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

2lE2l4

Internal Magnetic Probe Measurement in
Heating Experiment of FRC Plasma byLow-Frequency Magnetic Pulse
YOSHIMURA Satoru, YAMANAKA Koji, YAMAMOTO Shinichi, MASUMOTO Terutaka,

OKADA Shigefumi and GOTO Seiichi
Plasma Physics Laboratory, Graduate School of Engineering, Osaka University, Suita 565-0871, Japan(Received: I I December 2O0l I Acceoted: 8 Mav 2002)

Abstract
Internal magnetic probes are used for direct measurements of time-varying magnetic fields in aheating experiment of a field reversed configuration (FRC) plasma by a low-frequency magnetic pulse.
The low-frequency magnetic pulse is applied by an antenna which consists of two single-turn coils. Thefrequency of the applied magnetic field is lower than the ion cyclotron frequency at the separatrix. A
large amplitude oscillation is detected by an magnetic probe which is oriented with the axis in theazimuthal direction and located near the separatrix. Since the observed oscillation is transient, themagnetic probe signal is analyzed by the wavelet transform. The phase velocity of the oscillation in thedirection parallel to the equilibrium magnetic field is measured using the wavelet cross-spectrum function
and it approximately agrees with the Alfvdn velocity. The experimental results suggest that the shear
Alfv6n wave is excited.

Keywords:
FRC, plasma, magnetic probe, wavelet transform, Alfv6n wave

1. Introductionof plasma wave was verified by inserting magnetic
probes into the plasma. In this paper, we report theThe development of auxiliary heating methods haslong been one of the most important issues of the fieldreversed configuration (FRC) studies []. Recently, weproperties of the excited wave using the results of theinternal magnetic probe measurements. Since thereported that the application of the low-frequency
magnetic pulse was effective for the heating of a FRC
plasma [2]. The obvious increases of both pressurebalance temperature (sum of the electron and iontemperatures, Ttotil=7" + Ii) and ion temperature (21)observed wave signals are transient, we analyze themagnetic probe signals by the wavelet transform.

2. Experimental Apparatus
The experiment is carried out in the confinement
region of the FIX device [3]. In FIX, the FRC plasma isproduced by the theta pinch discharge after theintroduction of deuterium gas in the formation region
and then is translated to the confinement region. The
confinement region consists of quasi-DC magnetic fieldcoils and a metal vacuum chamber, as shown in Fig. 1.

obtained by the measurement of the Doppler broadeningof the spectral line of OV were observed during theapplication of the magnetic pulse. The increment of Z,oo1
was almost equal to that of Ir (AZ,*"r - LTi - 20 eY),suggesting that the energy of the magnetic pulse wasabsorbed mainly by ions. Although the heatingmechanism has been indistinct so far. excitation of a sort

@2O02 by The Japan Society of Plasma

Corresponding author's e-mail: yosirnura@ ppl.eng.osaka-u.acjp

2toScience and Nuclear Fusion ResearchYoshimura S. et aI., lntemal Magnetic Probe Measurement in Heating Experiment of FRC Plasma by Low-Frequency Magnetic Pulse

40,!4()

Umagnetic pulse coil(downstream)

200-20-440,4080.tttll-2.4 -t.2 0.0t.2Iime lpsec]

2.4

Fig. 2 The typical waveform of the coil current. Themagnetic pulse is started at t= 0lsec.

z [m]Fig. 1 Schematic drawing of the confinement region ofthe FIX device. The hatched region represents thetranslated FRC plasma.

axial direction.

3. Spectral and Cross-Spectral Analysis
using Wavelet Transform

The radius and the length of the straight section of themetal chamber are 0.4 m and 3.4 m, respectively. The
strength of the quasi-DC magnetic field is B, = 0.04 T.
The separatrix radius and the length ofthe plasma are r,= 0.20 m ard l, = 3.6 m. The lifetime of the plasma is

A time-frequency analysis of magnetic probe
signals is performed by the wavelet transform [4] using
the following simple analyzing wavelet

Y^1tv=#*r(-about 350 psec. The electron density and the pressurebalance temperature are i. = 3 - 4 x 10le m-3 and Z,o, =T" + Ti = 100 - 140 eV, respectively.
Two single-turn coils are placed coaxially with thery.t+)(1)where "a" is the wavelet scale which corresponds to theinverse of the frequency. The wavelet transform of adevice axis at z = -1.2 and -0.6 m, as shown in Fig. 1.
The radius of each coil is 0.33 m. Each coil is sealed bya Pyrex tube to prevent the serious interaction with theplasma. A serial couple of 3.3 pF capacitors isfunction/(r) is given by
w1 (a,x) =I, UrY ^(t - r)dtQ)

which is a function of both scale "a" and time "C'.
Choosing the oparameter in eq. (l), we can balance thetime and frequency resolutions as appropriate for a certain signal. We usually choose o = 1.0.
The delayed wavelet cross-spectrum function [5] isconnected to each coil as a power supply. The LC
configuration provides a damped sinusoidal current of60 psec duration. The typical waveform of the coilcurrent measured by a Rogowski coil is shown in Fig. 2.
The two coil currents are supplied with z radians out-ofphase. The frequency of the applied magnetic pulse isgiven byC,r(a, A,t) = | W; @,r)Wr(a,c + Lr)dc

about 80 kHz and is lower than the ion cyclotron(3)

where/(t) and g(t) are two signals obtained at two sepa-frequency near the separatrix (a"tl2n = 400 kHz).
In order 10 measure the time-varying magnetic
fields near the separatrix of the FRC plasma during theapplication of the magnetic pulse, small magnetic probes
are inserted into the plasma. Three magnetic probe

rated observation points. The Ar value maximizing theCry@, A,r) function gives the travel time of the component with frequency F = lla from one observation point
to the other separated point [6].

anays are located at z = 0.0, 0.6 and 1.2 m, as shown in
Fig. l Each array has magnetic probes oriented with theaxis in the azimuthal direction (be probe) in addition tomagnetic probes oriented in the radial direction (b,4. Experimental Results and Discussion
The low-frequency magnetic pulse is applied to aquasi-steady state of a translated FRC plasma. Figuresprobe). The intensity of these probe signals is calibrated
to each other. When we measure the z component of the3(a)-3(d) show the time evolution of signals of themagnetic fielcl (b.), the magnetic probe arrays arethe application of the magnetic pulse, a coherent

rotated through 90" and the De probes are oriented in theoscillation is observed on the De probe [Fig. 3(a)]. Oninternal magnetic probes located at z = 0.60 m. During

2tl

Yoshimura S. et al., lntemal Magnetic Probe Measurement in Heating Experiment of FRC Plasma by Low-Frequency Magnetic Pulse

2of the measurement show that the excited magnetic
oscillation has a strong component in the azimuthal(a)0-o -2

direction. In addition, the distance between the magnetic
probes and the magnetic pulse coils is so far that no!

r-: 2

signal is detected by the magnetic probes when themagnetic pulse is applied in the vacuum field. These(b)results suggest that a sort ofplasma wave is excited and,CIt. 0

propagated.

-t -z
0

Since the coherent oscillation can not be observedon the b. component and the observed oscillation on the20 40 60 80

100b, probe is less coherent, we mainly analyze the bs

Time [psec]tprobe signals for observing the wave characteristics. The

wavelet transform coefficients lWr(a, r)l of the signals of
the coil current and the three b6 probes at z = 0.0 m, 0.6m and 1.2 m are shown in Figs. a@)a@). The results of
the wavelet transform evidently show that the wave
observed on the be probes [Figs. 4(b)-4(d)] is excitedlater than the start of the magnetic pulse [Fig. 4(a)]. The
frequency of the excited wave is found to be about 80
kHz and it is the same as that of the applied magnetic
pulse. Figures 4(b)-4(d) show that the amplitude of theexcited wave on the be probes decreases as the distancefrom the magnetic pulse coils increases. The attenuation
length of the excited wave in the z direction is estimatedto be 2 = 0.65 m. Furthermore, Figs. 4(b)-4(d) also showthat another low frequency oscillation (F' < 50 kHz) iscoexisting with the excited wave. At z = 1.2 m, theamplitude of the another low frequency oscillation is(c)20p -2N(d)20-20 2a 40 60 80 100
Time [psec]
FlG. 3. The internal magnetic probe signals at z= 0.6 m.

They are'oriented with their axes in (a) the azimuthal direction (b, probe) and (b) the radial direction (4 probe) of the FIX device. The b, and b,probes are installed at the radial positions of r=larger than that of the excited wave. This another0.20 and r = 0.21 m, respectively. In figures (c) and(d), the magnetic probe arrays are rotated through90" and the b, probe is oriented in (c) the axial direction (4) of the FIX device. The magnetic pulse

oscillation is also observed on the b, and b, components
and is detected even in the case without the magnetic
pulse. Therefore, this oscillation is not excited by themagnetic pulse but is naturally existing in the FRC

isstartedatt=0llsec.

plasma.

The delay of the oscillation phase is clearly seenamong the raw signals of the three be probes at z = 0.0,

the contrary, the oscillation on the b, probe is less

0.6 and 1.2 m, suggesting that the excited wave ispropagated in the z direction. In order to measure thepropagation velocity of the excited wave, the delayed
wavelet cross-spectrum function lC4@, A,r)l is calcu-

coherent and its amplitude is smaller than that on the roprobe, as shown in Fig. 3(b). Next, the De probe isoriented with the axis in the z direction in order tomeasure the b. component. In this case no such coherent
oscillation can be seen on the D. component, as shown in
Fig. 3(c). On the other hand, the waveform of the b,probe signal tFig. 3(d)l is almost the same as that in Fig.
3(b). In the case without the magnetic pulse, no such
oscillation is observed on all internal magnetic probe
signals, showing that the observed magnetic oscillation

lated. As an example, the result of the calculation of thelCry(a, Lr)l from two b6 probes at z = 0.0 and 0.6 m isshown in Fig. 5. In this case, we choose o = 0.1 in Eq.
(1) for the improvement of the time resolution. The peakof the lCry@, Ac)l is clearly shifted from the Ar = 0 pointand can be seen at LT = 4 1tsec. Therefore, the phasevelocity of the propagation in the z direction isestimated to be Vpruse = LzJL,t = 1.5 x 105 m,/sec, which
is approximately agrees with the Alfv6n velocity, Vo.
These results suggest that the excited wave is theis excited by the magnetic pulse.
Although the magnetic field produced by the pulse
coil has no component in the azimuthal direction, results
212

Yoshimura S. et al., Internal Magnetic Probe Measurement in Heating Experiment of FRC Plasma by Low-Frequency Magnetic Pulse

N

200

J<200>'C)

100

(,)

100C)

0IL

00200
N

Delay Time Ar [psec]
FlG. 5. The delayed wavelet cross-spectrum function for
two b, probe signals at z = 0.0 and 0.6 m. The ra-100

dial location of the b, probes is r = 0.24 m. Theg

peak of the spectrum is shown by an arrow.

,M>.
CJ0a)

204Oc)oC)

LEi100105C)

a00.00200

0.10 0.20

0.30

radius [m]FlG. 6. Radial profile of the phase velocity of the excitedwave in the z direction. The dashed line is thetheoretical phase velocity of the shear Alfu6n

100

wave for the experimental condition.

004480applied magnetic pulse to the shear Alfv6n wave at theAlfv6n resonance layer where both wave types locallyhave the same wavelength in a direction parallel to theequilibrium magnetic field [7-10].
The excited wave is observed in the relatively wide
region around the separatrix. The radial profile of themeasured phase velocity is shown in Fig. 6. The phasevelocity outside the separatrix (r" = 0.20 m) is found to
be larger than that inside the separatrix, as shown in Fig.

Time [psec]

FlG. 4. The wavelet transform coefficients of the signalsof (a) the coil current and three b, probes at (b) z=0.0 m, (c) 0.6 m and (d) 1.2 m. The radial locationof these b, probes is r = 0.24 m. In the figures (c)and (d), the contour scale is enhanced twice thatin the figure (b). The magnetic pulse is started at f= 0,usec'

6. Outside the separatrix, the experimentally obtained
shear Alfv6n wave, since the shear Alfv6n wave istransverse magnetic (strong be and weak b.) at low wave

phase velocity approximately agrees with the theoreticalphase velocity of the shear Alfvdn wave in low B
plasmas (vpru." = ve [1 - 1ala"t121tt21 [7]. Although thelocal B value outside the separatrix is nearly zero, it
rapidly varies along the radial direction in the FRC
plasma and it exceeds even unity inside the separatrix. It
may be the reason of the deviation of the experimental

frequencies and its phase velocity in the direction
parallel to the equilibrium magnetic field is equal to Va[7]. The excitation of the shear Alfv6n wave may be dueto the mode conversion of the compressional wave
which is excited directly by the z component of the213

Yoshimura S. et al., Internal Magnetic Probe Measurement in Heating Experiment of FRC Plasma by Low-Frequency Magnetic Pulse

oscillation is detected by the bs magnetic probes. Since
the observed oscillation is transient, we analyze themagnetic probe signals by the wavelet transform. The
frequency of the oscillation is found to be the same asthat of the applied magnetic pulse. The phase velocity ofthe oscillation in the e direction is measured by
calculating the delayed wavelet cross-spectrum function
and it approximately agrees with the Alfv6n velocity.
These results suggest that the shear Alfv6n wave isdata from the theoretical value inside the separatrix. Oneof other possible reasons of the deviation is thedifference between the topology of the magnetic fieldlines inside the separatrix and that outside the separatrix
which separates the regions of open and closed magnetic
field lines. However, the attenuation length of theexcited wave inside the separatrix and that outside theseparatrix are almost the same (z - 0.65 m) and aremuch less than the length of the plasma (3.6 m),suggesting that the difference of the topology of themagnetic field lines does not have a primary role in thethe deviation of the experimental data from theexcited.

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low-frequency magnetic pulse. The large amplitude214