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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, UK
2 University of Tokyo, Japan
Workshop on MHD waves & reconnection, University of
Warwick, November 18-19 2010
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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
1 Ono
et al. Phys. Rev. Lett. 76, 3328 (1996)
2
Hsu et al. Phys. Rev. Lett. 84, 3859 (2000)
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MAST spherical tokamak (ST)
R
a
 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 & noninductive methods) ≤ 1.45 MA
 poloidal B at plasma edge ≤ 4 kG
 Electron & ion temperatures in plasma core ~ 106 - 107 K ( 0.1-1 keV)
 Particle density (~1018 – 51019 m-3) >> solar coronal values, but
 ~ 0.01 is comparable
 Ions mostly deuterium (mi = 2mp, mi /me = 3675)
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Merging/compression start-up in MAST
P3
t=2.0 ms
t=3.0 ms
t=3.4 ms
t=6.6 ms
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 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
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Reconnection in TS-3, TS-4
1
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 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)
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Temperature evolution in MAST
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Ti (keV)
Te (keV)
Ip (MA)
 No evidence of
super-thermal
electrons, from
either Thomson
scattering or hard
X-ray diagnostics
Imazawa et al. to be submitted
to Phys. Rev. Lett.
 Te increases from ~105 K to around 5106 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
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2D Te profiles in MAST
Hollow case
Peaked case
Yag @ 8 ms
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Te (eV)
200
Yag @ 9 ms
Yag @ 10 ms
z (m)
Yag @ 11 ms
0
R (m)
 2D Thomson scattering maps of Te show centrally peaked & hollow profiles;
in latter cases central peak may also be present
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f (kHz)
High-frequency instabilities in MAST
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 Instabilities in Alfvén frequency range
A ~ cA/R ~ 2102 kHz present
during & after reconnection → cf.
Alfvén eigenmodes excited by superAlfvénic 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
~ (ie)1/2 ~ 2200 MHz also
observed during reconnection
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Filaments in MAST
4.9 ms
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 Filamentary structures can be
seen during merging
compression in backgroundsubtracted optical images
 These are observed following
spikes in line-integrated density,
implying radial ejection of
plasma following reconnection
 evidence of turbulence in postreconnection plasma?
5.0 ms
5.1 ms
minimum subtracted
average subtracted
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Reconnection length & time scales (1)
 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 ~ 1s
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 (  ~ 410-5 ohm m)
 resistive timescale r ~ 10s ~ 10A
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

 η 2
B
j 
    v 

B
 B


t
ne 

 μ0
 two-fluid or kinetic analysis of reconnection process is necessary
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Reconnection length & time scales (2)
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 Based on rate at which plasma rings approach each other, assuming
Spitzer resistivity with Te~105 K, magnetic Reynolds number is of order
μ LU
Rm  0
~ 10
η
(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)
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Ion & electron heating
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 Neglecting radiative losses, electron & ion energy equations are
dT
3me nk
3
Ti  Te   ηj 2
nk e  pe   v e    qe  Pe : v e 
2
dt
mi τ e
3me nk
3
dT
Te  Ti 
nk i  pi   v i    qi  Pi : v i 
2
dt
mi τ e
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
1 Haas
2
& Thyagaraja Culham Report CLM-P 606 (1980)
Gimblett Europhys. Lett. 11, 541 (1990)
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Buneman instability
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 3rd possibility: heating due to turbulence driven by two-stream (Buneman) instability1
 Ampère’s law in reconnecting region
Bθ
 μ0 j φ  μ0 ne v i  v e φ
Z
 ,  - toroidal & poloidal components
 B-field mainly toroidal, so electron-ion drift parallel to B is
vi  ve


jφ

1 Bθ
 107 ms 1
μ0 ne Z
ne
 using B  1 kG, n  51018 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  6106 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)
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Summary
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 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?
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