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Charge exchange collisions of deuterium in a rubidium vapor target
NUCLEAR
INSTRUMENTS
AND
METHODS
143 ( 1 9 7 7 )
505-511
• ©
NORTH-HOLLAND
PUBLISHING
CO.
CHARGE EXCHANGE COLLISIONS OF D E U T E R I U M IN A R U B I D I U M VAPOR TARGET* R. J. GIRNIUS, L. W. A N D E R S O N and E. STAAB
Dept. o/ Physics, University of Wisconsin, Madison, Wisconsin 53706, U.S.A. Received 14 February 1977 The equilibrium fraction of D- ions formed when D + ions are incident on a Rb ergies of the incident ion in the range 1.1-40 keV. The equilibrium fraction of Dwhen D + ions with an energy of 1.1 keV are incident. The equilibrium fraction ion increases in the energy range of 1.1-40keV. The charge transfer D + + R b - - , D ° + R b + is also reported. The cross section is 1.14 x 10-14 cm 2 when 1.5 keV, and the cross section falls rapidly with increasing energy reaching the
1. Introduction The formation of high intensity H - or D - ion beams has long been of interest for injection into tandem accelerators or cyclotrons. Recently the interest in the formation of D - ion beams has expanded to the controlled thermonuclear reaction program, where the injection of fast D O atoms has been proposed for heating plasmas. The fast D O beam could be formed by producing low energy D - ions, accelerating these D - ions to a high energy, and then stripping the D - ions of an electron. Two methods exist for producing H - or D ions: (1) the direct extraction from an ion source, and (2) charge exchange collisions with H ÷ or D ÷ incident on a target that has a high equilibrium fraction for D - . Targets containing an alkali metal vapor have large H - or D - equilibrium fractions. The H - or D - equilibrium fraction for H ÷ or D ÷ ions incident on Cs (refs. 1-7), K (refs. 2 and 3), Na (refs. 3 and 8) and Li (refs. 3 and 8) has been reported previously. In this paper, we report the first measurements of the D - equilibrium fraction for D ÷ ions incident on Rb vapor. In addition we have remeasured the D - equilibrium fraction for D ÷ incident on Cs vapor. In addition to the measurement of the equilibrium fraction of D - ions when D ÷ is incident on a Rb target we have measured the electron capture cross section, a÷0, for the reaction D ÷ + Rb--,D O+ Rb+. This cross section is very large because the reaction is nearly resonant for the production of D O atoms in one of the n = 2 states. Our measurements of the cross section a+0 for D ÷ incident on Rb provides support for
vapor target has been measured for enions emerging from a Rb target is 19% decreases as the energy of the incident cross section a+0 for the reaction the incident D + ion has an energy of value 9.4 x 10-16 cm 2 at 40 keV.
Olson's theoretical model 9,1°) for near resonant charge exchange collisions.
2. Apparatus 2.1. GENERAL DESCRIPTION The apparatus used in this experiment is shown in fig. 1. It has been described previously. The apparatus consists of three parts: the ion source, the charge exchange target, and the detector chamber. A D ÷ ion beam is extracted from a duoplasmatron ion source accelerated to the desired energy, m o m e n t u m analyzed, and collimated. The ions enter the charge exchange target, where D O atoms D÷ ION BEAM
COLLIMATING f APERTURES f,jDIFFUSION PUMP SWEEP MAGNET
"
CESIUM TARGET ...._,U
I1
II jDEFINING CHARGEMAGNETANALYN Z[~/ lG APERTURE PV I OT D .F I FUSO I NPUMP MOVABLE WIRE SCANNER WIRE
=,FARADAY CUPS -NEUTRAL DETECTOR
,50 c m
* This research is supported AT(11-1) Gen.-7.
in part by ERDA
Contract
L_.= I~
~I "-I
Fig. 1. Schematic diagram of apparatus.
506
R.J.
GIRNIUS
and D - ions are formed. A magnet located after the exit aperture deflects the D + and D - ions emerging from the target into two suppressed Faraday cups at + 8 ° and - 8 ° from the beam axis. The fast D o atoms pass through the magnet undeflected. They are incident on a copper surface. The neutral atoms are detected by electron emission from the copper surface, 2.2. ALKALI TARGET The Rb target, which is descibed in detail in ref. 11, is a copper lined stainless steel container, maintained at a temperature of approximately 250°C. The temperature of the target is measured by two chromel P alumel thermocouples mounted on the wall of the target. A reservoir containing molten Rb is connected to the target by a tube 2.54 cm in diameter. The temperature of the reservoir is kept at least 25°C less than the temperature of the target. The Rb density in the target is varied by changing the temperature of the reservoir, The Rb vapor density in the target is measured by two surface ionization gauges each using an oxidized tungsten filament. One gauge, called gauge 1, is located inside the Rb target and is used to measure the low Rb densities in the cross section determination. This gauge has a guard ring geometry so that the length of the oxidized tungsten filament from which Rb + ions are drawn is accurately determined. The other gauge, called gauge 2, is located in an auxiliary chamber that is connected to the target by a 1 m m hole. The auxiliary chamber contains a large liquid nitrogen cooled surface that acts as a pump for the Rb vapor. As a result, the density of the Rb vapor in the auxiliary chamber is substantially reduced from the density in the target. Gauge 2 is used to measure the density in the target, when the density of Rb is so high that gauge 1 is space-charge limited, The density in the target prior to space charge limitation is determined using gauge 1 with the assumption that every atom that hits the hot wire is ionized. The current read from gauge 1 is
ng I~ = --~ e 27rrl,
where n is the average speed of the temperature charge, r is the
number of a t o m s / c m 3, ~ is the the Rb atoms ~ is determined by of the target), e is the electronic radius of the oxidized tungsten
et al.
wire, and / is the length of the wire from which the current is collected. Thus, n can be determined from the measured current using the relationship n = 4I~/ge 27rrl. When the density in the scattering chamber becomes so large that gauge 1 is space charge limited, then gauge 2 is used to determine the density. At low densities, we find that the current drawn by gauge 2, 12, is proportional to the current drawn by gauge 1, i.e., 12-~11. Measurement of Ij and 12 at low densities enables us to obtain the calibration constant/3 for gauge 2. At high densities we obtain the Cs target density from n-412/F)e 27rrlB. The target thickness, re, in ato m s / c m 2, is given by r e - n L , where L is the elfective length of the target as defined in ref. 11 2.3. DETECTION SYSTEM The detectors for the particles emerging from the target have been described previously~,S). They consist of two suppressed Faraday cups placed symmetrically with respect to the beam axis. The positive ions emerging from the target are deflected by a magnet into one of these cups, and the negative ions are deflected into the other cup. The ion currents to the two cups are measured. The D o flux emerging from the target is determined using an electron emission detector. This detector consists of a polished heated (180°C) copper disk and a ring of 2.54 cm diameter located in front of the disk and concentric with it. The ring was biased at + 180 V. The D o atoms strike the disk thereby ejecting electrons. The electron current is measured. The detection chamber also contains a wire scanner that is used to measure crudely the angular distribution of the D +, D - , and D o beams emerging from the target. The scanner consists of a 25 mil. tantalum wire that can be moved through the D ÷ beam, the D - beam, or the D o beam after these beams have been separated by the magnetic field. The scanner is used to determine whether or not the detector for a given charge state intercepts the entire beam that emerges from the target in that charge state. Each of the detectors intercepts an angle of about 1° as seen from the target. It was found that at low target thickness (rr<10 ~3atoms/cm 2) each of the three detectors completely collects the beam emerging from the target with the appropriate charge state. At target thicknesses 7r> 1014
CHARGE
EXCHANGE
a t o m s / c m 2 and energies less than 6 keV we observed that the beams are of different widths. The beams have an angular distribution that has a peak that lies within the 1° angle intercepted by the detectors but has wide wings so that a different fraction of each of the beams is collected by the detector for that beam. For target thicknesses r e > 2 × 10 ~5a t o m s / c m 2 and energies less than 6 keV it was found that the D + beam, D - beam and D o beam emerging from the target all have the same angular distribution. This angular distribution has wings that are wider than the detectors and only a fraction of each beam is collected by the detector for that beam. The fraction detected is the same for each of the three beams. As the energy of the incident beam is increased above 6 keV the angular distribution of the beams is confined to smaller angles, and a larger fraction of each beam is collected by the detector for that beam. 3. M e a s u r e m e n t
of the cross s e c t i o n O+o for D + i o n s i n c i d e n t on Rb
The charge transfer cross section a+0 for D + ions incident on Rb vapor target has been measured for incident D + ions with energies in the range 1.1-40 keV. The cross section a+0 was measured in the following manner. A beam of D ~ ions is extracted from the duoplasmatron ion source, accelerated to the desired energy, focussed into a nearly parallel beam and collimated. The incident D + ion current is measured in a retractable Faraday cup. This current is I s - N s e , where Ns is the number of D + ions incident per s, and e is the electronic charge. After measuring Is the Faraday cup is retracted and the D + ions enter the Rb t a r g e t - w h e r e charge exchange collisions occur. Emerging from the Rb target are D + ions, D ions, and fast D o atoms. A magnetic field after the target deflects the D + ions into a suppressed Faraday cup. The current to the D + cup is I+-N+e, where N+ is the number of positive ions per s emerging from the target. If the target thickness ~ is very small (~z< 1013 a t o m s / c m 2) the~ the positive ion current is given by l + - T + 0 I ~ [ 1 7~(a+0+a+_+a~)], where T+0 is the transmission of the incident ion beam through the target at zero target thickness, where a+_ is the total cross section for the reaction D + + R b ~ D - , and where ae is the cross section for elastic collisions that scatter a D + ion through an angle large enough that the D + ion does not enter the Faraday cup
COLLISIONS
507
used to detect the positive ions. Elastic scattering of the positive ions is not a signiicant loss mechanism (i.e. ~ c r + 0 + a + _ ) . The positive ion beam emerging from the target is observed using our movable wire detector to be much smaller than the size of the positive ion Faraday cup at the highest values of the target thickness used for measurements of a+0. The two electron pick up cross section a+_ is very small compared to the one electron pick-up cross section a+o. Thus l+/Is-T+0(1-~a+0). We measure (l+/ls) for 10-15 different values of ~z(~z< 10 ~3a t o m s / c m 2 for all the measurements). The quantity (I+/ls) is found experimentally to be a linearly decreasing function of ~ for ~z< 10 ~3 a t o m s / c m 2. The ~z = 0 intercept of (l+/ls) is T+0, and the slope is -T+0~+0. A least-squares fit to the data was used to determined T+0 and a+0. The values of T+0 obtained from these measurements were greater than 0.95 for energies of the incident ion above 2 keV and above 0.90 for energies of the incident ion in the range 1.1-2 keV. The cross section a+0 was measured from 1.1 to 40 keV. The measured values of cr+0 are presented in table 1. The errors shown in table 1 are based on statistical uncertainties in the data an on our estimate of possible systematic errors in the experiment. The values of a+0 for D + incident on Rb are plotted in fig. 2, together with the values of a+0 for D + incident on Cs by Meyer and Anderson12). Below 5 keV, the charge transfer cross section, a+0, for D + incident on Rb is smaller than TABLE 1
The variations of o'+0 and F ~° for D + ions incident on a Rb vapor target as a function of the energy of the incident ion. E(keV)
D+
1.1 1.5 2.0 3.o 4.0
5.0 6.0 10.0 15.0 20.0 28.5 H+
10.0 15.0 20.0
~+0( × 10-17 cm2) 1 039+ 84 1 140__+100 1 080__+87 1 065 _+90 1 010_+85 980 _+90 930_+76 653_+59 450+40 260+26 280_+ 28 121.2+11 93.5 + 9
Fr(%) 19.0__+2.9 17.0 + 2 . 6 16.0 __+2.4 13.5 _+2.0 10.0 _+1.5 6.6 + 1.0 3.4 _+0.52 1.2 -+0.18 0.59-+0.10 0.32-+0.05
0.22 +0.035
508
R.J.
GIRNIUS
the cross section for D + incident on Cs. Between 5 and 20 keV, the two cross sections are nearly the same. Above 20 keV the charge transfer cross section for D + on Rb is smaller than for D + on Cs. For energies of the incident ion less than about 20 keV the cross section tr+0 is primarily due to the near resonant charge transfer of the Rb valence electron to the D + ion in the reaction D ÷ + R b - D ~ + Rb + where the excited D ~ atom is produced in one of the n - 2 states. The energy defect AE (AE is the energy difference between the reactant and product states at infinite separation) for the reaction where the D ~ atom is formed in the n - 2 state is 0.8 eV. For comparison the energy defect to produce a D Oatom in the n - 1 state or one of the n - 3 states is 9.4eV of 2.7 eV respectively. Thus the production of states other than n - 2 is very non-resonant. The near resonant charge exchange process occurs because of the interaction of the near lying potential curves for the molecular ion states that have D + + R b ° and D ~ + R b ÷ as the separated atom ion limits. The theory of these near resonant processes have been discussed by several authors9,1°,13,14). In the theory due to Olson the interaction between the product and reactant states is taken as proportional to exp(-2r/ao), where r is ION SPEED (I06mlsec) , 0.3
0.5
l
1.0
i
,
,
,
,
I
2.0
3.0
v
,
A
~'-'5 E o
b o
~ i
2
1
i
i
i
i
t
iI
i
A
5 I0 20 D÷ION ENERGY (keV)
1
,
,
,
,,
50
Fig. 2. The cross section ~+o for D + +Rb--,D ° + Rb+. The symbol (it) represents our data. The symbol ,4 represents the data of Meyer and A n d e r s o n 12) for D + + C s - + D ° + C s +. The darkened points are for H + plotted at the same velocity, i.e. at half the energy. The error bars for the data of Meyer and Anderson are about + 10% which is nearly the same as for our data.
et al.
the internuclear separation a0 is the Bohr radius and 2 is a dimensionless parameter. It has been shown that 2 can be approximated by 2~-~
+
,
where I1 is the ionization potential of Rb, 12 is the ionization potential of the n = 2 state of the D O atom, and IH is the ionization potential of the hydrogen atom]5). Thus 2 ~ 0 . 4 5 . At low velocities, the charge transfer occurs at a radius r - R e , for which the matrix element of the interaction potential between the product and reactant states is equal to one half of the separation AV(Rc) of the potential curves for the product and reactant channels. This theory of near resonant charge exchange indicates that the cross section a+0 increases with increasing relative velocity, o until tr+0 reaches a m a x i m u m and then decreases. In this velocity region the cross section depends upon A V(Rc), Rc, 2 and o. At relative velocities that are high enough that or+0 is decreasing as o increases, the theory for the near resonant charge exchange cross section tr+0 becomes formally identical to the theory for resonant charge exchange. In this case tr+0 is independent of A V(Rc) and Re. Thus it depends only on 2 and o. We interpret our results as follows. For energies of the incident ion in the range 1.1-5 keV we believe that the cross section tr+0 is near its maxim u m value, and that (7+0 depends on A V(Re), Re, A, and v. The energy defect AE i s larger for D + + R b - - , D ° than for D + + C s - , D °. As r decreases from infinity the interaction potential increases and the separation of the product and reactant states decreases. The value of Rc at which the matrix element of the interaction potential equals one half of the separation of the potential curves for the reactant and product states is smaller for D + + R b - - , D ° than for D + + C s ° ~ D °. Thus tr+0 is smaller for D + + R b - - , D ° than for D + + C s °--,D O in this velocity range. For energies in the range 5-20 keV we believe that tr+0 is in the velocity region where the near resonant cross section behaves like the resonant cross section so that (7+0 depends only on 2 and o. In this velocity range the cross section tr+0 for D + + R b - - , D ° is a very similar function of o to t r + o for D + + C s - - , D O because 2 is nearly the same for the two reactions (2 = 0.45 for the reaction D + + R b ~ D O and 2 = 0 . 4 4 for the reaction D + + Cs ~ DO).
CHARGE
EXCHANGE
For energies of the incident ions in the range 20-40 keV the cross section a+0 decreases as o increases but with a rate of decrease that is less than in the energy range 5-20 keV and that is less than expected from the resonant charge transfer theory. We believe that this levelling off of the cross section at higher velocities is due to the increased participation of the core electrons, in the charge transfer reactions, as the incident ion velocity approaches the velocity of the core electrons. A number of theoretical calculations for the total charge transfer cross section for protons incident on alkali vapors show that the magnitudes and the velocity dependence of these cross sections at high velocities v >~ 108 cm/s) may be understood if allowance is made for capture of the target atom's core electrons. In the case of H ÷ + R b ~ H + Rb+, Vinogradov et al]6,]7), using a Brinkman-Kramers calculation, have shown that the contributions to the cross section from 4p6 and 4s 2 shells of the Rb atom are 90% and 10%, respectively, in the energy range of 20-40 keV. Olson has pointed out to us that the flattening of a+0 as a function of the velocity may also be the result of electron transfer due to rotational coupling at internuclear separations small enough that the potential curves are repulsive18).
COLLISIONS
The current to this plate is Io = RNoe, where No is the number of neutrals atoms emerging from the target per s and R is the number of electrons ejected from the copper surface per incident neutral atom. The particle flux emerging from the Rb target and entering one of the detectors is less than the incident particle flux. Particles fail to pass through the target and enter one of the detectors because of stray electric and magnetic fields, because of misalignment of the apparatus, and because of scattering through angles large enough that the beam misses one of the detectors. At the large values of the target thickness necessary for equilibrium a given particle has changed its charge many times and the fraction of the beam transmitted is independent of the charge state. Thus 1 Ns = T ( N + + No + N_),
where T is a number fact that the emerging incident particle flux. of the beam. We can the currents as
,(
Is=-~ 1.0
4. The equilibrium fraction of D- ions In addition to our measurement of a+0 we have measured the equilibrium fraction of D - ions emerging from the Rb target. These measurements were made as follows. The incident D + ion current, Is, is measured using a retractable Faraday cup located before the Rb vapor target. The Faraday cup is then retracted allowing the D ÷ beam to enter the Rb target where charge exchange collisions occur. The beam exiting the Rb target contains D + ions, D O atoms, and D - ions. The different charge states in the beam emerging from the Rb target are separated by a magnet. The D + and D - ion currents in the beam emerging from the target are measured using suppressed Faraday cups. The D + and D - ion currents in the beam emerging from the target are I + - N+ e and I_-N_e respectively, where N+ and N_ are respectively the numbers per s of positive ions and negative ions emerging from the target. The fast neutral D o atoms emerging from the target fall on a copper surface ejecting electrons from this surface. The ejected electrons are collected by a positively biased ring in front of the copper surface.
509
a / lad >.. _J <[ Z 0
,o )
I+ + ~ - + I _ T
•
|
i
i
u
iii
I
(5)
that takes into account the particle flux is less than the We call T the transmission express eq. (5) in terms of .
(6)
• oo '•°~°~'o'oA'ogg~,go
•
. .• . . . . .
I u
AA
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AA |A
(J < n" LL
-F. -E 0.01
i013
. . . . . . . . i~)i4
,
i
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i
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I016
I"I' (atomslcm z) Fig. 3. The variation of the fractions of the beam emerging from a Rb vapor target as D + ions (F+), D O atoms (F 0) and D- ions (F_) as a function of the target thickness n in ato m s / c m 2 w h e n a beam of D + ions is incident at an energy of 1.5 keV. An interesting feature of the data s h o w n in fig. 3 is that F 0 has a m a x i m u m value of about 90% at a value of n = 3 × 10 TM a t o m s / c m 2. The value of F0~ is 83%. The physical reason for the m a x i m u m is the following. The cross section a+0 is very large so that the positive ions incident on the Rb target are neutralized at relatively low values of n. The decrease in F 0 occurs, as some of the neutrals that have been made are converted to negative ions. The production of negative ions requires larger values of n since cr0_ is not nearly as large as a+0.
510
R.J.
GIRNIUS
We determine R from measurements with D + ions incident on the Rb target at very low values of 7r. Under these conditions dI+/drc--(1/R)dlo/drc. This expression is correct because at very low values of zc we find that dI_ ~AI+. Once R is known then T is obtained from eq. (6). It should be noted that in the measurement of a+0 as discussed in section 3 of this paper it is not necessary that R be measured nor it is necessary to assume that T is the same for each of the three beams. The fractions of the beam in the various charge states are given by F+-l./Tls, Fo-Io/RTIs, and F _ - I / T I ~ . It should be noted that F+ +Fo+F_- 1. At large values of ~r the quantities F+, F0, and F become independent of re. The values of F + , F0, and F when ~r is large enough that these fractions do not vary as rc varies are called the equilibrium fractions F+, F6~, and FT. We have measured F ~_ as follows. For a given energy we measure I~, I+, I0, and I as a function ~z. From these measurements we compute F+, F0, and F as a function of 7r. An example of our measurements of F+, F0, and F_ vs 7r are shown in fig. 3. As can be seen we increase rc by a factor of 2 or 3 after F_ reaches F=. Thus we feel confident that we have measured F up to values of zr large enough that F _ - F s . Our measurements of F___ as a function of the energy of the incident ion are tabulated in table 1 and are shown in fig. 4. As can be seen F7 is 0.19 at an incident ion energy of 1.1 keV, and F7 decreases as the energy increases from 1.1 keV up to 40 keV.
20
I0 -J W
5
et al.
In addition to making sure that rc is large enough that F - F ~_ we have made several other studies of possible systematic errors in our measurements. We have measured F~ both with and without an aperture located downstream from the exit aperture of the target. This aperture was chosen such that every particle that exits the target and passes through the second aperture must enter the detectors for that charge state. We find F = to be the same measured both with and without the second aperture. This leads us to the conclusion that focusing effects, resulting from that magnet that separates the different charge states leaving the target, are not important. We have crudely measured the angular distribution of the positive ion beam, the fast neutral beam, and the nagative ion bern after these beams have emerged from the Rb target and have been separated by the magnetic field. These angular distributions are measured with a moveable wire that is 25 mils in diameter. The wire can be moved across each of the beams. The current to the wire is measured as a function of the position of the wire. The current to the wire equals the ion current striking the wire plus the current resulting from the electrons ejected from the wire. We find that at values of the target thickness near r c - 1014 a t o m s / c m 2 the angular width of the positive beam is less than the angular width of the neutral beam and that the angular width of the neutral beam is less than the angular width of the negative beam. At the target thickness required for charge state equilibrium, however, the angular width of the three beams is identical. This indicates that our assumption that the fraction of the beam transmitted through the target is independent of the charge state when the target thickness is large enough for e(~uilibrium is correct i.e. our assumpnon that when rc is large enough for equi-
>TABLE 2
2
T he variation of F2 ° for D + ions incident on a Cs vapor as a function of the energy of the incident ion.
o
W
t
Q5
{ Q2 '
'~'
"lb
'
'
'~o
D+ION ENERGY (keV) Fig. 4. T h e D - e q u i l i b r i u m fraction F °° as a function of the energy of the D + ions incident on a Rb vapor target.
E(keV)
F 2 (%)
1.0 1.5 2.0 3.0 4.0 6.0
23.0±3.5 18.6±2.8 13.3±2.0 10.0±1.5 6.3±1.0 4.3±0.65
CHARGE
EXCHANGE
librium then T is the same for each charge state so that Ns - (I/T)(N+ +No +N_) is correct. Our belief that the fraction of the beam transmitted through the target is independent of the charge state for large values of rc is strengthened by the observation that we measure the same value for F_~ when we use different size apertures after the target. Each of the apertures is such that all the beam emerging from the target in a given charge state must enter the detector for that charge state. We have also studied the variation of R with time. We find that R varies less than 10% over the time required to measure F_. Thus we believe that variations of the ratio of the electron emission current to the flux of the neutral beam incident on the copper surface contributes an error of less than 10% to our measurement of F7 As a result of our experiments we believe that the errors assigned to F7 as a function of the energy of the incident ion are adequate to include both statistical errors and systematic errors. In addition to our measurements of F7 when D + is incident on Rb we have measured F_7 when D + is incident on a Cs vapor target. The results are tabulated in table 2 and are shown in fig. 5. Several previous measurements of F7 when H + or D ÷ is incident on Cs have been made. Our measurements are in agreement with the recent measurements of Schlachter et al. 7) and the earlier measurements of Khirnyi and Kochemasova4). Our confidence in our measurements of FS for D + incident on Rb are strengthened by the agreement
COLLISIONS
of our results for FS for D + incident on Cs with the very careful experiment of Schlachter et al. Our present measurements agree with the two previous measurements of F7 for D + incident on Cs carried out at the University of Wisconsin by Schlachter et al. ~) and by Meyer and Anderson 5) except at the lowest energy studied in each of the previous measurements. We believe that these previous measurements have a systematic error at the lowest energy for which F7 was measured. A comparison of F7 for D + incident on Rb and on Cs indicates that for energies of 1.1-3 keV the values of F_= are slightly higher for a Cs target than for a Rb target. For energies in the range 3-15 keV the values of F7 are higher for a Rb target than for a Cs target. We are indebted to Dr. A. S. Schlachter, for communicating his results prior to publication and for his helpful comments. We are also indebted to Dr. F. W. Meyer for his interest in these experiments and discussions of them.
References 1)
2) 3) 4) 5) 6)
3O
7) A
2O
8) ._I >.-
D
lO-
re_
8-
._.J ~
_
0u_l
6-
S
-
9) 10) 11) 12) 13) 14) 15)
41
16)
I
D÷ION ENERGY (keY)
Fig. 5. The D-equilibrium fraction F7 as a function of the energy of the D + ions incident on a Cs vapor target.
511
17) 18)
A. S. Schlachter, P. J. Bjorkholm, D. H. Loyd, L. W. Anderson and W. Haeberli, Phys. Rev. 177 (1969) 184. H. Bohlen, G. Clausnitzer and H. Wilsch, Z. Physik 208 (1968) 159. W. Grtiebler, P. A. Schmelzbach, V. KiSnig and P. Marmier, Helv. Phys. Acta 43 (1970) 254. Ya. M. Khirnyi and L. N. Kochemasova, Instr. Exp. Tech. 3 (1970) 693. F. W. Meyer and L. W. Anderson, Phys. Rev. A l l (1975) 589. C. Cisneros, I. Alvarez, C. F. Barnett and J. A. Ray, Phys. Rev. A14 (1976) 76. A. S. Schlachter, J. W. Stearns, D. L. Kagan and K. R. Stalder, Bull. Am. Phys. Soc. 21 (1976) 1265. B. A. D'yachkov and V. I. Zinenko, Sov. At. Energy 24 (1968) 16. R. E. Olson and F. T. Smith, Phys. Rev. A7 (1973) 1529. R. E. Olson, Phys. Rev. A6 (1972) 1822. F. W. Meyer and L. W. Anderson, Phys. Rev. A9 (1974) 1909. F. W. Meyer and L. W. Anderson, Phys. Lett. 54A (1975) 333. Yu. N. Demkov, Sov. Phys. JETP 18 (1964) 138. D. Rapp and W. E. Francis, J. Chem. Phys. 37 (1962) 2631. R. E. Olson, F. T. Smith and E. Bauer, Appl. Optics 10 (1971) 1848. A. V. Vinogradov, L. P. Presnyakov and V. P. Shevelko, JETP Lett. 8 (1968) 275. A. V. Vinogradov and V. P. Shevelko, Sov. Phys. JETP 32 (1971) 323. R. E. Olson, private communication.
INSTRUMENTS
AND
METHODS
143 ( 1 9 7 7 )
505-511
• ©
NORTH-HOLLAND
PUBLISHING
CO.
CHARGE EXCHANGE COLLISIONS OF D E U T E R I U M IN A R U B I D I U M VAPOR TARGET* R. J. GIRNIUS, L. W. A N D E R S O N and E. STAAB
Dept. o/ Physics, University of Wisconsin, Madison, Wisconsin 53706, U.S.A. Received 14 February 1977 The equilibrium fraction of D- ions formed when D + ions are incident on a Rb ergies of the incident ion in the range 1.1-40 keV. The equilibrium fraction of Dwhen D + ions with an energy of 1.1 keV are incident. The equilibrium fraction ion increases in the energy range of 1.1-40keV. The charge transfer D + + R b - - , D ° + R b + is also reported. The cross section is 1.14 x 10-14 cm 2 when 1.5 keV, and the cross section falls rapidly with increasing energy reaching the
1. Introduction The formation of high intensity H - or D - ion beams has long been of interest for injection into tandem accelerators or cyclotrons. Recently the interest in the formation of D - ion beams has expanded to the controlled thermonuclear reaction program, where the injection of fast D O atoms has been proposed for heating plasmas. The fast D O beam could be formed by producing low energy D - ions, accelerating these D - ions to a high energy, and then stripping the D - ions of an electron. Two methods exist for producing H - or D ions: (1) the direct extraction from an ion source, and (2) charge exchange collisions with H ÷ or D ÷ incident on a target that has a high equilibrium fraction for D - . Targets containing an alkali metal vapor have large H - or D - equilibrium fractions. The H - or D - equilibrium fraction for H ÷ or D ÷ ions incident on Cs (refs. 1-7), K (refs. 2 and 3), Na (refs. 3 and 8) and Li (refs. 3 and 8) has been reported previously. In this paper, we report the first measurements of the D - equilibrium fraction for D ÷ ions incident on Rb vapor. In addition we have remeasured the D - equilibrium fraction for D ÷ incident on Cs vapor. In addition to the measurement of the equilibrium fraction of D - ions when D ÷ is incident on a Rb target we have measured the electron capture cross section, a÷0, for the reaction D ÷ + Rb--,D O+ Rb+. This cross section is very large because the reaction is nearly resonant for the production of D O atoms in one of the n = 2 states. Our measurements of the cross section a+0 for D ÷ incident on Rb provides support for
vapor target has been measured for enions emerging from a Rb target is 19% decreases as the energy of the incident cross section a+0 for the reaction the incident D + ion has an energy of value 9.4 x 10-16 cm 2 at 40 keV.
Olson's theoretical model 9,1°) for near resonant charge exchange collisions.
2. Apparatus 2.1. GENERAL DESCRIPTION The apparatus used in this experiment is shown in fig. 1. It has been described previously. The apparatus consists of three parts: the ion source, the charge exchange target, and the detector chamber. A D ÷ ion beam is extracted from a duoplasmatron ion source accelerated to the desired energy, m o m e n t u m analyzed, and collimated. The ions enter the charge exchange target, where D O atoms D÷ ION BEAM
COLLIMATING f APERTURES f,jDIFFUSION PUMP SWEEP MAGNET
"
CESIUM TARGET ...._,U
I1
II jDEFINING CHARGEMAGNETANALYN Z[~/ lG APERTURE PV I OT D .F I FUSO I NPUMP MOVABLE WIRE SCANNER WIRE
=,FARADAY CUPS -NEUTRAL DETECTOR
,50 c m
* This research is supported AT(11-1) Gen.-7.
in part by ERDA
Contract
L_.= I~
~I "-I
Fig. 1. Schematic diagram of apparatus.
506
R.J.
GIRNIUS
and D - ions are formed. A magnet located after the exit aperture deflects the D + and D - ions emerging from the target into two suppressed Faraday cups at + 8 ° and - 8 ° from the beam axis. The fast D o atoms pass through the magnet undeflected. They are incident on a copper surface. The neutral atoms are detected by electron emission from the copper surface, 2.2. ALKALI TARGET The Rb target, which is descibed in detail in ref. 11, is a copper lined stainless steel container, maintained at a temperature of approximately 250°C. The temperature of the target is measured by two chromel P alumel thermocouples mounted on the wall of the target. A reservoir containing molten Rb is connected to the target by a tube 2.54 cm in diameter. The temperature of the reservoir is kept at least 25°C less than the temperature of the target. The Rb density in the target is varied by changing the temperature of the reservoir, The Rb vapor density in the target is measured by two surface ionization gauges each using an oxidized tungsten filament. One gauge, called gauge 1, is located inside the Rb target and is used to measure the low Rb densities in the cross section determination. This gauge has a guard ring geometry so that the length of the oxidized tungsten filament from which Rb + ions are drawn is accurately determined. The other gauge, called gauge 2, is located in an auxiliary chamber that is connected to the target by a 1 m m hole. The auxiliary chamber contains a large liquid nitrogen cooled surface that acts as a pump for the Rb vapor. As a result, the density of the Rb vapor in the auxiliary chamber is substantially reduced from the density in the target. Gauge 2 is used to measure the density in the target, when the density of Rb is so high that gauge 1 is space-charge limited, The density in the target prior to space charge limitation is determined using gauge 1 with the assumption that every atom that hits the hot wire is ionized. The current read from gauge 1 is
ng I~ = --~ e 27rrl,
where n is the average speed of the temperature charge, r is the
number of a t o m s / c m 3, ~ is the the Rb atoms ~ is determined by of the target), e is the electronic radius of the oxidized tungsten
et al.
wire, and / is the length of the wire from which the current is collected. Thus, n can be determined from the measured current using the relationship n = 4I~/ge 27rrl. When the density in the scattering chamber becomes so large that gauge 1 is space charge limited, then gauge 2 is used to determine the density. At low densities, we find that the current drawn by gauge 2, 12, is proportional to the current drawn by gauge 1, i.e., 12-~11. Measurement of Ij and 12 at low densities enables us to obtain the calibration constant/3 for gauge 2. At high densities we obtain the Cs target density from n-412/F)e 27rrlB. The target thickness, re, in ato m s / c m 2, is given by r e - n L , where L is the elfective length of the target as defined in ref. 11 2.3. DETECTION SYSTEM The detectors for the particles emerging from the target have been described previously~,S). They consist of two suppressed Faraday cups placed symmetrically with respect to the beam axis. The positive ions emerging from the target are deflected by a magnet into one of these cups, and the negative ions are deflected into the other cup. The ion currents to the two cups are measured. The D o flux emerging from the target is determined using an electron emission detector. This detector consists of a polished heated (180°C) copper disk and a ring of 2.54 cm diameter located in front of the disk and concentric with it. The ring was biased at + 180 V. The D o atoms strike the disk thereby ejecting electrons. The electron current is measured. The detection chamber also contains a wire scanner that is used to measure crudely the angular distribution of the D +, D - , and D o beams emerging from the target. The scanner consists of a 25 mil. tantalum wire that can be moved through the D ÷ beam, the D - beam, or the D o beam after these beams have been separated by the magnetic field. The scanner is used to determine whether or not the detector for a given charge state intercepts the entire beam that emerges from the target in that charge state. Each of the detectors intercepts an angle of about 1° as seen from the target. It was found that at low target thickness (rr<10 ~3atoms/cm 2) each of the three detectors completely collects the beam emerging from the target with the appropriate charge state. At target thicknesses 7r> 1014
CHARGE
EXCHANGE
a t o m s / c m 2 and energies less than 6 keV we observed that the beams are of different widths. The beams have an angular distribution that has a peak that lies within the 1° angle intercepted by the detectors but has wide wings so that a different fraction of each of the beams is collected by the detector for that beam. For target thicknesses r e > 2 × 10 ~5a t o m s / c m 2 and energies less than 6 keV it was found that the D + beam, D - beam and D o beam emerging from the target all have the same angular distribution. This angular distribution has wings that are wider than the detectors and only a fraction of each beam is collected by the detector for that beam. The fraction detected is the same for each of the three beams. As the energy of the incident beam is increased above 6 keV the angular distribution of the beams is confined to smaller angles, and a larger fraction of each beam is collected by the detector for that beam. 3. M e a s u r e m e n t
of the cross s e c t i o n O+o for D + i o n s i n c i d e n t on Rb
The charge transfer cross section a+0 for D + ions incident on Rb vapor target has been measured for incident D + ions with energies in the range 1.1-40 keV. The cross section a+0 was measured in the following manner. A beam of D ~ ions is extracted from the duoplasmatron ion source, accelerated to the desired energy, focussed into a nearly parallel beam and collimated. The incident D + ion current is measured in a retractable Faraday cup. This current is I s - N s e , where Ns is the number of D + ions incident per s, and e is the electronic charge. After measuring Is the Faraday cup is retracted and the D + ions enter the Rb t a r g e t - w h e r e charge exchange collisions occur. Emerging from the Rb target are D + ions, D ions, and fast D o atoms. A magnetic field after the target deflects the D + ions into a suppressed Faraday cup. The current to the D + cup is I+-N+e, where N+ is the number of positive ions per s emerging from the target. If the target thickness ~ is very small (~z< 1013 a t o m s / c m 2) the~ the positive ion current is given by l + - T + 0 I ~ [ 1 7~(a+0+a+_+a~)], where T+0 is the transmission of the incident ion beam through the target at zero target thickness, where a+_ is the total cross section for the reaction D + + R b ~ D - , and where ae is the cross section for elastic collisions that scatter a D + ion through an angle large enough that the D + ion does not enter the Faraday cup
COLLISIONS
507
used to detect the positive ions. Elastic scattering of the positive ions is not a signiicant loss mechanism (i.e. ~ c r + 0 + a + _ ) . The positive ion beam emerging from the target is observed using our movable wire detector to be much smaller than the size of the positive ion Faraday cup at the highest values of the target thickness used for measurements of a+0. The two electron pick up cross section a+_ is very small compared to the one electron pick-up cross section a+o. Thus l+/Is-T+0(1-~a+0). We measure (l+/ls) for 10-15 different values of ~z(~z< 10 ~3a t o m s / c m 2 for all the measurements). The quantity (I+/ls) is found experimentally to be a linearly decreasing function of ~ for ~z< 10 ~3 a t o m s / c m 2. The ~z = 0 intercept of (l+/ls) is T+0, and the slope is -T+0~+0. A least-squares fit to the data was used to determined T+0 and a+0. The values of T+0 obtained from these measurements were greater than 0.95 for energies of the incident ion above 2 keV and above 0.90 for energies of the incident ion in the range 1.1-2 keV. The cross section a+0 was measured from 1.1 to 40 keV. The measured values of cr+0 are presented in table 1. The errors shown in table 1 are based on statistical uncertainties in the data an on our estimate of possible systematic errors in the experiment. The values of a+0 for D + incident on Rb are plotted in fig. 2, together with the values of a+0 for D + incident on Cs by Meyer and Anderson12). Below 5 keV, the charge transfer cross section, a+0, for D + incident on Rb is smaller than TABLE 1
The variations of o'+0 and F ~° for D + ions incident on a Rb vapor target as a function of the energy of the incident ion. E(keV)
D+
1.1 1.5 2.0 3.o 4.0
5.0 6.0 10.0 15.0 20.0 28.5 H+
10.0 15.0 20.0
~+0( × 10-17 cm2) 1 039+ 84 1 140__+100 1 080__+87 1 065 _+90 1 010_+85 980 _+90 930_+76 653_+59 450+40 260+26 280_+ 28 121.2+11 93.5 + 9
Fr(%) 19.0__+2.9 17.0 + 2 . 6 16.0 __+2.4 13.5 _+2.0 10.0 _+1.5 6.6 + 1.0 3.4 _+0.52 1.2 -+0.18 0.59-+0.10 0.32-+0.05
0.22 +0.035
508
R.J.
GIRNIUS
the cross section for D + incident on Cs. Between 5 and 20 keV, the two cross sections are nearly the same. Above 20 keV the charge transfer cross section for D + on Rb is smaller than for D + on Cs. For energies of the incident ion less than about 20 keV the cross section tr+0 is primarily due to the near resonant charge transfer of the Rb valence electron to the D + ion in the reaction D ÷ + R b - D ~ + Rb + where the excited D ~ atom is produced in one of the n - 2 states. The energy defect AE (AE is the energy difference between the reactant and product states at infinite separation) for the reaction where the D ~ atom is formed in the n - 2 state is 0.8 eV. For comparison the energy defect to produce a D Oatom in the n - 1 state or one of the n - 3 states is 9.4eV of 2.7 eV respectively. Thus the production of states other than n - 2 is very non-resonant. The near resonant charge exchange process occurs because of the interaction of the near lying potential curves for the molecular ion states that have D + + R b ° and D ~ + R b ÷ as the separated atom ion limits. The theory of these near resonant processes have been discussed by several authors9,1°,13,14). In the theory due to Olson the interaction between the product and reactant states is taken as proportional to exp(-2r/ao), where r is ION SPEED (I06mlsec) , 0.3
0.5
l
1.0
i
,
,
,
,
I
2.0
3.0
v
,
A
~'-'5 E o
b o
~ i
2
1
i
i
i
i
t
iI
i
A
5 I0 20 D÷ION ENERGY (keV)
1
,
,
,
,,
50
Fig. 2. The cross section ~+o for D + +Rb--,D ° + Rb+. The symbol (it) represents our data. The symbol ,4 represents the data of Meyer and A n d e r s o n 12) for D + + C s - + D ° + C s +. The darkened points are for H + plotted at the same velocity, i.e. at half the energy. The error bars for the data of Meyer and Anderson are about + 10% which is nearly the same as for our data.
et al.
the internuclear separation a0 is the Bohr radius and 2 is a dimensionless parameter. It has been shown that 2 can be approximated by 2~-~
+
,
where I1 is the ionization potential of Rb, 12 is the ionization potential of the n = 2 state of the D O atom, and IH is the ionization potential of the hydrogen atom]5). Thus 2 ~ 0 . 4 5 . At low velocities, the charge transfer occurs at a radius r - R e , for which the matrix element of the interaction potential between the product and reactant states is equal to one half of the separation AV(Rc) of the potential curves for the product and reactant channels. This theory of near resonant charge exchange indicates that the cross section a+0 increases with increasing relative velocity, o until tr+0 reaches a m a x i m u m and then decreases. In this velocity region the cross section depends upon A V(Rc), Rc, 2 and o. At relative velocities that are high enough that or+0 is decreasing as o increases, the theory for the near resonant charge exchange cross section tr+0 becomes formally identical to the theory for resonant charge exchange. In this case tr+0 is independent of A V(Rc) and Re. Thus it depends only on 2 and o. We interpret our results as follows. For energies of the incident ion in the range 1.1-5 keV we believe that the cross section tr+0 is near its maxim u m value, and that (7+0 depends on A V(Re), Re, A, and v. The energy defect AE i s larger for D + + R b - - , D ° than for D + + C s - , D °. As r decreases from infinity the interaction potential increases and the separation of the product and reactant states decreases. The value of Rc at which the matrix element of the interaction potential equals one half of the separation of the potential curves for the reactant and product states is smaller for D + + R b - - , D ° than for D + + C s ° ~ D °. Thus tr+0 is smaller for D + + R b - - , D ° than for D + + C s °--,D O in this velocity range. For energies in the range 5-20 keV we believe that tr+0 is in the velocity region where the near resonant cross section behaves like the resonant cross section so that (7+0 depends only on 2 and o. In this velocity range the cross section tr+0 for D + + R b - - , D ° is a very similar function of o to t r + o for D + + C s - - , D O because 2 is nearly the same for the two reactions (2 = 0.45 for the reaction D + + R b ~ D O and 2 = 0 . 4 4 for the reaction D + + Cs ~ DO).
CHARGE
EXCHANGE
For energies of the incident ions in the range 20-40 keV the cross section a+0 decreases as o increases but with a rate of decrease that is less than in the energy range 5-20 keV and that is less than expected from the resonant charge transfer theory. We believe that this levelling off of the cross section at higher velocities is due to the increased participation of the core electrons, in the charge transfer reactions, as the incident ion velocity approaches the velocity of the core electrons. A number of theoretical calculations for the total charge transfer cross section for protons incident on alkali vapors show that the magnitudes and the velocity dependence of these cross sections at high velocities v >~ 108 cm/s) may be understood if allowance is made for capture of the target atom's core electrons. In the case of H ÷ + R b ~ H + Rb+, Vinogradov et al]6,]7), using a Brinkman-Kramers calculation, have shown that the contributions to the cross section from 4p6 and 4s 2 shells of the Rb atom are 90% and 10%, respectively, in the energy range of 20-40 keV. Olson has pointed out to us that the flattening of a+0 as a function of the velocity may also be the result of electron transfer due to rotational coupling at internuclear separations small enough that the potential curves are repulsive18).
COLLISIONS
The current to this plate is Io = RNoe, where No is the number of neutrals atoms emerging from the target per s and R is the number of electrons ejected from the copper surface per incident neutral atom. The particle flux emerging from the Rb target and entering one of the detectors is less than the incident particle flux. Particles fail to pass through the target and enter one of the detectors because of stray electric and magnetic fields, because of misalignment of the apparatus, and because of scattering through angles large enough that the beam misses one of the detectors. At the large values of the target thickness necessary for equilibrium a given particle has changed its charge many times and the fraction of the beam transmitted is independent of the charge state. Thus 1 Ns = T ( N + + No + N_),
where T is a number fact that the emerging incident particle flux. of the beam. We can the currents as
,(
Is=-~ 1.0
4. The equilibrium fraction of D- ions In addition to our measurement of a+0 we have measured the equilibrium fraction of D - ions emerging from the Rb target. These measurements were made as follows. The incident D + ion current, Is, is measured using a retractable Faraday cup located before the Rb vapor target. The Faraday cup is then retracted allowing the D ÷ beam to enter the Rb target where charge exchange collisions occur. The beam exiting the Rb target contains D + ions, D O atoms, and D - ions. The different charge states in the beam emerging from the Rb target are separated by a magnet. The D + and D - ion currents in the beam emerging from the target are measured using suppressed Faraday cups. The D + and D - ion currents in the beam emerging from the target are I + - N+ e and I_-N_e respectively, where N+ and N_ are respectively the numbers per s of positive ions and negative ions emerging from the target. The fast neutral D o atoms emerging from the target fall on a copper surface ejecting electrons from this surface. The ejected electrons are collected by a positively biased ring in front of the copper surface.
509
a / lad >.. _J <[ Z 0
,o )
I+ + ~ - + I _ T
•
|
i
i
u
iii
I
(5)
that takes into account the particle flux is less than the We call T the transmission express eq. (5) in terms of .
(6)
• oo '•°~°~'o'oA'ogg~,go
•
. .• . . . . .
I u
AA
0.1
AA |A
(J < n" LL
-F. -E 0.01
i013
. . . . . . . . i~)i4
,
i
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i
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i
i
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AI
I016
I"I' (atomslcm z) Fig. 3. The variation of the fractions of the beam emerging from a Rb vapor target as D + ions (F+), D O atoms (F 0) and D- ions (F_) as a function of the target thickness n in ato m s / c m 2 w h e n a beam of D + ions is incident at an energy of 1.5 keV. An interesting feature of the data s h o w n in fig. 3 is that F 0 has a m a x i m u m value of about 90% at a value of n = 3 × 10 TM a t o m s / c m 2. The value of F0~ is 83%. The physical reason for the m a x i m u m is the following. The cross section a+0 is very large so that the positive ions incident on the Rb target are neutralized at relatively low values of n. The decrease in F 0 occurs, as some of the neutrals that have been made are converted to negative ions. The production of negative ions requires larger values of n since cr0_ is not nearly as large as a+0.
510
R.J.
GIRNIUS
We determine R from measurements with D + ions incident on the Rb target at very low values of 7r. Under these conditions dI+/drc--(1/R)dlo/drc. This expression is correct because at very low values of zc we find that dI_ ~AI+. Once R is known then T is obtained from eq. (6). It should be noted that in the measurement of a+0 as discussed in section 3 of this paper it is not necessary that R be measured nor it is necessary to assume that T is the same for each of the three beams. The fractions of the beam in the various charge states are given by F+-l./Tls, Fo-Io/RTIs, and F _ - I / T I ~ . It should be noted that F+ +Fo+F_- 1. At large values of ~r the quantities F+, F0, and F become independent of re. The values of F + , F0, and F when ~r is large enough that these fractions do not vary as rc varies are called the equilibrium fractions F+, F6~, and FT. We have measured F ~_ as follows. For a given energy we measure I~, I+, I0, and I as a function ~z. From these measurements we compute F+, F0, and F as a function of 7r. An example of our measurements of F+, F0, and F_ vs 7r are shown in fig. 3. As can be seen we increase rc by a factor of 2 or 3 after F_ reaches F=. Thus we feel confident that we have measured F up to values of zr large enough that F _ - F s . Our measurements of F___ as a function of the energy of the incident ion are tabulated in table 1 and are shown in fig. 4. As can be seen F7 is 0.19 at an incident ion energy of 1.1 keV, and F7 decreases as the energy increases from 1.1 keV up to 40 keV.
20
I0 -J W
5
et al.
In addition to making sure that rc is large enough that F - F ~_ we have made several other studies of possible systematic errors in our measurements. We have measured F~ both with and without an aperture located downstream from the exit aperture of the target. This aperture was chosen such that every particle that exits the target and passes through the second aperture must enter the detectors for that charge state. We find F = to be the same measured both with and without the second aperture. This leads us to the conclusion that focusing effects, resulting from that magnet that separates the different charge states leaving the target, are not important. We have crudely measured the angular distribution of the positive ion beam, the fast neutral beam, and the nagative ion bern after these beams have emerged from the Rb target and have been separated by the magnetic field. These angular distributions are measured with a moveable wire that is 25 mils in diameter. The wire can be moved across each of the beams. The current to the wire is measured as a function of the position of the wire. The current to the wire equals the ion current striking the wire plus the current resulting from the electrons ejected from the wire. We find that at values of the target thickness near r c - 1014 a t o m s / c m 2 the angular width of the positive beam is less than the angular width of the neutral beam and that the angular width of the neutral beam is less than the angular width of the negative beam. At the target thickness required for charge state equilibrium, however, the angular width of the three beams is identical. This indicates that our assumption that the fraction of the beam transmitted through the target is independent of the charge state when the target thickness is large enough for e(~uilibrium is correct i.e. our assumpnon that when rc is large enough for equi-
>TABLE 2
2
T he variation of F2 ° for D + ions incident on a Cs vapor as a function of the energy of the incident ion.
o
W
t
Q5
{ Q2 '
'~'
"lb
'
'
'~o
D+ION ENERGY (keV) Fig. 4. T h e D - e q u i l i b r i u m fraction F °° as a function of the energy of the D + ions incident on a Rb vapor target.
E(keV)
F 2 (%)
1.0 1.5 2.0 3.0 4.0 6.0
23.0±3.5 18.6±2.8 13.3±2.0 10.0±1.5 6.3±1.0 4.3±0.65
CHARGE
EXCHANGE
librium then T is the same for each charge state so that Ns - (I/T)(N+ +No +N_) is correct. Our belief that the fraction of the beam transmitted through the target is independent of the charge state for large values of rc is strengthened by the observation that we measure the same value for F_~ when we use different size apertures after the target. Each of the apertures is such that all the beam emerging from the target in a given charge state must enter the detector for that charge state. We have also studied the variation of R with time. We find that R varies less than 10% over the time required to measure F_. Thus we believe that variations of the ratio of the electron emission current to the flux of the neutral beam incident on the copper surface contributes an error of less than 10% to our measurement of F7 As a result of our experiments we believe that the errors assigned to F7 as a function of the energy of the incident ion are adequate to include both statistical errors and systematic errors. In addition to our measurements of F7 when D + is incident on Rb we have measured F_7 when D + is incident on a Cs vapor target. The results are tabulated in table 2 and are shown in fig. 5. Several previous measurements of F7 when H + or D ÷ is incident on Cs have been made. Our measurements are in agreement with the recent measurements of Schlachter et al. 7) and the earlier measurements of Khirnyi and Kochemasova4). Our confidence in our measurements of FS for D + incident on Rb are strengthened by the agreement
COLLISIONS
of our results for FS for D + incident on Cs with the very careful experiment of Schlachter et al. Our present measurements agree with the two previous measurements of F7 for D + incident on Cs carried out at the University of Wisconsin by Schlachter et al. ~) and by Meyer and Anderson 5) except at the lowest energy studied in each of the previous measurements. We believe that these previous measurements have a systematic error at the lowest energy for which F7 was measured. A comparison of F7 for D + incident on Rb and on Cs indicates that for energies of 1.1-3 keV the values of F_= are slightly higher for a Cs target than for a Rb target. For energies in the range 3-15 keV the values of F7 are higher for a Rb target than for a Cs target. We are indebted to Dr. A. S. Schlachter, for communicating his results prior to publication and for his helpful comments. We are also indebted to Dr. F. W. Meyer for his interest in these experiments and discussions of them.
References 1)
2) 3) 4) 5) 6)
3O
7) A
2O
8) ._I >.-
D
lO-
re_
8-
._.J ~
_
0u_l
6-
S
-
9) 10) 11) 12) 13) 14) 15)
41
16)
I
D÷ION ENERGY (keY)
Fig. 5. The D-equilibrium fraction F7 as a function of the energy of the D + ions incident on a Cs vapor target.
511
17) 18)
A. S. Schlachter, P. J. Bjorkholm, D. H. Loyd, L. W. Anderson and W. Haeberli, Phys. Rev. 177 (1969) 184. H. Bohlen, G. Clausnitzer and H. Wilsch, Z. Physik 208 (1968) 159. W. Grtiebler, P. A. Schmelzbach, V. KiSnig and P. Marmier, Helv. Phys. Acta 43 (1970) 254. Ya. M. Khirnyi and L. N. Kochemasova, Instr. Exp. Tech. 3 (1970) 693. F. W. Meyer and L. W. Anderson, Phys. Rev. A l l (1975) 589. C. Cisneros, I. Alvarez, C. F. Barnett and J. A. Ray, Phys. Rev. A14 (1976) 76. A. S. Schlachter, J. W. Stearns, D. L. Kagan and K. R. Stalder, Bull. Am. Phys. Soc. 21 (1976) 1265. B. A. D'yachkov and V. I. Zinenko, Sov. At. Energy 24 (1968) 16. R. E. Olson and F. T. Smith, Phys. Rev. A7 (1973) 1529. R. E. Olson, Phys. Rev. A6 (1972) 1822. F. W. Meyer and L. W. Anderson, Phys. Rev. A9 (1974) 1909. F. W. Meyer and L. W. Anderson, Phys. Lett. 54A (1975) 333. Yu. N. Demkov, Sov. Phys. JETP 18 (1964) 138. D. Rapp and W. E. Francis, J. Chem. Phys. 37 (1962) 2631. R. E. Olson, F. T. Smith and E. Bauer, Appl. Optics 10 (1971) 1848. A. V. Vinogradov, L. P. Presnyakov and V. P. Shevelko, JETP Lett. 8 (1968) 275. A. V. Vinogradov and V. P. Shevelko, Sov. Phys. JETP 32 (1971) 323. R. E. Olson, private communication.