disturbance: a pair of fast MHD waves impinging on both sides of CS.

Simulation A Initially: hot plasma in a Harris-type CS Cold uniform plasma background 1D hybrid code: ions treated as macroparticles, electrons as cold massless background; self- consistent electromagnetic fields. Simulation domain 3 times larger that the CS thickness.

Results - decay of a non- equilibrium discontinuity with field reversal and

- fast MHD waves ahead of slow switch-off MHD shocks

- formation of a finite field E

- formation of a switch-off shock front - convection towards CS between the MHD fast and slow fronts - fast (v~V A0 ) convection along x at the center

- diminishing B x : “dipolarization” CONSISTENCY WITH THEORY - energy transformation at the shock fronts - wave speeds E + [vB]/c = 0

Simulation B Initial thinning violates the force balance over x: may be set Disturbance is induced by collisionless fast shocks incident on both sides of CS

A very thin CS is formed at the central plane This is a stationary Forced Kinetic Current Sheet (FKCS)

Current sheet thinning: cumulative effect of non- stationary convection Weak external MHD trigger wave produces a cumulative nonlinear effect of CS thinning and its transformation into the anisotropic Forced Kinetic Current Sheet (FKCS) This specific steady-state solution corresponds to possibility of momentum balance in CS over x by means of anisotropy – prevalence of the field- aligned ion motion.

Earlier work S.W.H.Cowley and R.Pellat, 1979, Planet. Space Sci., v.27, 265. J.W.Eastwood, 1972, Planet. Space Sci., v.20, T.W.Hill, 1975, J.Geophys. Res., v.80, T.W.Speiser, 1970, Planet. Space Sci., v.18, 613. Semi-qualitative solution P.Frankfort and R.Pellat, 1976, Geophys. Res Lett., v.3, 433.

Self-consistent theory A.P.Kropotkin and V.I.Domrin, 1996, Theory of a thin one- dimensional current sheet in collisionless space plasma. J. Geophys. Res., vol. 101, р A.P.Kropotkin, M.I.Sitnov, and Ch.V. Malova, 1997, The self- consistent structure of a thin anisotropic current sheet. J. Geophys. Res., v.102 (A10), p M.I.Sitnov, L.M.Zelenyi, H.V.Malova, and A.Sharma, 2000, Thin current sheet embedded within a thicker plasma sheet:self- consistent kinetic theory, J. Geophys. Res., 105 (A6), p V.I.Domrin and A.P.Kropotkin, 2002, A kinetic model of thin current sheet generation and its role in magnetic reconnection in space plasmas. Proc. Sixth International Conference on Substorms (ICS-6), Univ. of Washington, Seattle, USA, p

Trajectory of an ion forming the anisotropic current sheet Current sheet

Inside the CS: motion in the y direction and oscillations under action of restoring force Outside the CS: motion along x; v 0 >>v T Ion distribution function: I is the adiabatic invariant of z-oscillations, Generally the CS profile B(z) determined by arbitrary functions P,  Far from CS: set Maxwellian counter-streaming ion beams separated by 2V A The structure scale length:

Consistency with theory - B(z) profile - finite energy transformation rate: electric field E and the Pointing vector

The process becomes independent of the triggering disturbance, and appears to be spontaneously self-sustained, as a finite magnitude MHD disturbance of a rarefaction wave type propagates back over the background plasma outside the CS. [V.I.Domrin and A.P.Kropotkin, 2004, Geomagn. and aeronomy, No.2]

Like at the Alfvenic discontinuity in MHD, transformation of electromagnetic energy into the energy of plasma flows occurs at the FCS. However, unlike the MHD case, generation of "free" energy takes place in the course of that transformation: a strongly anisotropic ion distributions, with counter-streaming ion flows, are produced. That "free" energy should then dissipate, in the course of the distribution relaxation, through particle interaction with turbulent waves generated by unstable ion distribution. In this way, an effect of magnetic field "annihilation" takes place, which is a necessary constituent of fast magnetic reconnection.

“FREE ENERGY” SOURCES IN THE TRANSITION REGION High p gradient in the quasi-dipole subregion High j in the taillike subregion Both are associated with enhanced B in lobes in the near-Earth portion of tail

ALTERNATIVE DISTURBANCES: A INITIALLY: nonlinear ballooning-type instability in the quasi-dipole subregion Fast “sausage”-type disturbance propagates inside CS with velocity ~V A0 and provides a disbalance of the magnetic tension and the pressure gradient component Formation of FAST RAREFACTION – SLOW SHOCK pairs Spontaneous magnetic field “annihilation” and “dipolarization” BBF Bifurcated CS

ALTERNATIVE DISTURBANCES: B INITIALLY: nonlinear tearing-type instability in the tail subregion Fast trigger signal in the fast MHD mode propagating towards CS Formation of FORCED KINETIC CURRENT SHEET with extremely anisotropic ion distributions Spontaneous magnetic field “annihilation” and “dipolarization”