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Dynamical plasma response during driven magnetic reconnection in the laboratory. Ambrogio Fasoli * Jan Egedal MIT Physics D pt & Plasma Science and Fusion Center Ackn.: W.Fox, J.Nazemi, M.Porkolab *Now at EPFL Physics D pt & Centre de Recherche en Physique des Plasmas.

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dynamical plasma response during driven magnetic reconnection in the laboratory
Dynamical plasma response during driven magnetic reconnection in the laboratory

Ambrogio Fasoli*

Jan Egedal


Physics Dpt & Plasma Science and Fusion Center

Ackn.: W.Fox, J.Nazemi, M.Porkolab

*Now at EPFL

Physics Dpt &Centre de Recherche en Physique des Plasmas

our definition of magnetic reconnection
Our definition of magnetic reconnection
  • Change of magnetic field topology in the presence of plasma
  • Reconnection rate: value of E-field along X-line, perpendicular to plane over which flux annihilates
  • Driven reconnection in the VTF open cusp
    • Conditions to create a current channel
    • Dynamical evolution of j and E
    • j||and dE/dt linked through ionpolarization current
    • Size of diffusion region (EB0)
    • Orbit effects
  • Future work on VTF
    • New diagnostics
    • Closed cusp configuration

Magnetic Reconnection on VTF



2 m

  • Origin of fast time scale for reconnection, mechanisms behind breaking of frozen-in flux
      • Particle orbits ?
      • Instabilities / waves ?
      • ….

Diagnostic ‘workhorses’ on VTF

45 heads L-probe

40 Channels B-probe

vtf configuration

Ex. of target plasma profiles

Bcusp = 50mT, Bguide= 87mT; PECRH ~ 30 kW

VTF configuration
  • lmfp>>L, tcoll>torbit,tA;ri<<L
  • S = m0LvA/h>>1
  • Plasma production by ECRH separate from reconnection drive

J.Egedal, A.Fasoli et al., RSI 71, 3351 (2000)

reconnection drive
Reconnection drive
  • Ohmic coils driven by LC resonant circuit
  • Flux swing ~ 0.2 V-s, duration ~ 6 ms (>>treconnection)
  • Vloop ~ 100 V, vExB ~ 2km/s ~ vA/10

Sketch of poloidal flux during reconnection drive

No reconnection

as in ideal MHD

Fast reconnection

as in vacuum

plasma response to driven reconnection 3
Plasma response to driven reconnection(3)
  • Current layers develop for l0=Bguide/Bcusp~3m
  • No steady-state
  • Questions:
    • How much max current / min anomalous resistivity (though ratio E/J is not constant!)?
    • What determines the size and time evolution of the diffusion region where ideal MHD breaks?
a nomalous resistivity

Ipmax [kA]

l0=Bguide/Bcusp [m]

Anomalous resistivity

- Current sustained in plasma determines reconnection rate

- For l0=Bguide/Bcusp<3m

Ip ~ 0  reconnection rate is same as in vacuum

hmeas/hSpitzervs le/l0

First observation of strongly anomalous parallel resistivity (hmeas = Ef/Jfmax)

electrostatic potential away from the x line

Ideal region:

E + v×B= 0

E · B = 0



-l0 l0

2x 2y

Electrostatic potential(away from the X-line)

E= Ezz - 

B=b0 ( x x – y y + l0 z)


E = Ez ( x + y + z)

observation of self consistent e s potential




Ez 0 Poloidal Drift

w/o e.s. potential: charge separation

No charge separation if

EtotB =½Ezl0log(x/y)

Observation of self-consistent e.s. potential

J.Egedal and A.Fasoli, PRL 86, 5047 (2001)

Deviations from EB=0 are observed close to separatrix  diffusion region

the size of the diffusion region 1
The size of the diffusion region(1)



Frozen in law is

broken where EB0

EB=(E -) B

Fit extending form valid in ideal region

d = 3.5 cm

the size of the diffusion region 2





The size of the diffusion region(2)
  • The size of thediffusion region is clearly independent of ionmass and ne
  • It cannot be related to c/wpi,e or ri,s
temporal evolution of the current channel
Temporal evolution of the current channel


in steps

of 12 ms

Time response of the toroidal current


f ~20-30 kHz


plasma response to an oscillating drive 2

In phase withVloop

900 ahead of Vloop

0 – 1.2 kA/(Vm2)

0 – 20 mAs/(Vm2)

Plasma response to an oscillating drive(2)
  • The current profile
  • can be separated in
  • two parts:

What causes the out of phase current?

ion polarization currents due to d dt
Ion polarization currents due to d/dt

Ion polarization current:

Quasi neutrality:

 fits exp. Data with  = 3.5 cm


Interpretation with polarisation current predicts time evolution and shape of current channel

MEASURED change in f and  j dt between t=0 and 30ms


circuit model for vtf plasmas 2



the observed dependence






Circuit model for VTF plasmas(2)
  • Total current is measured in each
  • shot by a Rogowsky coil
  • Values of R j1 and Cj2 obtained
  • by curve fitting
what breaks the frozen in condition

Would give c/wpe

too small (<103) & can’t explain phase

far too small with strong guide field, would give c/wpi

Only off-diagonal terms (toroidal symmetry)

What breaks the frozen in condition?

The plasma frozen in condition

is violated where:

Generalized Ohms law:



Breaking the frozen in law

  • All electrons are trapped 
  • limiting macroscopic current channel
  • Electrons short circuit electric
  • fields along their orbits
  • The frozen in law is broken in areas
  • where the orbits do not follow the
  • field lines: E•B0

Orbit width, cusp= (g l0)0.5

J.Egedal, PoP 9, 1095 (2002)

  • Fast, collisionless driven reconnection directly observed
    • Bguide <~ Bcusp
      • No current channel, trapped orbits; self-consistent plasma potential
    • Bguide>>Bcusp
      • Dynamic evolution of current profile and self-consistent potential
      • Classical collisions: not important
      • Ion polarisation current (analogy with RLC circuit) explains observed reconnection dynamics
      • Key parameter is
      • Diffusion region does not scale with el./ion Larmor radius, el./ion skin depth, but with characteristic particle orbit size
      • Direct measurements of different terms in generalised Ohm’s law suggest that pe (off-diagonal) and/or dJ/dtterms are needed (kinetic effect)
future developments
Future developments
  • Energy and velocity distributions
    • Laser Induced Fluorescence
      • fi(v) at one position; planar LIF fi(v, x) with intensified CCD
    • E.s. energy analyzer
  • Systematic analysis of e.s. and e.m. fluctuations
    • Spatial and temporal correlations; effect on plasma effective resistivity
  • Combined reconstruction of Y(x,t) and fe,i(v,x) around X-point

 particle energization mechanism

  • Machine upgrades
    • Increase strength of reconnection drive (reduce ECRH frequency)
    • Installation of in-vessel coils
      • Reduction in direct plasma losses: from collisionless to collisional regime
vtf diagnostics lif e g planar set up f i v k laser x y
VTF Diagnostics: LIFE.g. planar set-up: fi(vklaser,x,y)
  • Pulsed dye laser (Lambda Physik Scanmate pumped by Nd:Yag) pumps 611.5 nm line Elaser ~ 20 mJ in 10 ns
  • LIF detected at 461 nm (intensified CCD?)




first observation of lif on vtf arii plasma
First observation of LIF on VTF ArII plasma

Broad band, Elaser ~ 5 mJ/pulse, Dtlaser~ 15 ns

e s fluctuations during reconnection weak i p

Plasma edge

time (10-5 s)







Increased turbulence close to current channel, where gradients are large f < 100 MHz << fpe



E.S. fluctuations during reconnection, weak Ip

J(r) vs .time