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Nuclear Instruments and Methods in Physics Research A 513 (2003) 99–102

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doi:10.1016

Spatial profile measurements of ion-confining potentials usingnovel position-sensitive ion-energy spectrometer arrays

M. Yoshida*, T. Cho, M. Hirata, H. Ito, J. Kohagura, K. Yatsu, S. Miyoshi

Plasma Research Centre, University of Tsukuba, Ibaraki, Japan

Abstract

The first experimental demonstration of simultaneous measurements of temporally and spatially resolved ion-

confining potentials fc and end-loss-ion fluxes IELA has been carried out during a single plasma discharge alone by the

use of newly designed ion-energy-spectrometer arrays installed in both end regions of the GAMMA 10 tandem mirror.

This position-sensitive ion-detector structure is proposed to obtain precise ion-energy spectra without any perturbations

from simultaneously incident energetic electrons into the arrays. The relation between fc and IELA is physically

interpreted in terms of Pastukhov’s potential confinement theory. In particular, the importance of axisymmetric fc

formation is found for the plasma confinement.

r 2003 Elsevier B.V. All rights reserved.

PACS: 52.25.Fi; 52.55.Jd; 52.70.Nc

Keywords: Ion-energy spectrometer array; Ion-confining potential profile; Position sensitive plasma diagnositics

1. Introduction

Recent findings of the importance of optimizedplasma spatial profiles for plasma confinementenhance the requirements of measurements ofplasma parameters. For the purpose of clarifyingthe spatial structures of plasma potentials and ion-energy distribution functions, multigridded elec-trostatic energy analyzers [1] including multi-gridded Faraday cups are widely utilized.However, energetic electrons, for instance, pro-duced by strong electron–cyclotron heatings(ECH) for producing plasma-confining potentialsin tandem-mirror plasmas [2–7] provide serious

onding author. Tel.: +81-298-53-6231; fax: +81-

.

ddress: yoshida@prc.tsukuba.ac.jp (M. Yoshida).

- see front matter r 2003 Elsevier B.V. All rights reserve

/j.nima.2003.08.010

problems so as to obtain precise information fromthe ion data accompanied with such electronincidence. In order to solve such serious problemsfor precise ion diagnostics, we develop a novelelectrostatic ion-energy spectrometer. These im-provements provide complete suppression of theelectron-current fluxes onto ion signals.In this article, we describe the characteristic

properties of the novel position-sensitive ion-spectrometer arrays for simultaneous observationsof the spatial-profile symmetries in end-loss-ionfluxes IELA; ion temperatures Ti; and fc: Further,the first report on the relation of the profile shapesof IELA and fc with plasma-confinement capabil-ities is made by the use of a single plasmadischarge alone in the world-largest tandem mirrorGAMMA 10 [3–19].

d.

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M. Yoshida et al. / Nuclear Instruments and Methods in Physics Research A 513 (2003) 99–102100

2. The characteristic features of the position-

sensitive ion-energy spectrometer arrays

In Fig. 1, a schematic view of the ion-energyspectrometer is illustrated. The differential ion-energy-spectrum measurements are achieved usingan applied-bias difference DV between the ion-repeller grid and the ion-energy-control grid[Fig. 1(a)]. This voltage difference cuts out anarrow ‘‘ion-energy window’’ that has the energywidth (resolution) of eDV=cos2 y from a totalion-energy-distribution spectrum. Under suchoperational conditions, lower-energy ions belowthe voltage of an ion-energy-control grid VC arereflected away due to a uniform electric fieldformed between this control grid and an entrancegrid located in front of it, while electrons andhigher-energy ions over VC þ DV=cos2 y are trans-mitted away through the ion-repeller grid towardsan exit grid. Consequently, an exact relation ofdetectable ion energies Ei within the ‘‘ion-energywindow’’ cutting out of a broader total ion-energydistribution is written as

eVCoEipeVC þ e DV=cos2 y: ð1Þ

Such an energy window is then scanned byvarying both an ion-repeller-grid voltage VIR

Fig. 1. (a) A novel ion-energy-spectrometer unit on the plane of

the plasma incidence. (b) Schematic drawing of the locations of

a novel position-sensitive ion-energy-spectrometer array and a

similarly structured movable ion-energy-spectrometer.

(¼ VC þ DV ) and VC simultaneously, so as toobtain a whole ion-energy-distribution functionwith the energy resolution of eDV=cos2 y: Thetemporal evolution of ion-energy spectra in aplasma discharge is obtained by several scans ofthese biases without any disturbances over ionspectra due to incident energetic electrons. Iontrajectories in the spectrometer unit are numeri-cally simulated so as to optimize the locations ofeach grid and a collector by varying the electricfields produced by the biased grids and theambient magnetic fields in the spectrometer unit.The total detection efficiency is cross-checked bythe use of a monochromatized ion-beam line, andis consistently attained to be 42% as anticipatedby the grid transmissivities.In Fig. 1(b), the locations of the ion-energy

spectrometer array which consists of five spectro-meter units and a similarly structured movableion-energy spectrometer are depicted along with apart of the GAMMA 10 vacuum vessel. Themovable spectrometer is utilized for confirming thedata at various radial positions including the onaxis (rc ¼ 0) location in an operation with a single-ended magnetoplasmadynamic (MPD) gun placedon the opposite end region to the movablespectrometer. The radial positions of the five-spectrometer units are mapped along the mag-netic-flux tubes into the central-cell plasma radiusrc of 2.6, 5.3, 8.2, 11.2, and 14.6 cm. Accordingly,by the use of these spectrometers, radial profiles ofend-loss ions flowing into both end regions areobserved at every 90� around the magnetic axis(rc ¼ 0) horizontally and vertically.

3. Temporally and spatially resolved plasma

parameters by the use of the ion-energy

spectrometer arrays

The experiments have been carried out inGAMMA 10, which is a minimum-B anchoredtandem mirror with outboard axisymmetric plugand barrier cells [3–5]. It has an axial length Lz of27m, and the total volume of the vacuum vessel is150m3. The central cell has a length of 6m and afixed limiter with a diameter of 0.36m, and themagnetic-field intensity at the mid-plane Bm is

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M. Yoshida et al. / Nuclear Instruments and Methods in Physics Research A 513 (2003) 99–102 101

0.405T with a mirror ratio Rm of 5.2. The plugand barrier cells are axisymmetric mirrors(Lz ¼ 2:5m, Bm ¼ 0:497T, and Rm ¼6.2). Formore detail, see Ref. [3–19].In Fig. 2, a typical data set of a plasma

discharge is shown. The target plasmas areproduced by fast-wave ion-cyclotron range-of-frequency (ICRF) heatings in the anchor cells(9.9MHz, 100 kW), initiated with both endedMPD guns. Slow-wave ICRF heatings(6.36MHz, 100 kW) in the central cell are thenapplied to produce a few keV hot-ion plasmas.Higher harmonic fast-wave ICRF heatings(41.5MHz, 100 kW) are employed for producinghigher density plasma. Gyrotrons (28GHz,130 kW) are used for producing magneticallytrapped hot electrons with a temperature of 50–60 keV in the barrier region due to the secondharmonic ECH [20,21], and the other two gyro-

Fig. 2. A data set of temporal evolution of (a) the central-chord

central-cell line density nlc; and (b) an output signal from the

ion-energy-spectrometer array unit at rc ¼ 2:6 cm in a bias-

scanning operational mode (see text). Here, the envelope of this

signal traces total end-loss-ion currents IELA into the spectro-

meter unit. (c) The ion-confining potential fc at rc ¼ 0: Two-dimensional displays of (d) IELA and (e) fc using horizontally

and vertically placed ion-energy spectrometer arrays are

represented during the plug and the barrier ECH injection

period in each plug and barrier region, respectively [at 110ms in

Figs. 2(a)–(c)], the axisymmetric profile of IELA related to the

axisymmetric fc profile peaked on the magnetic axis is

observed.

trons (28GHz, 100 kW) are applied to the plugregion for producing warm electrons in the energyrange of a keV due to fundamental ECH [22–26](hereafter referred to as barrier ECH and plugECH, respectively). A neutral-beam injection(NBI; 25 keV, 20A) is prepared for producinghot ions in the central cell.The central-chord line density, nlc; [Fig. 2(a)]

increases with reducing end-loss-ion currents IELA[Fig. 2(b)] due to a 0.4-kV fc formation [Fig. 2(c)]in the period with the barrier and the plug ECH(t ¼ 100� 150ms). After the whole ECH isswitched off, a quick disappearance of fc resultsin significant outward flows of potential confinedions (see IELA just after the ECH switched-offtime) along the lines of magnetic force into bothend regions. In Figs. 2(d) and (e), detailed two-dimensional radial-profile data on IELA and fc

from the spectrometers in both horizontal andvertical directions are shown. During the ion-plugging period [Figs. 2(a)–(c)], the axisymmetriclarge fc formation peaked on the magnetic axis isobtained [Fig. 2(e)]. Simultaneously the data fromour developed ion-energy spectrometer arrays giveinformation on the axisymmetric profile of IELA inFig. 2(d), associated with the above-describedpeak-on-axis fc formation. Such axisymmetricplasma profiles may be produced by the E�Bplasma rotation in the azimuthal direction due toaxisymmetrically formed plasma potentials [27].Here, E and B denote the radially formed electricfields due to potential F (i.e., E ¼ �rF) and theaxially directed (z) ambient magnetic fields,respectively. These data in Fig. 2 thus providethe physics essentials for the potential confinementdue to the symmetrically formed fc:

4. Physics interpretations of the plasma data

observed with the ion-energy spectrometer arrays

from the viewpoint of potential confinement

In Fig. 3, data in Fig. 2 are plotted in the scalingplane of nctpjj versus fc=Tijj; where the particleconfinement time and ion temperatures in the axialdirection are designated by tpjj and Tijj; respec-tively. Here, tpjj is calculated from the experi-mental data by the use of e

Rn dS dL=

PRIELA dS

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1016

1017

0 0.5 1.0 1.5

n cτ p

// [m

-3s].

φc /Ti//

Fig. 3. Data on nctpjj using the ion-energy spectrometers at

rc ¼ 2:6; 5.3, 6.0, and 8.2 cm are plotted as a function of fc=Tijj:Here, a similarly structured movable ion-energy spectrometer is

utilized for the data at rc ¼ 6:0 (see Ref. [3]). The solid and

dashed curves show the theoretical predictions from Pastu-

khov’s potential-confinement relation [see Eq. (2)] by the use of

the observed values of Tijj of 0.45 and 0.35 keV at rc ¼ 2:6 and8.2 cm, respectively. Here, the data at t ¼ 110ms in Fig. 2 are

plotted.

M. Yoshida et al. / Nuclear Instruments and Methods in Physics Research A 513 (2003) 99–102102

where the total particle number multiplied by theelectronic charge of e is integrated along the fluxtube that is connected to the collector area dS ofan ion-energy spectrometer unit [2,3]. This integralis then divided by the total end-loss current IELAflowing into the spectrometer collectors in bothend regions.In addition to qualitative global researches in

the relation between IELA and fc; data in Fig. 2 att ¼ 110ms along with the observed values of Tijj

deduced from the ion-energy spectra at rc ¼ 2:6;5.3, 6.0, and 8.2 cm along with nc are plotted inFig. 3 so as to investigate the quantitative relationbetween IELA and fc:The data are then compared to the predicted

values from the Pastukhov theory of the plasmaconfinement due to plasma-confining potentials[28]. Also, the modification term from Rognlienand Cutler’s formula [29] is added. The theore-tical-axial confinement time in seconds is, thus,written as

tpjj ¼ 2:28 tiiðfc=TijjÞexp ðfc=TijjÞ1þ 0:25ðfc=TijjÞ

�2

1þ 0:5ðfc=TijjÞ�1

þ 1:06� 10�4 T�1=2ijj exp ðfc=TijjÞ ð2Þ

where tii represents the ion–ion collision time inseconds. For fc and Tijj in Eq. (2), the unit of keVis employed.

The solid and the dashed curves in Fig. 3 arecalculated from Eq. (2) using the observed valuesof Tijj ¼ 0:45; and 0.35 keV, respectively. Here,these two values are chosen as the representativeparameters of monotonically decreasing Tijj fromrc ¼ 2:6 to 8.2 cm. It is noted that a smallcorrection of a few percent from the second termon the right-hand side of Eq. (2) is estimated to thetotal tpjj in the parameter regime of Fig. 3. Thus,these data are consistently interpreted by Pastu-khov’s theoretical prediction in Eq. (2). This resultindicates that these tandem-mirror plasmas inFigs. 2 and 3 are confined and controlled by thepotential formation, as proposed in the originaltandem-mirror scenario.

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