J. Plasma Fusion Res. SERIES, Vol.5 (2002) 100-105

Research on High-Beta Plasmas Basedon Two-Fluid Relaxation Theory
OGAWA Yuichi, HIMURA Haruhikor, HIROTA Makotor, HORI Danr, ITOH Atsushi2,
KONDOH Shigeor, MORIKAWA Junji, NAKASHIMA Chihiro2, NIHEI Hitoshi2,
NUMATA Ryusuker, OHHASHI Manabur. OHKUNI Kohtaro, OHSAKI Shuichir, SAITOH Haruhikor,
SHATASHVILI Nana, VOLPONI Francescol, WAKABAYASHI Hidenoril and YOSHIDA Zenshol
High Temperature Plasma Center, The University of Tolqo, Tolqo 113-8656, Japant School of Frontier Sciences, The University of Totcyo, Tolq-o 113-8656, Japan
2
School of Engineering, The (Iniversity of Tokyo, Tokyo 113-8656, Japan(Received: 11 December 2001 / Accepted: 15 May 2002)

Abstract
Relaxation phenomena have been observed in many plasma experiments, and some theoreticalexplanations have been presented. Recently Mahajan-Yoshida has discovered a new relaxation statebased on two-fluid plasma theory, and proposed a possibility for confining high-beta plasmas. In thistheory two fluids (electron and ion) shouldrelax to the conditions;V - VxB = aB,B + VxV = FV,
resulting in a relation given by B + (VlV)2 = constant. This is called Beltrami/(generalized) Bernoulli
condition. To explore this new relaxation state experimentally, a toroidal device with an internal coil issuitable, where strong plasma flow in the toroidal direction is induced by E x B drift by introducing aradial electric field. Since the E x B flow velocity increases as the minor radius is increased, a high-beta
plasma could be confined in the core region. A torus device called S-RT is planned with a floatingsuperconductor coil. This paper describes its engineering design and discusses expected plasma
parameters. At present, a device with a normal conductor, called Proto-RT, has been constructed, andexperiments of electron injection have been carried out. In addition, a small-scale torus device with asuperconductor coil, called Mini-RT, are under construction, where a high-temperature superconductor(HTS) made of Bi-2223 tape is employed as a floating coil. This is the first challenge to explore thefeasibility of HTS coils for fusion plasma devices.

Keywords:
High-beta plasma, two-fluid relaxation theory, plasma flow, intemal coil device, high temperature superconductor (HTS)

1. Introduction
Relaxation plays an important role in plasma

to the so-called Taylor state due to the strong toroidal
magnetic field. In REPUTE-I device (R=0.82 m, a=0.22
m, 8,-0.35 T, 1n=4gg kA) a new relaxation state has

dynamics. In Reversed Field Pinch (RFP) plasmas theforce-free condition (i.e., j // B) is established and J.B.
Taylor has theoretically explained by the energy
minimum condition with the constraint of the helicity
conservation [1]. While, tokamak plasmas do not relax

been discovered experimentally at the parameter region

between RFP and tokamak (i.e., 0 < q(a) < 1), and iscalled as Ultra-low-q (ULO configuration [2]. In ULQ@20U2by The Japan Society of Plasma
Science and Nuclear Fusion Research100

Ogawa Y. et al., Research on High-Beta Plasmas Based on Two-Fluid Relaxation Theory

plasmas the profile of the safety factor is not
monotonical, but has a pitch minimum in the outerregion of the plasma column (r/a - 0.7). This is very
similar to the negative shear configuration in tokamak
plasmas t3l. Ul-Q plasmas are categorized into a kind ofrelaxed plasmas, and many interesting phenomena
related with the dynamo effect have been observedhigh-temperature superconductor (HTS) made of Bi2223 tape is employed as a floating coil [13]. This is thefirst challenge to explore the feasibility of HTS coils forfusion plasma devices.

In this paper the two-fluid relaxation theory isbriefly explained, and an idea how to apply thisrelaxation theory for a torus device with an internal coilis presented. Next the engineering design of the S-RT

t4,sl.

In the Taylor state, the plasma current becomesparallel to the magnetic field; namely the relaxation
between the electron flow (plasma current) and themagnetic field takes place. Recently a relaxation theory
including the plasma flow (i.e., ion flow) has beendeveloped, and a new relaxation state has been
identified [6,7]. Hereafter let us call this two-fluid

device and expected plasma parameters are discussed.
Finally, the present status of the Proto-RT device isreviewed and the design of the Mini-RT device ispresented.

2. Two-Fluid Relaxation Theory andApplication for a Torus Device withan Internal Coil(electron and ion flows) relaxation.

Equations of motion of the electron fluid and theion one are given as follows;

In Taylor's one-fluid relaxation state, the pressure
gradient perpendicular to the magnetic surface should be

zero, yielding a quite low beta plasma, if some

E+V"xB+*ro"=0,

improvements were not taken into account. While, in the
two-fluid relaxation state, the plasma pressure could besustained by the dynamic pressure due to the plasma(1a)v) y,= ab*v,xB)-.f
Y*ft,t Mn vr, 1lu;dtM|flow, resulting in a confinement of an ultra high-beta

plasma. To study this new relaxation state

Here an inertial term is omitted for electron equation,and the ion flow velocity is retained for the ion equation. Conventional notations are employed. These two-

experimentally, a toroidal device with an internal coil issuitable, where strong plasma flow in the toroidal
direction is induced by E x B drift by introducing a

fluid equations can be easily modified as follows;radial electric field.

,j =(V_yxB)xB +v(p"-A). ea,t

A. Hasegawa has also developed another new
relaxation theory, and proposed a dipole field

dt\

configuration with an internal coil [8]. In his theory theplasma relaxes to a high beta state under the constraintsof the conservations of two adiabatic constants (tt and J)[9]. To explore this concept, MlT/Columbia group is
now constructing a large-scale torus device called as
Levitating Dipole eXperiments (LDX) t101.

Ictt (v*;')= v x(E +Y x v)-" (+ v'+ n,+ o). (2b)Although these two relaxation phenomena are

where the electric field E is replaced with vector andscalar potentials (A and p). The magnetic field B, theplasma flow velocity Vp and electron/ion pressure p"/p1
are normalized by Bs, Va, magnetic pressure, respec-

independent with each other, the internal coil device istively.

As mentioned above, Mahajan-Yoshida andHasegawa have proposed new relaxation theories.

suitable for studying these relaxation theories. To
explore these new relaxation phenomena, it is planned toconstruct a torus device with a floating superconductor
coil called Superconductor-Ring Trap (S-RT). Prior tolarge-scale experiments a normal conductor device
called Proto-RT has been constructed [1,12]. The

Mahajan-Yoshida has examined these two
equations at the steady-state condition and derived thefollowing conditions as a new relaxation state [7].

confinement tirne of plasmas is, however, quite limited

due to the support structures of the internal coil. A
small-scale torus device with a superconductor coil,called Mini-R'f, is now under construction, where aI-\
n=a\v_vxB),(3a)

B+Vx V= bV

(3b)

.

These are corresponding to the so-called force-free con-ditions; i.e., the first terms of the right hand side in eqs.
(2a) and (2b) should be zero. This is corresponding to101

Ogawa Y. et a/., Research on High-Beta Plasmas Based on Two-Fluid Relaxation Theory

the Beltrami condition of a vortex dynamic system. We
should notice that the first condition includes the Taylor
state, when the plasma flow 7 is zero; i.e., E = a(V -discovered [4]. In these devices the plasma is confinedin the inner region of the torus (i.e., good curvature
region), while in our device the plasma is produced andVxB) =-aVxE=1,j.

confined in the outer region of the torus (i.e., badThis force free conditions yield the followins

relations;curvature region). We expect to realize a new relaxedstate predicted by two-fluid relaxation theory under theF"-Q=const,(4a)*.v'* fii-Q = const(4b)

condition of the strong toroidal plasma flow. In general,
the interchange mode is unstable at the bad curvature
region, but the stability is not so clear for the plasma
accompanied by a strong plasma flow. Stability of the

By combining these two relations, the following condition is obtained;

V'* F= const.

new relaxed state is important, and theoretical study isunder way.
Next let us discuss on the radial electric field E.. Intokamak H-mode plasmas the radial electric field seems(5)

to play an important role at the plasma boundary.
Mahajan-Yoshida has extended two-fluid relaxation
theory for the pedestal region of tokamak H-mode
plasmas, and found a good agreement between

This is called as Beltrami/(generalized) Bernoulli condition. This means that the sum of the dynamic pressurei' andthe static pressure p is constant, and is very similar to the Bemoulli law. Here we should notice that thiscondition is satisfied for the radial direction (i.e., theperpendicular direction to the plasma flow), as well,while the Bernoulli law is valid only along with theexperimental characteristics and theoretical predictions

tlsl.
In the torus device with an internal coil we areconsidering several methods to produce the radial
electric field. Most straight forward method is theflow.

In the case of no plasma flow, this gives thecondition that B - constant, yielding a low/zero beta
plasma because of the low/zero beta at the plasma
surface. While, we could confine a high beta plasma inthe core region if the plasma flow is induced in the outerinsertion of the electrode inside the plasma column, justas demonstrated by the CCT device [16]. While, in L-H
transition phase the role of high energy ion loss ispointed out to explain the build-up of the radial electricfield [7]. This idea might be applicable for the internalcoil device, as well. The Electron Cyclotron Heating

region of the plasma column.

Here a torus device with an internal coil is
introduced, to explore this new relaxation state. Figure I
shows the schematic drawing of the magnetic field
produced by the internal coil, where the dipole magnetic;\'

field with the separatrix is shown. Going away from thepoloidal magnetic field coil, the poloidal magnetic fieldstrength Bo by the internal coil is monotonicallydecreasing. If a radial electric field is induced in the'!\1r

Orbil los$inner region of the plasma column, the plasma begins toflow in the toroidal direction due to the ExB drift. The

drift velocity becomes faster in the outer region of theplasma column, because the amplitude of the drift
velocity is given by EtBr. This results in confining ahigh beta plasma in the core region, if the relation 72 +is realized. This is the reason why we areF="orst.
toroidalutilizing adevice with an intemal coil to study a
two-fluid relaxation theory experimentally.
Several devices with a floating superconductor coil(e.g., Spherator, Levitron) have been constructed in thepast, where many interesting physics issues such as
Min-B concept have been verified, and very good

B votue

Fig. 1 Schematic drawing of an idea for confining a highbeta plasma with an internal coil device.

plasma confinement characteristics have been102

Ogawa Y. el a/., Research on High-Beta Plasmas Based on Two-Fluid Relaxation Theory(ECH) is planned to produce a high temperature plasma,

and the coil current is 500 kAturns. The minor radius ofand could yieid a high energy component at a low
density plasma [18]. The poloidal magnetic field is very
weak in the outer region of the plasma column, andbecome zero at the separatrix point, as shown in Fig. 1.
We could, therefore, expect an orbit loss of high energy
electrons, yielding a radial electric field.
In addition, by considering that the magnetic fieldis zero at the separatrix, an interesting idea has been
proposed for injecting an electrons into the torus
plasmas. At the separatrix region the electron has achaotic motion because of the non-conservation of theadiabatic constant. By utilizing this chaotic motion,some part of electrons can travel into the torus [19].

the coil might be around 8 cm. The maximum magnetic

field strength is estimated to be - 3 T around the
conductor. It is expected that the internal ring coil islevitating during a few hours or more.
The toroidal field coil is also equipped in order tointroduce a magnetic shear, because some instabilities
related with flow shear and non-neutralized plasmas
might be stabilized by the magnetic shear. The total
current of the toroidal field coil is 1.4 MAturns, which
produces the toroidal magnetic field B, to be 0.7 T at R
= 0.4 m.
The internal ring coil produces the dipole magnetic

field. By combining external poloidal field coils, several
magnetic field configurations are available; for example,
the plasma confinement configuration bounded with themagnetic separatrix located in the outer (or top/bottom)

3. Design of the Torus Device with anlnternal Coilregion of the torus can be produced. The typicalmagnetic configuration is shown in Fig. 3. The

Figure 2 shows a bird's-eye view of the device,
which is composed with floating internal ring coil,several poloidal field coils and toroidal field coil.

levitation coil current is 120 kAturns, and the verticalcoil current located upper and lower positions is 50
kAturns. The separatrix is produced in the outer regionof the torus around R = 1.2 m.
The maximum magnetic field becomes larger than
2 T at the conductor, and is around I T in the coreplasma region. In the outer region of the torus the

Feedback coils are located inside the vacuum vessel, andcharging coil is put at the bottom of the torus. The
diameter and height of the vacuum vessel is 3 m and 2.5m, respectively.
The basic specification of the levitated intemal ringcoil is as follows; the major radius of the coil is 40 cm,

magnetic field decreases rapidly, and becomes around
0.1 T at R = 0.7 m. If the plasma relaxes to the two-fluid
relaxation state, the relation (VolVo)'+ f = constant issatisfied at the whole region of the plasma column. Herethe plasma velocity Vo is given by E,/Br. By assumingthat the beta value is set to be zero at the plasma
Height GD
0.75

{,5
{.75
0.?5

1.25

1.5

Radius (m)Fig. 2 A Bird's-eye view of an internal coil device withan superconductor floating coil, called S-RT.

Fig. 3 Typical magnetic configuration of the S-RT device.
103

Ogawa Y. et a/., Research on High-Beta Plasmas Based on Two-Fluid Relaxation Theory

Table 1 Expected Plasma Parameters of the S-RT device
at B=0.1T and n,= 1018 m-3.

A Bi-2223 Ag-sheathed multifilamentary wire, atpresent, seems to be a most promising candidate for the

Beta value: B

100 Vol0 Vohigh magnetic field coil. For example, a 7T solenoid

Temperature: Z'

12 keV

1.2 keV

Radial electric field: E

220kYlm

69 kV/mNonneutrality: Anln

2.4x10'5

0.76x10r

confinement time: ?8,

120 msec

12 msec

coil with an averaged major radius of 17.6 cm and a coilcurrent of 1.5 MAturns has already been constructed1211. Bi-2223 is a thin tape and the critical current
density strongly degrades as the magnetic field isincreased at the relatively high temperature regime (e.g.,
T > 40 K). There exists a residual voltage of the HTS
coil, and n-yalve around the critical current density isrelatively small. We should, therefore, pay attention to
the coil cunent decay due to the residual voltage.
Operation temperature regime is set to be between
20 K to 40 K. During levitating operation for a few
hours the heat input to the levitated internal coil should
be compensated with the temperature increase of thestructural materials of the coil. So as to increase the heat
capacity of the coil itself, some heat reservoir with alarge heat capacity should be equipped; e.g., lead,cooled helium and cooled nitrogen.

boundary and the flow velocity is zero at the plasma
center, the necessary radial electric field E. is given withthe relation. E,/Br= VofB. Expected plasma parameters

are estimated in Table l. Here it is assumed that themagnetic field strength B is 0.1 T, and the plasma minor
radius is 0.5 m. The plasma nonneutrality Lnln to indtce
this radial electric field is also evaluated, as shown in
Table 1. When the heating power is assumed to be
P=100 kW, the necessary energy confinement time torealize above-mentioned plasma parameters is evaluatedto be 12 - 120 msec.
Low-Tc and high-Tc superconductor coils are taken
into account for the floating coil. There were, in thepast, several experiences of construction and operationof the low-Tc superconductor floating coil, and a new

Based on these considerations, it is concluded thatthe levitation during a few hours could be available with
the HTS coil.

superconductor (HTS) coil in the fusion plasma

4. Present Status of High Beta Plasma
Study with Small Devices
A normal conductor device called Proto-RT has

experiments. If the HTS coil could be employed as abeen constructed ft2| equipping an internal coil with alarge device is now under construction in MIT [20].
There is no experience of the high temperature

major radius of 30 cm and the coil current of l0

floating coil, it seems to be quite attractive from theviewpoints of plasma experiments and machine

kAturns. The electron injection through the separatrix
has been carried out to examine the feasibility of thebuild-up of the radial electric field. Experimentally theradial potential of - I kV has been established, yielding
a radial electric field of - 10 kV/m or more. The
electron density is estimated to be of the order of lOta
m-3, which is close to the Brillouin density limit of an

operation.

In the case of low-Tc superconductor coil, three
superconductor cables NbTi, Nb3Sn and Nb3Al arecompared, and Nb3Al is selected because of its large
temperature margin and mechanical stress. It isestimated that the current decay time of the floating coilis quite long (50 days).
The design of the HTS coil has been carried out, as

electron plasma.
In the Proto-RT device the support structure of theinternal coil and the current feeder are crossing themagnetic surface of the dipole field, which might beafraid of causing a loss of plasma. In addition, themagnetic field is relatively weak due to the limitation of
the coil current. To overcome these problems, a small
size device with a floating internal coil called Mini-RT

well. Advantages of HTS coils are summarized asfollows;* Large heat capacity; i.e., specific heatcapacity at2040 K is around 100 times as high as that at 4 K, results in the remarkable improvement of the thermal
stability of the superconductor coil, giving a chance ofhigh power and/or long pulse plasma heating experi-

is now under construction. The detail of the Mini-RT
device is described in ref. [13].

ments.

* High cooling efficiency of refrigerators; i.e., the effi-

The Mini-RT device is equipping a HTS floating
coil (R=0.15 m). The Ag-sheathed Bi-2223 tape with aciency of refrigerators at 2040 K is around l0 times
as high as that at 4 K, results in easy maintenance andremarkable reduction of the operation cost.

coil current of I l7 A (50 kAturns in total) is employed.
The magnetic field strength at the plasma confinementr04

Ogawa Y. et al., Research on High-Beta Plasmas Based on Two-Fluid Relaxation Theory

region is around 0.1 T, giving a plasma production andheating by 2.45 GHz ECH system. In order to drive aradial electric field, the loss of high energy electrons
produced by tbe ECH might be a useful technique, in
addition to the electron injection through the separatrix.
This is the first challenge to apply the HTS coil for

Scientific Research (No. 12308019) from the Ministryof Education, Culture, Sports, Science and Technologyof Japan.

a fusion plasma confinement device. Several

I2l Z.Yoshida, et al., J. Phys. Soc. Jap., 55, 450

References[1] J.B. Taylor, Phys. Rev. Lett.,33, ll39 (1974).

engineering del'elopments for the HTS coil are required.

(1e86).

At first, the persistent current switch (PCS) with thet3l F.M. Levinton, et al., Phys. Rev. Lett., 75, 4417

HTS tape is requisite, because the HTS coil current isdirectly driven by the demountable electrode in the
Mini-RT device. There are few experiences for the PCS
with the HTS tape. Here the Ag-sheathed Bi-2223 with
O.3wtVo Mangernese is adopted, because this gives asufficiently high resistance at the elevated temperature(0.27 A at the critical temperature). We have measured
the characteristics of this PCS-HTS tape, and confirmedthat this tape is satisfactory for the PCS [22].
Next, the levitation of the HTS coil itself is very

(19e5).

[4] T. Fujita, et al., Nucl. Fusion, 31,147 (1991).
[5] Z. Yoshida, et al., J. Plasma Phys., 59, 103 (1998).
t6l L.C. Steinhauer and A. Ishida, Phys. Rev. Lett.,79,3423 (1997).
l7l S.M. Mahajan and Z. Yoshida, Phys. Rev. Lett., 81,
4863 (1998).

t8l A. Hasegawa er a/., Nucl. Fusion, 30,2405 (1990).
t9l A. Hasegawa et al., Fusion Technology, 22,27(1992\.

challenging. A small HTS coil (4 cm radius, 2.6[10] J. Kesner, et al., lTth IAEA Fusion Energy Conference, (Yokohama, 1998), IAEA-FI -CN-69/ICP/

kAturns) has been fabricated and the levitation experiment has been carried out. The HTS coil is immersed09.

with liquid nitrogen, and the coil current is kept during[11] Z. Yoshida, et al., Non-Neutral Plasma Physics III,AIP Conf. Proc.,397 (1999).
|21 C. Nakashima, e/ a/., Non-Neutral Plasma Physics
III, AIP Conf. Proc., 4ll (1999).
tl3l Y. Ogawa, et al.,in this conference
ll4l S. Yoshikawa, Nucl. Fusion, 13,433 (1973).
t15l S.M. Mahajan and Z. Yoshida, Phys. Plasmas, 7,

the evaporation of the liquid nitrogen. The levitation coil

is located at the upper region of the floating coil. In thissituation, the floating coil is unstable for the verticalmotion. The coil position is detected by the laser sensor,
and the levitation coil current is controlled with PID
feedback system. It has been demonstrated that the HTS
coil has successfully floating during a few minutes witha positioning accuracy of635 (2000).

- 30 1tm[23].

[16] R.J. Taylor, et al., Phys. Rev. Lett., 63, 2365
(1989).

Acknowledgements

U7l S.-I. Itoh and K. Itoh, Phys. Rev. Lett., 60,2276(l988).

The author acknowledges for Profs. T. Mito and N.
Yanagi in National Institute for Fusion Science and forllSl H. Ikegami, et al.,Phys. Rev. Leu., 19,778 (1967).
Il9)2. Yoshida, et al., Phys. Rev. Lett., 81, 2458

Prof. N. Iwakuma in Kyushu University for designingand constructing a superconductor coil. The author
thanks engineers of Fuji Electric Corporation, Toshiba(1998).

[20] H. Schultz, et al.,IEEE Trans. Appl. Supercond. 9,

Corporation, Mitsubishi Electric Corporation and
Sumitomo Electric Industries on designing high378 (1999).
[2llT. Kato et al., Proceeding of ISS, (1997).
t22l N. Yanagi et al.,MT-17, Geneva, 2001.
[23] J. Morikawa, Jpn. J. Appl. Phys.,40, L1029 (2001).

temperature superconductor coils.
This work was supported by a Grant-in-Aid for105