Forced reconnection studies in the MAST

spherical tokamak M P Gryaznevich1, A Sykes1, K G McClements1

T Yamada2, Y Hayashi2, R Imazawa2, Y Ono2

Reported by K G McClements with acknowledgements to

A Thyagaraja1 & C G Gimblett1

1 EURATOM/CCFE Fusion Association, UK2 University of Tokyo, Japan

Workshop on MHD waves & reconnection, University of Warwick, November 18-19 2010

1/14

CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

Introduction

Magnetic reconnection can be studied in laboratory experiments under conditions approximating those of space plasmas including solar corona

Dedicated experiments include TS-3/4 at Tokyo University1 & MRX at Princeton2

Reconnection can also be studied in magnetic fusion experiments, such as Mega Ampère Spherical Tokamak (MAST) at Culham → higher magnetic field, stronger heating & more detailed diagnostics than those available in dedicated experiments

Reconnection can occur spontaneously in tokamak plasmas due to MHD instabilities, leading to sawtooth oscillations & magnetic island formation

I will present experimental signatures of forced reconnection that occurs in MAST during one particular method of plasma start-up:

→ merging-compression

2/14

1 Ono et al. Phys. Rev. Lett. 76, 3328 (1996) 2 Hsu et al. Phys. Rev. Lett. 84, 3859 (2000)

CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

MAST spherical tokamak (ST)

Unlike conventional tokamaks, aspect ratio R/a ~ 1 in STs

In MAST R 0.85 m, a 0.65 m Current in centre rod & external coils

produces toroidal B field 5 kG Current in plasma (produced by

combination of inductive & non-inductive methods) ≤ 1.45 MA

poloidal B at plasma edge ≤ 4 kG

3/14

R a

Electron & ion temperatures in plasma core ~ 106 - 107 K ( 0.1-1 keV) Particle density (~1018 – 51019 m-3) >> solar coronal values, but

~ 0.01 is comparable Ions mostly deuterium (mi = 2mp, mi /me = 3675)

CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

Merging/compression start-up in MAST4/14

P3

t=2.0 ms

t=3.0 ms

t=3.4 ms

t=6.6 ms

MAST shot #15929: two plasma rings, inductively formed around P3 in-vessel coils (t=2.0ms), merge (t=3.0ms), & eventually produce plasma current of up to 0.45 MA (t=6.6ms)

Right-hand frames show same images but with closed poloidal magnetic flux contours superposed

reconnection of poloidal flux occurs in midplane

accompanied by rapid heating of ions & electrons, with some evidence of ion acceleration

toroidal (guide) field unaffected by reconnection

CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

Reconnection in TS-3, TS-4 15/14

Rise in ion temperature found to increase approximately as B2 where B is initial magnetic field conversion of field energy to thermal energy

In these cases toroidal field reverses at X-line → no strong guide field No electron temperature measurements 1 Ono et al. Phys. Rev. Lett. 76, 3328 (1996)

CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

Temperature evolution in MAST6/14

Te increases from ~105 K to around 5106 K while Ti rises to 1.3 107 K in ~10ms (caveat: Ti measurements based on neutral particle analyser data, which may have been affected by fast ions)

In another merging-compression shot Te > 107 K was measured

Imazawa et al. to be submitted

to Phys. Rev. Lett.

Te (

keV

)T

i (ke

V)

I p (

MA

)

CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

No evidence of super-thermal electrons, from either Thomson scattering or hard X-ray diagnostics

2D Te profiles in MAST7/14

R (m)

z (m

)

Yag @ 8 ms

Yag @ 9 ms

Yag @ 10 ms

Yag @ 11 ms

Peaked caseHollow case Te (eV)

200

0

2D Thomson scattering maps of Te show centrally peaked & hollow profiles;

in latter cases central peak may also be present CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

High-frequency instabilities in MAST8/14

CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

Instabilities in Alfvén frequency range A ~ cA/R ~ 2102 kHz present during & after reconnection → cf. Alfvén eigenmodes excited by super- Alfvénic beam ions in tokamaks - but, no beam injection occurs during merging-compression in MAST

Frequency-sweeping modes also observed; seen in MAST only when fast ions are present

evidence that reconnection is accelerating ions to E ~ 102 keV

in this case Alfvénic instabilities could be producing fast ions rather than vice versa

Instabilities in lower hybrid range ~ (ie)1/2 ~ 2200 MHz also observed during reconnection

f (k

Hz)

Filaments in MAST9/14

Filamentary structures can be seen during merging compression in background- subtracted optical images

These are observed following spikes in line-integrated density, implying radial ejection of plasma following reconnection

evidence of turbulence in post-reconnection plasma?

4.9 ms

5.0 ms

5.1 ms

minimum subtracted average subtracted

CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

Reconnection length & time scales (1)

CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

10/14

Both electrons & ions strongly heated during merging compression in MAST, but at unequal rates; generally ions are heated more rapidly

results cannot be explained by MHD alone

Some estimates of length & time scales:Alfvén timescale A ~ 2/A ~ 1s

Thickness of current sheet (based on 2D Te profiles) ~ 2 cm

Identifying this as reconnection length scale, assuming Spitzer resistivity & setting Te equal to pre-reconnection values ~105 K ( ~ 410-5 ohm m)

resistive timescale r ~ 10s ~ 10A

Ion skin depth c/pi ~ 14 cm, electron skin depth c/pe ~ 2 mm,

ion Larmor radius ~ 1 mm, electron Larmor radius ~ 0.01 mm

electron inertia & finite Larmor radius effects negligible, but Hall term cannot be neglected in induction equation

two-fluid or kinetic analysis of reconnection process is necessary

BBj

vB 2

0

μ

η

net

Reconnection length & time scales (2)11/14

CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

Based on rate at which plasma rings approach each other, assuming Spitzer resistivity with Te~105 K, magnetic Reynolds number is of order

(NB Rm << Lundquist number since inflow velocity << Alfvén speed)

highly dissipative plasma

Post-reconnection electron-ion collisional energy equilibration time

E ~ tens of ms >> r , but comparable to actual equilibration time

(E >> r also found by Hsu et al. in MRX, in which there is no guide field)

10~0

η

μ LURm

Ion & electron heating12/14

CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

Neglecting radiative losses, electron & ion energy equations are

q – heat flux; P – stress tensor; e – electron collision time

Temperature evolution cannot be explained by Ohmic term (j2) since this only heats electrons (measurements indicate that ions heat up first)

If mechanism were found for heating ions alone, rise in Te could be largely accounted for by equilibration term ( Ti -Te)

Possible ion heating mechanisms: damping of turbulent ion flows associated with magnetic fluctuations –

proposed by Haas & Thyagaraja1 & Gimblett2 as explanations of Ti >Te in reverse field pinches

23:P

2

3jTT

nk

m

mp

dt

dTnk ei

ei

eeeeee

e ητ

vqv

ieei

eiiiii

i TTnk

m

mp

dt

dTnk

τ

3:P

2

3vqv

1 Haas & Thyagaraja Culham Report CLM-P 606 (1980)

2 Gimblett Europhys. Lett. 11, 541 (1990)

Buneman instability 13/14

CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

3rd possibility: heating due to turbulence driven by two-stream (Buneman) instability1

Ampère’s law in reconnecting region

, - toroidal & poloidal components B-field mainly toroidal, so electron-ion drift parallel to B is

using B 1 kG, n 51018 m-3, Z 0.01 m (from 2D Te profiles)

Threshold drift for instability is (kTe /me)1/2 106 ms-1 if Te = 105 K Conditions for Buneman instability may exist in pre-reconnection plasma

Maximum growth rate at frequencies comparable to that of observed wave activity in lower hybrid range

Instability saturates when (kTe/me)1/2 initial drift Te,sat 6106 K, which is close to measured values

However, Buneman instability expected to heat mainly electrons – cannot explain why rise in Ti precedes that in Te

1 Lampe et al. Phys. Fluids 17, 428 (1974)

φφθ μμ einej

Z

Bvv

00

17

0

ms 101

Z

B

nene

jei

θφ

μvv

Summary14/14

CCFE is the fusion research arm of the United Kingdom Atomic Energy Authority

Merging-compression method of start-up in MAST spherical tokamak provides opportunity to study reconnection in high temperature plasma with strong guide field

Information available on Ti, Te, bulk plasma motions & fast particles

Reconnection associated with rapid heating of ions & (on slightly longer timescale) electrons; Te often has hollow profile

High frequency instabilities & filamentary structures observed during & following reconnection, suggesting presence of fast ions & turbulence

Detailed theoretical model of reconnection during merging-compression in MAST yet to be worked out; any such model would need to include two-fluid (& possibly kinetic) effects

Preliminary analysis suggests that ion & electron heating could be due to turbulence &/or streaming instabilities, but there any many unresolved issues, e.g. origin of hollow Te profiles, filaments & ion acceleration

Is this telling us anything useful about reconnection in solar flares?