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Erratum: “A simple, analytical model of collisionless magnetic 
reconnection in a pair plasma” [Phys. Plasmas 16, 102106 

(2009)] 


Michael Hesse, Seiji Zenitani, Masha Kuznetsova, and Alex Klimas 


All at: Space Weather Laboratory, Code 674, NASA Goddard Space Flight Center, 
Greenbelt, Maryland, 20771, USA 

The following describes a list of errata in our paper, “A simple, analytical model of 
collisionless magnetic reconnection in a pair plasma.” 1 It supersedes an earlier erratum 2 . 


We recently discovered an error in the derivation of the outflow-to-inflow density ratio. 
Specifically, eqn. (23) contains an erroneous, additional factor of n 0 ~' . This error leads to 
three changes to subsequent equations, and to quantitative changes in the figures. We 
regret this error. The correct version of (23) should read: 


f 


u : 


1 -n o — ~n 0 

V U„ 


7-1] /-I 


r ) 


r 


-Pc 


— I - n 

J 


(23) 


This result changes two additional equations. Eqn. (24) now becomes: 


u t 27-1 7-1 

!-«—-« 


(i+«„ 2 ) 


' u Q ' 7 2 7 

which now leads to a quadratic rather than cubic equation for n 0 . 


(24) 


2 2 7 

n„ H m„ 


7-1 


_2y_ 

7-1 


= 0 


(26a) 


1 



This equation is readily solved analytically: 


n„ = -- 


Y 


r - 1 


■£ + 


r 


\ 2 


Vy-l J 


+ 1 + 


2 / 

7-1 


n-1/2 


(26b) 


The subsequent analysis is unchanged. The revision of (26) leads to qualitatively very 
similar results, and all original conclusions remain valid. The revised figures are shown 
below. 


REFERENCES 


1 M. Hesse, S. Zenitani, M. Kuznetsova, and A. Klimas, Phys. Plasmas 16, 
102106 (2009) 

2 M. Hesse, S. Zenitani, M. Kuznetsova, and A. Klimas, Phys. Plasmas 16, 
129906 (2009) 


2 



3 



Figures and captions 


reconnection electric field 


0.35 



Figure 1 (color online). Reconnection electric field depending on inflow plasma /? 
and polytropic index y. 


outflow/inflow density ratio 



1.2 

1 1.5 gamma 2.5 3 


Figure 2 (color online). Ratio of outflow and inflow density, depending on inflow 
plasma f5 and polytropic index y. 


4 


Inflowfouflow entropy ratio 


06 
0,7 
0.6 
0.5 
0-4 
0.3 
0.2 
0-1 
0 

1.2 1.4 1.6 gamma 2 2.2 2.4 




— S(bela=0 00} 

S(beia=0-10) 

— — S(bela=0.20} 

S(bela=0 ,40) 

# 



/ 


1 


Figure 3 (color online). Entropy ratio pjn 0 r /p 0 n/ depending on inflow plasma ) 3 and 
polytropic index y. 


0-75 


0.7 

0-65 

0.6 

0,65 

o.o 

0.45 


diffusion region thickness 



Figure 4 (color online). Diffusion region thickness d depending on inflow plasma (3 
and polytropic index y. 


0.6 

0.7 


0.4 

0-5 

0.2 

0.1 

0 


diffusion region aspect ratio 


: ' i 
t I 
. * t 

/ t t 

t 4 t * 

if/ / 

j 

/ 

t 

doL(beta-[}.00) 

— doL{beta=0.1D) 

doL{beta=0,20) 


OQL|DeLa— Li.J'Lri 

doU,bela=Q.4D) 


/' / 

/ / / 


1 1.5 gamma 2.5 3 



5 



Figure 5 (color online). Diffusion region aspect ratio d/L depending on inflow 


plasma / 3 and polytropic index y. 


0.5 


0.45 


0.35 


0.3 


outflow velocity 



0.25 

1 1.5 gamma 2.5 3 


Figure 6 (color online). Outflow velocity depending on inflow plasma [1 and 
polytropic index y. 


outlfow velocity in units of outflow Alfven speed 

0.8 



1 1.5 gamma 2.5 3 


Figure 7 (color online). Outflow velocity based on outflow density depending on 
inflow plasma /? and polytropic index y. 


6 


035 


inflow energy flux densities, |t=0.3 


0.3 

0.25 

0.2 

0.15 

0.1 


kinetic energy flux(beta=0.30) 

enthalpy flux(t>eta=0.30) 

Poynting flux(beta*0 30) 




0.05 



1.3 1.4 1.5 gamma 1.7 1.8 1.9 


Figure 8 (color online). Inflow energy flux densities for upstream J3= 0.3. 


1.4 


outflow energy flux densities, |i=0.3 


1.2 

1 

0.8 

0.6 

0.4 

0.2 

0 


\ 

\ 

X 

X 

X 

X 



X 

x 


kinetic energy flux(beta=0 30) 

Enthalpy flux(beta=0 30) 

Poynting (lux(beta=0 30) 



1.3 1.4 1.5 gamma 1.7 1.8 1.9 


Figure 9 (color online). Outflow energy flux densities for upstream 0.3. 


0.3 

0.25 


015 

0.1 

0.05 

0 

0 


outflow kinetic energy vs. outflow enthalpy flux 


/ .// 

/ / / 
/ f / 

/ 

' / ' 

/ / / 
}/// 




t / / ■ 

Ekia_o{beta“0,QQ) 

f / * 

Ekin o(beta-O.IO) 

i *t 

Ekin_D{beta=0.20) 

/// 

Ekin_o{lMta=0.30) 




0.5 outflow enthalpy flux 1.5 2 


7 


Figure 10 (color online). Outflow kinetic energy flux density plotted versus enthalpy 
flux density for all parameters. The lower fluxes are obtained for larger values of the 
polytropic index y, with the exception of the J3=\ calculation. Here, lower values of y 
yield larger kinetic energy but lower enthalpy flux densities. 


outflow Poynting Hux v* outflow enthalpy flux 



Foyn j34.beLa=l}.M>) 

PoynjcHt*ta=0.l0) 

Poyn_<Hbeta=D.20) 

— - Pcyn_o{lw!te=O.30) 

Poyn_u{beta=D.4D) 


0,5 outflow enthalpy flux 1.5 


Figure 1 1 (color online). Outflow Poynting flux density plotted versus enthalpy flux 
density for all parameters. Here higher Poynting fluxes are obtained for smaller values of 
the polytropic index y, again with the exception of the J3= 1 calculation. Here, lower 
values of y yield larger kinetic energy but lower enthalpy flux densities. 


8