Erratum: Collisionless magnetic reconnection with arbitrary guide-field [Phys. Plasmas 11, 4713 (2004)]

This paper is in error due to the neglect of the gyroviscous contribution to the electron equation of motion. Adopting the normalization described in the paper, the electron fluid velocity takes the form

where $VE$ is the $E×B$ velocity, and

The electron equation of motion can be written¹ 

This equation differs from Eq. (1) in our paper due to the inclusion of addition terms arising from the electron gyroviscous tensor. These terms are of order $di∇P$⁠, and must, therefore, be included in any treatment of electron motion that takes pressure into account. As is well known, the net effect of the inclusion of the gyroviscous terms in the electron equation of motion is to cancel out part of the inertial term.

Redoing the analysis of Secs. II.B and II.C in our paper, our modified set of reduced equations take the form

where $∇2ψ=U$ and $ψe=ψ−de2∇2ψ$⁠. These equations only differ from Eqs. (25)–(28) in our paper in the respect that $Ze=Z−cβ2dβ2∇2Z$ has simply become $Z$⁠. In the paper, the $−cβ2dβ2∇2Z$ component of $Ze$ ultimately derives from the $[∂∕∂t+(Ve∙∇)]V*$ component of the inertial term in the electron equation of motion. However, it turns out that this component is canceled out by the gyroviscous contribution to the equation of motion. Hence, the $−cβ2dβ2∇2Z$ correction to $Z$⁠, appearing in Eqs. (25)–(28) of our paper, is spurious.

Redoing the remainder of the analysis in our paper, our modified general dispersion relation takes the form

This differs from Eq. (95) in our paper due to the absence of a $G(g∕cβdβ)$ factor in the second term on the right-hand side. In the large-$Δ′$ limit, the above dispersion relation yields³ 

for $β⪡(me∕mi)1∕4$⁠, and⁴ 

for $β⪢(me∕mi)1∕4$⁠. In the small-$Δ′$ limit, we obtain³ 

for all $β$ values. Note that our modified results are now not in agreement with Mirnov et al.,² since this paper also neglects to take the electron gyroviscous contribution to the electron equation of motion into account.

The importance of gyroviscous terms in the electron equation of motion was pointed out to the authors by Prof. F. Pegoraro.