Transcript Comparing classical and lab plasma dynamos

Comparing classical and lab plasma dynamos
S. Prager
University of Wisconsin
useful discussions with
D. Craig, H. Ji, J. Sarff, E. Zweibel
• The classical dynamo
well-posed problem(s)
• The lab plasma dynamo
well-posed
• The astrophysical field generation problem
maybe less clear
The classical dynamo problem
velocity-driven
V
energy source
˜v  B˜
fluctuations
(with seed B)


B
mean, large-scale
Poynting flux
Poynting flux is outward from plasma volume
P
V
d
dt

B
2
20
dV    E  B  dS 
<0

j  E dV
> 0, source term
   j 2 dV 

j  v˜  B˜ dV
>0


Magnetic helicity flux
Magnetic helicity flux direction is unclear
dHm
   B  dS 
dt

E  B dV

J  B dV
using Ohm’s law
dHm
   B  dS 
dt
> 0 in all lab
cases
< 0 in sodium expts
< 0 in Taylor state
unclear in astrophysics
The classical dynamo
P
V
Hm
or
P
V
Hm
The lab plasma dynamo
Magnetically-driven
B
energy source
˜v  B˜
fluctuations
B
mean, large-scale
two cases:

•Free relaxation (no energy or helicity injected)
•Driven relaxation (energy and helicity injected)
Free relaxation
Poynting flux = 0 = helicity injection
large-scale field, <B>, transported by fluctuations
( v˜  B˜ in MHD)
200
magnetic
energy
(kJ)
Helicity
(Wb)
150
100
50
0
0.08
0.06
0.04
0.02
0.00
-3
-2
-1
0
1
Time (ms, relative to crash)
Time (ms)
2
3
Driven relaxation
Poynting flux  0  helicity injection
Hm
P
Magnetic field grows and redistributes
Experimental examples
in a torus (e.g. reversed field pinch)
dHm
˜ torV˜tor  2  E˜  B˜ dV
 
dt
helicity injection
through surface

E˜
pol ( 0 )
E˜
tor ( 0 )
˜ tor

V˜tor
˜
EÝ
pol
= toroidal flux ~
= toroidal loop voltage
~ E˜ tor

dc injection of
helicity
fluctuations

v(,k)  B(,k)
B
experimental result
MST
McCollam, Blair,
Sarff

another experimental example
dHm

dt
 (B dS)  
spheromak
E˜  B˜ dV
One physics link between the
classical and lab dynamos
˜ can be driven by instability
In both cases, v˜  B
or nonlinear coupling
lab dynamo shows alpha effect can be large,
 that dynamo quenching predictions are not
Indicates
universal
The astrophysical field generation problem
B fields are observed or deduced to
•Grow from a seed field (Earth, ISM…)
•Oscillate in time (Earth, Sun….)
•Be transported in spatial scale or wavenumber (ISM….)
•Be transported through space (Extragalactic jets…)
Lab relaxation processes can contribute to the latter
three
What are the most important problems in the
generation of magnetic fields in astrophysics?
Coupling of two dynamo processes
e.g., discussed by Blackman
velocity-driven
dynamo
P
Hm
magnetic-driven
dynamo
(relaxation)
velocity-driven dynamo on LHS drives relaxation
or field growth on RHS
Coupling of two dynamo processes
e.g., discussed by Blackman
velocity-driven
dynamo
Hm
P
Hm
magnetic-driven
dynamo
(relaxation)
velocity-driven dynamo on LHS drives relaxation
or field growth on RHS
Solar fields
P
V dynamo
Disk/Jet/lobe system
disk engine
velocity-driven
dynamo
Jet/lobe
P
magnetic-driven
dynamo
(relaxation)
Disk/Jet/lobe system
P
Jet/lobe
magnetic-driven
dynamo
relaxation, transport of B over over space, transport
of B from high to low k
Magnetic energy in the universe
other
1
2
jets/lobes
Magnetic energy in the universe
other
is this
correct?
1
2
jets/lobes
so, magnetic transport and consequent creation of largescale field may be important
(the lab plasma
dynamo or magnetic dynamo)
Summary
Two B generation mechanisms can work together
velocity-driven engine (dynamo)
internal energy source in flow
contains little magnetic energy (?)
occupies small space (?)
magnetically-driven relaxation
driven by boundary condition
produces large-scale field via transport
contains large magnetic energy (?)
occupies large space (?)
Summary
Two B generation mechanisms can work together
velocity-driven engine (dynamo)
internal energy source in flow
contains little magnetic energy (?)
occupies small space (?)
magnetically-driven relaxation
driven by boundary condition
produces large-scale field via transport
contains large magnetic energy (?)
occupies large space (?)
Should the astrophysical “dynamo problem” be broadened to
include both effects about equally?