J. Plasma Fusion Res. SERIES, Vol.2 (1999) 195-197

Physics lssues of a Proposed Progroffi, SPIRITJI Hantao and YAMADA Masaaki
Princeton Plasma Physics Laboratory
P.O. Box 451, Princeton, New Jersey 08654. IISA
(Received: 12 lantary 1999 I Accepted: 28 June 1999)

Abstract
Physics issues of the proposed program, SPIRIT (Self-organized Plasmas with Induction,Reconnection, and Induction Techniques) are discussed. The main purpose of this program is to explore
the physics of global stability and sustainment of compact toroids, including FRC (field reversedconfiguration) as well as low-aspect-ratio RFP (reversed field pinch), spheromak and spherical torus.

Keywords:
compact toroid, MHD stability, dynamo effect

1. lntroduction

SPIRIT - Side view (E=0.8)

Compact toroidal plasma configurations, such as
FRC's, spheromaks, spherical toruses, and RFP's havebeen extensively studied in search of a cost-effective,

Flux Coaes

high-performance, high-power-density reactor core.
Since such configurations have characteristically highbeta plasmas, they hold promise for opening the road toan advanced fuel reactor, provided confinement issufficiently favorable. Among these compact toroidal
configurations, the FRC is a particularly attractive
candidate for a compact fusion reactor core. It has thehighest beta (near unity) conceptually attainable inequilibrium. If questions regarding formation, stability,Shaping PF Coils Passive Stabilizers
2.0 m

sustainment, and confinement are successfully resolved,

then FRC's may offer a high-power-density and easily

Fig. 1 Schematic view of SPIRIT device. Two pairs offlux cores are installed to form two spheromaks

maintainable alternative approach to fusion power

before they are forced to merge into an FRC(counter-helicity merging) or a larger spheromak(co-helicity merging). When a center stack withtoroidal field coils is installed, finite toroidal field
can be introduced at the edge of plasma to form

production.

The SPIRIT (Self-organized Plasmas with
Induction, Reconnection, and Induction Techniques) [1]device, shown in Fig. 1, has been proposed to explore
the physics of these compact toroids. The uniquenessand significance of the SPIRIT device are: (l) the novel

an RFP or ST plasma during co-helicity merging.

inductive formation scheme by merging co- andcounter-helicity spheromaks; (2) wide-range@1999 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchCorre sponding autho r's e -mail : hj i @ pppl. gov

195

JlH. et al., Physics Issues of a Proposed Program, SPIRIT

accessibility of the global stability and confinement
characteristics of FRCs; (3) utilization of ohmictransformer and/or neutral beam injection to sustain CT
plasmas for a significantly longer time than the energy
confinement time; (4) great flexibility to address effectsof aspect ratio on the RFP configuration.
The compact toroid plasmas in SPIRIT will beformed by merging two spheromaks. Each spheromak
will be generated by induction using a pair of flux coresl2l at each end of the vessel by properly programming

shift instabilities.
An initial study [4] on the global FRC stability has

been performed using a rigid body model in theparameter space of s (ratio of separatrix radius toaverage ion gyro-radius) and plasma elongation E (ratioof separatrix length to separatrix diameter). Tilt stability
is predicted, independent of s, for FRC's with low E(oblate), while the tilt stability of FRC's with large E(prolate) depends on slE.It is found that plasma rotation

due to ion diamagnetic drift (a two-fluid effect) andcollisionless ion gyro-viscosity can stabilize the tiltmode when slE < 2.8 (see Fig. 2). Increasing stability
with decreasing s is due to strong two-fluid and ion

currents inside the flux cores. Then these two
spheromaks, which carry identical toroidal currents withthe same or the opposite toroidal field, are forced tomerge along a common axis by controlled external coilcurrents. FRC can be formed by merging of counterhelicity spheromaks [3] while a larger spheromak (orRFP and ST) can be formed as a result of co-helicity

kinetic effects while a larger E further enhances stability
by increasing tilting inertia. A small additional rotation(e.g. a Mach number of C.2) can improve tilt stability
significantly at lar ge E.
Existence of a small number of energetic ions canalso improve tilt stability by lowering effective s by afactor of \il + a(FAf, - t), where a is the fraction ofenergetic ion density and s5 is the parameter s for themerging.

2. Global Stability of FRC Plasmas
The most striking feature of an FRC is the absenceof a toroidal field. The internal plasma current flows

energetic ions. For example, if the energetic ions have a
50 time higher energy than background ions, then s2ls2n =50, the s can be lowered by a factor of 5 with d, = l7o.

toroidally, essentially perpendicular to the local field,
which is in the poloidal direction. The resulting Lorentz

force balances with pressure gradient in the radial

It is also found that radial shift is unstable when E< I while axial shift is unstable when E > 1 However,direction, confining a plasma with a nearly unity beta.
However, such a configuration will subject to tilt andunlike tilt stability, gyro-viscosity has little effect on
shift stability. Both tilt and shift stability is required for
FRC plasmas to be experimentally studied in detail.

3. Sustainment of FRC plasmas
Another important goal of FRC research in theSPIRIT is the sustainment of FRC plasmas over a much
longer time (1-10 ms) than the energy confinement timeby an OH transformer and/or an neutral beam injection(NBI). The OH transformer in the SPIRIT with singleswing will have a flux of 0.1 Vsec, with a maximum
one-turn loop voltage of 200 V.
According to a zero-D analysis, an NBI with 2-5
MW with help of an additional particle source maysustain the FRC plasma in a quasi steady-state fashion,satisfying requirement for balances of energy, particle,
and magnetic flux. An intriguing feature of FRC
sustainment via a heat source at the magnetic axis ispossible activation of a cross-field thermoelectric force
arising from electron temperature gradient to counter act

Unsta

Stable10tlFig. 2 Stability diagram in s and elongation for tilt modeof FRC plasmas. Stabilizing effects from ion

against resistive diffusion [5]. In addition to this 2Deffect, the 3D dynamo effect may also help to sustain

additional E x B rotation (represented by Machthe FRC configuration through conversion of kinetic
energy from the beam to magnetic energy.

diamagnetic drift, ion gyro-viscosity, andnumber Ml are taken into account.
196

IIH. et al., Physics Issues of a Proposed Program, SPIRIT

relatively larger distances between them (Fig. 3(b)).
When the aspect ratio approaches unity, it is expectedthat the number of unstable modes decreases to 2 andthe distance between their rational surfaces increasesignificantly, as illustrated in Fig. 3(c) where aspectratio is 1.25. This physical intuition has been supported
by preliminary results of nonlinear resistive MHD
simulations in which the aspect ratio can be varied in a4. Low Aspect Ratio RFP
A growing consensus in the RFP community is thatsuppression of magnetic fluctuations and stochasticity
will lead to significant improvement in confinement.
Recent inductive poloidal current drive experiments inMST RFP have proven [6] that a modification of edge

current profile can reduce magnetic fluctuation
amplitudes and improve the confinement. A

locations are very close to each other, as shown in Fig.
3(a). With an aspect ratio of 3, such as in MST, thecylindrical geometry [7]. More recent studies using full
3D toroidal MHD codes are underway to explore
possible advantages of a low aspect ratio RFP. The
unique formation method employed in SPIRIT bymerging can generate RFP's with lowest possible aspectratio of 1.05, since only a small TF coil is needed in thecenter stack. With the OH transformer in the center
stack, an aspect ratio of 1.3 can be obtained with anumber of unstable modes is reduced to 6 withsustained discharge.

complementary approach to suppress the stochasticityinduced transport is to reduce the number of unstablemodes and increase the distance between neighboring
resonant surfaces at the lower limit of aspect ratio. InRFP with an aspect ratio of 6 (such as in ZT-40M), thenumber of unstable modes is around l0 and their

5. Conclusions
With its novel inductive formation scheme, unique
FRC sustainment methods, and great flexibility, the0.15'ol=ti=l, -^0.10

Fi/a=6SPIRIT experiment will provide fundamental physics ofglobal stability and sustainment of CT plasmas,
especially FRC and low-aspect-ratio RFP plasmas. Aq o.o50successful demonstration of favorable properties ofstability, sustainment, and confinement will open a new-0.05 E
0path towards high-power-density and easily

0.3

maintainable fusion reactor concepts.

0.2

qq0.1

References

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-0.1

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-o.2(1999).
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Y.L. Ho et al., Phys. Plasmas 2,3407 (1995).

and unstable modes in RFP.

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