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