IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. PS-12, NO. 4, DECEMBER 1984
An Improvement of Secondary Emission Detector forEnergyAnalysis of Charge-Exchange Neutrals Emitted
from High-Temperature Plasma
KAORU OHYA
Abstract-Secondary emission detector (SED)' is improved for ion tem-perature measurement of high-temperature plasma by charge-exchangeneutral analysis. This improvement is based on the incident energy (E)dependency of the ratio of secondary electron yield for an incident angle0 to that for normal incidence, defined as k(0, E). The ratio k(0, E) isinvestigated as functions of E and 0 for hydrogen atom incidence. Toexamine and demonstrate the usefulness of the improved SED, both ex-perimental simulation and computer simulation of the charge-exchangeneutral analysis with the improved SED are used. In the experimentalsimulation, facsimile neutrals are produced by neutralization of an ionbeam on a solid surface and are analyzed by the improved SED. 'Theresult is compared with that obtained by using normal charge-strippingtype analyzer. In the computer simulation, a smnple model ofthe charge-exchange neutral emission of high-temperature hydrogen plasma isassumed and the usefulness of the improved SED as a hydrogen plasmadiagnostic technique is evaluated under the influences of strong plasmaradiation conditions.
I. INTRODUCTIONE NERGY analysis of the charge-exchange neutral flux in
Tokamaks and other plasma devices is a well establisheddiagnostic technique for measuring ion temperatures. Analysisof the neutrals is, however, not as easy as that of ions and elec-trons. In most cases the charge-exchange neutrals are ionizedthrough collisions with neutral gases in a charge-stripping celland are then analyzed with an electrostatic or magnetic analyzer.This analysis system, however, has various intractable problems.First, the stripping efficiency of the gas cell is largely depen-dent on the incident neutral energy. It produces a distortionin the energy distribution of the neutrals. Second, this typeof measuring system contains a large vacuum pump to preventgas molecules in the cell from flowing into the plasma andanalyzer regions which are kept under high vacuum. This leadsto complexity and requires a high-production and operationcost. Third, high energy tail of the charge-exchange neutralenergy distribution is important to determine the ion tempera-ture. In this process only a fraction of the neutrals enteringthe measuring system are involved. In addition, the efficiencyof the gas cell is less than of the order of 10-2. The number ofions detected after the energy analysis is, therefore, very smalland a multiplication function ion detector is necessary, for ex-ample a Channeltron and Dary.We proposed an application method of secondary electron
Manuscript received March 29, 1984; revised June 19, 1984.The author is with the Faculty of Engineering, Tokushima University,
Ninami-Josanjima, Tokushima, Japan.
emission to energy analysis ofkeV neutrals [1], [2]. Secondaryelectron emission from a metal surface is useful for the detec-tion of all the particles, especially neutrals, and this type ofparticle detector is known as "secondary emission detector"(SED). The number of secondary electrons emitted from themetal surface bombarded by neutrals, however, depends bothon the number of the incident neutrals and on their energy.It occurred to us to bombard the metal surface at two differ-ent angles of incidence with the same neutrals and measurethe ratio of the secondary electron current for an incident angle0 to that of normal incidence (0 = 0O), defined as K(0). Thenwe eliminated the effect of the quantity ofthe incident neutralsfrom the measurement of the secondary electrons and wereable to abstract the information on neutral energy. The mea-suring system required by our proposed method for energyanalysis of the neutrals is similar to the normal SED exceptthat the emitter electrode, which emits secondary electrons byneutral bombardment, is improved to be bombarded by theneutrals at two different angles and to measure each currentseparately. Thus the use of rotatable or separated emitters isnecessary. The above mentioned problems result to a greateror lesser degree from the use of the charge-stripping cell asthe neutral analyzer. It is significant that this system obviatesthe need for such use of the cell.This paper describes experimental and numerical investiga-
tions of the application and the adaption of our proposedenergy analysis method for kiloelectronvolt neutrals. Thismethod is discussed as to its application to analysis of charge-exchange neutrals from high-temperature plasma, especially toion temperature determination.
II. PRINCIPLE OF CHARGE-EXCHANGE NEUTRALDIAGNOSTICS WITH THE IMPROVED SED
The number of charge-exchange neutrals emitted with theenergy of E to E + dE, per unit time and unit plasma volume,is expressed as
N(E) dE = n0nifi(E) dEa. (E)M
(1)
where no and ni are the number densities of the remainingneutrals and the plasma ions, respectively, and mi is the ionmass, then vex (E) is the charge-exchange cross section. fi(E)is the plasma ion energy distribution. We think about themeasurement of the charge-exchange neutrals using the im-
OHYA: ANALYSIS OF NEUTRALS EMITTED FROM HIGH-TEMPERATURE PLASMA
proved SED mentioned above, with which we measure K(O)defined by the ratio of the secondary electron current Ie(G)for an incident angle 0 for an incident angle 0 to that for nor-mal incidence Ie (00). If the entrance aperture of the improvedSED subtends a solid angle dQ2 as seen from the plasma volumeV which it sees, the measured Ie(0) and Ie(00) can be writ-ten by
I(0) = eV -no ni J o(0,E) a" (E) fJ(E) dE
(2)
d92 2EIe(0o) eV- noni 7o(00, E) ae. (E) -if(E) dE
(3)
where 'y(0, E) is the secondary electron yield of the emitterin the improved SED bombarded by neutrals with the energyof E and the incident angle of 0, and 7yo(O0, E) is the yieldwith normal incidence. It is well known that the secondaryelectron yield depends not only on the incident particle energybut on the incident angle. We define k(f, E) with the ratio of'yo(0, E) to 7o(O', E), then for the asked K(0) we have
k(0,E) ¢)(E) dEK04
¢(E) dE
To
Cell
slitEmitter(Cu)
Collector
To PumpFig. 1. Schematic diagram of experimental apparatus for the investiga-
tion of k(O, E) of Cu with hydrogen atom incidence.
TABLE Ia(8), b(6) AND Eth (0) OF Cu FOR AR AND HE0 INCIDENCES AS A
FUNCTION OF INCIDENT ANGLE 0
Species of e a(W) b(6) Eth(e)incident neutrals (deg.) (keV- ) (keV)60 0.125 1.53 3.76
Ar070 0.0601 2.01 15.2
60 0.0882 1.53 5.34
He0 70 0.192 1.51 7.36
80 0.336 1.51 13.7
were incident on Cu. We approximately write k(0, E) with athreshold energy Eth (0) as a function of 0, as follows
where
¢(E) - 7o(0, E) aex (E)s fi(E). (7)
Equations (4) and (5) do not include both the remainingneutral density no and the plasma ion density ni.To obtain the relation between K(8) and the ion temperature
T, we assumed that the ion energy distribution fi(E) was Max-wellian. Then
K(0);k(0 ,E) 7o(00,E) urx (E)E exp (-E/kB Ti) dE
00 TO(Oo, E) ae. (E)E exp (-E/kB T1) dE
(6)The right-hand side of (6) is considered to be a function only ofTi for fixed 0 after the integration with E, if k(0 ,E), 70(00, E)and a,,, (E) are well known.
It is said that k(0, E) is almost equal to the value of sec 0and is independent on E for high energy region of more than afew hundred kiloelectronvolts or for small incident angle. We,however, found previously [1], [21 that k(0, E) linearly de-pended on E and no longer followed the sec 0 law for lowerenergy of less than a few tens of kiloelectronvolts and largerincident angles of more than 600 when Ar and He neutrals
Here, a(0) and b(0) are constants with given 0, which have dif-ferent values for different species of incident neutrals as shownin Table I. Table I was experimentally determined and also in-cluded Eth(0). Atomic hydrogen escapes with the charge-exchange process from hydrogen plasma, which was generallyproduced in the plasma experiments for nuclear fusion research.If k(0, E) depends on E also for hydrogenatom incidence withthe energy of several keV, it becomes possible to determinethe ion temperature Ti with the measured K(0) and (6) whichis inversely solved for T,.So we initially experimentally investigated k(0, E) for hy-
drogen atom incidence on Cu.
III. MEASUREMENT OF E- AND 8-DEPENDENCES OFk(0,E) FOR HYDROGEN ATOM INCIDENCE ON CU
Fig. 1 shows the experimental set up for the investigation ofk(0, E) of Cu with hydrogen atom incidence. A hydrogen ionbeam which was extracted from abeam plasma discharge (BPD)type ion source with the discharge room filled with hydrogengas, was introduced into a large vacuum chamber. In thechamber the hydrogen ion beam was mass-separated with amagnet, then only H+ was selected and was neutralized with anitrogen gas cell. The remainder of the ions not neutralized
255
I I
k(O . E) =
a(0)E + b (0), for E < Eth (0)(5) sec 0 for E> Eth (0)
IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. PS-12, NO. 4, DECEMBER 1984
3.0
2.5
w
. 2.0
1.5
1.0 I I I I
0 1 2 3 4 5 6E (keV)
Fig. 2. Dependence of k(o, E) on incident angle and incident energy
E of hydrogen atoms bombarding Cu surface. Solid lines representsec 0 law.
were excluded by electrostatic deflection plates and only thehydrogen atoms Ho entered into a small measuring chamber.The dependence of k(0, E) on the incident angle 0 and theenergy E of H0 was then investigated. The flux intensity ofH0 entering the measuring chamber was of the order of 108
CM-2atoms -s-cThe measuring system was composed ofthe rotatable emitter,
a cylindrical collector and a circular slit. The emitter was con-
nected to the earth through a picoammeter to measure second-ary electron current. And the rotation of the emitter causes
the incident angle of Ho to be adjusted. DC voltage of +50 Vwas supplied to the collector to collect the secondary electronsefficiently. The entrance aperture of the collector for H0 in-
cidence was 1 cm in diameter, in front of which the slit with3 mm in inner diameter was set and collimated the incidentH0. All of the electrodes were made of commercial gradecopper, and the emitter surface was polished with metal polishand was washed with acetone. The large chamber containingthe mass-separating system and the measuring chamber were
separately pumped from the BPD ion source by 1500 1/s and600 1/s oil diffusion pumps, respectively, with water-coolingbaffles, and liquid nitrogen cold traps. The background pres-sure in the measuring chamber was 1 X 10-6 torr; throughoutthe experiment the pressure was kept at about 10-6 torr.
Fig. 2 corresponds to the results of the E- and 0-dependencesof k(0, E) for several keV and 0 = 500, 600, 700, and 800.
The solid lines are theoretical values given the sec 0 law. Ex-
cept for a little dispersion of the experimental points, whichmay be caused by the measurement error of a very small cur-
rent (less than a few tens of picoamperes), the results approxi-mately show linear dependency on the incident energy E untilthe value of k(0, E) reaches that of the sec 0 law, as observed
TABLE IIa(6), b(6) AND Eh(O) OF CU FOR HYDROGEN ATOM INCIDENCE AS A FUNCTION
OF INCIDENT ANGLE 6
Species of a (0) b (9) Eth (e)incident neitrals (deg.) (keV-') (keV)
50 0.0873 1.22 3.81
60 0.0887 1.61 4.37H0
70 0.180 1.88 5.81
80 0.299 1.83 13.2
for Ar and He incidences. a(0), b(0), and Eth (0) in (7) are
determined as shown in Table II from such experiments.
IV. AN EXPERIMENTAL SIMULATION OF ENERGYANALYSIS OF CHARGE-EXCHANGE NEUTRALS
WITH THE IMPROVED SED
A. Production ofFacsimile Neutrals
In this section the proposed method is investigated experimen-tally. We planned to produce facsimile neutrals with wide en-
ergy distribution (i.e., Maxwellian) instead of charge-exchangeneutrals from high-temperature plasma. We analyzed them
with the proposed method, comparing it with that of a normalcharge-stripping type neutral analyzer. Then we investigatedthe experimental possibility of its practical use.
The facsimile neutrals require energies higher than severalkiloelectronvolts and the energy distribution broadens in a Max-
wellian manner. Now the following facts are well known: whenion beams with monochromatic energy bombard a solid surface,
a proportion of them are neutralized. The neutrals have a
slightly lower mean energy than the incident ions and the en-
ergy distribution is very wide. Although it is normally advis-able to use a proton beam as the incident ion beam to the solidsurface, ion beams of rare gas elements, i.e., Ar+ and He', wereused because the mass-separation of the extracted ion beamfrom the ion source was unnecessary. The result of our use ofrare gas beams facilitated counting of the neutrals.A schematic diagram of the scattering chamber used is shown
in Fig. 3. A monoenergetic ion beam was extracted from the
above-mentioned BPD ion source and was introduced into the
scattering chamber by ion transport electrodes. The ion beam
was collimated through a circular slit and bombarded a Cu tar-
get mounted at the center of the scattering chamber. The inner
diameter of the slit was of fairly large size (3 cm) because we
wished to obtain as many neutrals as possible. The bombardingion fluxes were of the order of 1013 atoms s-1 cm2 for He+and 1014 atoms s-1 cm-2 for Ar+. The incident angle of the
ion beam to the target was fixed at 67.50 as shown in Fig. 3.
The limiter with an aperture of 4 cm in diameter was set around
the target. He and Ar atoms neutralized on the Cu target are
emitted in various directions. Therefore the limiter also had
an aperture of 2 cm in diameter to allow the escape of the
neutrals emitted at the angle of -67.50 (Fig. 3). At the rear
of the aperture, deflection plates were mounted, excludingcharged particles emitted from the target, and only the neutrals
entered into the improved SED. The neutral flux enteringthe improved SED located 50 cm away from the target was of
the order of 109 atoms -s- cm-2 for He0 and 1010 atoms
ol
, sec70"
* 6=50° ,° -,,o
60° ,1* 70° , /'*O 80°,/ D ,
,° ,@
o
-
* -0
I., 'sec6O0
^A Asec50
,-
_,A
o
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OHYA: ANALYSIS OF NEUTRALS EMITTED FROM HIGH-TEMPERATURE PLASMA
those of the neutrals produced here. Sufficient quantitites are,however, produced for use in the simulated feasibility studyfor the proposed analysis method.
B. Analysis of the Facsimile Neutrals with the Improved SED
DeflectionPlates
.Neutrals
Fig. 3. Schematic diagram of scattering chamber used for the produc-tion of facsimile neutrals. The facsimile neutrals are produced withneutralizations of He+ and Ar+ on a Cu surface.
Ei -5keV
Eg 4.5keV
E =45keVnA......... ..
..... ......
Ei=2keV
Ei =25keV
Ei-7keV
E, G5keV1....... ..
...............
InA.[... ...6.
Ei=55keV..S.......
Ej-5keV..........................
Ei=4.5keV
I
0 1 2 3 4 5 0 1 2 3 4 5 6E (keV) E (keV)
(a) (b)Fig. 4. Energy distributions of the facsimile neutrals as a function ofthe incident ion energy Ei: (a) He, (b) Ar. These are measured with anormal charge-stripping type neutral analyzer. The ordinates corre-spond to the output current of ion detector in the analyzer.
s-i * cm-2 for Ar0 at the incident ion energy of several kilo-electronvolts which corresponded to the secondary electroncurrent of 0.1 nA to a few nanoamperes in the improved SED.These currents are sufficiently measurable with a picoammeter.The neutrals produced were analyzed with the normal neutral
analyzer before experiments with the improved SED. Fig. 4(a)and (b) represent the results for Heo and Aro, respectively.These are described as a function of the incident ion energy Eito the Cu target: Ei = 2.5, 3, 3.5, 4, 4.5, and 5 keV, respectively,for He, while Ei = 4.5, 5, 5.5, 6, 6.5, and 7 keV, respectively,for Ar. The normal neutral analyzer used consisted of a gascell, a parallel-plate type electrostatic ion energy analyzer anda scintillation type ion detector as adapted by Kimura et al.[3]. The energy resolution AE/E of the analyzer was 0.15.The ordinate axis in Fig. 4(a) and (b) corresponds to the detec-tor output current. For both cases (He and Ar) mean energiesof the neutrals are about 20 percent lower than the incidention energy, and the energy distribution, whose medians are
half as wide as the mean energies for maximum, becomes widermainly toward lower energy. On the other hand, for Max-wellian distribution approximating the charge-exchange neutralenergy distribution from high-temperature plasma, the medianis about as wide as the mean energy and the distribution has a
long high energy train. These are somewhat different from
In this case the energy distribution of the neutrals produceddoes not approximate to a Maxwellian curve and we cannot use(6) to determine ion temperature for a hypothetical plasma.We can, however, analyze the energy of the neutrals by using(4) (the source of (6)), (7), and a measuring value of K(O) fora fixed 0, then compare it with the results ofthe normal neutralanalyzer process (Fig. 4(a) and (b)). The method of energyanalysis for neutrals was described in [1], in which the de-scriptions were partially inaccurate.
If energy distribution of neutrals is assumed as ; (E), thequantity ¢(E) in (4) of this paper or in (3) of [1] is equal notto (E) as described in [1] but to (E) multiplied by yo(00,E) and a square root of E, i.e.,
¢(E)-- yo(O0 E) W (E). (8)
Substituting (7) into (4) as described in [1 , we have
rEth ()fE| 4(E) dE
K(0) a(0)E b(0)- X + sec 041(E)dE
41(E) dE
c( (9)
f,( ¢(E) dE
where
fEth ()
EO(E) dE
(10)E=I 7(E)dE
If 41(E) has no energy component of more than Eth (0), thethird term in the right-hand side of (9) disappears and thesecond term is simplified, thus as we have seen in [11
E = (K(0) - b(0))/a(0) (11)
is obtained. This is a simple description and is important forthe energy analysis of neutrals with the improved SED. Wecan easily determine a "mean energy" E of neutrals using con-stant values of a(0) and b(O) in Tables I and II together withK(0) measured with the improved SED for a fixed 0. The"mean energy" E obtained here, however, does not correspondto real mean energy (E) defined as an average value of E forthe energy distribution function (E)
To Pump
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. PS-12, NO. 4, DECEMBER 1984
3-
2-
1
4,e
1W
5
4
3
2
He T
.Ii
82
0 1 2 3 4 5 6 7E; (keV)
(a)
Ar i
i, I
0 1 2 3 4 5 6 7Ei(ieV)
(b)Fig. 5. "Mean energies" E of the facsimile neutrals determined withthe improved SED (error bars: I), as a function of the incident ionenergy Ei. Circle points and triangle points correspond to E and realmean energies (E) obtained with averages of Fig. 4 using (10) and(12), respectively. Dashed straight lines show paths of energies equalto the incident ion energy (E = Ei): (a) He, (b) Ar.
co
EOE(E)dE
(F)- (12)
(E)dE
and E gives another average value ofE for 4(E) (Eyo(00, E)X;if4(E)). As the secondary electron yield yo(O0, E) increaseswith the rise of the incident energy E for less than a few hun-dred kiloelectronvolts, it is found that is larger than (E) forthis energy range.
In our case the energy of sample neutrals depends on, and isobviously less than the energy of the ions bombarding the Cutarget. In Fig. 4(a) and (b) the maximum energy of the bom-barding ions is 7 keV. When we, therefore, choose 700 or 800as 0 from Table I, we can estimate the "mean energy" F ofthe neutrals with measured K(0). Then the "mean energy" Eof the neutrals produced by the neutralization of He' and Ar+on the Cu surface was determined with a(0) and b(O) repre-
sented at 0 = 800 for He and 0 = 700 for Ar.For this experiment we used the same type of improved SED
as that used in the determinations of a(0) and b(6), whichconsisted of the ratatable emitter, the positive biased collector,and the earthed slit. The results are shown in Fig. 5(a) and (b)as a function of the ion energy Ei bombarding the Cu target.The data are shown by error bars which represent the range offive or more experiments, considering the setting errors of theincident angles and the changes of the secondary electron cur-
rents themselves. The measurements with 0 = 70° for He and0 = 600 for AR were also carried out and all of the results fell
within the error bars in these figures. The dashed straight linesdescribe the path of energy equal to the incident ion energy.
For comparison of the results with those of normal neutral
analyzer, the energy distributions of Fig. 4(a) and (b) were
averaged by the numerical integrations of two different equa-
tions, i.e., (10) and (12). Here, Fig. 4(a) and (b) must be cor-
rected to allow for the characteristic of the normal neutralanalyzer. The complications caused by the stripping gas cellwere described in Section I. The characteristic of the normalneutral analyzer were measured using neutral beams. Thesewere produced with the neutralization of the ion beam in a gas
cell and had the energy spread of less than 100 eV. The nor-
mal secondary electron yield yo(0, E), which was also neces-
sary to evaluate (10), was assumed as follows: It was equal,whether the impinging atom was neutral or ionized, becausefor ions with energy of several hundred electronvolts or higherthe dominating mechanism of secondary electron emission was
not Auger neutralization but the kinetic process that was
similarly applied to neutrals. So, 'y(O0, E) for ions [41, [5]was used instead of yo (00, E) for neutrals.We have drawn the final results of the "mean energy" E and
the real mean energy (E) calculated with the above mentionedassumptions also in Fig. 5(a) and (b) as a function of the in-cident ion energy El; circle points and triangle points corre-
spond to and (E), respectively. In the figures the values ofE are roughly 10 percent larger than those of (E). Now, theenergy-difference of E from (E) depends on the energy widthof the distribution function of the neutrals. Then it was esti-mated with the assumption of ideal rectangular distributionfunction of any width. And it was found that the correlativedifference divided by (E) increased as the distribution functionwas broadened, but it approached the value of 43 percent andnever exceeded it.In Fig. 5(a) and (b) the measured "mean energies" of surface-
neutralized atoms with the improved SED (I) seem to be a
little larger than the calculated ones from Fig. 4(a) and (b)obtained with the normal neutral analyzer. We cannot, how-ever, say whether results from the improved SED or the nor-
mal neutral analyzer have major errors, but we can say thatthe improved SED allows easy estimation of the mean energyof neutrals with unknown energy distribution within errors
of 50 percent.
V. A COMPUTER SIMULATION OF ENERGY ANALYSISOF CHARGE-EXCHANGE NEUTRALS WITH THE
IMPROVED SED
A. A Simple Modelfor the Computer Simulation
The derivation process of (6) in Section II, which gave the
relation of K(O) measured with the improved SED to the ion
temperature of the high-temperature plasma, was greatlysimplified. This was in order to easily illustrate the proposedmethod. We aim to consider here some complicated and im-
portant problems in real high-temperature plasma experiments.The first problem concerns radial variations of plasma param-
IThese were normalized by y0(0°, E) for contaminated surfaces bom-barded by less than 1 keV in [61, because the Cu emitter used was notatomically clean as used in [41 and [51 but was contaminated asin 161l.
258
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(
LI I
OHYA: ANALYSIS OF NEUTRALS EMITTED FROM HIGH-TEMPERATURE PLASMA
eters. The second concerns that the neutral density receivingthe charge-exchange collision in the plasma center is ratherlower than that near the plasma edge. These radial variationsof the plasma parameters and the neutral density lead to dis-tortions of the energy distribution shape of the escaped charge-exchange neutrals.
In order to understand effects of the problems connectedwith the improved SED, it is necessary to understand thetransport of the neutral gas and the emission of the charge-exchange neutrals in nonuniform high-temperature plasmas.Several authors [7] - [11] have thoroughly investigated thembecause they have been important also from the view pointsof energy loss and balance of the plasma. In our investigationwe assumed a simple model. We did not address the questionsof the recharge-exchange effect of the charge-exchange neu-trals back into ions in the plasma. In our model hydrogenatoms (H0), the source of which was the outside of the plasma,were considered as background neutrals acting on the charge-exchange reaction in hydrogen plasma. The charge-exchangeneutrals (H1) are produced by their collisions with the plasmaions when they diffuse from the plasma edge to the plasmacenter. On the other hand, a proportion ofthe hydrogen atomsare lost at the diffusion due mainly to the following three re-actions. The first is their ionization by plasma electrons: H0 +e -* H + 2 e. The second is their ionization by plasma ions:H0 + H+ -+ 2H+ + e. The last is their charge-exchange withplasma ions, in which we are interested: H0 + H -+ Hi + H0 .
Only these processes could be applicated to a cylindricalplasma.Let us assume now that the improved SED is perpendicularly
seeing a portion of a cylindrically symmetrical plasma columnwith a radius of a; radial position r is measured from the centeraxis to the outer region, i.e., r = 0 implies the plasma center,and r = a the plasma surface. Also assume ne, i(r) and Te, i(r)to be the electron and the ion density and temperature profiles,respectively. The charge-exchange neutral fluxwiththe energyof E to E + dA, entering the improved SED with the entranceaperture of the unit area, is approximated by
r(E) dE =- tf - no(r)nj(r)Ij(r,E)dE(uexvi)dr (13)
where no(r) is the hydrogen atom density profile penetratingthe plasma, fi(r, E) the local ion energy distribution functionassumed as of Maxwellian distribution; (a, vi) is the rate coef-ficient for charge-exchange obtained by averaging over the dis-tribution function (the Maxwellian curve) of the interactingpopulations. Space isotropy of the velocity is assumed also forthe charge-exchange neutrals and is represented as a factor of4 . An addition of rla means that the surface area passed throughby the neutrals increases with the increase of r in the plasmacolumn which stretches infinitely; the charge-exchange neutralflux per unit area decreases with the increase of the surfacearea. We only considered it as the differences between cylindri-cal and slab geometries in the present study.Now, the hydrogen atom density profile no(r) contained by
(13) is established as the above-mentioned processes of partialdiffusion reach a dynamically steady state with the plasma
density and temperature profiles typically peaked in theplasma center, and it is well approximated by
r2 Vn(()
+ ( nii1i)(r') + (ax inKr)) drj .
Un Un(14)
Here, no(a) is the atom density assumed only as a source ofthe hydrogen atoms at the outside of the plasma, and vn istheir velocity considered as a constant value. (aie,v) and(aiivi) are the rate coefficients for the ionizations of the atomsby plasma electrons and ions, respectively.Both the output current (secondary electron current) Ie (0)
for an incident angle 0 and its ratio K(0) to that for normalincidence, measured with the improved SED with an entranceaperture of the unit area, are expressed with 17(E) dE in (13)as follows
(15)Ie(0) = e k(0, E) yo(O0, E) 17(E) dE
k(0, E) y0(00, E) r(E) dEK(0) ='e(0_Ie( 0) =J
0 (16)'yo(O, E) r(E) dE
Ie(0) with (15) is the output current assuming improved SEDto be set at the plasma surface (r = a), and that the current tobe measured with actual experiments decreases in inverse pro-portion to the position of the improved SED (r> a).We simulated the analysis of the charge-exchange neutrals
from high-temperature plasma with the improved SED, using(13), (14), (15). and (16), which were numerically solved byassuming the profiles of the plasma parameters as follows:
n (r) = ni(r) = te(0)(1n
T1(r) = Ti(0) ( _-n Te(r) = 2 Ti(r). (17)
n was 1, 2, or 4. These profiles were named as r-, r2-, or r-distribution inhomogeneities, respectively, assuming a = 100cm and ne(0) = 1014 cm-3 . The source of the hydrogen atomsat r = a was also assumed to have an energy of 3 eV (=mvA/2)and a density of 4 X 109 cm-3 [11]. Riviere [12] has sum-marized the cross section data ofhydrogen atoms for the charge-exchange and the ionizations by electrons and ions, and haspresented formulas which has fitted the experimental data well.We quoted them for the calculations of (13) and (14). Thevalues shown in Table II for k(G, E)and the data in [13], [14],and [15] for Pyo(00, E) ('y+(00, E) in E>5 keV) were alsoused with the Cu emitter.
.
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. PS-12, NO. 4, DECEMBER 1984
10
a)
g-
0.1
1 2 3 4 5 6K(o)
Fig. 6. Relation between the ion temperature Ti ofhomogeneous hydro-gen plasma and K(e) measured with the improved SED, as a functionof 0.
B. Numerical Analysis of the Improved SED MeasuningCharge-Exchange NeutralsThe output current of improved SED was numerically in-
vestigated with the simple model of the charge-exchangeneutral emission from high-temperature plasma, mentionedin the last section. Firstly the relation between K(O) mea-sured by the improved SED and the ion temperature of theplasma were discussed. Fig. 6 shows this relation for homoge-neous plasma as a function of 0, in which the plasma parametersare held constant with the radial variation. As was expectedwith the E- and 0-dependences of k(0, E) the variation ofK(0) with the ion temperature Ti becomes remarkable forlarge 0 and keV-energy ranges. This limits measurable lowtemperature to about 500 eV with the improved SED. On theother hand, the E-dependence of K(0) remains for higher iontemperature than Eth (0) (at greater energy than this k(0, E)is constant) though it levels off slightly because the charge-exchange neutrals have a wide energy distribution near theMaxwellian type. This raises upper limit of measurable tem-perature with the improved SED. Where the plasma parametersare radially inhomogeneous, K(0) is related to ion temperaturesat every position of neutral generation by (13) and (16). Fig. 7shows local ion temperature Ti corresponding to the same valueof K(0) as that calculated in inhomogeneous plasma as a func-tion of maximum ion temperature T7(0) occuring at r = 0, forinhomogeneities of r, r2, and r4 (17). From this figure it isfound that the ion temperature of the local plasma approxi-mately overviewed by the improved SED is 1 I as high asthe maximum ion temperature. Thus it corresponds to thatof the radial position of r = 0.93 a 0.98a, very close to theplasma surface. So we claim that the improved SED gives aninformation on peripheral plasma and does not directly showmaximum ion temperature occuring at the plasma center. Thisis significant since most charge-exchange neutrals are generatedfrom peripheral plasma. On the other hand, the normal charge-stripping type neutral analyzer can measure the central iontemperature by sampling a very few neutrals generated nearthe plasma center. The simplicity of the method obviates theuse of the improved SED, but its use for both the measured
0.1
1 10 100Ti(0) (keV)
Fig. 7. Local ion temperature Ti corresponding to the same value ofK(O) as that obtained for inhomogeneous hydrogen plasma, as a func-tion of the central ion temperature Ti(O). The results are representedby those for radial inhomogeneities of r, r2, and r4.
-
0
1 2 3 4 5K(80°)
Fig. 8. Relation between the central ion temperature Ti(0) and K(0)measured with the improved SED for radial inhomogeneities of r,r2, and r4 of hydrogen plasma. K(0) is represented by K(80).
K(0) and the computer simulation results may be possible ifthe radial variations of the plasma parameters are either knownor assumed.The relation between the central ion temperature Ti(O) and
K(8), expected from the computer simulation with our simplemodel, is shown in Fig. 8 for r-, r2- and r4 -inhomogeneities;K(0) is represented by K(80°). The expected Ti(O) is differ-ent in all cases with the assumed radial inhomogeneity of theplasma parameters. Plasma produced experimentally by manylarge Tokamak devices has a radial inhomogeneity factor whichcan be expected as r2- or r4-inhomogeneity. From Fig. 8,therefore, it is expected that the estimation error of the centralion temperature with the improved SED due to the differenceof inhomogeneities of the plasma parameters is less than 30percent, and basically a measurement accuracy of a factor of2 is guaranteed even if r-inhomogeneity is also considered to-
gether with r2- and r4-inhomogeneities.The expected Ti(O) does not depend on the density no(a) of
260
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OHYA: ANALYSIS OF NEUTRALS EMITTED FROM HIGH-TEMPERATURE PLASMA
us
1 10 100
Ti (0) (keV)Fig. 9. Variation of the secondary electron current Ise in the improvedSED with the central ion temperature Ti(O) of inhomogeneous hydro-gen plasma, as a function of radial inhomogeneity. The improved SEDhas an entrance aperture of the unit area and is set at the plasma sur-face (r = a).
the hydrogen atoms because no(a) was eliminated from (16)by substitutions of (13) and (14). It depends, however, on theenergy (=mv'/2) of the atoms as found in (14). It has beensaid that the hydrogen atoms at the outside of the plasma havebeen almost all generated with Franck-Condon dissociation ofmolecular hydrogens. The Franck-Condon dissociation occursonly for a particular molecular energy, so the energy of hydro-gen atoms thus generated is determined only by the specialenergy which we assumed as 3 eV in our study.Recently a method has been proposed and examined for local
ion temperature measurement by a charge-exchange processof intense high energy neutral beams injected toward a smallportion on the plasma [161, [17]. This method makes itpossible to determine the local ion temperature with the im-proved SED because the difference of its output current forneutral beam injection from that for noninjection is due to thecharge-exchange neutrals produced in the portion seen by theneutral beam. With this active diagnostic technique, therefore,we may obtain the central ion temperature Ti(0) without anyassumptions.Next, the output current (i.e., the secondary electron current)
for normal incidence Ie(00), renamed as ISe, with the improvedSED which had an entrance aperture of the unit area and wasset at the plasma surface (r = a), was investigated numericallyas a function of the central ion temperature in the inhomo-geneous plasma. The results are shown in Fig. 9 for the inho-mogeneities of r, r2, and r4. The secondary electron currentI,, increases with the rise of the central ion temperature Ti(0),for exarnple it is about 0.1 mA for Ti(O) = 5 keV. Generally,in large devices such as Tokamaks, diagnostic tools are consider-ably separated from the produced plasma by numerous largemagnetic coils, e.g., toroidal field coils, vertical field coils, etc.These surround a torus vacuum chamber to control the plasma.The charge-exchange neutrals entering the improved SED,therefore, diverge and consequently decrease in quantity. The
secondary electron current, however, still remains larger than10 ,uA and is large enough to measure by means of direct mea-surement without any electron multipliers, even ifthe improvedSED was located 4 m away from the plasma center. On theother hand, the improved SED is so compact that it may beset in narrow gaps between the large magnetic coils and beclose to the vacuum chamber. In this case the secondary elec-tron current is expected not to be much smaller than Ise inFig. 9.
C. Influences ofStrongRadiations ofHigh-TemperaturePlasma on the Improved SEDA very important problem is still to be discussed for practical
use of the improved SED for charge-exchange neutral analysis.This is the effects of strong lights radiated from high-tempera-ture plasma onto it. Its emitter, which faces the plasma tomeasure the quantity of charge-exchange neutrals, is directlyirradiated by these lights and emits many photoelectrons. Thenthe output current of the improved SED is not only the second-ary electron current with charge-exchange neutral bombard-ment, but is the sum of it and the photoelectron current withthe plasma light irradiation. To make the current measurablewith the improved SED, therefore, it is necessary either toknow the rate of the secondary electron current in relation tothe total output current or to be able to ignore the photo-electron current measured with the improved SED and to com-pare it with the secondary electron current in this study.Various mechanisms of ion-electron interactions contribute
to photo-radiation of high-temperature plasma. Two radiationswith continuous spectrums, i.e., Bremsstrahlung of electronsand recombinative radiation of ions, are relevant here. Theradiation intensity of the recombinative radiation is so muchsmaller than that of the Bremsstrahlung to be ignored for purehydrogen plasma with the temperature of more than severaltens of electronvolts. We, therefore, considered only theBremsstrahlung in our numerical investigation.The radiation energy of the Bremsstrahlung per unit wave-
length, per unit time and per unit volume of the plasma isknown to be expressed for hydrogen plasma as follows
dE1.9 X 10-2 8neni exp [- 12398/(XkB Te)] (18)
dX (kBTe)l/2X2where kB Te is the electron temperature in electronvolts and theunit of dEBIdX is W. cm-3 - A-1. The photoelectron currentmeasured with the improved SED with an entrance aperture ofthe unit area set at the plasma surface is named Iph. This valuecan be obtained with dEBId;X by
~a 00
dEB eX rIph dr d QdX -- (19)Pj0j0 ~dX hc a
for cylindrical geometry. Here, Q is the quantum efficiencyof the photoelectron emission as a function of wavelength X,which also depends on the emitter material.According to (18) and (19) the photoelectron current Iph
was evaluated in the case ofinhomogeneous plasha with plasmaparameters depending on radial position r as r4. The result isshown in Fig. 10 as a function of the central ion temperature
261
IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. PS-12, NO. 4, DECEMBER 1984
1 10 100Ti(O) (keV)
Fig. 10. Photoelectron current 'ph, secondary electron current ISe, andthe ratio of Iph to Ise in the improved SED, as a function of the cen-tral ion temperature Ti(O) of inhomogeneous hydrogen plasma. Theradial inhomogeneity is represented by r4-dependency.
Ti(O) (= Te (0)/2), where smoothly-connected values of [18],[19], and [20] were used for the quantum efficiency Q in(19). In this figure the secondary electron current Ise calculatedin the last section (Fig. 9) and the ratio of Iph to Ise are alsoshown together. The photoelectron current Iph decreases withthe rise of the plasma temperature for this variation range. Thisis caused by the decrease of the vacuum-ultraviolet-frequencycomponent with quantum efficiency Q for the photoelectronemission at maximum. This causes the frequency shift of theBremsstrahlung spectrum to higher frequency regions, i.e.,X-rays. On the other hand the secondary electron currents Iseincrease with the rise of Ti(0). So finally the ratio IphlIserapidly decreases with the rise of the plasma temperature. Itis, for example, about 0.06 for T,(0) = 5 keV(Te(0) = IOkeV),which implies that the photo effect on the improved SED isnegligible for ion temperature measurements of pure hydrogenplasma of more than several kiloelectronvolts.High-temperature hydrogen plasmas produced now are not
perfectly pure and to a greater or lesser degree contain impuritiesdue to the plasma-wall interaction. Thus the total intensitiesof their recombinative radiations have reached approximatelytwenty times as large as that of the Bremsstrahlung in some de-vices which has radiated most. For such devices the improvedSED may be difficult to use. So, we propose an additionaladaption of the improved SED for these cases in order toestimate the rate of the photoelectron current to its outputcurrent. It requires either an additional experiment of placinga metallic foil in front of it or an adjacent apparatus of an
identical SED with a metallic foil. The metallic foil is chosento be of the correct thickness to be transparent to radiation ofvacuum-ultraviolet from close range whilst stopping most ofthe charge-exchange neutrals. Then the output current isalmost reduced to the level of the photoelectron current. Ifthe transmission efficiency of the chosen foil is well known,we shall be able to evaluate the photoelectron current with-out foil.
TABLE IIISECONDARY ELECTRON CURRENT I,e AND PHOTOELECTRON CURRENT Iph INTHE IMPROVED SED WITH Be FOIL IN FRONT OF IT, AS FUNCTIONS OF THECENTRAL ION TEMPERATURE T(0) OF THE PLASMA AND THE FOIL THICKNESS
T. (0) Thickness of Be I Iph1 se p(keV) (mg/cm ) (A/cm ) (A/cm
0.1 6.47X10 9 1.69x10-60.3 1.27X 10'1 5.63X 10-7
1 1.0 1.9910 24 3.89X 10-7
3.0 7.12 x lo 5 2.11 X 10-7
10.0 - 8.96x10 8
0.1 9.81 x 10o 1.63x 10o60.3 1.60x l 11 6.44x 10-7
0.1 3.42 x 10-5 7.80 x 10-70.3 7.381x107 3.96X 10-7
20 1.0 7.82X 10l11 3.22x10-73.0 8.32x10o19 2.38X 10-710.0 5.30 x 10o43 1.64 x 107
0.1 1.43 x 10-4 5.22 x10-70.3 8.201x106 2.75 10-7
50 1.0 5.70x10 9 2.28X10-7
3.0 2.44 x 1016 1.73 x 10o'10.0 2.43 x 1040 1.24 x 10 7
For the sake of an examination of this proposal, we calculatedboth secondary electron current Ise and photoelectron current'ph to be measured by the improved SED with Be foils of vari-ous thickness. The data in [21] were used as the absorptioncoefficient of the Be foil for radiation. Then the decrease ofthe neutrals due to the foil was calculated with an equation ofthe stopping power of protons in Be obtained by Lindhardet al. [22]. The results are shown in Table III as functionsboth of the thickness of the foil and of the central ion tem-
perature of the plasma. With the increase of the Be foil thick-ness the secondary electron current Ise decreases rapidly whilethe photoelectron current 'Ih decreases only gradually. Thisfact may prove the practical utility of our proposal. The ap-propriate foil thickness at which Ise to 'ph becomes negligible,slightly increases with the rise of the ion temperature of theplasma. The photoelectron current I'h, however, remainsseveral hundred nanoampere per square centimeter even if the
thickness is 10 mg/cm2, and is large enough to directly measurewithout any electron multiplier systems.Now, the measurement of the radiation intensity of high-
temperature plasma is important from a viewpoint of its purityand is indispensable for identification and quantification ofcontained impurity. We can thus borrow its data to evaluate
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OHYA: ANALYSIS OF NEUTRALS EMITTED PROM HIGH-TEMPERATURE PLASMA
the rate of the photoelectron current to the total output cur-rent of the improved SED, instead ofusing the above-mentionedproposal. On the other hand, higher levels of plasma purityhave become necessary largely due to the production of higherplasma temperatures than before. In future, therefore, therecombinative radiations together with the impurities willconsiderably decrease and only the Bremsstrahlung will be-come important.
VI. CONCLUDING REMARKSThe adaption and the application of the secondary emission
detector (SED) for the ion temperature measurement of high-temperature plasma by charge-exchange neutral analysis, wereinvestigated both experimentally and numerically. In the ex-perimental investigation, first k(O, E) was investigated as func-tions both of the incident neutral energy E and of the incidentangle 0 for hydrogen atom incidence. Here, k(0, El was de-fined by the ratio of the secondary electron yield for an inci-dent angle 0 to that for normal incidence, based on the proposedsimple method with SED for the energy analysis of the charge-exchange neutrals. Then it was found that k(0, E) for Cubombarded by hydrogen atoms showed linear dependenceon the incident energy E both for several keV and for largeangles as observed in Ar incidence and He incidence [1], [2],and it was possible to apply k(0, E) to energy analysis of thehydrogen atoms. Second, a simulated experiment ofthe charge-exchange neutral analysis with the improved SED was carriedout, in which the facsimile neutrals were produced by theneutralization of an ion beam on a Cu surface. The resultwas compared with that obtained with a normal charge-strip-ping type neutral analyzer and approximately agreed with it.In the numerical investigation a computer simulation was
carried out for the sake of the discussion of problems in prac-tical use of the improved SED to the ion temperature measure-ment of high-temperature plasma. In this calculation we usedsimple models of the charge-exchange neutral emission ofhydrogen plasma and its vacuum-ultraviolet radiation; the lat-ter produced photoelectrons on the emitter electrode of theimproved SED and was considered as the most important noisecreated in the improved SED. As a result, it was found that;
1) The ion temperature directly determined by the improvedSED is that which is found near the plasma edge and isff as high as that at the plasma center. The lower and upperlimits of measurable temperature are 500 eV and a few tensof kiloelectronvolts, respectively. It is, however, possible toestimate the central ion temperature with accuracy of betterthan a factor of 2, with no clear knowledge of the spatial vari-ation of the ion temperature in the plasma. We can, of course,accurately determine the central ion temperature with addi-tional computer simulation if the spatial variations of theplasma parameters are well known.
2) The influence of Bremsstrahlung of high-temperatureplasma on the improved SED can be ignored for hydrogenplasma with a temperature of more than several kiloelectron-volts, for which the secondary electron current is large enoughto directly measure without using electron multiplier such as aChanneltron or Dary. Recombinative radiations with impuritiescontained in the plasma are important for recently producedhigh-temperature plasma and their influences on the improvedSED cannot be ignored in some cases. In these cases we have aproposal for its exclusion from the output current of the im-proved SED using a metallic foil. On future plasmas for thermo-nuclear fusion, however, it is expected that the contained im-purities will considerably decrease and their influences on theimproved SED will become unimportant.
ACKNOWLEDGMENT
The author would like to thank Prof. H. It6 and Prof. T.Ishimura of the Plasma Physics Laboratory of Osaka Universityfor helpful discussions and criticisms in this work. Thanksare also due to Prof. I. Mori of Technical College ofTokushimaUniversity for his continued encouragement.
REFERENCES
[1] K. Ohya and I. Mori, Japan J. Appi. Phys., vol. 19, p. L281,1980.
[2] -, Japan J. Appl. Phys., vol. 19, p. 2027, 1980.(31 T. Kimura and H. Akimune, Japan. J. Appl. Phys., vol. 17, p.
2129, 1978.[4] R. A. Baragiola, E. V. Alonso, and A. 0. Florio, Phys. Rev. B,
vol. 19, p. 121, 1979.[5] G. D. Magnuson and C. E. Carlston,Phys. Rev., vol. 129, p. 2403,
1963.[61 A Rostagni, Z. Phys., vol. 88, pp. 55, 1934.[7] Y. N. Dnestrovskij, D. P. Kostomarov, and N. L. Pavlova, MATT-
TRS, p. 107, 1971.[81 S. Rehker and H. Wobing, Plasma Phys., vol. 15, p. 1083, 1973.[9] M.H.HugesandD.E.Post,J. Compt. Phys., vol. 28,p.43, 1978.
[101 H. Yip, S. Yano, and H. Nishihara, in Proc. Int. Conf: PlasmaPhysics, vol. 1, p. 351, 1980.
[11] K. Murase, Japan. J. Appl. Phys., vol. 21, p. 109, 1982.[12] A. C. Riviere, Nucl. Fusion, vol. 11, p. 363, 1971.[131 N. Noda, J. Phys. Soc. Japan, vol. 41, p. 625, 1976.[14] N. Campbell, Philos. Mag., vol. 29, p. 783, 1915.[15] A. G. Hill, W. W. Buechner, J. S. Clark, and J. B. Fisk, Phys. Rev.,
vol. 55, p. 463, 1939.[16] V. V. Afrosimov, M. P. Petrov, and V. A. Sadovnikov, JETPLett.,
vol. 18, p. 300, 1973; A. M. Kudryavtsev and A. F. Sorokin,JETPLett., vol. 18, p. 286, 1973.
[17] M. Brusati, S. Davis, H. P. Eubank, P. Moriette, and R. Smith,Bull. Amer. Phys. Soc., vol. 22, p. 1076, 1977.
[181 R. B. Cairns and J. A. R. Samson, J. Opt. Soc. Amer., vol. 56,p. 1568, 1966.
[19] A. M. Tyutikov and Y. A. Shuba, Opt. and Spectrosc., vol. 9, p.332, 1960.
[20] A. P. Lukirskii, M. A. Rumsch, and I. A. Karpovich, Opt. andSpectrose., vol. 9, p. 343, 1960; A. P. Lukirskii, M. A. Rumschand L. A. Smirnov, Opt. Spectrosc., vol. 9, p. 265, 1960.
[211 R. H. Huddlestone and S. L. Leonard, Ed., Plasma DiagnosticTechniques. New York: Academic, 1968, ch. 8, p. 369.
[22] J. Linhard and M. Scharff, Phys. Rev., vol. 124, p. 128, 1961.
