J. Plasma Fusion Res. SERIES, Vol.4 (2001) 82-90

Heavy lon Beam Probe Diagnosticof Static and Dynamic Potential Structure
IGUCHI HarukazuNational Institute for Fusion Science, 322-6 Oroshi-cho, Toki-shi 509-5292' Japan(Received: 5 December 2000 / Accepted:2'7 September 2001)

Abstract
A heavy ion beam probe (HIBP) is a unique diagnostic method to measure the electric potential inmagnetically confined high temperature plasmas. Its fine probing beam and well-collimated secondary
beam detector give this diagnostic good spatial resolution, which together with the good time resolution
make it powerful in probing plasma interior both in steady state and transient state. There are many
excellent review papers [for example, 1,2], but these mostly concentrate on HIBP applications intokamak research. The radial electric field or space potential structure is more important in stellarators orother non-axisymmetric tori, because particle fluxes are intrinsically non-ambipolar in these devices. This
paper reports examples of HIBP measurements of potential structures in non-axisymmetric tori - thebumpy torus NBT-IM and the heliotron/torsatron CHS - following brief reviews of the development
history and basic principles of the HIBP.

Keywords:
heavy ion beam probe, HIBP, plasma diagnostics, electrostatic potential, magnetic vector potential, ExB
drift, reduced MHD equation

an m = 2 tearrng instability [6,7]. The systematic

1. Introduction

development of the HIBP diagnostic was continued by

The idea of using a heavy ion beam to probe theplasma interior originates from the work by R.L. Hickok

R.L. Hickok and his colleagues at Rensselaer

and F.C. Jobes in 1960's. They injected a molecularhydrogen beam (H2*) at an energy of 2 MeV into a

Polytechnic Institute (RPI). In the late 1970's, theysucceeded in measuring a two-dimensional spacepotential map in the ELMO Bumpy Torus (EBT) [8,9].
This attracted the attention and made this diagnostic
popular, especially in the research of bumpy tori andtandem mirrors in the 1980's. HIBP's are now
operational on the Nagoya Bumpy Torus (NBT) [10],the TMX tandem mirror [11], the RFC-XX tandem
mirror with radio frequency plugging [12], the
GAMMA-6 [l3] and GAMMA-I0 tandem mirrors [14]'In ISX-B the HIBP was applied to a tokamak plasma
with neutral beam heating, where the consistency ofthe
plasma potential profile measured with the HIBP withhollow cathode arc plasma, and detected protons
produced by molecular break-up in the plasma, tomeasure plasma density and density fluctuations [3,4].
After that, they proposed to use a heavy ion beam withlower energy instead of a molecular hydrogen beam tomeasure plasma space potential and plasma density
simultaneously [5]. The first application of the heavy
ion beam probe (HIBP) to a magnetic confinement
device was on the ST tokamak in early 1970's. Here,singly charged thallium ions (Tl*) with an energy of 200
keV were used successfully to measure the spacepotential profile and density fluctuations associated with

02001 by The Japan Society of Plasma*

Science and Nuclear Fusion Research

Corresponding author's e-mail: iguchi@ nifs.acjp82

Iguchi H., Heavy Ion Beam Probe Diagnostic of Static and Dynamic potential Structure

the radial momentum balance equation and plasma
toroidal/poloidal rotation velocity was demonstrated

potential of m = 2 rotating magnetic islands wasmeasured [30].

[5]. Recently, the radial momentum balance equation

In all of these HIBP set-ups, the beam trajectoryhas been examined more precisely in the CHS heliotron/

was basically two-dimensional. The beam displacement

torsatron using a HIBP and charge exchange
spectroscopy (CXS) tl6l. Because ofits high spatial andin toroidal direction was compensated by a toroidal
beam deflector, in either the primary or the secondary
beam line.
Compared to the situation in tokamaks, the radial

temporal resolution, and the capability to simultaneously
measure the density and potential fluctuations together

with their phase relations, the HIBP is considered as a
key diagnostic for turbulent transport in the core plasma

electric field or space potential structure is more[7]. In addition, thanks to the fact thar the HIBP canmeasure the t-spectrum of fluctuations (by using

tori, because in these devices the particle fluxes are
intrinsically non-ambipolar. A 160 keV HIBP wasapplied in the helical device ATF torsatron [31,32].
Since the beam trajectories are fully three-dimensionalin helical magnetic configurations, the geometricalarrangement of the beam injector and the energy

important in stellarators and other non-axisymmetricmultiple entrance slits on the energy analyser), thediagnostic has been used extensively in the research ofanomalous transport in tokamak plasmas. Leading
experiments have been carried out on the TEXT and
TEXT-Upgrade tokamaks with 500 keV and 2 MeV
HIBPs, respectively [8,19], and later with a 500 keV

analyser is not flexible. The energy analyser has to beplaced close to the plasma. The magnetic stray-field

HIBP on the JIPPT-IIU tokamak t20,211. In these

affected the measurement accuracy in absolute potential
measurements. The observation points in the plasma
cross-section were limited as well. At CHS a 200 keV

studies, a comprehensive comparison of the fluctuation
ft-rrr spectrum and phase velocities obtained by HIBP
and other diagnostics, especially electromagnetic wave

HIBP has been developed with the aim to actively

scattering, was carried orrt 1221. However, thedifferences still remain as open questions. In the T-10

control the trajectory. Sweep plates (octapole type) havebeen installed in the secondary beam line as well as intokamak the potential structure in tokamak plasma
heated by Electron Cyclotron Resonance waves wasstudied with a 200 keV HIBP [23].
Since the discovery of the H-mode in the ASDEX
tokamak [24], much attention has been paid to the radial
electric field in the edge region125,26l. Efforts to study
the H-mode transition using the HIBP have been carriedout on TEXT and JIPPT-IIU, but no clear results havebeen reported. Recently, a 500 keV HIBP was installed

the primary beam line. The combination of the electricfields in the two deflectors is used to control the
injection angle of the secondary beam in the energy
analyser [33]. Full radial scanning for the potential
profile measurement was achieved with this method
1341.

Reviews of the basic principles and the potential ofthe diagnostic are found in the excellent papers by A.J.
Wootton and P.M. Schoch [], and by T.P. Crowley andon the JFT-2M tokamak, where a fast change of theedge potential associated with the H-mode transition

RPI team l2l. A review by Y. Hamada treats theturbulence measurements in the JIPPT-IIU tokamak

was observed [27]. However, the causal relation
between the radial electric field and transport barrier[21]. Those review papers are basically limited to HIBP
applications in tokamak research. The reference [2] is information has not yet been clarified.

the special issue of the IEEE Transactions on Plasma
Science published on the occasion of Prof. Hickok's
retirement. This issue includes other review papers from

The idea to measure the poloidal magnetic fieldusing the HIBP [28] goes back to the proposal for themeasurement of current density profile on the ST
tokamak [6], which was not successful at that time.

various HIBP groups in the world. Recent progress in
HIBP and contributions to physics understanding fortoroidal helical plasmas are found in a series of papers
by A. Fujisawa and H. Iguchi, et al. 135-381.

Current profile measurements have been demonstrated
in the TEXT tokamak [29], but the accuracy is not yet
as good as the MSE (Motional Stark Effect) diagnostic

In this paper, two examples of HIBP applications in
non-axisymmetric tori are presented to emphasise theor the Faraday rotation measurement using a FIR (Far
Infra-Red) laser. Less demanding than a current profile
measurement is the detection of fluctuating magnetic
fields associated with MHD modes. In the TEXT
tokamak, the radial profile of the magnetic vector

diagnostic capabilities which have not been discussed indetail in the previous review papers. These are themeasurements of the potential structure in the bumpy
torus NBT-lM and the heliotron/torsatron CHS.
83

Iguchi H., Heavy Ion Beam Probe Diagnostic of Static and Dynamic Potential Structure

current is about 10 to 100 nA, which is large enough toallow a time resolution in the microsecond range.
Figure 2 shows a typical beam injector, consistingof an ion gun, an accelerating tube, a quadrupole lens

2. Basic Principles and Hardware
The diagnostic principle of the HIBP is based on
the motion of heavy ions in the electromagnetic field(Fig. 1(a)). A singly ionised heavy ion beam is injected
into a magnetically confined plasma. Doubly charged
secondary ions are produced by ionisation in the plasma.
Their trajectory differs from that of the primary ions dueto their smaller Larmor radius. A detector locatedoutside the plasma can select a local position in theplasma by selecting a secondary beam trajectory.
The Lagrangian of the beam ions in electromagnetic field in the non-relativistic limit isfor beam focusing and shaping, and toroidal and radial

beam deflectors. The accelerator tube and thequadrupole lens are not necessary for beams at energy
less than tens of keV, because focusing can be obtainedwith the lens inside the ion gun. Octapole beam
defectors can be used instead of a two-stage deflector
t341.

A is the magnetic vector potential. The secondary beam

The energy analyser used so far for HIBP
diagnostics is the Green-Proca type parallel plateelectrostatic energy analyser as shown in Fig. 3 t391.
The advantage of this type of analyser is its secondorder focusing characteristic. A split plate detector is

carries information on the field quantities, Q and A at thegenerally used, which consists of four metal plates for ar=jmv2-qQ+qi.A
where q is the ion charge, @is electrostatic potential andionisation point.

The spatial resolution or the sample volume isbasically determined by the primary beam size and theaperture of the detector, which are both typically of theorder of mm. It also depends on the magnetic field
configuration and the locations of the beam injector andthe detector. Trajectory calculation with finite beam sizeis necessary to optimise the sample volume. In general,

Ion Gunthe sample volume is elongated along the beam
trajectory as shown in Fig. 1(b). The spatial resolution isbetter in the direction perpendicular to the beam

Energy Analyzer

trajectory.
The temporal resolution depends on the signal levelof the secondary ions. The secondary beam intensity isgiven as [2](b)(7")1,,n"(r)I, = d po alo
1' F,F,o,",p-frIIIl"

where 1o is the primary beam current, F, F, are theattenuation factor

4=exp

l-[o1",""0t1

Sample Volume,lEil(j = e.i\Fig. 1 (a) Basic principles of the heavy ion beam probe'(b) Typical shape of observation volume (sample

due to ionisation etc., o;,, is the ionisation cross-section,
which is a function of the electron temperature, l"u is the
sample volume length along the primary beam

volume).

trajectory, z" is the electron density at the ionization

point and r is the amplification factor due to thesecondary emission coefficient of the detector plates.
The primary beam current is typically l0 to 100 pA

Ion Gunwhen a thermo-ionic alkali-metal ion source is used. The
beam energy so far ranges from 10 keV up to 2 MeV.
For plasmas with an electron density of 101e m-3 and anelectron temperature above 100 eV, the secondary beam

Accelerator

Focusing I-ens Quadrupole

Toroidal Deflector

l.ens

Radial Deflector

Fig. 2 Typical arrangement of beam injector with athermoionic ion source.
84

Iguchi H.' Heavy Ion Beam probe Diagnostic of Static and Dynamic potential structureHigh Voltage Top plate

potential at the ionisation point, because the stripped
electron removes an amount of energy equal to -eQ. Theenergy change is resolved at the energy analyser interms of the difference current lro. lt is noted that themeasurement is direct and local. When there are

SecondaryBeam

i?l'j":,:?:.

rFl

UGleftDown-Lcft
Ielectromagnetic fluctuations in the plasma, the possible
change of the beam energy caused by the acceleration
due to dA/dt term should be evaluated for all relevant
fluctuation models, but it is generally small [43].

UD-RiEbt

Down-Risht

svu- (1,,2* I u, ) * (I DL+ IDR)

C. The Magnetic Vector potential

IuD- (Iw+ Iu*) - (IDL+ IDR)Iu

The left-right shift of the secondary beam on the- (IuL + Iy ) - (IuR+ IDR)

split plate detector carries the information on thepoloidal magnetic field. This idea has so far only been
discussed for axisymmetric tori, for which the canonicalFig. 3 Parallel plate energy analyzer with split plate
detectors.

angular momentum is conserved. If the symmetry axis istaken in the z direction and the toroidal anele as (. it issingle entrance slit. The sum of the beam current on four

expressed as

plates, IsuM, corresponds to the total secondary beam
intensity. The beam motion on the detector in the up_

P,,dC= * = mr2 i + qrA r= const.

down direction, i.e. the up-down difference current(1y2), corresponds to the change of the beam energy.

Then, the magnetic vector potential at the ionisation
point can be expressed as

The beam motion in the left-right direction, i.e. the left_right difference current (-I.*), corresponds to the toroidal
deflection of secondary beam trajectory if the analyser.--1,.

AAs, =-m7i l'dt-

lttn

plates are placed horizontally.

;-r

f-

s,t - '

I.

td' id]+ 2 t A sd

\a

A

*

where 0, i and, d denote the initial, ionisation anddetector positions, respectively. All parameters on the

A. Electron Density Fluctuations
In low density plasmas, beam attenuation isright-hand side can in principle be measured, and the
local vector potential is obtained. The poloidal magnetic

negligible and the secondary beam intensity Isura isfield or plasma current can be calculated if A6i is
measured. In an actual experiment, however, it is

proportional to the local electron density. The condition

for this simple interpretation to hold has been examined,difficult to m'easure the beam velocity in the toroidal
direction at the detector. The left-right displacement isfor example, in [40,41]. When attenuation is not
negligible, some reconstruction process is required tomeasured instead, which is a path integral of the toroidal

obtain the local electron density. A HIBP is seldom usedvelocity along the beam trajectory. The fluctuating

for this purpose because there are other diagnostic
methods with better accuracy for the electron density
measurements. However, the HIBp has been used fordensity fluctuation measurements because of its goodcomponent of 46;

Ar,=

f i'oO,is more easy to measure because the static part can bespatial and temporal resolution. The problem arising

dropped.

from the path integral effect has been resolved by

In real confinement devices there is toroidal field
ripple due to the finite number of toroidal coils, so thatthe system is not truly axisymmetric. In the TEXT

utilising a multiple point detection method and taking
cross-correlation. Further details on density fluctuation
measurements can be found, for example, in 12I,421.

tokamak, computer codes were used to derive the local
magnetic vector potential [30].

B. Electrostatic Potential
From the total energy (kinetic energy + potential
energy) conservation before and after the ionisation

3. Fine Potential Structures
3.1 Static Potential Structures in NBT-IM

reaction, the doubly charged secondary ion has anadditional energy equal to the local electrostatic

A bumpy torus is a closed-line magnetic

confinement device containing electrons with energy
85

Iguchi H., Heavy Ion Beam Probe Diagnostic of Static and Dynamic Potential Structurefrom tens of eV to hundreds of keV' The last bumpy

Jd.

""4

--.%,

torus was shut down more than a decade ago, but bumpy
tori have been a treasury ofplasma physics. The idea ofdrift rotational transform due to E x B poloidal drift as
well as grad B and magnetic curvature drifts was tested.
The radial electric filed (which is determined by theradial space potential profile) induces poloidal drifts.
Closed ExB drift surfaces are essential for theconfinement. Figure 4 shows a grid map of the"\observation point for the 30 keV HIBP on NBT-IM. By
selecting the beam energy and sweep angle, full two-

dimensional observation is possible. Figure 5 shows
typical contour plots of the space potential for two
different operational modes, the C-mode and T-mode. In
the collisional regime, the C-mode, the electron
temperature was low (10-20 eV) and toroidal drift

Fig. 4 Detection grid on the poloidal cross section tn
NBT-1M.

dominated poloidal drifts. The potential is positive in theupper half of the torus and negative in the lower half ofit, which produces a downward electric field resulting inan outward ExB plasma flow. In the collisionlessregime, the T-mode, in which a hot electron ring isformed and the core electron temperature was in therange 50 to 100 eV, poloidally closed potential surfaces
are formed. The presence of mirror trapped energetic
electrons plays an important role in the formation of theclosed ExB drift surfaces. Figure 6 shows anothercomparison of potential and density profiles in two

T-modeC-modeFig. STwo dimensional potential profiles in two

different ECH schemes. Poloidal symmetry of thepotential profile was improved in this two-frequency
ECH operation, which should improve closed contour ofdifferent operation regimes in NBT-1 M.

the ExB drift surfaces. Actually a peaked density profileand steeper density gradient were observed. Relation

1 BGHzECH

1 8GHz+8.5GHzECH(30kw)(4skw)

between closed ExB drift surfaces and particle
confinement was also tested using an artificial external
error filed. External field was applied artificially by thene (xl01h-3)

ne (x1017m-3

6

use of the field correction coils, which were equipped on

CHS to cancel intrinsic error field in toroidal average.
When the vertical or horizontal field error in the level of
LBIB - 2 x l}-a was applied, closed equi-potential
contours were destroyed, resulting depression of central
electron density and a flattened density profile. Further

2

10

10

x(cm )

X(cm )

t00

discussions are found in reference [44].

0s (v)

1

3.2 Static Potential Structures in CHS

oo {s

\
\

\\,

The heliotron/torsatron device CHS is also a nonaxisymmetric torus and radial fluxes of electron and ion
are not necessarily ambipolar. Effect of space potential
profiles or radial electric field on confinement has to bestudied. In contrast to the bumpy torus, it has magnetic

(V)

-100

-roo

051015

x(@)

-t0

10

x(d)

Fig. 6 Comparison of density profiles and potential
profiles in two different ECH schemes in NBT-1 M'

rotational transform produced by a pair of helical86

Iguchi H., Heavy Ion Beam probe Diagnostic of Static and Dynamic potential

windings. Figure 7 (a) shows the schematic diagram ofstructurepoloidal cross section is achieved by the use of thethe 200 keV HIBP at CHS. The beam trajectory is

active trajectory control method as shown in the Fig. 7

completely three-dimensional in this case. Full radial
scanning from the top to the bottom of the plasma in(b). Various types of potential profile are observed
depending on the operational conditions as shown in
Fig. 8. The positive p corresponds to upper side and thenegative p, the lower side. A full profile is obtained bysweeping beam in every 2 ms. The electron temperature
ranges from 200 eV to 800 eV. The radial electric field

is positive in the high T"ECH plasma and negative in a

NBI plasma with comparable T" and,I,. For the Mexican
hat shape, it is considered that electron root and ion root

are simultaneously realized in spatially separated
regions. The observed potential profiles and the radial
electric fields are well explained by neoclassical theory.

This does not suggest that electron and ion loss
processes be dominated by neoclassical process. In facttransport analysis have shown that anomalous transport

dominated in most operation regimes. They are,however, ambipolar and do not effect the flux balance todetermine the potential structure. The potential profiles
shown in the figure are typical in CHS plasmas, but finestructure changes depending on the heating scheme andeplasma collisional parameters.

(b)

3.3 Potential Dynamics in CHS
Potential structure in CHS is not always stable, but

in some conditions, it exhibits dynamic changes. Figure9(a) shows temporal variation of the central space*'ml lH-E",fY'lpotential during a combined ECR+NBI heating. In thiscase probing beam is fixed to observe the spacepotential at the plasma center. The time resolution inthis operation is of the order of microseconds. Repetitive
crush of the central potential is observed approximately
in every 2 ms in quasi-steady state. The drop of the

0.8 0.9 1 1.1 1.2 o 5 10 15 20 25
Rpmlectlon(m)Toroidal Angle

Fig. 7 (a) Schematic of 200 keV HIBP on CHS.

central potential reached to 600 eV. Crush occurs in the(b) Projection of the observation points on thepoloidal cross section for the central scanning
chord. Toroidal distribution is also plotted.

300kw EcH
ng=J; I Ql 8rn-3
Te>>Titime scale in the range of several tens microseconds asshown in Fig. 9(b), which clearly suggests that theprocess is not a diffusive one (- a few milliseconds).
Figure 9(c) is the radial structures of the potential
profiles in the two states. It is interpreted as bifurcation
phenomena between the two steady state, which ispredicted by the neoclassical theory. Because of
nonlinear dependence of radial particle fluxes on theradial electric field, multiple steady states solutions can

ECH+NBl

ne=8xl Ol 8m-3

TPTi

be realized in a non-axisymmetric torus. Detailed
physics associated with this bifurcation nature of thepotential profiles or radial electric field in a toroidal
helical plasmas are described in reference [38 ] as wellFig. 8 Typical potential profiles in different operational

as in this conference [47].

regimes in CHS.
87

Iguchi H., Heavy Ion Beam Probe Diagnostic of Static and Dynamic Potential Structure

(u)
m

c

ll)-

cto

70

(b)

-jz
vn
€'o

x
co

t (ms)(")

i 7'uu"Repetitive
Transition

1+@t=73pst (msFig. 9 (a) Self-sustained osscillation of space potential observed in a combined ECR+NBl heating.
(b) Fast time scale of the potential crush and recover , suggesting bifurcation phenomenon.
(c) Potential profiles before and after the transition.

q (vaccum field)

-:
)3

m2

---

-1 r=110.0 msili

t=110.2 ms/ ", \h\-'

?/A

(t
120

122

126

124

128

---=1"o.2

130(...1-"'-. t=110.4 hs

0.4

0.6

0.8

p

t (ms)of space potential

Fig. 10H|BP raw signals.during the MHD bursts
together with a Mirnov coil signal in CHS.

Fig. 11 Radial distribution

3.4 Internal Strusture of MHD Modes in CHS
Magnetic perturbations associated with MHD

are well correlated with the Mirnov coil signals. 15vv
includes density fluctuation information but is a pathintegrated value. For reconstruction a detailed analysis is

oscillation during the growing phase of the
MHD burst in CHS.

instabilities affect the particle trajectory of probing
heavy ions. In CHS, the HIBP measurement has been
carried out during bursting MHD activity [43]. Figure
10 shows the time behaviour of the raw HIBP signals'
Isu*, Iuo and Is, together with the Mirnov coil signal,
durine the MHD bursts. It is seen that all three signals

required, as mentioned in the previous section. /{,,2shows the local potential fluctuation. Figure I I shows
radial profiles of the oscillating space potential, which
has a peak around the q = 2 magnetic surface' The
potential oscillation is related with the growth of an m =88Iguchi H., Heavy Ion Beam Probe Diagnostic of Static and Dynamic potential Structure

2 interchange instability. 1.o includes toroidal deflection

conference [47].

of the beam which comes from the fluctuating vector

Reduced MHD equations have often been used for
MHD studies in which the key parameters are the stream
function and the poloidal flux function [48]. The stream

potential 45. Since the signal is a path-integrated value
and magnetic field configuration is not axisymmetric inthis case, the radial profile analysis is not

function is related with the electrostatic potential asstraightforward. New algorithms for the reconstructionof the local vector potential are required.

@o#and the poloidal flux fluctuation is related with thetoroidal component of the magnetic vector potential as

4. Discussion and Summary
Systematic experimental studies on the effect of theradial electric field on confinement have been carriedout in the closed-line toroidal system, the bumpy torus
NBT-IM. The theoretical framework for the particle
confinement in the presence of a radial electric field has
been discussed in detail by Kovrizhnikh [45] andY e RoAr+Y,o"
Toroidal angular momentum of the probing beam is notconserved in non-axisymmetric toroidal devices.

Determination of 46 from toroidal displacement of thesecondary beam is not direct as in an axisymmetric
torus. However, in the heliotron/torsatron configuration,
the magnetic structure is mostly determined by theexternal coils and the vacuum flux function is well

Hasting [46]. Multiple solutions of the steady stateradial electric field structure were predicted. Steady statesolutions are referred to as the electron root and an ion
root. The neo-classical theory developed in the bumpy
torus research has been extended to the present day

determined. The data from CHS show that theoscillating leftright displacement is well correlated with
the Mirnov coil signal. The experiment suggests thediscussion for heliotron/torsatron or stellerator
confinement physics.

possibility to measure the toroidal component of vector

In the toroidal helical system CHS, which has
magnetic rotational transform, the potential wasobserved to be constant on the flux surfaces, inagreement with the general assumption that spacepotential, if the algorithm to reconstruct the vector
potential fluctuation component is developed. When thetwo key parameters of the reduced MHD equations
simultaneously with a HIBP, improved understanding of
the MHD phenomena in toroidal helical plasmas ispotential is a flux function. The poloidal symmetry of
the profiles of the potential or the radial electric field in

expected.

a non-axisymmetric torus with magnetic rotational

In summary, a heavy ion beam probe is a powerfultool to study the effects of the radial potential structureor the electric field structure on magnetic confinement,
especially in non-axisymmetric tori such as a bumpy

transform are confirmed in rather wide range of electron

or ion collision parameters. However, it is pointed out

here that the relation between a small poloidal
asymmetry and particle confinement is still an issue tobe studied in the present day high temperature

torus or a stellarator. Short reviews of HIBp
development history and basic principles as well as

confinement devices, like tokamaks and stellarators. The

experimental observations are presented emphasising theadvantage of the HIBP diagnostic is that measurements

potential structure measurements in non-axisymmetric

are local and direct and do not require the assumption

tori, which have not been treated in previous HIBp

that the potential is a flux surface quantity.

review papers.

Dynamical structural reformation of potential
profiles has also been observed in certain operational

Acknowledgement

regimes. The change of the potential profile occurred in
the time scale of several tens microseconds, which ismuch faster than the time scale of diffusion processes. It
is interpreted as a bifurcation phenomenon ofthe radial

The author would like to thank co-workers of HIBp
diagnostics, Drs. K. Takasugi, F.M. Bieniosek for NBTlM experiments and Drs. Fujisawa, T.p. Crowley, S.

Lee for CHS experiments. Long years support fromelectric field in toroidal helical plasmas. It has been

Rensselaer Polytechnic Institute, especially by profs

theoretically predicted, because in such non-

K.A. Connor and R.L. Hickok as well as continuous

axisymmetric tori, multiple solution for the electron andsupport and encouragement by Profs. H. Ikegami, M.
Fujiwara, Y. Hamada, K. Matsuoka are acknowledged.

ion flux balance equation can be realised. Different
radial electric field corresponds to the different solution.
This topic is presented in the separate paper at thisHe also thanks to theoretical contributions andsuggestions by Prof. K. Itoh and Drs. H. Sanuki and K.
89

lguchi H., Heavy Ion Beam Probe Diagnostic of Static and Dynamic Potential Structure

Ichiguchi. Finally critical reading of the manuscript byrefrees is aknowledged.

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