J. Plasma Fusion Res. SERIES, Vol.5 (2002) 163-166

A Gomputational Model for He* lons in a Magnetized
Sheet Plasma: Comparative Analysis between
Model and Experimental Data
BLANTOCAS Gene Q.r, RAMOS Henry J. and WADA Moroi2
National Institute of Physics, College of Science, University of the Philippines, Diliman
12Quezon City 1101, Philippines
West Visayas State [Jniversity, Lapaz" Itoilo City 5000, Philippines

Department of Engineering, Doshisha Llniversity, Kyoto 610-0321, Japan(Received: ll December 2001 / Accepted: 12 July 2OO2)

Abstract
An ExB probe was used to extract He* ions from a magnetized steady state sheet plasma. Plasma
parameters 7", n.and extracted He* ion current were analyzed vis-i-vis a modified Saha population
density equation of the collisional-radiative model. Numerical calculations show that at low discharge
currents and in the hot electron region of the sheet plasma, relative densities of He* ions show somedegree of correlation with ion current profiles established experimentally using the ExB probe. Bothexperimental and computational results indicate a division of the plasma into two distinct regions eachwith different formation mechanisms of He* ions.

Keywords:sheet plasma, ExB probe, coltsional-radiative model, MSPDE - modified Saha population density equation

2. Experimental Set-Up and Principles ofthe Method
A schematic diagram of the MSPIS facility is

1. lntroduction
The collision and capture processes of He* ionswith other charged particles play vital roles in the studyof astrophysical phenomena and in fusion and beamtransport research [1]. In this work, He* ions wereextracted using an ExB probe from a magnetized sheet
plasma ion source (MSPIS). In most researches He* ionswere extracted from multicusp sources. This reportfurnishes new insights to He* ions produced in sheet
plasmas. Experimental data were analyzed vis-ir-vis a
modified Saha population density equation (MSPDE) ofshown in Fig. 1, while that of the ExB probe is shownin Fig. 2(a). A representative He'peak detected by theprobe is shown in Fig. 2(b). Detailed descriptions of theion source and the ExB device are found in refs. [2,3].
Base pressure was typically in the order of 1xl0-6 Torr.
Helium gas at 0.02 Ton fed into the production chamber
diffused into the extraction chamber via a small aperture
between limiters E1 and E2. The existence of a pressure
gradient between these two regions facilitated thediffusion process. The initial gas filling pressure in theextraction chamber before discharge was 0.002 Torr. A

the collisional-radiative (CR) model, providing analternative physical representation of He* particle
distribution in the sheet plasma. In contrast with direct
measurements of the ExB probe, the MSPDE method

potential of 20 V (Va) was applied across the hot
cathode assembly, with corresponding filament current

offers a choice of numerical and diagnostic simplicity.

@200.2by The Japan Society of Plasma
Science and Nuclear Fusion ResearchCorresponding author's e-mail: plasma@ nip.upd.edu.phr63

Blantocas G.Q. et al., A Computational Model for He* Ions in a Magnetized Sheet Plasma

and radiative processes. One of the salient features ofranging from 20 to 25 A. Energetic electrons emitted
from the filament are further accelerated by the fields ofY (90-120 V) and % (100V), ionizing helium neutrals
thereby generating helium plasma in the extraction

the model is that for hydrogenic ions at levels above theground state, the probability of collisional processes

becomes greater while that of radiative processes
becomes smaller. Hence there is always some level
above which the effect of radiative processes isnegligible. Under these circumstances a modified formof the Saha equation can be used to evaluate thepopulation densities of upper level hydrogenic ions. [4].
The equation in its generalized form is given byregion. The cylindrical plasma initially formed iscompressed into a sheet configuration by a pair ofstrong Sm-Co dipole magnets (-1.5 kG). The plasma
discharge current 1a in the extraction region was varied
from 1.5 to 4.5 A by increasing V1 from 90 to 120 V.
Experimental parameters such as electron temperature2", density z" and He* ion current were measured by theLangmuir and ExB probes at locations orthogonal to thesheet plasma. These data were investigated using theN z-r@) = | / 2 @z lD I azE) N z(E)nI (2Tcm"fh2KT")13t2

exp[Ep(p)lKT"], where N2-1(p), NzG) are the numberdensities of hydrogenic ions in the quantum level p andbare nuclei in the ground state, a7-1Qt), rthG) are thestatistical weights ofhydrogenic ions and bare nuclei intheir designated levels, Eo@) is the ionization potential

MSPDE of the CR model. It is a model for optically thinplasmas of moderate density where the loss mechanism
results from the combination of interactine collisionalof a hydrogenic ion in its quantum level p, K is
Boltzmann Constant, m, T.and n" are electron mass,temperature and density, respectively. For hydrogenicions, the energies depend only on the principal quantum
number hence the statistical weight can be substitutedby 2pt.Bare helium nuclei, because of the absence ofvalence electrons, are considered to have single quantum

states hence the weight factor is taken as unity.
Imposing the condition of macroscopic neutrality suchthat n.= 7N. and replacing Ep(p) by Eslp2 where Esis
the ionization potential of hydrogen; the final expression
for the MSPDE takes the approximate form; N-t(pt) =p2 n.2 I z1h2 | 12nmKT
exp [Esl (p2 KT")]. Substituting")f3t2
plasma parameters 7", n, in the MSPDE at each data
point for each discharge current used and numericallyvarying the values of p in a stepwise permutation from Ito 30, yields density plots of He* ions as functions ofv2

V1Fig. 1 Schematic diagram of the Magnetized Sheet
Plasma lon Source

distance from the sheet plasma core. The density plots(MSPDE curves) are then compared with theexperimental curves of extracted He* ions (ExB probecurves) to see whether or not some degree ofCollimator,",8s ##icorrespondence exists between them.

{* Electrometer="*'-ffi

3. Results and Discussion
Investigations were conducted to establish thespatial distributions of T,andn" (Figs. 3(a) and (b)) andcurrent profiles of He* ions (Fig. (a)) by successively
positioning both Langmuir and ExB probes at various
distances from the sheet plasma core using threedifferent plasma discharge currents (I), viz,1o = 1.5 A,
3 A and 4.5 A. The probe's extraction voltage was set at
65 V; this is the calibrated potential that limits theextraction of He' ions only. The calibration of the probe
was reported in ref. 3. Values of p from 1 to 30 wereFaraday cupa(b) :eFbg-l-30 -20 -10 010 2030

Deflector voltage (V)Fig. 2 (a) Schematic diagram of the ExB probe. (b) Typical signal peak of He. detected by the probe.

r64

Blantocas G.Q. et al., A Computational Model for Het Ions in a Magnetized Sheet plasma

permuted 3 at a time. Each value of p for all possible

observed within this vicinity. The set of coupled
differential equations linking both collisional andsequence, together with f" and z" values coffesponding

to each discharge current used were substituted into theMSPDE to calculate the density profiles of He* ions,Fig. @). However, calculations were discontinued atp
values above .10 since beyond this limit, pronounced
differences with the spatial curves of Fig. 4(a) are seen,
as shown in one of the density plots for excited He+ions, Fig. 5. A.t the p value of 2 for 16 current 1.5 A,

radiative processes in the CR model need not be actuallysolved, since only a representative plot of ion
concentrations in the direction transverse to the sheet
plasma core is desired. It is necessary only to note that
the MSPDE can be applied to states above the groundlevel where radiative processes become quite
insignificant. The MSPDE is an exponential function of
the ionization potential Eo@) which in turn is inversely
proportional to p2.Hence, implicit in the equation, theexperimental and calculated curves showed unequal butcorrelated values except at the periphery (7 cm) whereslight dissimilarities are manifested (Figs. 4(a) and (b)).
This could be ascribed to some wall effects. At p valuesof 3 and 4 for 16 cunents 3 and 4.5 A respectively, slightdisagreements are seen. These differences are likely
caused by the presence of doubly excited metastable^70g60o5U.
ao..3ta) -".030

states of helitrm atoms (He.-) which decay throughthrough: He-. + He+(ls) + e. The probe detects He*(ls)ions but they are not captured in the MSPDE curves

UO

01234567

because of ttre built-in constraint that it is only
applicable to upper level He* ions. Experimental andcalculated curves show that ion concentration increases
steadily from the center reaching an optimum value, andthen gradually tapers off at the peripheral region of theplasma, where cold electrons are predominant. Theselow energy electrons with low thermal velocities have ahigher probability of being captured in therecombination process involving He** to form He*: He+++ 2e -+ He* + r:. Hence a higher concentration of He* isoIn- 2ooo.9

I 0000123

0ac.oi500
400+'1.5ASg too9c-200

2E+'11(b)UoFig. 4 (a) He* ion current profile in the sheet plasma as
detected by the ExB probe using the three plasma
discharge currents la= 1 .5A,3A and 4.5A. (b) Relative density profile of He* corresponding to thethree /o's calculated using the MSPDE of the CR
model. (lnset) He- density profile in the hot electron region i.e., from the center (plasma core) up
to 2cm away perpendicular to the sheet.

2E+11FC

Distance from core of sheet plasma (cm)E-94000got

Distance from core of sheet plasma (cm)o5000o(b) i 'g3000r 4.5A
06000

oI

A34EU.9

O 1.5A

6o-9

Distance from core of sheet plasma (cm)

86(a)_-_l-_ 4.5AEzo810

radiationless transition into ground state He+ ionsoo---9- 1.5A---*-34

1E+1'l;5E+1 0p-.A-3A---r--- 4.5A

100

Dstance from core of she€tplasnE(cm)0o2468Distance from core of sheet plasma (cm)Fig. 5 Relative densities of He* ions calculated using theMSPDE at large values of p (i.e., p = 10, 20 and 30
for /o= 1.5, 3 and 4.5 A respectively). The same
plasma parameters were used as in Fig. 4(b).

Fig. 3 Spatial configurations of electron (a) temperaturesand (b) densities of the sheet plasma at discharge
currents Id= 1.5, 3 and 4.5A.
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Blantocas G.Q. et al., A Computational Model for He* Ions in a Magnetized Sheet Plasma

a970
860

(a) -" ""r30

Ezo810necessary. In this region, the main formation mechanismof He* is through electron impact collisions: e + He ->---e---0cm

Nh?:;"" {}:..a,*:-:::5
regFn'io 0246oischargo current lo (A)-----g----- 1cm-----*----2cm}J.e' + 2e.In this particular region, higher discharges are---*-3cm----r(-4cm

essential to strip helium neutrals of their boundelectrons. This in turn translates to a modest increase in
He* yield. This assertion is further substantiated by thedensity curves in the hot electron region using the--4+5cm-----l- 6cm........_7cm

MSPDE (Fig. 6(b) and inset of Fig. 4(b)). The plot
supports the fact that indeed high discharges are needed;93

here to increase He* ion concentration.

----+- 1.5A----*-3A---]--4,qOt(b)a '?too04. Conclusions
The MSPDE is valid at very low discharge
currents, numerical calculations of the density curve(plot of Id= 1.5 A in Fig.4(b)), albeit crude, bear aE,o -lE.

plasma (cm)certain degree of correlation with the experimentallymeasured spatial distributions of He* ions (plot of 1o =1.5 A in Fig. 4(a)). This is actually the condition for aquiescent steady state sheet plasma at optimum He+Fig. 6 (a) He* yield as a function of the discharge current/0, the plots represent the position of the probewith respect to the plasma core. {b) Relative den-sity profile of He* ions in the hot electron region(0-2 cm away orthogonal to the plasma core) at
the same discharge currents. The plots were cal-extraction. Secondly, the MSPDE has also captured thehot electron region of the sheet plasma; there is strong
correspondence here between experimental observation

culated using the MSPDE.

(hot electron region of Fig. 6(a)) and numericalcalculations (Fig. 6(b)). Thirdly, MSPDE curves showthat the number density of He* ions is much smaller
than the number densities of free electrons and barenuclei He**; the predominance of He** species has been
experimentally demonstrated in ref. 3. Subsequently, atheory for He+ formation mechanism in the sheet plasma
was formulated. These findings have established the set
parameters as bases for future enhancement and beam
conversion of extracted He* from the sheet plasma
source. Modifications of the facility for this purpose aredensity of He* is a decreasing function of the quantum
level (p level) it occupies. He* ions produced at highplasma discharge currents are more energetic, thus theyoccupy relatively higher quantum levels than those

produced at lower discharges. The production of He'
from He** at high discharge currents proceeds at aslower rate. Hence, a much lower flux of He* ions isdetected at high discharge conditions. The relationshipbetween He+ yield and discharge current shown in Fig.
6(a) indicates a division of the sheet plasma system into
two distinct regions each with different formation
mechanisms of He* ions. In the region comprising cold(slow) electrons from 2to1cm, the production of He* isdone more effectively through low discharge currents. In
this region, the main formation mechanism of He+ ionsnow ongoing.

References[1] D.E. Post e/ al., Fusion Technol. 1, 355 (1987); M.
Sasao et al., ibid 10,236 (1986).

tzl Y. Abate and H. Ramos, Rev. Sci. Instrum.71,

is through the electron-ion recombination channel: He'*+ 2e -+ He* + e. On the other hand, the opposite applies
to the hot (fast) electron region, i.e., from the center up
to 2 cm away, it is seen that, to affect a significant

3689 (2000).

[3] G. Blantocas, H. Ramos and M. Wada, Rev. Sci.
Instrum. 73, 97 6 (2002).
[4] Huddlestone et al., Plasma Diagnostic Techniques,(Academic Press. New York. 1965).

increase in He* yield, high discharge currents are166