J. Plasma Fusion Res. SERIES, Vol.5 (2002) 373-376

A New Design of a Tandem Mirror
KATANUMA Isao, TATEMATSU Yoshinori, ISHII Kameo, SAITO Teruo,NAKASHIMA Yousuke, ICHIMURA Makoto and YATSU Kiyoshi
Plasma Research Center, University of Tsukuba, Tsukuba 305-8577, Japan(Received: 1 1 December 2OOl I Accepted: l0 July 2002)

Abstract
Tandem mirror experiments have proved that the plug potential is created by a""ECRH only, whereions and electrons in the central cell have been confined axially well. On the other hand the radial loss ofplasma in a tandem mirror has lately drawn considerable attention. Therefore, we are designing a new
tandem mirror improving axial and radial confinement of plasma.

Keywords:
design, tandem mirror, radial transport, electrostatic potential

1. lntroduction

designing the tandem mirror improving the radial andTandem rnirror experiments have proved that theaxial plasma confinement.

plug and thormal barrier potentials are created
2. On the Radial Transport

successfully by a".ECRH only. Ion axial confinement
has been improved greatly by the plug potential. Thephysical mechanism, which remained unknown for along time, has been found by ourselves recently [-3].

The mechanism of a large radial transport in thethermal barrier region of a tandem mirror is unknown atpresent. However the transport is accompanied with@""ECRH, so that the most plausible mechanism isThat is, the non-Maxwellian electron distributionfunction in the plug/thermal barrier region, two-supposed as follows.

There is no magnetic flux surface in the open-component electron distribution function in the central
cell, and ion coulomb collisions are required for the plug

ended system such as a tandem mirror. Noting that therelation c\rr ) corrn > rovn holds in the present tandem
mirror, the equilibrium state is realized along eachand the moderately deep thermal barrier potential
formations [1]magnetic field line firstly. Here 4411 is the bounce
frequency along a magnetic field line, are'g and ohR arc
the bounce frequencies due to the E x B drift and VB
drift in the azimuthal direction, respectively. In the nextstage the equilibrium state will be realized along eachequi-potential surface due to the E x B drift. The VB

However. the tandem mirror experiments haverevealed the existence of a larger plasma radial transport

in the plug/thermal banier region. In the thermal barrier
region the plasma density is considerably lower thanthat in the central cell. This large radial transport exists
even in the axisymmetric end-mirror cells such as theGAMMAI0 t:rndem mirror [4]. Therefore the radialtransport is r:onsidered not to come from a nonaxisymmetric magnetic field such as a neoclassicaltransport (axii;ymmetric electrostatic potential + nonaxisymmetric magnetic field). As the radial loss may
extend to the central cell in a tandem mirror, we aredrift is much smaller than the E x B drift. The
discrepancy between the equi-potential surface and the
Mod-B surface makes a particle feel an effective nonaxisymmetric magnetic field, which causes theneoclassical transport (non-axisymmetric electrostatic

C o r r e sp o ndin g' aut ho r' s e - mail : kat anuma @ p r c. t s ukub a. acjp

JIJ

@2002 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchKatanuma L et aI., A New Design of a Tandem Mirror

potential + axisymmetric magnetic field).

particle the energy and magnetic moment satisfy theFigure I displays the mechanism of generating thediscrepancy between the equi-potential surface and theMod.B surface even in an axisymmetric magneticmirror. Firstly, the equi-potential surface is assumed
circular as shown in Fig. 1. In general, plasma
equilibrium state is realized on the equi-potentialsurface. The ionization, however, occurs non-uniformly,
on the cross section surrounded by the equi-potential
surface. The ionized ions and electrons drift in theopposite azimuthal directions to each other due to VB
drifts as shown in Fig. 1 The resultant charge separation
does not lead to the outward plasma drift because themirror system is assumed to have an average minimum
B magnetic configuration to assure MHD stability.
Instead, the high-m modes appear on the equi-potential

relation t = IlBt + qcp., wherc B, and rp, are the magnetic
field and electrostatic potential at the turning point. If
the relation ttB.> lqqrl is satisfied, the magnitude Bt isconserved during the drift.
Because the Mod-B surface is open in theaxisymmetric magnetic mirror while the surface isclosed in the minimum B magnetic configuration, theminimum B magnetic configuration can confine theparticles within the Mod.B surface even in the equipotential surface such as Fig. l. The magnetic field issurfaces.

The minimum B magnetic configuration has a great
benefit to the plasma radial confinement even in thelocal minimum at the center of the minimum B
magnetic configuration so that the Mod-B surfaces areclosed around the center.

4. Single Minimum B Tandem Mirror

Ions and electrons drift along a winding equipotential surface in Fig. l. The VB drifts cause the ion
and electron motions across the winding equi-potential
surfaces, where the orbits become chaotic in case of alarge amplitude of the high-m mode on equi-potential
surfaces [5]. Therefore, a large radial transport ofcase that the winding equi-potential surfaces appear
such as that in Fig. 1. The drift orbits ofion and electron
are restricted within the surface satisfying B(x,y,a) = Br.

Figure 2 shows the schematic diagrams of thesingle minimum B tandem mirror coils. The magnetic

field is plotted in Fig. 3, where the magnitude ofplasma is anticipated.

magnetic field is displayed in shading in Fig. 3(a) andthe magnetic field on axis is plotted in Fig. 3(b). The

3. Goncept of a New Open-ended System
In the previous section we have mentioned thata large radial transport is expected when 4611

central cell of the tandem mirror is inside the innermirror throat and the plug/thermal barrier region isbetween the inner and outer mirror throats. The mirror
ratio of magnetic field at the inner mirror throat to thatat the midpoint of the central cell is about six in Fig. 3.
The micro-wave, indicated by ECRH in Fig. 3(a),is injected around the midway from the thermal barrier
to the outer mirror throat and creates the plug potential
by heating electrons there [1]. The end-mirror cell has
the open contours of magnetic field so that the ionstrapped in the end mirror cell drift out radially. The) olBrr )>ovn. The relation of oo^n > atvn exists in the case ofhigh f", that is, when plasma heating such as ECRH andICRF is introduced in the operation.

It is necessary to suppress the large radial transporteven in the configuration of Fig. 1. Ions and electrons
drift radially through E x B drifts and VB drifts, whereenergy e and magnetic moment 1t of a particle areconserved during its drift. At the axial turning point of a(b)(a)

1.** tb-' .*.

tqFnLtng

gre,Y j J}rfid,Bblack: equi-potential

Fig. 1 Schematic diagram of equi-potential surfaces inan axisymmetric mirror, and mechanism of gener-Fig. 2 Schematic diagram of single minimum B tandem
mirror coils, where left figure is a top view andright figure is bird's eye view.

ating the high-m modes on equi-potential surfaces.

374

Katanuma I. et al.. A New Desien of a Tandem Mirror

"T(a)

4\r$

Fis. 4 Schematic diagram of linked minimum I mirror
coils.

o)

ECRH-305zo
Fr l00.0Z2.254.5tm)

Fig. 3 Magnetic field configuration. (a) is magnetic fieldlines and contours of magnitude of magnetic
field. (b) is the magnetic field on axis.
Fig. 5 Schematic diagram of each component of linked
minimum B mirror coils, left figure is a top viewand right figure is bird's eye view.

thermal barrier potential, therefore, are created and so
the electrons are confined within the minimum B central
cell magnetically and electrically.
The weak point of this single minimum B tandem
mirror is that the volume of the central cell is rathersmall in Figs. 2 and 3, so that input power (ECRH) tocreate the plug potential may be expensive per the unit
volume confining plasma.

(a)

5. Linked Minimum B Mirror
The linked minimum B is designed in order tomake the volume of the central cell region larger and to

gain the power efficiency in Fig. 4. The essential part ofthe linked minimum I mirror is to link the single
minimum B tandem mirror in a line, where Fig. 4 is an
example set four unit single minimum I mirrors in aline. The plug and thermal barrier potentials are created30

in the outermost end mirror cells by ECRH as shown inFig. 4. The injected power (ECRH), therefore, isrequired only in the outermost mirror cells, whichV\improves the power efficiency compared to the single
minimum B tandem mirror.
Each component of the linked minimum B mirror isshown in Fig. 5, where the coils are plotted. The coilsystem is more complicated than that of Fig. 2 in orderthat the outernrost magnetic field lines are bended tolink to the neighbor mirror cell as can be seen in Fig. 6,0E-4. 5-2.25 0.0 2.25 4.5Z@)

Fig. 6 Magnetic field configuration. (a) is magnetic fieldlines and contours of magnitude of magnetic fieldin each component of linked minimum B mirror
coils. (b) is the magnetic field on axis.
3',15Katanuma I. et al., A New Design of a Tandem Mirror

6. Summary

where the equi-contour surfaces of magnetic filed are
drawn in Fig. 6(a) and the magnetic field on axis isplotted in Fig. 6(b). The mirror ratio of magnetic field at
midpoint of central cell of each component to the innermirror throat of each component is about six.

The new design of a tandem mirror has shown inthis manuscript. The detailed calculation of ion andelectron confinement times have to be carried out fromnow on. However, the essential idea of the design that

The ions trapped in the central minimum I mirror

the ions and electrons are tried to be confined by amagnetic well radially is very new. And the confinement
time of plasma in the present tandem mirror is expected

cell of each component drift within the minimum B
magnetic field, where Mod.B surfaces are closed, so thatare confined radially by the magnetic well. The ionsgoing through the inner and outer mirror throats ofeachcomponent, which are called passing ions, reach theplug region in the outermost end-mirror cells. Because
the passing ions do not feel the minimum B magnetic
field, these passing ions drift radially and are lost
finally. However the passing ions have to travel a long
distance from the plug to another plug, and then are
expected to feel the smoothed out winding equipotential surface and are expected to drift out very
slowly. So the confinement time of the passing ions areto be improved greatly.

References[1] I.Katanuma et al., J. Plas. Fus. Res. 77, 1085
(2001).

[2] L Katanuma et al., Phys. Plasmas 9,3449 (2002).
[3] I. Katanuma et al., in preparation (2002).
t4l K. Yatsu et al., Nucl. Fusion, 39, l7O7 (1999).
[5] I. Katanuma et al., Plasma Phys. Rep. 28,734(2002). (Fizika Plazmy 28,798 (2OO2)).

expected to be long.

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