Multiple reconnections and explosive events and in MST and solar flares
Gennady Fiksel
CMSO workshop, Princeton, NJ, Oct 5-8, 2005
CMSO
Outline
• Explosive character of many MST plasma parameters is associated with abrupt growth of internally resonant resistive tearing modes.
• Presence of non-linearly driven poloidally symmetrical (m=0) modes is crucial.
• Some new data and observations.• Similarity with solar flares models by Kusano
et al
CMSO
MST Reversed Field Pinch
• Toroidal, current-carrying
• Density, n ~ 1013 cm–3
• Temperature, Te,i ~ 1 keV
• B / B ~ 2% (B ≤ 0.5 T)~
MST
CMSO
MST equilibrium field and resonances
kgB=0
q=
mn
m - poloidal mode numbern - toroidal mode number
1,61,7 1,8
0,n
-0.1
0.0
0.1
0.2
0.3
q
0.0 0.2 0.4 0.6 0.8 1.0r/a
q=
rBt
RBp
Multiple resistive tearing modes can exist
non-linearly driven
linearlyunstable
CMSO
010203040Time (ms)Ip (kA)Φ ( )WbBt =1, =6 ( )m n GBt =0, =1 ( )m n G010004000.040100200CoreEdge
Toroidal flux
Continuous dynamo and discrete events
• RFP magnetic configuration is generated and supported against resistive decay by continuous coherent action of multiple tearing modes.
• On top of that regular discrete events are observed during which mode amplitude explodes and additional flux is generated.
CMSO
We can control position of resonances (somewhat)
1,51,6
1,71,6
1,7 1,8
0,n
-0.1
0.0
0.1
0.2
0.3
q
0.0 0.2 0.4 0.6 0.8 1.0r/a
non-reversed
reversed q=
rBt
RBpControlq(a)
CMSO
We can control position of resonances (somewhat)
1,51,6
1,71,6
1,7 1,8
0,n
-0.1
0.0
0.1
0.2
0.3
q
0.0 0.2 0.4 0.6 0.8 1.0r/a
non-reversed
reversed q=
rBt
RBpControlq(a)
CMSO
Discrete events of modes amplitude burst
30
20
10
015010050
00 10 20 30 0 10 20 30 40Time (ms)Time (ms)
q(a) = 0 q(a) > 0 q(a) < 0
Core modem=1 n=6
Edge modem=0 n=1
m = 0 is small in non reversed plasmasm = 1 remains the same
ReversedNon reversed
CMSO
Core plasma rotation remains unaffectedwithout m=0 modes
5 10 15 20-20
0
20
0
0
20
40
20
40
Time (ms)
q(a) = 0 q(a) > 0
non reversed
CMSO
Ion heating reduced for non-reversed shots
q(a) > 0
reversed
0 10 20 30 40Time (ms)
0
100
200
300
400
CMSO
Ti (eV)
Flux generation
Magnetic energyreleased
m=1, n=6m=0, n=1
“Abnormal” events in reversed plasmas
• “Abnormal” events - the core modes amplitude remains high but there is no burst in edge m=0 modes even in reversed plasmas. Why?
• No change in Ti
Toroidalflux
Mag energy(kJ)
Modesamplitude (G)
CMSO
Fusion neutrons with and without m=0
Toroidalflux
Mag energy(kJ)
Modesamplitude (G)
Flux generation
Magnetic energyreleased
m=1, n=6m=0, n=1
Fusiond-d neutrons
CMSO
Without m=0 the changes in equilibrium B and E are small ==> no free energy source
• No generation of toroidal flux and equilibrium electric field.
• No release of magnetic energy. • Ion temperature (impurities and bulk) and core
rotation remain unaffected.
CMSO
What about fluctuation induced drive terms?
MHD dynamo
EM torque
Ion heating ⟨%J i ×%E⟩
⟨%J ×%B⟩
⟨%v×%B⟩
CMSO
Fluctuation induced torque is low in the corewithout m=0 ...
Fluctuation induced torque is measured in the plasma core
by FIR polarimeter (Weixing Ding)
%J×%B
CMSO
... and edge
The torque is also measured at the edge by insertable probes (with A. Almagri)
300 events with m=0 15 events without m=0
m=0,n=1
m=1,n=6
%J×%B phase
%J×%B
CMSO
... and edge
The torque is also measured at the edge by insertable probes (with A. Almagri)
300 events with m=0 15 events without m=0
m=0,n=1
m=1,n=6
%J×%B phase
%J×%B
CMSO
Conclusions
• Plasmas without m=0 edge resonant fluctuations do not exhibit bursts of ion heating and abrupt change in the rotation even that the core resonant m=1 fluctuations are large.
• In addition - no change in the energy of equilibrium B and no induced equilibrium E.
• Fluctuation induced torque JxB also remains small. The phase shift is close to /2.
• Is this the case for other quadratic fluctuation terms (e.g. ion heating JixE, MHD dynamo vxE )?
CMSO
mutual excitation of reconnections(observation)
1
2
3CS1
CS1 CS2
CS2
CS1
B
tearing reconnection
B
collapsing
30/ ≈L
21/ ≈L
12/ ≈L
flarespontaneous driven
(Kusano et al. 2004, ApJ)
CMSO
erup
tion
inte
rnal
col
laps
e
numerical simulation
tearing instability
eruption
time
kinet
ic en
ergy
mag
netic
ener
gy
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