J. Plasma Fusion Res. SERIES, Yol.2 (1999 6246

Magnetic Reconnection and Self-organized Plasma Systems
YAMADA Masaaki and JI Hantao
Princeton Plasma Physics Laboratory
P.O. Box 451, Princeton, New Jersey 08654. USA(Received: 14 April 1999 / Accepted: 9 June 1999)

Abstract
In this paper the recent results from the Magnetic Reconnection Experiment (MRX) at PPPL arediscussed along with their relationship to observations from solar flares, the magnetosphere, and current

carrying pinch discharges such as tokamaks, reversed field pinches, spheromaks and field reversed
configurations. It is found that the reconnection speed decreases as the angle of merging field lines
decreases, consistent with the well established observation in the dayside magnetosphere. Thisobservation can also provide a qualitative interpretation of a generally observed trend in pinch plasmas,
namely that magnetic field diffuses (or reconnects) faster when magnetic shear is larger. A recently
conceived research project, SPIRIT (Self-organized Plasma with Induction, Reconnection, and Injection
Techniques), will also be discussed.

Keywords:
magnetic reconnection, compact toroids, self-organization

1. lntroduction

toroidal plasmas.

Magnetic field generated by current in a plasma caneffectively confine high temperature plasmas by

2. Magnetic Reconnection Experiments
The MRX device is the most recent device

generating a stable toroidal pinch configuration. But thisconfiguration is often susceptible to relaxation

dedicated to investigating the fundamental physics ofmagnetic reconnection. The primary objective of MRX
is the fundamental study ofreconnection utilizing a very

phenomena which always invoke changes in themagnetic field topology and magnetic reconnection.
Also in the solar physics community there has been

growing interest in magnetic reconnection -flexible merging toroidal plasma configuration. The

MRX device creates an environment to satisfy thecriteria for MHD plasmas (the Lundquist number .! -atopological change of magnetic fields in solar flares [1].
In this paper, experimental findings on magneric

103 >> l, and the ion gyro-radius is much smaller thanthe plasma size p1 (reconnection are briefly reviewed to elucidate thet), and the boundary condition canbe controlled externally. The initial MRX experiments

fundamental physics mechanisms of magnetic
reconnection. Then the basic features of selforganization of toroidal pinch plasmas caused bymagnetic reconnection are presented. Based on thehave been carried out in the double annular plasma set-

up in which two toroidal plasmas with annular crosssection are formed independently around two flux coresfindings of recent merging experiments, this paper also[2] and reconnection is driven in the quadrupole field;
Fig. 1(a). By pulsing currents in the TF coils after a

discusses a recently conceived research project, SPIRIT(Self-organized Plasma with Induction, Reconnection,and Injection Techniques), in the context of studying
confinement physics of low aspect ratio current carrying

quadrupole poloidal magnetic field has been established,@1999 by The Japan Society of Plasma
Science and Nuclear Fusion Research

62

Yamada M. et al., Magneric Reconnection and Self-organizedplasmas are inductively created around each flux core
due to poloidal electric fields' Then the PF coil current
can be decreased to drive magnetic reconnection aroundthe x-point. Magnetic reconnection has been intensively
studied with and without the third vector component(toroidal or azimuthal direction) of the magnetic field'
To document the internal magnetic structure of thereconnection on a single shot, a two-dimensional
magnetic probe array with 90 channels is placed on an

Plasma Systems

R-Z plane or toroidal cut-off plane, as shown in Fig'
1(a). Plasma parameters ate B - 0.5 l'0kc, T.
(O.l 1.0) x l0racm-3'
30eV, and n.

--- l0 --

Two distinctively different shapes of neutral sheet
cunent layer are identified, depending on third vector
components of reconnecting magnetic fields' Fig' l(b)and Fig. l(c) show the time evolution of the poloidal
flux contours during reconnection processes of null-helicity and co-helicity plasmas. The contours arederived assuming axisymmetry (assured by a center
conductor placed at the major axis) in a R-Z plane'
Other operational conditions are held constant for eachdischarge. As poloidal flux is driven toward theCo[cd bY 2'O

diffusion region, a neutral sheet is formed. Without thethird component (null-helicity reconnection), a thindouble-Y shaped diffusion region is clearly identified;Fig. 1(c). With a sizable third component (co-helicity
reconnection), an O-shaped sheet current appears; Fig'l(b). This O-point current channel grows into aspheromak configuration.

Quantitatively, it has been found that the measured
reconnection rates agree well with a generalized Sweet-

Parker model, which incorporates compressibility'
downstream pressure, and the effective resistivity [3]'(b) Co"holclty pull nconncctlon
10

A quantitative study of the merging angleodependence of reconnection speed Vp and current sheet€ o 610z (cm)

thickness 6 is being carried out' By controlling themagnitude of the axial field component' 81, the angle
inbetween merging field lines can be varied' As shown
as
of
2'5
factorbyaFig. 2, Vp increases as 6decreases

HHH

the angle is increased from 55 degree to 180 degree'
While this data is preliminary, data points between 0
draw
and 55 degree will be added in the future' We can$-li-o o .,0.,!fi#'o.ihtt-J5
Z(cm)
Z(c||)

a comparison between our preliminary study and

Z(cm)

in

observations at the dayside magnetopause' Variations
the interplanetary magnetic field (IMF) cause the(c) Null-hcllctly pull nconnectlon

impinging field to alternate between having a northwardand southward component. It is observed that "fluxtransfer events", likely signatures of magnetic

'l)

o

s

reconnection, are clearly correlated with southward
antiparallel wind in agreement with the present results'

3. Magnetic Reconnection and Self'
organization of Toroidal Pinch Plasmas
9,t1f

s"i*t'it.riiffi -i-i6 €0Z (cm)

Z(cnr)z(cm)Magnetic reconnection occurs whenever electric
current is induced in a plasma with finite dissipations'Typical examples of such plasmas are laboratory
toroidal pinches, where a toroidal current is induced toheat and compress the plasma through the well known
pinch effects. Tokamak, reversed field (toroidal) pinch05
Z (crn)Experimental setup including 2-D magnetic
Fig.
- 1 (a)(b)probe array. Poloidal flux contour evolution for(c)reconnection'null-helicity
co-helicity and63

Yamada M. et al., Magnetic Reconnection and Self_organized plasma

10

Systems

continuously supplies the poloidal flux (or equivalently
drives the toroidal current). The process ofpoloidal flux
resistive diffusion at the magnetic axis can be regarded
as field line annihilation or..magnetic reconnection,, in a
general sense. Supply of new flux from the outside
resembles the external drive of magnetic reconnection.
Then the merging process of field lines at the magnetic

a

v4
G

2

axis belongs to the category of ..co_helicity,'

0
5reconnection for tokamaks, RFp's and spheromaks,
since the merging angle is less than lg0 degrees, but
their angles vary for the case of a tokamak to an RFp
and/or a spheromak plasma. On the other hand, theJ)3

plasmas. The rate of magnetic reconnection or diffusion"null-helicity" reconnection happens in the FRC
can be measured by the toroidal electric field, or thequantity usually referred to as the one-turn loop voltage&o2needed to sustain the plasma. The larger the loop

voltage is, the faster the diffusion happens.

050

Experimentally, it is a general observation that an

100 150 200

ohmically driven tokamak can be sustained by a much

Merging Angle (degrees)

lower loop voltage than an RFp for the same given

toroidal plasma current. Although the usualFig.2 Dependence of (top) rgqe.r.ction speed V. and(bottom) current sheet thickness 6'on themerging
angle between magnetic field lines.

interpretation is that the quality of energy confinement

is much poorer in low-q pinch plasmas, anotherinterpretation can be given that the rate of reconnection
or diffusion is much faster with larger merging angles,
qualitatively consistent with MRX results.

(RFP), spheromak, and field reversed configuration(FRC) belong to this category. However, toroidal

fieldsAnomalous diffusion or poor energy confinement isare supplied differently in these systems; the tokamak,sgenerally regarded as a consequence of large

toroidal field is very strong and is primarily created byexternal coils, while the toroidal field of the RFp iscreated by the combined effects of internal current andsmall external field and is much weaker than that of afluctuations associated with self-organization activities,

which is a remarkable common feature for all of these
low-q pinch plasmas. After an initial highly turbulent
state, t}le plasma settles into a relatively quiescenttokamak. The toroidal field of a spheromak is generated

stablefinal state, which is insensitive to initial conditions.

entirely by the internal current. To another extreme. the
FRC plasmas does not have a significant toroidal

4. Current Garrying plasma Systems for
Gompact Fusion Reactor

field atall throughout the plasma. There is a sharp contrast in
the direction of magnetic fields in these pinch plasmas:
in high-q tokamaks, the angle of field lines vary little
throughout the plasma (or equivalently the magnetic
shear is low), and they are primarily in the toroidal

In addition to confinement quality, the achievablebeta is critical to the cost-effectiveness of a f-usion
reactor. However, in general, the highest betas are notnecessarily achieved with the best confinement

direction. In the RFp and spheromak plasmas, the angle

characteristics. Often, the opposite trend is seen among
the pinch plasmas discussed in the previous section.

of field lines vary over a wide range (or the magnetic

shear is large), and they change from primarily toroidal
at the magnetic axis to primarily poloidal at the plasmaedge. In the FRC plasmas, the angle of magnetic fieldchanges 180 degrees across the magnetic axis orthemagnetic null.

Figure 3 schematically presents the achieved beta
regime of representative toroidal configurations
generated by external and internal magnetic
field withrespect to an internal field factor. The horizontal axis
can be considered to be a self-organization factor,

All these pinch plasmas are mostly produced andsustained by an external transformer, whichsince

the internal field is created by self_organization ofplasmas. Among these compact toroidal configurations,64

Yamada M. et al., Magnetic Reconnectionand Self_organized plasma Systems

OPERATION REGIME ON SPtRtT(0.5<E<4,and4<S-<60)

Itramd d[

un!6le qb(1htr,)@m>/--\ q!9(.:"-ii:tl@-*9

Elongation E

Internal current(S€lt Organization Eftscls)

Fig. 4 Operation regimes of SplRlT

are shown withregards to s'(gyro-radius factor) and E(elongation). Tilt stability conditions

0.1

Fig. 3 Diagram for magnetic confinement

systems inplasma beta and ratio of internal
to externalareemphasized in this figure.

current.

passive stabilizers. (3) Sustain thethe FRC which does not have toroidal field
and isdominated by perpendicular currents, isuniquely
attractive for a compact fusion reactor core.
It has thehighest beta (near unity) conceptually attainableinequilibrium. However, the nature of its self_organization
process is qualitatively different fromthat happening in

RFP's and spheromaks, where parallel currents

an FRC has
been successfully attained in relatively
small devices,
although its lifetime is limited to the orderof the energy

time (< lms).
formed FRC
plasmas appear experimentally tobe quite stable toglobal modes. If questions regarding formation,
stability,
sustainment, and confinement are successfully
resolved,
then FRC's may offer a high_power_densityand easily
properly

maintainable alternative approach to fusion

production.

MRX [7]. The FRC plasmas were formed by merging

counter-helicity spheromaks whose opposing

power

conventional fast shock heating nor electrode
discharges, has significant advantages for

We have proposed a concept exploration
called SPIRIT to investigate comprehensively

stability and the confinement features ofdevelopment of a compact reactor core.

device

FRCs inplasma size. It is expected that counter_helicity

confinement

Form FRC's with large flux (50mWb) bymerging two
spheromaks made by the flux core induction
schemestability andconfinement characteristics of the new regimesof FRC

configuration by varying the importantto themergingof two spheromaks will lead to the formationof FRC
plasmas with a toroidal current of
up to 300kA and witha separatrix radius R, of up to 50cm. The gyro_radiiofions can be significantly smaller than R, and their ratio
s will be varied over a wide range (24O).
Here s _ 4 s.
Important questions are for what s values
are these CT

research are: (l)with opposite helicities, and (2) Assess thethe

SPIRIT will be dedicated to the explorationof new
regimes of compact toroid configurations,in particular,
FRCs with variable ratio of the ion gyro_radius

the MHD

comparison with other CT plasmas, by
maintaining suchplasmas much longer than their energy

parameter s- and the elongation factor

toroidalflux is annihilated during the merging to acceLrate
ionsfrom l0 to 200eV thus allowin1 p _ l. This novel
inductive formation scheme, which invokes
neither

5. Proposed Device SplRlT

times. Primary features of the proposed

firm base for assessing confinement characteristicsof
FRC plasmas. (4) Investigate comparatively
the global
characteristics of all compact, current_carrying
toroidalconfigurations.
In the proposed SpIRIT device, FRC plasmas
andother compact toroidal plasmas can be generatedbyutilizing inductive formation schemes followedbymerging of co- and counter helicity spheromaks,
basedon the previous experiments in the TS_3
[4,5,6] anddominate. The high-beta equilibrium ofconfinement

FRC for asignificantly longer time (l_10 msec) thanthe energy
confinement time using a center stackohmic_heating(OH) transformer and/or NBI current
drive to provide astability

plasmas susceptible to a tilt mode,and under what
conditions can they be made stable with
conductive

E and by using
65

Yamada M. et aI., Magnetic Reconnection

SPIRIT areshells? In Fig. 4, operation regimes forwithshown versus s and E (elongation) and compared
the previous regime [8].
A center stack which contains an OH transformer
plasmas towill be inserted to extend the lifetime of FRC
theincrease
further
and/orthan one millisecond

more
can beplasma current, so that a confinement study
MHD
The
carried out in a quasi steady-state regime'ofthecharacteristics and global confinement featuresdifferent compact toroid plasmas with additional

four

be
ohmic current drive by the center stack willcomparatively investigated in the Phase I research

stage'

Furthermore, this project will be designed

toaccommodate an upgrade consisting of

neutral-beamtheinjection (NBI) of a few megawatts to extend
one
the plasma for much longer thanlifetime ofthe scope ofof plasma
control
activeby enabling

millisecond. This will significantly broaden

the experiment
providing an
stability with toroidal rotation and also byheating' If abeam
additional means of current drive and30-60kVofhigh-fueling (- 100Amps) neutral-beamrange is injected into the FRC plasma' it isand Self-organized Plasma Systems

possible to sustain this configuration fora long period ofti-" (> l0ms). This NBI would induce spinning of theplasma with high velocity up to the Alfven

speed' whichmodes'
would in turn help stabilize the global MHD
Additionally's'of
NBI would also decrease the value

RFP (Rla = 1'O5 SPIRIT can create a low aspect ratio1.5), which has never been studied before [9]'References[1] S. Tsuneta, Astrophys' J' 456'840(1996)'-

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