Magnetic Weibel field generation in thin collisionless current sheets in reconnection in space plasma

In collisionless reconnection in space plasma like the magnetospheric tail or magnetopause current layer, magnetic fields can grow from thermal level by the action of the non-magnetic Weibel instability driven in thin (∆ < few λi) current layers by the counter-streaming electron inflow from the ‘ion diffusion’ (ion inertial Hall) region into the inner current (electron inertial) region from where the ambient magnetic fields are excluded when released by the inflowing electrons which become non-magnetic on scales < few λe. It is shown that under magnetospheric tail conditions it takes ∼ 40 e-folding times (∼ 20 s) for the Weibel field to reach observable amplitudes |bW| ∼ 1 nT. In counter-streaming inflows these fields are predominantly of guide field type. In non-symmetric inflows the field may possess a component normal to the current which would be capable of initiating reconnection onset. Introduction. – Space observations in situ [1–4] and kinetic numerical simulations [5–7] unambiguously prove that magnetic reconnection in the collisionless space plasma proceeds under the following two conditions: • The first condition is that the current sheets – that separate the involved oppositely directed (‘anti-parallel’) magnetic fields ±B to both sides of the current – become ‘thin enough’, where under ‘thin enough’ it is understood that the effective half-widths 2 ∆ . λi of the current sheets fall (approximately) below the ion inertial scale-length λi = c/ωpi (with c velocity of light, ωpi = e(N/ε0mi) 1 2 ion plasma frequency, e elementary charge, N plasma number density, mi ion mass). In fact the real limit on the width is not precisely known. Observations [4] suggest for instance that the width can reach values up to ∆ . 4λi. This condition is commonly (for example in [8, 9]) taken as sole indication that one is dealing with reconnecting collisionless current sheets. • The second condition is that plasma must flow in into the current sheet from both sides along the normal to the current sheet at a finite (though possibly low) velocity ±Vn. This condition is frequently ignored or is taken for granted without explicit consideration. In numerical simulations it (a)Visiting the International Space Science Institute, Bern, Switzerland is usually taken care of by starting the simulation with a prescribed reconnection configuration which is either assumed an X-point or by locally imposing an electric field or resistance for sufficiently short time in order to ignite reconnection. From the first condition it follows that ions in the current sheet become inertia-dominated and are demagnetised, while electrons remain magnetised. Since magnetised electrons are tied to the magnetic field, it follows that in the ion inertial region the magnetic field is carried along by the electrons becoming a region of Hall current flow [11]. From the second condition it is clear that reconnection cannot proceed continuously on time scales shorter than inflow time τin ' ∆/Vn ∼ fewλi/Vn. If reconnection turns out to be faster, it will necessarily be non-stationary and probably pulsed. These conditions just represent necessary conditions still being insufficient to describe the onset of reconnection. A mechanism is missing so far that either demonstrates, in which way the electrons become scattered away from the magnetic field in order for letting the oppositely directed magnetic field components slide from the electrons and reconnect, or that forces reconnection to occur in some other way. Quite generally, any model that scatters electrons away from the magnetic field turns out to be in trouble because of the following reason: Assume that the electrons have transported the p-1 ar X iv :0 90 3. 03 34 v2 [ ph ys ic s. sp ac eph ] 1 3 M ar 2 00 9