J. Plasma Fusion Res. SERIES, Vol.4 (2001) 595_599

Measurement of Anomalous Resistance Induced by chaotic
Motion of Electrons in a Magnetic Null pointYAGI KEitA' YOSHIDA ZCNShO, HIMURA HAruhiKO*, MORIKAWA
JUN.,i,NAKASHIMA Chihiro, SAITOH Haruhiko, TAHARA Shigeru,
FUKAO Masayuki and UCHIDA Taijiror
Graduate school of Frontier sciences, university of rokyo, Tolqo

IULVAC Japan,

rI3-0033, Japan
Ltd. Hagisono, Chigasaki 253_g543, Japan(Received: 5 December 2000

/ Accepted: 1g August 2001)

Abstract
Chaotic motion of particles in magnetic null regions can produce a large collisionlessresistivity. Inorder to measure the macroscopic resistivity, a new instrument using a pockels
crystal has beendeveloped. This measurement can detect a high frequency electric field in plasmas.
The pockels probesatisfies the frequency response with 13.56 MHz and the sensitivity as low as
the capability of measuring the local electric fields in a plasma discharged by

3x102 V/m, which provesa radio-frequency method.

Keywords:
chaos-induced entropy, anomalous resistivity around magnetic null, anisotropic electric fieldmeasurement, pockels effect, neutral loop discharge plasma

1. Introduction

induced resistivity may be the reason why a plasma canbe discharged around a magnetic neutral toop (calledOver the past several decades, plasma resistivity
has been one of the most puzzling problems in plasma
physics. In most cases, the observed resistivity isanomalous, which shows a higher value than theclassical value expected from Coulomb interactions. A
typical example can be seen in the event of magnetic

Neutral Loop Discharge) [5] with a lower fillingpressure (- l0 4 Torr) than other methods of plasma
discharges such as the inductively coupled plasmas [6].

To verify the above mechanism, we have produced
an NLD plasma in the prototype ring trap device (proto-reconnection ul where some mechanism to enhance theresistivity plays a role around the magnetic null region,RT) t7l and developed a new diagnostic of an electricfield E since.E - 4J at the magnetic neutral loop, where
4 and J are plasma resistivity tensor and current,respectively. Usually, it is very hard to measure E inplasmas. Many works on E of plasmas have been
performed in several research areas such as sheared
E x B flow [8] and toroidal equilibrium of nonneutral
plasmas [7]. Generally, E consists of both electrostatic
E, and inductive do components. For the E", case, theand as a candidate mechanism, turbulent wave-particle
interactions [2] or effects arising from two-fluid Hall
dynamics [3] have been considered to explain the fasterreconnection rate. However, recently, a new mechanismof anomalous resistivity around magnetic null regions
was theoretically presented [4]. In fact, the paper clearlyshows a possibility of existence of large enhancement

resistivity produced by the charged particles which arescattered around a magnetic null point even in acollisionless plasma. Also, it points out that this chaos-conventional methods using particle flux or ion
processes [9] can be applied to determine it. In fact, the*Corresponding author's e-mail: himura@ k.u-tolcyo.ac jp595@2001 by The Japan Society of Plasma
Science and Nuclear Fusion Researchyagi K. et al., Measurement of Anomalous Resistance Induced by chaotic Motion of Electrons

particle flux method investigated by Langmuir and hiscoworkers [9] has still been the most convenient tool tolocally measure the value of E", for low temperatureplasmas. In higher temperature plasmas where the probe
itself cannot survive, on the other hand' ion processes
such as the charge exchange technique [9] and an

appropriate model calculation have been used todetermine E"r. However, for the plasmas with Ei6
besides E"r, there are as yet no methods to directly

between the two components and the phase shift
between them occurs correspondingly' Assuming that/n is constant during the light passes through it' thephase shift /0 is given bY

Ae=ryAn,(3)

where I is the wave length of the light and I is thelength of the crystal along the light path' Thus, if thePockels crystal is placed between a pair of twopolarizers, the corresponding phase shift can bemeasured as light intensity fluctuation. Furthermore'measure E in plasmas and actually, the NLD plasmas
are produced by an inductive coupling technique with amagnetic field. On Proto-RT, the inductive field isgenerated by a high power (- 1 kW) radiofrequencyRF) with 13.56 MHz. To answer the chaos-induced
resistivity around the neutral loop, a new method iswhen the polarization orientation of them is orthogonal
to each other, the output light intensity 1o normalized by
the input one I is given bY

required for the Proto-RT experiments.
In this contributed paper, a new instrument using aPockels crystal is presented, which has been so far used
only in the researches of high-voltage engineering [10]'For the first time, the Pockels crystal is applied toI1="t"'f'(4)where the lights decay through the sensor is neglected'

3, Experimental Setup

measure an anisotropic E which oscillates with highfrequency in plasmas. In Sec. 2, the Pockels effect isbriefly explained. The instrument developed here canmeasure E with up to 15 MHz. In Sec' 3, the diagnostic
system designed to detect such a small signal from theWe have applied the Pockels crystal to measure E
in plasmas for the first time. As described in Fig. 1' thesystem consists of main three components: a lightsource with SLD (Super luminescent diode, .1, = 840
nm), a Pockels (BiaGqO12) sensor, and a pin PD (pinPockels crystal is described. In Sec. 4, the characteristics

photo diode) detector to measure light intensity. Thoseparts are connected with optical fibers each other. Figureof the Pockels probe and the preliminary results arepresented. Finally, a summary is appeared in Sec. 5.

2 shows an enlarged photograph of the Pockels sensor
indicated in Fig. 1. The light launched from the source
passes through the PANDA (Polarization-maintaining

2. Pockels Effect
The Pockels effect is one of the electro-opticaleffects and has been used to measure a high voltage in
research areas of electric engineering [10]. When an
electric field is applied to such crystals that exhibit theAND Absorption-reducing) fiber and at first, enters in
PBS (Polarization Beam Splitter) where the light ispolarized linearly. This polarized light is immediately
circular polarized by the il4 plate before entering in thePockels sensor in order to obtain maximum sensitivityof it. Thus, the eq. (4) reads

Pockels effect, birefringence occurs. The difference inthe two refractive indices for each orthogonal
polarization component changes as the first orderfunction of E as follows;

An=Ano+AaE,

in a Magnetic Null Point

ti=Lu-sinAd)-lo-rct
(1)

(5)

where /O'equals to /0 + ttll, in this system. The output

where Ans and AaE term represent the naturallight coming out from the sensor finally reaches thebirefringence and the Pockels effect, respectively. Here,detector through the GI (Grated Index) fiber.

h can be written as

The values of Pockels coefficient ya1, relat\vedielectric constant q, and refractive index z6 are
1.03x10-t2 m/V, 16, and 2.O7, respectively. Also, thelength of the crystal along the light path is 2 cm(1cmx2). Since no natural birefringence occurs,

Aa = no3Tp,(2)where n6 is the normal refractive index and ?zo is thePockels coefficient of the crystal. When a light passes
through it, the birefringence causes a velocity difference

substituting those parameters into eqs. (l), (2)' and (3)'the value of 1g is calculated to be 8.54x10-8 E. Here it596IYagi K' et al'' Measurement of Anomalous

Resistance Induced by chaotic Motion of Electrons

in a Magnetic Null point

Light source
DC-cutPANDA
l'iberl',*Sfi^

C-type caPacitor'
Antenns| |_r1-

tF:sensor @Vbias

RF PowerSourcve-|rlBand-Pa-ss

amplifierLight Intensi(r' detector
Fig' 1 A schematic diagram of the Pockels probe system. A pairof pockels cells is used for the sensor.

frequency response is enough to measure the high_frequency electric field oscillating with 13.56 MHz for
the NLD experiments on Proto-RT. The output voltage
from the current amplifier is described as 3.43x10-6 E
when the biased voltage is 2.5 V. Thus, for the case of E- I kV/m, the signal voltage would be about 2.l4xl0-a

V which seems to be too small to be measured.

Therefore, we have employed a band-pass amplifier justafter the current amplifier. The gain of the band-pass
amplifier is about 212 and the q-value is about 7.5 sothat the output voltage is expected to be - 50 mV for thecase of E - 1 kV/m.

4. Characteristics of Pockels probe
To examine the characteristics of this new
instrument, we have applied this probe to measure anelectric field which is produced by a pair of parallelsquare metal plates. The size of the plates is 30 cmx30
cm and the distance between the two plates is 10 cm. As

Fig. 2 An enlarged photograph of the sensor indicatedin Fig. 1.

seen from the data plotted in Fig. 3, the output voltage
against the strength ofE shows linear dependence ar any

should be mentioned that the electric field strength
inside the crystal decreases to Edsr. The sensitivity ofpin PD is constant (0.55 A/W) in the range between DCand 100 MHz for the case of L = 840 nm. The currenr
from the pin PD is converted to the corresponding
voltage by a high-speed current amplifier which also hasa constant gain (50 kV/A) from DC to 50 MHz. Thisfrequencies varying between 20 Hz and I kHz, which isalso consistent with eq. (5). From the fitting line in Fig.

4, the value of phase shift can be expressed as A0 =5.20x10-e E. The directional sensitivity is also wellattained. Fig. 3 indicates the output voltage measured atdifferent angles a between the pockels sensor and E.
The fitted curve on the measured values is sinusoidal as597

yasi K. e, al., Measurement of Anomalous Resistance Induced by chaotic Motionof Electrons in a Magnetic Null Point

expected, allowing E to be broken down into
thecomponents which determines anisotropy ofits

tf,oscillating field.
isHowever, the output voltage in experiments V"*othelower than expected V-1. As mentioned in Sec' 3'

1.0

a0.5;t-'j'jia0.0.

-- -.' - --.._"'i i'__'-'-"_'-" " " __- - -_.''__-,'- - -'_- " "-analytical value of /g is calculated from /g - 8'54x10{
E and thus the value of %nr without the band-pass
amplifier is expected to be - 0'24 mV for E - 1 kV/m'On the other hand, in experiments the probe outputs_ _6-0. 5

Ia-1.0-1. 5

only V"*n - 0.015 mV for E - 1 kV/m if we extrapolate
it from ihe measured data in Fig' 4' The value of V"*n/rl120 180 210 300

ooo

V-1is so far 1116. The reason is still unknown' however'
it is probably owing to the sensitivity of the Pockels
crystal itself.
With the present sensitivity of the Pockels crystal'
the lower limit of detection against E would be about
300 V/m where V""o is about 1 mV' This value360

d (desee)Fig. 3 Plots of %,p at various angles a between thePockels sensor and E. The plotted data are wellfitted by a sinusoidal, showing that the sensor candistinguish the three component of E in a goodcorresponds to E* - 0.4 in the NLD experiments' Here'E* is the normalized electric field used in NLD studies'
Since the chaotic effect is enhanced at E* 1, even withresolution.

-1.4

the lower sensitivity this Pockels probe could be applied
to measure the oscillating electric fields with 13'56 MHz(a)..41.0-'? o'-t.J

0.6

t'

0.4
0.2
0.0

in a neutral loop produced in Proto-RT.
In fact, we have installed the Pockels probe inProto-RT and tried to measure the 13'56 MHz of E bythe probe. The electric field is produced by a capacitive
coupled technique with a pair of torus plates made ofSUS304. Under this setting in Proto-RT, the Pockels"t' I'l..1

probe so far successfully detects E with 3'3 kV/m atwhich the value of the S/N is about unity, determining
the lower limit of detection inside the Proto-RT device'.,.jaa

1060

This limit is higher than the calculated value as alreadydescribed. However, the limit can be improved about 16times better by fixing the sensitivity problem of theE (kv/m)current Pockels crystal, which actually decreases lowerlimit of detection limit down to 330 V/m enough to be
employed in Proto-RT for not only NLD but also
nonneutral plasma experiments.

5. SummarY
A new diagnostic for measuring anisotropy of highfrequency E in plasmas has been develqped using aPockels crystal. The test of the probe shows a good
performance to distinguish directional components(three, vector components) of oscillating electric fields
up to 13.56 MHz which is too fast to be detected by aFig. 4 Plots of the output voltage %"o at various

conventional probe technique. The lower limit ofdetection against E is so far about 3x102 V/m that is
restricted possibly owing to the sensitivity of thestrengths of oscillating electric fields E: (a) f O.O2-1 .O kHz (b) f - 13'56 MHz. The dotted andsolid lines show a least square fitting from thedata, which shows that values of V"*o increaselinearly with E as expected.

Pockels crystal. In the Proto-RT device, the lower limit598

Yagi K. et al., Measurement of Anomalous Resistance Induced by Chaotic Motion of Electrons in a Magnetic Null Pointof detection increases up to - 3x103 V/m with presentt3l M.A. Shay, J.F. Drake, R.E. Denton and D.

settings because of the S/1.{ problem. In this case, thevalue of the lower limit corresponds to E* - 3.8 which

Biskamp, J. Geophys. Res. 103,9165 (1998).

[4] Z. Yoshida, H. Asakura, H. Kakuno, J. Morikawa,is the normalized electric field in the NLD studies.

K. Takemura, S. Takizuka and T. Uchida, Phys.
Rev. Lett. 81, 2458 (1998).
[5] T. Uchida, Jpn. J. Appl. Phys. 33,L43 (1994).

Although the chaos induced thermalization is occurredin E* - O(l) l4), this probe could be employed in NLD
experiments to measure E and, with measurements ofhigh-frequency current this Pockels probe would answer
the anomalous resistivity observed in magnetic null.
With better S/1.{ values the first experiment of it is now
going to be conducted on Proto-RT.

t6l T. Shirakawa, H. Toyoda and H. Sugai, Jpn. J.
Appl. Phys. 29, Ll0l5 (1990).

t7l H. Himura, C. Nakashima. H. Saito and Z.
Yoshida, Phys. Plasmas 8,4651 (2001).

[8] for example, S.M. Mahajan and Z. Yoshida, Phys.
Plasmas 7, 635 (2000); K.H. Bunell, Phys. Plasmas
6,4418 (1999).

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s99