The lith Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

Estimation of Charge Exchange Cross Section for Multiply Charged Ions Accelerated
in the JAERI AVF Cyclotron
Yoshiteru NAKAMURA, lkuo ISHIBORI, Kazuo ARAKAWA and Takayuki NARA
Advanced Radiation Technology Center, Japan Atomic Energy Research Institute,Takasaki, Gunma, 370-12 JAPAN

Abstract
An estimation of charge exchange cross section wasexperimented With the JAERI A VF cyclotron. The beamloss of accelerating ions was mare to occur intentionally bygas feeding into the vacuum chamber of the cyclotron. Thecharge exchange cross sections for various heavy ions werecalculated based on the attenuation of beam intensity on themain probe. These cross sections largely recrease withincrease the energy of the accelerating ions. Furthermore, wealso tried to get a preliminary empirical formula.

original acceleration process, independents of pressure in thecyclotron. The other, fc(n), shows the attenuation term
induced by the charge exchange reaction.
7~~~-:~~~~~~~==~~
Pr~s~ute level -P1 -P2 - P a """"~- P4I''''--------------------··f···--·----------·-----·-·f········--················f············

ilp2ni___i:_________________________ t·····-------------------

1 Introduction
The charge exchange reactions which occur with highprobabilities in ion-atom collision have been studied [1]-[3]from a standpoint of theoretical and experimental situations
since the 1960s. A charge.exchange cross section (CECS)
for heavy ions is one of the important data to resign thevacuum re<pirement for accelerator as an A VF cyclotron, it
may bring a serious beam reduction in the initial acceleration
process especially. However, reliable experimental data andcomprehensive empirical formulae for many kinds of ionsalmost have been not reported so far.
In general, it has been well known that the CECS
strongly depends on energy and charge state of the ion beam.
Therefore, the AVF cyclotron is very convenient machine toinvestigate the energy dependence on the CECS because theenergy of the ion increases gradually with increase of a radiusof the cyclotron. In consideration of this advantage, weexperimented to get the CECS which is estimated from anattenuation of beam intensity by aggressive gas feeding into
the vacuum chamber of the JAERI A VF cyclotron.

2

Method of Estimation for Charge Exchange
Cross Section

General shape of ion beam intensity observed on a mainprobe, in case of the increase of feeding gas <pantity into thevacuum chamber of the cyclotron, will be varied as shown in
Fig. 1. The vertical and horiwntal axes indicate the beam
intensity and the number of turns of ion beam.
First, four values of beam intensity, when the position of
the ion is n-th tum and where theirpressuresarePto P 2 , P 3 andP 4, are put as IPtn, IP2n, IP3n and IP4n, respectively. Theattenuation of the beam intensity along the radius of thecyclotron is thought that it can be expressed by the product oftwo functions. One of two, fa(n), is the effect related to50n
100150The number of turns (n)200Fig. 1 A calculationmodelforattenuated beam intensities bygas feeding.
We assume that IPtn is given asI Pin= lo• f 0 (n)• ftc(n).

(1)

In addition, f 1c(n) for Ip In is written by next formula.

=e-k•P,•{.E(cr;•X;)}

(2)

I= I

Where k is a constant, equal to [6.023x 1023 /(22.4x 103)/(lx105 )x 273/(273+T)]. T is temperature in the vacuumchamber. The values of PI> cri and Xi correspond to thepressure in the vacuum chamber (Pa), the cross section ofcharge exchange reaction (cm 2) and the traveling distance ofion (em), respectively. Then, the ratio of lp 1n and lp2n is
introduced because of the elimination of the terms fa(n) andfo.

I Ptn//fP2n=e-k•(Pt-P2)•{ E(cr; • X;)}

(3)

i=l

Finally, the value of O'n which should be obtained isderived from a following formula.
1
1 •[crn=•ln( 1Ptn/)-{ni(cr;•X;)}](4)
Xn -k•(P -P/Inni=t
12)

The value of O'n can be calculated in tum, if the ratio of two
intensities of lp tn and IP2n, the summation of the product of O'iand Xi are given. In case of other pressure levels, another ancan be also calculated in combination with their beam
intensities, for instance, IPtn and IP3n or IPtn and IP4n.
On the other hand, the average orbit radius of accelerating
ion in the cyclotron, rn, is expressed generally based upon themotion of the ion in magnetic field.

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The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

~En2 +2moEn r:-{.i2rn= o.2998•Q•Bo •vl-p(5)Where, Illo is the rest mass of ion in unit of MeV, En kineticenergy (MeV), Q charge state, Bo base magnetic field (kG) and~ the ratio of ion velocity to light speed.
In onb" to confirm the certainty of rn, the beam tum
pattem retected by differential head of the main probe wasanalyzed. An example of the relationship between calculated
and measured radii of the beam trajectory is shown in Fig. 2.
A linear relation is kept completely within the radius of 330
mm with the exception of first tum.
350

EIll.8l/300

oe 250~~ 200The number of turns
I.!B"'0 u150!!-~1111!!
: ; - 100.Y~50I&

050~100__/'~~ ~5

4He 2+, 50 MeV (h=2}:

Radius of the cyclotron (em)
150

200

250

300

350

Measured radius of beam trajectory (mm)Fig. 2 A relationship between calculated and measured radiiof the beam trajectory.

3 Pressure Control, Distribution and Calibration
Pressure control in the vacuum chamber, measurement ofpressure distribution along the radius and calibration for a
vacuum gauge have to be carried out for estimation of theCECS.
A block diagram for pressure control is shown in Fig. 3.
Nitrogen gas was selected as the feeding one from theviewpoint of p~ical effectiveness. The gas feeding line
constituted of copper pipe through two valves and a mass flow
meter was connected to the sire of the vacuum chamber.
Actually the pressure in the vacuum chamber was controlled
only by flow rate regulationofnitrogen gas.

Fig. 4 Pressure distributions along the radius of thecyclotron.
To obtain the absolute values of the CECS, a calibrationof the cold cathode gauge was perfonnedin comparison with anure BA gauge. A clear linear relation is observed along
both logarithmic axes in Fig. 5, its inclination of straight line
is slightly different from 1.0 apart.

2~/IY""'.{!;].....

l.P~--"~~

l10"510"410-3

Indication of cold cathode gauge (Pa)Fig. 5 A calibration line for cold cathode gauge used inexperiment.

4 Beam Attenuation by Gas Feeding

Fig. 3 A block diagram for pressure control in the vacuum
chamber of the cyclotron.
For the purpose of measuring the pressure distribution in
the vacuum chamber, the head of the main probe was replaced

Figures 6 and 7 show the beam intensities on the mainprobe when internal pressures by nitrogen gas feeding increase
up to about two orders from the normal condition. The beam
intensities at 50 mm of the cyclotron radius are rediced
because of the beam loss along a petpendicular injection line
where the pressure is mare to rise on account of thecontribution from the vacuum chamber.

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The 11th Symposium on Accelerator Science and Technology, Harima Science Garden City, 1997

7.---~-.~----------------~r-----~
lon beam : 36Ar8+, 195 MeV (h=3)<( 6 E--8;:::----t-~eeding gas: Nitrogen-+-----~§ 5 ~~~~------1-----~~----~~-­~4h~~+-~=+~~~=--~-~::O:::FaE-sa·a;little big variations appear in a lot of data points, wholetendmcy shows that the CECS 's for various ions d!crease
with increase of the ion velocity. Furthermore, the CECS's
for highly charged ions are relatively larger than that oflowly
charged one.

~3hc-T-'lt---t',.......,----1-----~-------+=~;---l.ss2~~-t--""..------+------=:llo.....J,------+---l"' 1 ~~~~~~~~~~~----~~~~~~~~

oo~~~~~~~~~~~~_J200

400600Radius of cyclotron (mm)8001000

Fig. 6 The beam attenuation for 36 Ar8+, 195 MeV ion bynitrogen gas feeding into the vacuum.chamber.

Velocity ratio to light speed (beta)

Fig. 9 Typical charge exchange cross sections estimatedbased on beam attenuation.

6 Derivation of Empirical Formula/•

4006008001000
Radius of cyclotron (mm)attenuation for 16100 MeV ion byd+,
Fig. 7 The beam
nitrogen gas feeding into the vacuum chamber.
5Estimation of Charge Exchange Cross Section

As mentioned before, the beam loss in the injection line
needs to be consirered carefully. The relative attenuation of
the beam intensity at several pressure levels can be corrected
surely by the exP<>,11ential functions as shown in Fig. 8.

We tried to get a reliable empirical formula which isavailable over the range of ion energy and charge state as wide
as possible based on above data. As a result, we d!rived afollowing preliminary formula which is given as a function of~ and the rate ofionization, Qr. within the range of ~which isless than 0.1.
(J = 1.5 X 10 -22 e Qr -6.2 • p-(3.9+4.3•logQr)

Where Qr eq~als Q/Q0 , and Q0 is charge state at full-strip
condition of the ion.

7 Further plan

. . . . . .l

1.0 r-!!:::::!!~~~~=::1----~ 0.95§So far, experimental data making use of cyclotrons, sometheoretical and semi-empirical formulae have been alreadypresented [5]-[8]. We are planning to acquire more excellent
empirical formula and reliable experimental data in future.

0.90 ~----------1----~--__,~~~"--------..:j~ 0.85 ~....:...r-o-::;::::;4-;:;H::::e2:;:+1,5;-;;0~M:.:e:;:v~----~~~\-:-----~
i-o--12C5+,220'iii--6-1604+,1 00~20Ne6+,120~References-<>-20Ne8+,350-t1-36Ar8+,195-!51-40Ar8+,175,.,£(6)0.65 ~__.........................L -_ _ _...........wL-.....z----....,;j10'5
104
10'3
10'2

Pressure in vacuum chamber (Pa)Fig. 8 The beam attenuation for various ions in the injectionline.
A FORTRAN program for estimation of the CECS wasmare newly by ourselves. The values of the CECS arecalculated with oouble precision by two manners ofinterpolation using Akima's methoc{4] and polynomial
approximation .
Figure 9 summarizes the CECS for typical kinds of ion
beams computed by polynomial approximation. Although a[1] H. D. Betz,Rev. Mod.Phys., vol. 44, No.3, (1972)465.
[2] C. L. Cocke, Phys. Rev. A, vol. 20, No.3, (1979)749.
[3] P. D. Miller, IEEE Trans. on Nucl. Sci. vol. NS-26,No. 1, (1979) 1111.
[4] H. Akima, Journal of the ACM, vol. 17, (1979) 589.

[5] D. Elo, D. Morris, et al., IEEE Trans. Nucl. Sci.,
NS-26, No.2, (1979) 2179.
[6] R. A. Gough andM. L. Mallory, IEEE Trans. Nucl. Sci.,
NS-26, No. 2, (1979) 2384.
[7] N. Bohr and J. Lindlard, Kgl. Danske Vied!nskab.
Selskab, Mat.-Fys. Medd. 28, No.7 (1954)[8] H. C. Hensh, I. Feigenbaum, et d., IEEE Trans. Nucl.
Sci., NS-32, No. 5, (1985) 3797.

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