Transcript Progress in Low-Aspect-Ratio RFP Research in RELAX

27. Apr. 2010
Helically deformed plasma in RELAX
-experiments and 3-D MHD simulation-
Akio Sanpei, Sadao Masamune
and
RELAX group
Kyoto Institute of Technology, Kyoto 606-8585, Japan
Background:Helical Deformation of RFP
Conventional RFP
Many n of m = 1 (helical) fluctuations (Multi-Helicity)
Magnetic Chaos (break closed magnetic surface)
QSH(Quasi-Single-Helicity) RFP
Single n mode has much higher amplitude than others
Good confinement inside helical magnetic island
SHAx(Single Helical Axis) RFP
Higher amplitude of single dominant mode
Separatrix (X-point) Disappearance
Helical deformation and Good
confinement in wider area
realized in RFX-mod (Ip > 1MA)
[1] D. F. Escande et al., PRL 85, 1662 (2000)
[2] D. F. Escande et al., PRL 85, 3169 (2000)
[3] R. Lorenzini et al., Nature Physics 5, 570 (2009)
not-SHAx
SHAx
Lower A has a possibility to easy access to QSH
Dependence of q-profile on A
Lowering A leas to …
0.4
A= 2
A= 3
0.3
1/4
1/5
1/6
...
q
0.2
0.1
q in the core region
: Up ↑
m=1 modes resonant surfaces are less
densely spaced in the core region.
0
-0.1
0
0.2
0.4
0.6
0.8
1
Avoidance of overlap of
magnetic islands (chaos).
r/a
・ A simpler magnetic mode dynamics
expected
・ Easier access to the QSH RFP state
Single dominant helical mode (m=1/n=4) is realized
in shallow reversal discharge

1
0.5
B p (a)
B
F
B (a)
B
QSH
F
0
-0.5
-1
MH
-1.5
0.5
1
1.5
2
2.5
3
3.5
4
Theta
The toroidal mode spectrum is narrowed by reducing the
toroidal field reversal, and the QSH state tends to be realized
in shallow reversal discharges.
Inner magnetic field profile in shallow-reversal discharge
Radial arrays of magnetic probes
inserted from outward-port
into the plasma region
Large oscillation of profile is observed
in shallow-reversal discharge.
To explain such oscillation….
Comparison of inner magnetic field profile
with HOE
Theoretical cylindrical Helical Ohmic Equilibrium (HOE) [4] [5]
• have Helical symmetry
• solved using helically symmetric Grad-Shafranov Equ. and Ohm's law
Bi (r, , z)  B
( 0,0)
i
~
(r)  bi (r) sin(m  kz  i )
symmetry
component
helical component bi
For satisfy ∇・b = 0
   z   r   / 2
If HOE rotate, at the radial array ...
non-oscillatory component (< 2kHz)
oscillatory component
b (2kHz ~ 50kHz)
・Phase of br is differ from b , b by ~  / 2
[4] R. Paccagnella, presented at IEA/RFP
Workshop, Madison, 2000
[5] J. M. Finn et al., Phys. Fluids B 4, 1262
(1992)
We confirm this in following pages.
Magnetic measurement suggests HOE in RELAX
Comparison of profile of measurement with
each component in HOE [4].
Non-oscillating component
oscillating component
[4] R. Paccagnella, presented at IEA/RFP
Workshop, Madison, 2000
Good agreement is observed.
Core Resonant mode
is m =1, n =－4
(consistent with edge
measurement)
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Original magnetic axis
still remain.
(Calculated with ORBIT)
•Helical Ohmic state has been observed.
2D image of SXR diagnostic suggests
existence of hot helical core
In order to study the plasma structure in very shallow reversal region,
we have taken SXR tangential images using a SXR pin-hole camera.
Z [m]
2.0
1.0
R [m]
Experimental result
A poloidal cross section of
the model SXR emission
intensity contours.
The existence of the helical hot region has been indicated in shallow
reversal, QSH discharges in RELAX.
Contours of magnetic surfaces and temperature
from data obtained with
magnetic probe
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Radial position of peak is similar.
Width of island is different.
Amplitude of br is assumed.
(We don’t have information of br)
SXR emission intensity contours
estimated from SXR image
Residual errors remain
Two different measurements indicate realization
of helically magnetic surface in RELAX.
3-D MHD simulation
We are interested in theoretical formation of such helical deformation
in fully toroidal system.
Direct numerical simulations of the fully three-dimensional,
nonlinear MHD equations in a low-A RFP plasma.
(1979) Sato and Hayashi
(2000) Hayashi and Mizuguchi
for Spheromac
for ST
This simulation code successfully reproduces several key features of Internal Reconnection
Event in spherical tokamak.
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(Now) Mizuguchi and RELAX group
[6] Mizuguchi et al.,
Phys. Plasmas, Vol. 7,
940 (2000)
for RFP
Set up of 3-D MHD simulation on A=2 RFP
Boundary condition
The boundary condition is put as a perfectconducting and no-slip wall at all boundaries of
the computation region.
•B⊥=const. V=0, j=0 at the boundary
•meshes: (NR×Nφ×NZ) = (153×128×153)
Initial distribution
Reconstructed equilibrium from experimental
result of RELAX with Fit code.
(torus symmetric)
Perturbations
The simulation starts from a linearly unstable configuration which causes initial tiny
perturbations to grow spontaneously. The perturbation is introduced on the plasma
velocity field at t = 0 as a random white noise.
First result of 3-D MHD simulation is demonstrated.
Visco-resistive MHD equations of the simulation

   ( V )
t
Equation of continuity
Fluid viscosity
V
1


   ( V V)  j  B  p    2 V    V 
t
3


E  V  B  j
Equation of motion
Generalized Ohm’s low
j  B
resistivity
B
   E
t
Maxwell equations
p
   ( pV )  (  1)( p  V    j 2 )
t
Energy conservation
1

2
  2 eij eij    V  
3


1  Vi V j
eij 


3  x j xi




Time is normalized with Alfven time.
Helical deformation of equi-pressure surface
Equi-pressure surface
Pressure at center of
poroidal cross-section
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In the early stage of the growth until t=60,
fluctuations grows exponentially.
Pressure profile on poroidal
cross-section
In t~60, relaxation event occurs.
In the later stage, Helical deformation (m=1/n=4) remains.
Dependence on initial distribution
1
n=4
0.5
QSH
0
F
F~0
MH
-0.5
Growth of single mode
-1
-1.5
0.5
1
1.5
2
2.5
3
3.5
4
Theta
0.1
n=8
n=5
F~-1
magnetic energy
n=4
F=0
F=1
0.08
0.06
0.04
0.02
0
1
In the early stage of the growth until t~60, each of
the components grows exponentially with its
linear growth rate.
2
3
4
5
6
7
toroidal mode number
8
Mode spectrum at t=150
Consistent with experimental results
Dependence of mode spectrum on Prandtl number
P=5
P=10
n=4
Prandtl number
P
n=5
n=6
F~0
Magnetic Energy
P=1
n=4
n=5
n=6
n=4
n=5
n=6
n=4
n=5
n=6


10-2
P=1
P=5
10-4
P=10
10-6
10
-8
10-10
3
4
5
n (mode number)
6
Mode spectrum at t=150
Growth of single mode (QSH) is observed.
Increasing of Plandtl number does not effective on dominant mode but reduce other mode.
The toroidal mode spectrum is narrowed by increasing the Plandtl number.
Dependence of Ns on Hartmann number
[6] S. Cappello et al., Phys. Rev. Lett, 85, 3838
(2000)
Spectral index Ns
 nmax 
b 21,n


Ns   

b 21,n
n

n

min
n


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



2  1



When a single mode is excited, Ns becomes 1.
In MH state, Ns becomes large number.
1.3
1.25
Hartmann number
H 1
Ns
1.2
1.15
(relatively)
MH
QSH
1.1

1 3
10
Transition QSH to MH by increasing H is observed.
(weak QSH?)
1.05
4
10
H
5
10
Summary of 3-D MHD simulation
• First result of 3-D MHD simulation is demonstrated
Helical deformation (m=1/n=4) is observed.
Dependence on initial distribution is
consistent with experimental result.
The toroidal mode spectrum is narrowed by
increasing the Plandtl number.
Transition QSH to MH by increasing H is observed.
We have to continue parameter survey.
Summary of talk
experimental
• Helical deformation is observed in RELAX
Magnetic measurement
SXR measurement
simulation
•First result of 3-D MHD simulation is demonstrated
The simulation has the possibility to explain the
transition to m=1/n=4 deformation.