Transcript ppt-file

“Ambipolar Diffusion” and
Magnetic Reconnection
Tsap Yu.T. , Stepanov A.V.
Crimean Astrophysical Observatory
Central (Pulkovo) Astronomical Observatory
1.
Diffusion and dissipation of the
magnetic field in the partially
ionized plasma is an important
physical process in many
cosmic objects
Star formation
Mestel&Spitzer (1956) - magnetic
force prevent star formation if the
mass of the magnetic cloud M < 500
Msun since magnetic flux is
conserved.
2. Dynamo – alpha-effect due to the
magnetic reconnection
3. Flare energy release on the Sun and
stars
Zaitsev-Stepanov (1991) circuit model of
flares
Giardini Naxos 2010
What is the “ambipolar diffusion” in the weakly ionized
plasma according to Mestel&Spitzer?
Three-fluid approximation

 ene  
 
 

dVe
 ene E 
Ve  B  ne m ea (Va  Ve )  ne m ei (Vi  Ve );
ne m
dt
c


 eni  
 
 

dVi
n
M

en
E

V

B

n
M

(
V

V
)

n
m

(
V
 i
i
i
i
ia
a
i
i
ei
e  Vi );
dt
c


 
 

dVa
n
M

n
M

(
V

V
)

n
M

(
V
 a
a
ai
i
a
a
ae
e  Va ).
dt

 

 ene  

j  eni (Vi  Ve )  equation for the electric current
 ene E  c Ve  B  0;
 
 
 
en E  eni V  B  n M (V  V )  0.
i
i
ia
 i
 
a  i
c
 
j B
Vi  Va  cnM
but
ia

Vi  B
E
c
“Ambipolar diffusion” (collisional plasma) is the motion of
ions through a gas of neutral particles under action of
Ampere’s force but classical (real) diffusion is caused by
the inhomogenity (two types of diffusion)
Mestel and Spitzer (1956)
considered star formation in magnetic dust
cloud due to gravity
• Main problem: since the field is frozen into the
contracting cloud the star formation becomes
impossible because of the magnetic forces
• Solution: the distorted magnetic field is able to
straighten itself, dragging the ions and
electrons with it , while the bulk of the cloud
contracts across the magnetic energy
This scenario suggests that the magnetic field is
frozen into ions, i.e.

 
B
 rot Vi  B
t
Very popular expression beginning from Parker (1963)
cloud
What is the Joule dissipation
in the collisional plasma?
The Joule dissipation is the work of the electric field on
electric current without the mechanical energy caused
by Ampere’s fоrсe, which is equal to the thermal energy
release due to ion-neutral, electron-neutral, and ionelectron collisions, i.e.
jB
V B


V  E 
j  E j 
c
c 

 nM in (Vn  Vi ) 2  nm ei (Vi  Ve ) 2  nn m ni (Vn  Ve ) 2
Q  Ej 
Mestel&Spitzer(1956), Parker(1963) and others.
On the Magnetic Flux Conservation
 
 

jB
V V 
 

i
a cnM
en




ia
i V B  jB
  eni E 
c i
c
 eni  



en E 
V  B  n M (V  V )  0
i
i
ia a i
c i


 


B
jB
 rotV  B  rot
i
t
en
i
But Parker (1963)

 
B
 rot Vi  B
t
Magnetic flux does not conserved due to Joule dissipation
Cowling Conductivity (1957)
The degree of ionization is not important as distinguished from
Mestel&Spitzer(1956)
Main suggestions:
1. Collisional plasma



 na maVa  ni miVi  ne meVe 
v



na ma  ni mi  ne me   v  vk
  

Vk  v  vk

2. Plasma must be non-stationary over time or space


dv v  

 ( v  )v  0
dt t
Generalized Ohm’s Law
  

j  eff ( E  v  B) ,
 C S
c Mn in
ne
 eff 
,  S
,  C
.
2 2
 C S
m( ei  en )
B F
2
2
Cowling conductivity
Sweet-Parker magnetic reconnection
Sweet-Parker [Sweet 1958, Parker 1957]
Main features:
1. L>>l – the current
sheet is long and thin;
2. Plasma is evacuated
from the current sheet
because of the gas
(magnetic) pressure.
Plasma evacuation may be caused by
Lorentz force due the strength of the
magnetic field lines (effect of slingshot)
B0 – perpendicular component
Scaling Laws and the Slingshot Effect
LV  lV0  0 - mass balance equation
B2
p
 p0 - pressure balance across the magnetic field
8
V02
0
 p0  p - coponent of the momentum equation along the sheet
2
B
VB  С - induction equation  uniform elctric field
l
V02
BBL
0
 p0  p  0
2
8 l
VB  V0 B0  continuity equation for electric field - Å  const
B B0

 continuity of the magnetic field lines - divB  0
L
l
B B0



L
l
  VB   0V0 B0 - contradict ion
LV  lV0  
Energy Balance of Plasma
j2
B 2 VA

 4 L
3nkT
J  2
B / 4
0
- energy releace rate due to Joule dissipatio n

L
L 

- heating time
VA VA  0
L
- dynamical plasma cooling
V
A 
  0    
J
d
d 
Qr  nnH F (T )  radiative losses


7
  negligibly small
T 2
Qt   2  losses caused by thermal conductivi ty 
L

Thickness of the Current Sheet under Solar
Chromospheric Conditions
L
l ~ C
VA

11
3 
nH  10 cm 

7
F 1

l
~
10
cm


T  10 4 K


L  108 cm
B  30G
Solar Chromospheric Ejections
observations with SOT/Hinode in lineСа
Shibata etal.07, De Pontieu et al.07
H
Spicules
Chromospheric jets
Thickness < 200 km
thickness - 150-300 km,
Hinode Ca H
Models
Shibata et al. 1992
Shock waves push plasma
Proposed model
Magnetic pressure pushes plasma
Токовый слой
Conclusions
1.
There are two types of ambipolar diffusion in plasma
physics – real and formal.
2.
The Joule dissipation in partially ionized plasma is
determined by collisions between neutrals and ions
too.
3.
Approach proposed by Cowling (1959) is more
adequate than approach proposed by Meste&
Spitzer~(1956) in the case of the collisional plasma.
4.
Plasma evacuation is an effective cooling mechanism
of the current sheet.
5.
The Sweet-Parker reconnection in partially ionized
plasma can play an important role in the solar
chromosphere.
Thank you!
RT-22, Crimea