J. Plasma Fusion Res. SERIES, Vol.3 (2000) 498-501

Source Plasma Formation of Field Reversed
Gonfiguration for a Long Pulse Operation
TAKAHASHI Tsutomu*, IWATA Kaoru and NOGI Yasuyuki
College of Science and Technology, Nihon (Jniversity
1-8 Kanda Surugadai, Chiyoda-ku, Tolqo l0l-8308, Japan(Received: 18 January 2000 / Accepted: I May 2000)

Abstract
The poloidal flux of a field reversed configuration (FRC) needs to increase more than the present
experimental regime to inject a neutral beam into a tangential direction for the plasma heating. Since thepoloidal flux of the rigid rotor profile model is proportional to the cube of the separatrix radius. the FRC
plasma with a large separatrix radius is produced by the enhancement of the axial contraction. The
enhancement is induced by a mirror ratio and a magnetic field index of the compression field. The
plasma radius of 1.3 times lager and a poloidal flux of 2.2 times larger than the present experiment status
are obtained by high mirror ratio of 1.8 and high magnetic field index of 0.3. The field index is possible
to contribute to the adjustment of a radial implosion strength and an axial contraction one and to thecontrol of the ratio of an ion temperature and an electron temperature.

Keywords:
field reversed configuration (FRC), radial compression, axial contraction, mirror ratio, magnetic fieldindex, ratio of ion to electron temperature

1. Introduction

compression field of 0.5 T and a coil radius of 0.17 m,
requires the normalized plasma radius more than 0.65 on
basis of the rigid rotor model [8]. The FRC plasma isalso needed to be formed in several times larger bias
magnetic field than the present experiment.
In this paper, we propose the FRC plasma formation method with the large X" and fo by an adjustment of

There are several proposals for a long pulse
operation of a field reversed configuration (FRC) [1-6].
In the proposals, the plasma of the FRC is heated by aneutral beam injection (NBI) [-4], an OH transformer[4,5] or a rotating magnetic field (RMF) [6]. The FRC
plasma parameters, required for a tangential injection ofa deuterium neutral beam with the energy of l0 keV on
FIX experiment [2], are as follows. An electron density(2") is -1.0 x 1020m-3, a normalized separatrix radius (aratio of a separatrix radius (r,) and a coil radius (r,)) X"

the radial compression and the axial contraction. The
adjustment is controlled by the mirror ratio (Ry) and themagnetic field index of the confinement field (n,= zdB,lB.Dz). Preliminary experimental results is presented in= -0.6, a poloidal flux p, = -3.0 mWb, an ion

the following sections

temperature T; = 300 eV, an electron temperature Z, =100 eV and the s-number of injection ion s = 2.
The plasma parameters except the poloidal flux, are

2. Experimental Apparatus
The theta pinch coil of NUCTE III device isattained by the translation [6] and the usual pinch

modified. Stepped theta pinch coil elements with 36, 34,

technique [7]. The poloidal flux of -3 mWb, under the*Corresponding author' s e-mail: tom@ pyxis.phys.c st.nihon-u.ac jp498@2000 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Takahashi T. et al., Source Plasma Formation of Field Reversed Configuration for a Long pulse Operation

Table 1 Coil Configuration and Plasma Parameterlllt sI

Case R, n-. tu n^ A@s tr* t, r"(O) l, tnr, rn-z(trs)(cmlps)(mWb) (ps)(ps) (cm)(cm) (ps) (ps)

1 1.10 0.O3 6.5 3.8 0.1s l2.S 30 6.2 62 65 28
2 1.35 0.16 5.O 4.5 0.17 tL.O 22 6.s 49 65 28
3 1.38 0.r5 4.s s.5 0.25 8.5 15 6.8 45 60 2s
4 1.80 0.24 3.5 6.0 0.2 7.5 ls 6.9 60 60 2ss 1.80 0.28 3.0 8.5 0.4 7.O 12 7.8 39 50 22
6 1.80 0.30 3.0 8.s 0.4 7.0 12 8.0 38 so 22=.
F

aEq,cGt0=?
@HeN€l.gidMe

Fig. 1 Schematic overview of the experimental set up on
NUCTE-III

0.100.ffi
0-80 {0 -40 -20 0 20 40 60 80

32,30,28,26 cm diameter are ilrayed symmetrically tothe midplane, shown in Fig.1. An averaged decay index

z [cm]

1nr=l_u2 njz/L".L"= 1.35 m: length between the mirror

Fig. 2 Time evolution of profiles of a separatrix radius
and an intensity of bremsstrahlung in case 6points) and Ry of the present experiments are listed inTable l. The theta pinch coil is connected with a 5 kV1920 pF slow bank and a32 kV-67.5 pF fast one. The
bias field has the maximum strength of 0.09 T and therise time of 90 ps and the compression field has those of
0.6 T and 4 ps. A transparent quartz discharge tube witha length of 2.0 m and an inner diameter of about 0.23 m
is evacuated till l.5xl0-4Pa and is filled with deuteriumgas of 1.33 Pa. A pre-heating plasma is formed by aringing I,-discharge method.

temperature (T), T, = Ti + T") is estimated from theequation of the average beta value <F> = l-x,212 .

An excluded flux array, a single path side-on HeNe interferometer and an visible fiber array are used toobserve the plasma. The sensitivity of the optical arrayis limited to 550+50 nm by band pass filters [9]. It isconfirmed that a dominant component of plasma

The FRC plasmas which have the same fr"= 2.2 x l02l
m-3 and T,= 120 eV are coinpared to clarify the relation
between the axial dynamics and the plasma behavior.
The time history of rJz) and lu,(z) of case 6 are shownby closed and open circles, respectively, in Fig.2. The

radiation la,(z) is bremsstrahlung in this region. From a
profile of the excluded flux (AD, a time history of theseparatrix radius profile r,(2) is obtained. An averaged
electron density at the midplane (n"=ln"dl/2r"(0)) iscalculated from the interferometer. The electron
temperature (2") is estimated by the following equation,

plasma implodes to the center axis by the radial1r,(o)*t#:

3. Experimental Results
The FRC plasma is produced on the six
configurations of the theta pinch coil listed in Table l.

compression. The radial velocity is faster in the coil end

region than that in the center one. At 3 ps, the magnetic
reconnection between the bias field and the compression

field has been already completed. Then the axial
contraction has started from the end region. The humpof la,k), which indicates the axial contraction, appears at(1)

z = 44 cm. The front of the contraction arrives to themidplane at 6 ps. The plasma reaches the equilibrium
state at l0 ps. The value of r"(0) and separatrix length(/,) are about 8 cm and 40 cm, respectively.

The value of Z"x is effective charge number. The total
plasma temperature (the sum of the electron (7,) and ion
499

Takahashi T. et aI., Source Plasma Formation of Field Reversed Configuration for a Long Pulse Operation
70

^la6o

^11I'.l50^lE40

a Coil-l
I coit-lrcoit-oo:€acarl.teO

alaal.
.IaN20F6E

l0oo.ro2468101214

l60.1 50.2

0.25

0.3

0.35

Magnetic InderTime lns ]Fig. 4 Relation between an electron temperature and aFig. 3 Time history of front positions of ah axial
contraction in case 1, case 4 and case 6

magnetic field index

The Figure 4 shows the dependence of the electron

temperature on the magnetic field index fi,. The
contribution of Z*to 16. is consider as the same level

On the other hand, in case l, the radial compression

is occurred uniformly over the full length of the coil.
The radial velocity is faster than that of case-6 except inthe coil end. The hump is formed at 5 ps in the coil end
and the axial contraction starts at 7 ps. The front of thehump arrives to the midplane at 15 ps. The equilibrium

because of the same T, and n". Open triangles, circles

and squares show the dependence at the plasma
temperature of 195 + 15, 120 t 10, 100 + 10 eV. The
electron temperature increases with the index of n..

state is delayed to 25 ps. The separatrix radius and4. Discussion and Summary
The FRC having a large separatrix radius islength is about 6 cm and 60 cm.
Figure of 3 shows the position of the front of thehump in cases 1,4 and 6. Each front travels to z = 30cm with the same velocity of -0.1 m/ps in the threecases. After that, the front arrives at the midplane withthe same velocity in case 6. But with decrease of Rry and
Q the velocity is damped and the arrival time is delayed.
In Table l, the parameters of the axial dynamics,
such as the average velocity (7*) from z = 30 cm toproduced by the enhancement of the axial contractionthat induced by a using a compression field with a highmirror field ratio and/or a large axial magnetic index.
Typical value of the separatrix radius at Ru= 1.8 and zz= 0.30 is r(0) = $.6 cm which corresponds to 1.3 timesr"(0) at Ru= l.l andn,= 0.03. Since the poloidal flux inthe separatrix surface is proportional to r"3{0) on thebasis of the rigid rotor profile model [8], 1.3 times r,(0)means a 2.2 times increase of the poloidal flux. That is,
it reaches I .l mWb at the former case.
The radial implosion and axial contraction are

midplane, the strength of the axial contraction atmidplane (/@,), onset time (2,,), the arrival time at
midplane (Tyo,) and etc., are summarized at every coils.
The value of /p" is calculated from the equation of /p"= AQn- AQ"o(AQo: AQ at the peak contraction and, AQ"n:occurred at the formation phase. The former shock heats
ions strongly and the latter heats both ion and electron

at the equilibrium state) [10]. The early onset time

adiabatically lll,l2l. If the former is stronger than thelatter, the electron temperature becomes low comparing
to the ion one. The present experiment shows that thecarries the strong contraction. The maximum of thecontraction velocity is about 0.1 m/ps at Z. = Q.lQ 3n6
RY = 1'80'

With increase of n, and Ry, the FRC plasmastrong implosion is formed before axial contraction overreaches the equilibrium phase at earlier time and has a

the full length of the case 1 at nz = 0.03. The fi,
dependence of the electron temperature seen in Fig.4

larger separatrix radius and a shorter length. The formed
plasma has a elliptical shape. The onset time of the n=2
instability (t,=2) is earlier with increase of n.. The life
time of the plasma (r';p) is limited by the growth of thecan be roughly explained from the heating steps.

Further studies will be pursued to produced a target
plasma for the neutral beam heating

instability.
500

Takahashi T . et al., Source Plasma Formation of Field Reversed Configuration for a Long pulse Operation

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