In thin ($\Delta<$ few $\lambda_i$) collisionless current sheets in a space plasma like the magnetospheric tail or magnetopause current layer, magnetic fields can grow {from thermal fluctuation level by the action of the non-magnetic Weibel instability \citep{weibel1959}.}The instability is driven 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 smaller than the electron gyroradius and $<$ few $\lambda_e$. It is shown that under magnetospheric tail conditions it takes $\sim$ 20-40 e-folding times ($\sim$ 10-20 s) for the Weibel field to reach observable amplitudes $|{\bf b}_{\rm W}|\sim 1$ nT. In counter-streaming inflows these fields are predominantly of guide field type. This is of interest in magnetic guide field reconnection. Guide fields are known to possibly providing the conditions required for the onset of bursty reconnection \citep {drake2006,pritchett2005a,pritchett2006a,cassak2007}. In non-symmetric inflows the Weibel field might itself evolve a component normal to the current sheet which could also contribute to reconnection onset.
Deep Dive into Magnetic guide field generation in thin collisionless current sheets.
In thin ($\Delta<$ few $\lambda_i$) collisionless current sheets in a space plasma like the magnetospheric tail or magnetopause current layer, magnetic fields can grow {from thermal fluctuation level by the action of the non-magnetic Weibel instability \citep{weibel1959}.}The instability is driven 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 smaller than the electron gyroradius and $<$ few $\lambda_e$. It is shown that under magnetospheric tail conditions it takes $\sim$ 20-40 e-folding times ($\sim$ 10-20 s) for the Weibel field to reach observable amplitudes $|{\bf b}_{\rm W}|\sim 1$ nT. In counter-streaming inflows these fields are predominantly of guide field type. This is of interest in magnetic guide field reconnection. Guide fields are known to possibly pr
In this communication we investigate the self-consistent generation of a so-called magnetic guide field in a thin collisionless current layer that initially lacks the presence of any guide field. For this we render responsible the Weibel instability (Weibel, 1959).
Correspondence to: R.A.Treumann (rudolf.treumann@geophysik.uni-muenchen.de) Guide fields are believed -and have been shown by numerical simulations (see e.g. Drake et al., 2006;Pritchett, 2005Pritchett, , 2006;;Cassak et al., 2007, and others) -to be of prime importance in collisionless reconnection. Their presence in a thin collisionless current sheet is not evident. In a collisionless plasma the state of magnetisation is determined by the history of the plasma. External magnetic fields are unable to penetrate it; they have to be present in the plasma from the very beginning. It is thus of vital interest in reconnection to understand whether guide fields can arise in collisionless current sheets.
Space observations in situ (Fujimoto et al., 1997;Nagai et al., 1998;Øieroset et al., 2001;Runov et al., 2003;Nakamura et al., 2006;Vaivads et al., 2004) and kinetic numerical simulations (Ramos et al. , 2002;Drake et al., 2003Drake et al., , 2005) ) unambiguously prove that magnetic reconnection in a collisionless space plasma proceeds under the following two conditions:
that the current sheet that separates the oppositely directed (‘anti-parallel’) magnetic fields ±B to both sides of the current becomes ’thin enough’. Under ’thin enough’ it is understood that the effective half-widths 1 2 ∆ λ i of the sheets fall (approximately) below the ion inertial scale-length λ i = c/ω i (with c velocity of light, ω i = e(N/ 0 m i ) 1 2 ion plasma frequency, e elementary charge, N plasma number density, m i ion mass). The real limit on the width is not precisely known. Observations (Nakamura et al., 2002;Vaivads et al., 2004;Nakamura et al., 2006;Baumjohann et al., 2007) suggest that it can reach values ∆ 4λ i . This condition is commonly (for example in Retinò et al., 2007;Sundqvist et al., 2007) taken as sole indication that one is dealing with collisionless reconnection.
that plasma flows in into the sheet from both sides along the normal to the current at a finite (though low) velocity ±V n , explicitly considered only in treatments of ‘driven reconnection’. Numerical simulations usually take care 2 R.A. Treumann, R. Nakamura, and W.Baumjohann: Weibel fields in thin current layers of this condition by starting the simulation with a prescribed reconnection configuration either assuming an initially present X-point or by locally imposing a temporary parallel electric field or finite resistance for sufficiently long time in order to ignite reconnection.
The first condition implies that ions in the sheet become inertia-dominated and thus are demagnetised, while electrons remain magnetised. Since magnetised electrons are tied to the magnetic field, the magnetic field in the ion inertial region is carried along by the electrons causing Hall current flow (as was realised first by Sonnerup, 1979).
From the second condition it is clear that reconnection cannot proceed continuously on time scales shorter than the inflow time τ in ∆/V n ∼ fewλ i /V n . If reconnection turns out to be faster, it will necessarily be non-stationary and probably pulsed.
These just represent necessary conditions still being insufficient to describe the onset of reconnection. A collisionless 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. Prime attention in this respect is attributed to the action of guide fields, i.e., a magnetic field component in the direction of current flow.
Magnetic guide fields have two implications which in a thin current sheet with unmagnetised ions affect basically only the electrons:
that the centre of the current sheet is not free of magnetic fields, as would be the case in the Harris current sheet model, and
that the sheet current J possesses a field-aligned component J which, when exceeding a certain threshold, undergoes instability and may cause either anomalous dissipation via generation of anomalous resistance or viscosity, or produces localised wave fields like solitons and (electron) holes. Both resistance and guide-fieldaligned electric fields violate the electron frozen-in condition and thus contribute to (localised) reconnection.
Quite generally, any guide-field-free current sheet 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 magnetic field from both sides some distance across the ion inertial region into the current sheet. During this transport the magnetic field lines have become b
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