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LIBRARY ‘
Michigan State
University This is to certify that the

thesis entitled

 

 

 

DEVELOPMENT OF HPGE DETECTOR
FOR THE LONGITUDINAL EMITTANCE MEASUREMENT

presented by
REIKO TAKI

has been accepted towards fulfillment
of the requirements for the

MS. degree in Physics and Astronomy

Major Professor’sfSignature
l1 [0 a} / 03,
Date

 

MSU is an Affirmative Action/Equal Opportunity Institution

 

PLACE IN RETURN BOX to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE

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6/01 c:/CiFiCJDateDue.p65-p.15

 

DEVELOPMENT OF HPGE DETECTOR
FOR THE LONGITUDINAL EMITTANCE MEASUREMENT

By
Reiko Taki

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Physics and Astronomy

2003

ABSTRACT

DEVELOPMENT OF HPGE DETECTOR
FOR THE LON GITUDINAL EMITTANCE MEASUREMENT

By
Reiko Taki

The longitudinal emittance of the beam from the RIKEN Ring Cyclotron (RRC) is
indispensable knowledge for the operation of the Radioactive Isotope Beam Factory,
which is now under construction and uses the RRC as an injector. We proposed to
employ a HPGe detector as a. compact and convenient energy detector for longitudinal
emittance measurements and studied the feasibility of its use with high-energy heavy
ions. A reasonably good energy resolution, (5E / E = 6.5x10‘4, has been observed for
1890-MeV 14N, which makes the HPGe promising. A new detector is being fabricated
to achieve a better resolution. Also the longitudinal emittances were measured for
3800-MeV 40Ar and 2420-MeV 22N e. It has been demonstrated that the measurement
of longitudinal emittance provides rich information on the acceleration condition, such
as the single-turn extraction and the effect of phase compression, and is very helpful

for the beam tuning of the present and new facilities.

Acknowledgement

First of all, I would like to express my appreciation to Prof. Martin Berz for preparing
the fascinating course of VUBeam and for his continuous support during my study.
I am deeply indebted to Dr. Akira Goto, the chief of Beam Dynamics Division at
RIKEN Accelerator Research Facility, for providing me an opportunity to make this
study. I am grateful to Prof. Toshio Kobayashi at Tohoku University who kindly
loaned us the HPGe detector, allowed us to modify the preamplifier and participated
in the experiment. Also my thanks go to Prof. Hiroyuki Okamura at Saitama Univer-
sity (presently at Tohoku University) who has been sincerely concerned about me and
gave me countless pieces of advice and comment in the course of the experiment, data
analysis and writing of this thesis. Theoretical discussions on the experimental results
with Dr. Nobuhisa F ukunishi are gratefully acknowledged. I sincerely appreciate the
help from Dr. Naruhiko Sakamoto, who provided me a supportive environment for
learning about accelerator concepts and made my life at RIKEN delightful. I would
like to thank Dr. Hiromichi Ryuto for his support in the experiments and for his
careful reading of my thesis. I am thankful to Dr. Kimiko Sekiguchi-Sakaguchi who
participated in the experiments and always cheered me heartily. I wish to express
my gratitude to all the staff members of the RIKEN Accelerator Research Facility,
particularly to the RIKEN cyclotron crew for their excellent machine operation, to
Dr. Yasushige Yano, the director of the RIKEN Accelerator Research Facility, who

generously accepted me for making a study at RIKEN, and to Dr. Masayuki Kase

iii

for his arrangement of the experiments. I am grateful to Prof. Harry Weerts for his
serving my defense committee and for his perceptive comments on my thesis. I am
much obliged to Prof. Kyoko Makino for her cordial advice through the course of the
study and for her serving my defense committee. Last but not least, I would like to

thank my family with my whole heart for their encouragement.

1v

TABLE OF CONTENTS

1 Introduction

1.1 Purpose of Experiment ..........................
1.2 Cyclotron .................................
1.2.1 Principle of Cyclotron ......................
1.2.2 Sector Focus Cyclotron ......................

1.2.3 Beam Extraction

ooooooooooooooooooooooooo

1.2.4 Single— and Multi—Turn Extraction ...............

1.2.5 Longitudinal Emittance .....................

1.2.6 Phase Compression ........................
1.3 HPGe Detector .....

1.3.1 Range of Particles

1.3.2 Simple Estimation

oooooooooooooooooooooooo

of Energy Resolution ............

1.3.3 Energy Loss Straggling ......................

1.3.4 Recombination Effect .......................

1.3.5 Radiation Damage

2 Experimental Arrangement

10

11

13

13

14

15

16

19

19

20

2.1 AVF Cyclotron .............................. 21
2.2 Ring Cyclotron .............................. 22
2.3 Beam TYansport .............................. 24
2.4 Target and Collimator .......................... 27
2.5 Magnetic Spectrometer SMART ..................... 28
2.6 Detector Systems ............................. 31
2.6.1 Energy Resolution Measurement ................. 31
2.6.2 Longitudinal Emittance Measurements ............. 32
2.7 Data Acquisition ............................. 35
2.7.1 Energy Resolution Measurement ................. 35
2.7.2 Longitudinal Emittance Measurements ............. 37
Analysis 38
3.1 Energy Calibration of HPGe ....................... 38
3.2 Veto by Active Slit ............................ 41
3.3 Time Calibration ............................. 42
3.4 Position Calibration ........................... 42
3.5 Time of Flight Correction ........................ 44
Results and Discussions 50
4.1 Energy Resolution of HPGe ....................... 50
4.2 Longitudinal Emittance of 40Ar Beam
' — case of single turn extraction — ................... 52
4.3 Longitudinal Emittance of 22Ne Beam

— case of multi-turn extraction -'-

vi

5 Conclusions

6 Future Prospects

Appendix

A Angular Distribution of Elastic Scattering

vii

62

64

66

67

1.1

1.2

2.1

2.2

2.3

2.4

3.1

4.1

6.1

LIST OF TABLES

Ranges of Ge for typical beams delivered from the RRC. ....... 15
Estimation of energy loss straggling for some materials. ....... 18
List of the experiments. ......................... 20
Accelerator parameters. ......................... 24
Energy spreads due to the angular acceptance of the collimator AB,“

and the energy-loss straggling in the target AEsmggle (FWHM). . . . 28

Typical optical characteristics of the SMART. ............. 29

Energies of 7 rays emitted by 60Co, 22Na, 137Cs and 40Kr, and the
corresponding ADC channels. ...................... 40

Peak width in observed energy spectra, the contributions from energy-
1oss straggling and the intrinsic energy resolution of HPGe at normal
and 43° injections for 1890—MeV 14N. ................. 51

Specifications of Ge detector (Princeton Gammatech: IGP1010185
Model). .................................. 65

viii

1.1

1.2

1.3

1.4

1.5

1.6

1.7

2.1

2.2

2.3

2.4

LIST OF FIGURES

Schematic layout of the new facility, RIBF, at RIKEN. ........ 1

Schematic drawings of the cyclotron. Vertical (left) and horizontal
(right) mid plane cross sections. .................... 3

Schematic drawings of AVF (upper panel) and Ring (lower panel) cy-
clotrons at RIKEN. Both of them have four sectors. ......... 6

Beam current versus radius measured with the differential probe for a

135-MeV/ A 28Si14+ beam at the RRC. ................. 9

Kinetic energy versus RF phase near extraction (solid curve) and en-
ergy profile of the extracted beam for the case of multi—turn extraction
(dots). .................................. 10

(T, t) correlation of 185—MeV Ar beam measured at VICKSI (presently
ISL), Hahn-Meitner Institute [4]. The right panel shows a high-resolution
measurement (presumably, labels on abscissa, 84.8 and 85.0, should

read 184.8 and 185.0). .......................... 11

(T, (1)) correlation of the extracted beam for the case of single-turn
extraction. Injection phases are displaced by 0°, :i:3° and :l:6° around

960. ..................................... 12
Schematic layout of RIKEN Accelerator Research Facility. ...... 21
Dependence of acceleration voltage on the relative phase (1). ..... 22
Beam configuration in the RRC in the case of the AVF injection. . . 24

'Itansport line components from the RRC to F2 of SMART together
with the extraction components of the RRC.

ix

2.5

2.6

2.7

2.8

2.9

2.10

2.11

2.12

3.1

3.2

3.3

3.4

3.5

3.6

3.7

A Typical beam envelope from the RRC to the target of scattering
chamber in E4 experimental area. ...................

Side view of the SMART scattering chamber. .............
Arrangement of SMART and the detector system. ..........

Setup of the HPGe detector and the slits for the energy resolution
measurement. ...............................

Setup of Si-PSD and the plastic scintillators for the longitudinal emit-
tance measurements. ...........................

A simplified equivalent circuit and the layout of Si-PSD. .......
Data acquisition system for the energy resolution measurement.

Data acquisition system for the longitudinal emittance measurements.

Energy spectra from 13"Cs, 22Na and °°Co sources which are used for
the energy calibration of ADC channels. The peak from the back-
ground, 40K, was also observed. .....................

Energy spectra for all events (unshaded) and for events without signals
from the active slit (shaded). ......................

Typical time spectrum used for time calibration (upper panel). Pulses
from a time calibrator had a 10 ns interval over 100 ns range. The
regression line is shown in the lower panel. ..............

Spectrum used for calibration of Left ADC (upper panel). The regres-
sion line is shown in the lower panel. ..................

Qlefi‘Qfight plot for different a: generated by the dedicated position cal-
ibrator. The inset is a closeup around the intersecting point.

Spectrum of :r: / L calculated by using Eq. (2.5) (upper panel). Discrete
peaks reflecting the strip structure are clearly seen. The lower panel
shows the regression curve to deduce the correct position determined
by the least squares method. ......................

Time spectra with the first-term correction only. The injection phase
with respect to the RF phase of the RRC, A¢inj, is displaced in step
of 2°.

ooooooooooooooooooooooooooooooooooo

26

27

30

31

33

36

36

39

41

42

43

44

45

3.8 Same as Fig. 3.7but with the correction assuming (1|6) = —35.5 cm/%.

3.9 The correlation between the time and momentum of particles detected
at F2 without the stripper (left) and with the stripper (right). . . . .

3.10 Beam spot on a ZnS scintillation target at the target position with
(right panel) and without the stripper foil (left panel). Ticks on the
target are marked in 5 mm step. ....................

4.1 Energy spectra with the active slit at normal and 43° injections, re
spectively. ................................

4.2 Longitudinal emittances of 3800-MeV ”AL The injection phase A¢inj
is displaced relative to the RF of the RRC in step of 2°. .......

4.3 Schematic illustration of phase compression effect for the case of narrow-
bunched beam. The extraction time is either relative to the RF of the
RRC (upper panel) or relative to the injection (lower panel).

4.4 Projected spectra of the extraction time relative to the injection. The
phase of the RF with respect to the injection, Arm“), is shifted in step
of 2°. ...................................

4.5 Shifts of time spectra deduced from Fig.4.4 plotted as a function of
Aqu. The solid line is a prediction from Eq. (1.13). The dashed curve
is a third order polynomial for eye-guide. ...............

4.6 Time spectrum (upper panel), the longitudinal emittances for the main
and adjacent turns at the nominal Dee voltage (middle panels) and at
a slightly lowered Dee voltage (lower panels). Straight lines are for
eye-guide. .................................

4.7 Schematic illustration of (ST-6t correlations for neighboring turns at
the nominal Dee voltage (upper panel) and at a slightly lowered Dee
voltage (lower panel). ..........................

6.1 Overview of the newly fabricated HPGe detector. ...........

A31 Angular distribution of 19"Au(1“N,” N)197Au elastic scattering at E /A =
135 MeV/ A compared with Rutherford scattering. The exponential
line is for eye-guide.

ooooooooooooooooooooooooooo

xi

47

48

55

56

57

59

65

Chapter 1

Introduction

1.1 Purpose of Experiment

The new facility, Radioactive Isotope Beam Factory (RIBF), is now under construc-
tion at RIKEN and is scheduled to be operational in 2006. The schematic layout of
the facility is shown in Fig. 1.1. The main accelerator of the present facility, RIKEN
Ring Cyclotron (RRC), will be used as a pre—accelerator in this new facility. The

typical injection energy is 60 MeV/ A, although the RRC is capable to accelerate up

RI Beam Factory (RIBF): Upgrading project of RIKEN Accelerator Research Facility (RARF)

RIBF Exp. Bldg.

 

RIHF Rl beam cxpcrnnunls Will he sluflctl in 2006.

Figure 1.1: Schematic layout of the new facility, RIBF, at RIKEN.

to 135 MeV/A for Z/A = 1/2 particles.

For designing new accelerator components, such as a re—buncher after the RRC,
the information of time structure and energy spread, i.e., the longitudinal emittance of
the beam coming from the RRC is needed. For successful operation of this accelerator
complex, it is also important to know the longitudinal emittance while beam tuning.
Because the typical time and relative energy spreads of the beam coming from the
RRC are 1 ns and 10—3, the required time and energy resolutions for the measurement
are (it 2 0.1 ns and 6E / E '2: 10-4, respectively. Such an energy resolution is usually
achieved by using a. magnetic spectrometer, but, for the routine beam tuning, the
use of a compact and convenient detector system is more desirable. We propose to
employ a High Purity Germanium (HPGe) detector for this purpose. The response of
HPGe to medium energy protons, g 150 MeV, was reported, for example in Ref. [10],
but that to energetic heavy ions is not well known. In the present experiment, the
energy resolution of HPGe has been studied for 135-MeV/ A 14N, the momentum of
which is defined by using a magnetic spectrometer. We also studied the longitudinal

emittances of 95-l\s‘IeV/ A 40Ar and 110-l\"1eV/A 22Ne beams.

1 .2 Cyclotron

Cyclotron is a circular particle accelerator first built by Lawrence and Livingston in
1930. The cyclotron employs a uniform magnetic field to guide particles along the
circular orbit, so that particles can be accelerated many times by the same acceler-
ating cavities. The principle of the cyclotron, however, is limited to non-relativistic
particles because of the change of revolution frequency. The technique of varying the
radio frequency (RF) of the accelerating cavity overcomes this limitation. This is the
principle of synchrocyclotron. In 1938, a significant breakthrough, strong focusing,

came out from H. A. Thomas. He found that the radial dependence of the magnetic

 

a + l: as

fl [economic/poo I

J i ”is c) , e

magnet Dee

D

 

 

 

 

 

 

 

.1,
C

 

 

 

 

 

 

 

Figure 1.2: Schematic drawings of the cyclotron. Vertical (left) and horizontal (right)
mid plane cross sections.

field makes the revolution frequency of particles constant. The machine employing
this principle is called isochronous cyclotron. In contrast to the synchrocyclotron,
the isochronous cyclotron provides a continuous thus high-intensity beam. Presently,
most of cyclotrons are isochronous type. Details of cyclotrons as well as other types

of accelerators can be found in textbooks, e.g., Refs. [1] and [2].

1.2.1 Principle of Cyclotron

The schematic configuration of an early cyclotron is shown in Fig. 1.2. The cyclotron
consists of magnets which generate a uniform magnetic field and two accelerating
cavities which extend over the whole aperture between the poles. These cavities form
semi-circles and generate the accelerating fields between them. Because of its shape,
the cavity is often called Dee. Since particles travel inside Dees, they are contained
in a vacuum box. The magnets have coils surrounding their poles and yokes which
reduce leakage field and resistance of magnetic field.

A particle which has the charge q and is moving at the velocity of v in the electric

and magnetic fields, E and B, feels the Lorentz force,

F=q(E+'va). (1.1)

Particles injected from the center of the cyclotron perpendicularly to the uniform

magnetic field B are guided along a circular orbit. Under this condition, Eq. (1.1) is

reduced to

F = (I’UB .

An equilibrium between Lorentz force and the centrifugal force,

 

defines the curvature of the orbit r as

_7’

— . 1.2
T (113' ( )

where m. and p are the mass and momentum of the particle, respectively. 7 is the
Lorentz factor defined by 7 = 1/\/1—(v/c)2. Particles are accelerated by an electric
field E every time when passing the gap between the accelerating cavities. Because
the momentum of the particle p increases after acceleration, the curvature of the orbit
r becomes larger and larger. Accordingly, the orbit of the particle forms in spiral.

The revolution time T and the revolution frequency f”.v are given by

27rr 27r p 27rmo/ 1
T : —— — — = —

v ‘qBE qB ‘f...’

 

 

(1.3)

They remain constant for non-relativistic case, where 7 2 1. The accelerating voltage

V(t) applied to the cavities is a sinusoidal function,

V(t) = VD cos th . (1.4)

The angular velocity cap 2 27Tfrf is chosen in such a way that the particles get the

maximum energy gain qVD when passing the accelerating gaps. This condition entails

qB

27rm7 ’

 

frf : h'frev : h (15)

where h is an integer called harmonic number. When the particles’ velocities become
relativistic, 7 > 1, the revolution frequency frev becomes smaller and smaller during
acceleration and the particles get out of synchronism with frf. This is a reason why
the early cyclotron is limited to non-relativistic particles. Maximum kinetic energy

Tmax obtained by acceleration is often represented by using K -value as

2
Tmax = Ii 7

A

where A and Q are the atomic mass of the particle and its charge in units of 8,

respectively. For non-relativistic case, K can be expressed as

(r3)? 3:

7
2 mu

K' =
where mu is the atomic mass unit.

1.2.2 Sector Focus Cyclotron

The sector focus cyclotron can accelerate relativistic particles using a constant f,; by
adjusting the magnetic field B. According to Eq. (1.5), the required modulation of

magnetic field is given by
B(r) 2 Boy, (1.6)

where BO is a magnetic field in the central region of the cyclotron. This equation

indicates that the magnetic field B must increase with r in proportion to 7. Such a

Cryo-Pump
Vacuum Chamber
Magnetic Channel

 

 
   
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gradient Deflector
Corrector
6::Zector
X /’ Probe
o
34
9" T!
6
v4
; Yoke
Phase Slit \>
[V <:> < ) Resonator
Beam ‘
O 1000 . Compensator
T— l ' Cryo-Pump Turbo-Pump

 

 

 

 

 

 

 

 

 

 

 

 

Figure 1.3: Schematic drawings of AVF (upper panel) and Ring (lower panel) cy-
clotrons at RIKEN. Both of them have four sectors.

field, however, causes a vertical defocusing of particles, while it provides a horizontal
focusing. This vertical instability can be compensated by an azimuthally alternating
varying field. Focusing powers arise at the boundaries between strong and week fields.
These fields can be formed by hill and valley on the poles. This type of machine is
called azimuthally varying field (AVF) cyclotron (upper panel of Fig. 1.3). The larger
difference of field strength makes the stronger focusing power. In order to provide
a maximumly varying field, the magnets are divided into some sectors as shown in
lower panel of Fig 1.3. Accelerating cavities are arranged in the field-free regions,
where much more spaces are available than magnet regions. Thus the cavities can be
designed to have higher quality factors and generate the RFs with higher voltages.
The orbit of particles becomes quadrangle-like because the particles go straight in the
field-free regions while they curve in the magnetic fields. The average of magnetic

fields in each turn,

__1
_27r

<B<r>> / flB(r,9)d6.

must satisfy Eq. (1.6) to keep the isochronal condition, where 6 is the azimuth.

1 .2.3 Beam Extraction

Several kinds of extraction methods are employed for cyclotrons [3]. Generally in
the case of positive ion acceleration, the beams can be extracted with the help of
extraction devices such as electrostatic and magnetic deflector channels (EDC and
MDC). The EDC consists of a septum, which is a thin inner electrode at the earth
potential, and an outer electrode at a negative high potential. Reaching the final
radius, particles enter between the septum and the outer electrode to be directed
away from the cyclotron magnetic field. In order to reduce the cyclotron magnetic

field along the extraction path, MDCs are employed. In the design of MDC, it is

important to keep the stray magnetic field as small as possible in the area of the
last acceleration orbit. For achieving a high extraction efficiency and a good beam
quality, a large separation between successive turns is desired. The radial position of

a particle at an azimuth f) in the cyclotron is given by

1(6) : r0(6) + 17(6) sin(1/,.9 + (90), (1.7)

where r0(6) is the radial position of the equilibrium orbit at that azimuth, .1:(6) is
the radial oscillation amplitude and 60 is an arbitrary phase angle. V, is a betatron
tune defined as the number of cycles of the radial oscillation during one turn. For

incoherent oscillations, the amplitude 1(6) is given by

x/fir0(0)€x,

where [3,0 is the radial beta function for radius 7‘0 and at azimuth 6, and 6x the radial
emittance. Rewriting Eq. (1.7) as a function of turn number n, the radial position at

a fixed azimuth i9, 2 27m. becomes

1‘(9,~) = 1'0(f),) + 1:(6,)sin(27m(1/,.—1) + 60), (1.8)

where for convenience 14—1 has been taken since V, is close to 1, which is the case
with most isochronous cyclotrons. The separation between two successive turns is

given by

A7161) : AT()(6,) + Al SiII(27T7l(l/r—1) "l” 60)

+27r(z/,.—1).rr cos(27m(1/r—1) + 60). (1.9)

The first term on the right-hand side in Eq. (1.9) represents the orbit separation due

 

to acceleration. Using the kinetic energy of particle T: \/(m02)2+(pc)2—mc2 and

Eq. (1.2), the turn separation due to acceleration becomes

Ar 7 AT
_= _ 1.1
7* 7+1 T ’ ( 0)

 

where f and AT are the average radius and the energy gain per turn, respectively.
The second term in Eq. (1.9) gives the orbit separation by an increase in the oscilla-
tion amplitude. This can be accomplished by providing a gradient of first harmonic
magnetic field, which leads to an increase in the beta function 6%. This method is
called regenerative extraction. The third term in Eq. (1.9) describes a turn separation
due to precessional orbit motion with the oscillation amplitude 1:. The maximum turn
separation produced by the precessional motion is given by 27r(r/,.—1):1:. The extrac-
tion using the precessional orbit motion is called precessional extraction. It can be
achieved by off-center injection, which generates a rotation of the orbit center around
the machine center, and thus, the oscillation pattern of the radius. A typical turn

separation is presented in Fig. 1.4.

Extraction

 

 

l . l . l - J 1 I
n r l r l ' r ' l

3100” 3200” 3300!! 3400" 3500!!!!

Figure 1.4: Beam current versus radius measured with the differential probe for a

135-MeV/ A 28$?“ beam at the RRC.

1.2.4 Single- and Multi-Turn Extraction

In general, particles with a different value of the accelerating RF phase experi-
ence a different number of turns before reaching the extraction radius. In a purely
isochronous cyclotron, RF phase of a particle remains constant. This leads to the
multi-turn extraction. The single-turn extraction can be achieved by restricting the
injection RF phase with a help of phase slits in the central region of cyclotron. This
reduces the energy spread of the extracted beam. The flat-top technique is also use-
ful, as described later. The kinetic energy T and the radius r of a particle on an ideal

orbit with accelerating voltage V(t) in Eq. (1.4) are

 

 

T(¢) = ToCOS¢ 1’ To (1—':-¢2) (1.11)
_ T(T+2mc2) ~ _1_7_ 2
71¢) _ TO\/T0(TO+2mc2) ‘ 7° [1 2 7+1¢ j

where To and m are the kinetic energy and radius at the central RF phase 450, and ()5 is

the phase difference with respect to 950. Figure 1.5 shows the energies for orbits near

 

1.ozo_es+......,....,
1.015:
1.010E
1.006

1.000’

Kinetic Energy [arb. units]

0.995

 

 

 

 

. . 1 i - . . 1 . . - r - .
-10 —5 0, 0 it; 5 10
Phase [deg]

 

0.990 '

Figure 1.5: Kinetic energy versus RF phase near extraction (solid curve) and energy
profile of the extracted beam for the case of multi-turn extraction (dots).

10

extraction and the energy pattern of the extracted beam as a function of RF phase.
It is seen that several turns get extracted when an energy gate opens between T1
and T2, which are mainly defined by the EDC and MDC apertures. The single-turn
extraction can be accomplished by restricting phase width S gbg—gbl. This is further

discussed for an actual case in Sec. 4.3.

1.2.5 Longitudinal Emittance

The motion of each particle at any given time is defined by the space coordinate
(1:,y,z) and the momentum coordinate (px,py,pz). Here the beam is assumed to
propagate in the z-direction. Particles in a beam occupy a certain region in phase
space which is called the beam emittance. The concept of describing a particle beam
in phase space is very powerful because the density of particles in phase space does not

change along a beam transport line (Liouville’s theorem). Since the coupling between

 

   

 

 

 

       
 

 

 

 

 

1. naming: 2
rinsli ,igymiep; ';
:11 l i“ >.
3e? 1; i 1' 35
= _ ii .5?! i
._ -- Is. 1: s
i‘f' 5%
1: il
2- ' 13'
- F
- i3. g .
I - _ .ii
1..§ as _ " l! Hg! _
[J : 113 éi‘élfi
I'1 1 15L!!! 1:1!1.‘i=
184.1. 184.6 184.8 84.8 85.0
EKlMeV]

Figure 1.6: (T, t) correlation of 185-MeV Ar beam measured at VICKSI (presently
ISL), Hahn-Meitner Institute [4]. The right panel shows a high-resolution measure-
ment (presumably, labels on abscissa, 84.8 and 85.0, should read 184.8 and 185.0).

11

 

1.010
1.005

1.000

Kinetic Energy [arb. units]

 

 

 

0.995

 

Phase [deg]

Figure 1.7: (T, 95) correlation of the extracted beam for the case of single-turn extrac—
tion. Injection phases are displaced by 0°, 2E3° and i6° around (1)0.

the transverse and longitudinal motion, as well as the coupling between the horizontal
and vertical plane, is being ignored in linear beam dynamics, six-dimensional phase
space can be split into three independent two-dimensional phase planes. In systems
where the beam energy stays constant, the slopes of the trajectory apr/p and
b E py /[) may be used instead of the transverse momenta and the transverse emittances
are usually defined as areas in ar-a and y-b planes. Likewise the longitudinal emittance
is defined as an area. in z-p plane or, as another set of canonically conjugate variables,
in t-T plane. The area alone, however, does not reflect the detailed quality of the
beam thus we will rather discuss the longitudinal distribution in t-T plane.

The beam extracted from the cyclotron is expected to have a quadratic correlation
between T and Q5, or equivalently time t, according to Eq. (1.11). Such a correlation
was actually measured at several facilities [4, 5]. An example at VICKSI (presently
ISL), Hahn-Meitner Institute, is shown in Fig. 1.6.

The phase width of the injection beam is often reduced by using a phase slit
and a buncher so that the single-turn is extracted easily. In this case, the quadratic
correlation is not observed, but it is useful to intentionally displace the injection phase
to see the correlation and to diagnose the acceleration condition conveniently (Fig.

1.7). This method is employed in the present experiment for 40Ar case (Sec. 4.2).

12

1 .2.6 Phase Compression

The phase compression was first mentioned by Miiller and Mahrt [6] and generalized
in Ref. [7]. A radial voltage distribution of the RF cavity produces a time varying
magnetic field. This field compresses the bunch size of beam for a radially increasing
voltage or expands it for a radially decreasing voltage. For an ideal isochronous

cyclotron, the effect of phase compression can be described by the Hamiltonian

H(T(n),¢(n)) = ql/(n) sin (15(n) ,

where q‘)(n) is the relative phase and qV(n) is the peak energy gain per turn at n-th
turn. Since the Hamiltonian H does not depend explicitly on the turn number n
(aH/Bn = 0), it is a constant of motion. This leads to an important relation between

peak energy gain and relative phase of acceleration,

(1V(711)Sin¢(n1) = qV(n2)sin $012) a (1-12)

where n1 and 71.2 are turn numbers in an isochronous cyclotron. According to this
equation, a voltage distribution increasing from Vin,- at injection to Vext at extraction

can compress the original phase spread quj into

l/in'
05m = V—Jt'q5inj - (1.13)

1 .3 HPGe Detector

In this section, matters related to operation of HPGe detectors are described. Detailed

review of them can be found in textbooks, e.g., Refs. [8] and [9].

13

1.3.1 Range of Particles

Heavy charged particles lose their energy by Coulomb interaction with the electrons
and the nuclei of absorbing materials. The collisions of heavy charged particles with
the free and bound electrons of the material are mainly responsible for the energy
loss of heavy particles and result in the ionization or excitation of the atom. The
scattering from nuclei also occurs, although not as often as electron collisions. Thus
the major part of the energy loss is due to electron collisions. The average energy

dE
loss per unit path length, —, was calculated by Bethe and Bloch. The Bethe-Bloch

(1:1:

formula is

 

(1E 2 .2 Z 22 2rr2.,._’y2122Wmax .2
_fi; : QWIVGTCTHRC p235 [In ( I2 — 2,6 , (1.14)

where
27r]\far'3m,.c"2 = 0.1535 MeV c1112/g
Na : Avogadro’s number = 6.022 X1023 mol‘1
re : classical electron radius = 2.817x10"23 cm

11),. : electron mass = 0.511 MeV/c2

Z : atomic number of absorbing material
A : atomic weight of absorbing material

p : density of absorbing material

2: : charge of incident particle in units of e

VVmax 2 2771,.3c21]2 : maximum energy transfer in a single collision
U . . .
[3 = — of the meldent particle

C

7) = 137 .

14

The mean range of a particle with a given energy E0 is obtained by integrating the

inverse of Bethe-Bloch formula over E,

3(a)) = A150 ($4.15.

The ranges in Ge for some typical beams calculated by Eq. (1.15) are listed in Table

(1.15)

1.1. The result indicates that the HPGe detector with thickness of 1 cm, which is
easily obtained commercially, can stop the beams of 60 MeV / A and serve as an energy

detector for the present purpose.

Table 1.1: Ranges of Ge for typical beams delivered from the RRC.

E/A = 135 MeV/A

E/A = 60 MeV/A

 

 

 

 

 

Particle Energy Range Particle Energy Range
[MeV] [cm] [MeV] [cm]

01 540 3.798 a 240 0.920
12C6+ 1620 1.265 12C6+ 720 0.307
”N” 1890 1.084 14N7+ 840 0.263
1608+ 2160 0.949 1608+ 960 0.231
20Ne10+ 2700 0.760 20Ne10+ 1200 0.186
28Si14+ 3780 0.546 2(“Si14+ 1680 0.136
40Ar18+ 5400 0.477 “(’Arlg+ 2400 0.122

 

 

 

 

 

 

 

 

 

1.3.2 Simple Estimation of Energy Resolution

The intrinsic energy resolution 66 depends on. the number of electron-hole pairs pro-
duced by incoming beam and the Fano factor. Assuming that all the energy deposited
by radiation E is used to create electron-hole pairs and that the number of those pairs
n follows the Poisson distribution, the expected relative energy resolution 66 / E can

be obtained by

— = 2.35 (1.16)

15

where n = E / w and w is the average energy for electron-hole creation, which is 2.96 eV
for Ge at 77 K. The F ano factor F is still not well determined, but is about 0.12. The
total energy resolution 6 E contains contributions from other sources, e.g., electronics
noise and fluctuation of leakage current. Denoting them by D, the resolution can be

expressed as

6E = x/o‘e? + D2. (1.17)

A simple estimation of energy resolution is obtained by neglecting D and by us-
ing certification values given in catalogs of commercial products. For example, the
DGP100-15 planer-type Ge detector of EURISIS MEASURES Inc., a typical charged-
particle detector with thickness of 15 mm and sensitive area of 100 mm2, has an energy
resolution of 6E0 = 20 keV (FWHM) for a particles with E0 = 5.486 MeV. On the

assumption that (560 = 6E0, the relative energy resolution for 1890-MeV 14N becomes

56 __ E0 550 __ . —4
E _ EEK -1.96><10 (FWHM).

This value makes HPGe very promising for the present purpose.

1.3.3 Energy Loss Straggling

In the measurement of heavy ions, one of major source of D is the energy loss strag—
gling in the entrance window of the detector, typically made of Be, and in other
materials which particles pass through. The amount of energy loss is not equal to the
mean energy loss because of the statistical fluctuations in the number of collisions of
charged particles with electrons and in the energy transferred in each collision. T here-
fore, after passing through a fixed thickness of material, an initially mono-energetic
beam has an energy distribution. Calculating the distribution of energy losses for a

given thickness of absorber is generally divided into two cases: thick absorbers and

16

thin absorbers.
For relatively thick absorbers, where the number of collisions is large, the total

energy loss distribution will approach the Gaussian form,

f(.17, A) o< exp [————

where :1: is the thickness of the absorber, A is the energy loss in the absorber, A is the
mean energy loss, and a is the standard deviation. In the case of relativistic heavy

ions, the spread a of this Gaussian can be calculated by

. — .1132) .
0'2 = gtfi—z-O'é and (1.18)
. Z Z
08 = 47rNarg(mecz)2pZ;r = 01569pr [MeVQ], (1.19)

where 00 is the spread of the Gaussian for non-relativistic heavy ions, Na is Avogadro’s
number, re and me are the classical electron radius and mass, and p, Z and A are the
density, atomic number and atomic weight of the absorber, respectively.

For thin absorbers or gases, where the number of collisions is small, the distribu—
tion of energy loss is complicated to calculate because of the possibility of large energy
transfers in a single collision. Since a long tail is added to the high energy side of
the energy loss probability distribution, the mean energy loss no longer corresponds
to the peak. One basic calculation of this distribution was carried out by Vavilov.

According to Vavilov’s theory, the spread a is given by

 

. 2 1 _ 2
02 = €— fl , (1.20)
h: 2
- _ 2 2 Z 22 . . .
where K. = A/ W max and A 2 f = 27rNa'remec pZ—B—Q-z, whlch IS the approx1mated

mean energy loss obtained by taking only the first term and ignoring the logarithmic

term in Eq. (1.14). Vavilov’s formula agrees with Eq. (1.18) for heavy particles.

17

Substituting K. and 6 to Eq. (1.20), a is reduced to

0‘ = C2, where

. Z
C = 27rNa‘rjmgc4er]

The energy loss straggling caused in a thin absorber is in proportion to the charge
of incident particle, but independent of the injecting energy E. Thus the relative
energy spread a / E becomes larger with E decreasing. It may be useful to rewrite the

formula as

 

Thus, for incident particles having the same injection energy per nucleon and the

same charge—to-mass ratio z/Ain, the relative energy spread becomes constant.

Table 1.2: Estimation of energy loss straggling for some materials.
Ener , thickness (SE/E

 

 

 

[MeV A] [rim] = 2.350/E
Be window
135 300 0.38X10’3
135 25 0.11x 10‘3
60 25 0.25x 10"3
Plastic Scintillator

135 100 0.18><10‘3
60 100 0.41x 10’3

 

Table 1.2 shows the energy loss straggling estimated for some materials. The
plastic scintillator is used as a timing detector. Since its contribution is relatively large
even with a thickness as thin as 100 nm, the use of a micro-channel plate combined
with a thin foil for secondary electron production may be considered. Contributions
from the vacuum window (Mylar, aramid, etc), as well as the gold target which is

used for elastic scattering, must be also taken into consideration.

18

1.3.4 Recombination Effect

Another possible source of D in Eq. (1.17) is the recombination effect. In the measure-
ment of heavy ions, the high density of charge carriers created along the ion tracks can
decrease the local electric field for charge collection, thus increase the magnitude of
the electron—hole recombination. A method usually employed for reducing the pulse
freight defect caused by this is to increase the bias voltage. However, the leakage
current, which will be increased by the radiation damage described in the next sec—
tion, may limit the maximum bias voltage and make this method impractical. The
recombination effect is expected to depend also on the relative orientation of the par-
ticle path with respect to the electric field. Therefore, in the present experiment, the
energy resolution has been measured for inclined particle injection as well as normal

injection with respect to the Ge crystal (Fig. 2.8).

1 .3.5 Radiation Damage

Incident particles collide with lattice atoms and knock them out of their normal posi-
tions with a certain probability. The resulting structural defects cause imperfection of
charge collection because they capture charge carriers in the semiconductors. T here-
fore after long irradiation, the degradation of energy resolution appears. A review
of the radiation damage of Ge detector for protons can be found in Ref. [10]. Ac-
cording to this review, Ge detectors lose their resolution after irradiation of ~ 109
protons/cm2, which corresponds to 10 days use at a rate of 1 kcps. It is also reported
that, in the case of Si detectors, the effect of radiation damage by heavy ions is re-
markable compared with that by light ions [11]. Thus, Ge detectors must be carefully

protected against heavy particle radiations.

19

Chapter 2

Experimental Arrangement

Table 2.1 summarizes the measurements discussed in this thesis. All the experiments
were performed in the E4 experimental area at RIKEN Accelerator Research Facility

(RARF). The schematic layout of RARF is shown in Fig. 2.1.

Table 2.1: List of the experiments.

 

 

Date Beam Energy Measurement
Nov. 16, 2002 14N 135 MeV/ A Energy resolution of HPGe
Jun. 26, 2003 40Ar 95 MeV/ A Emittance for various injection phase
Oct. 21, 2003 22Ne 110 MeV/ A Emittance for multi-turn extraction

 

 

 

 

 

 

 

The test of HPGe detector was carried out using the 14N beam from the RRC
in November, 2002. Though our interest is to estimate energy resolution of HPGe
for particles with energy around 60 MeV/ A, which is the injection energy in RIBF,
the highest beam energy 135 MeV/ A was chosen in order to reduce contributions
from energy-loss straggling. The 14N beam accelerated by the AVF cyclotron and
the RRC was transported to a scattering chamber in the E4 experimental area and
elastically scattered by a gold target. Scattered particles were momentum-analyzed
by the magnetic spectrometer SMART (Sec. 2.5) [12] and detected at the second focal
plane by a HPGe detector (EURISYS MEASURES: EGM 3800—30-R) with an active

slit for defining the momentum.

20

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

20m

AVFC clotron from UNAC
-. ,0
E6 --\ .2
k " " v
\
. Ring Cyclotron
E7
\
\ v v - ___ i
ii
l
; L
E2
E4 ll /
E3 E1
0 10
l l I

 

Figure 2.1: Schematic layout of RIKEN Accelerator Research Facility.

The longitudinal emittances of 40Ar at 95 MeV/ A and 22Ne at 110 MeV/ A from

the RRC were measured also utilizing the spectrometer in June and October, 2003,

respectively. After scattered by a gold target and momentum-analyzed, particles were

detected at the second focal plane by a pair of plastic scintillation counters followed

by a silicon position-sensitive detector. In the study of 40Ar, the injection time of the

beam to the RRC was displaced with respect to RF phase to cover the wide range

of beam distribution (see Fig. 1.7). Voltages applied to Dees of the RRC were also

varied for the same purpose in the measurement of 22Ne beam emittance.

2. 1 AVF Cyclotron

The AVF cyclotron has K = 70 MeV. It consists of four spiral sectors and two Dees

with an angle of 85° (Fig. 1.3). The pole diameter is 1.73 m and the gap between

21

the poles is 300 mm. The maximum flux density is 1.7 Tesla. The mean extraction
radius is 714 mm, which is the four-fifth of the mean injection radius of the RRC. RF
is tunable from 12 to 24 MHz, which corresponds to the accelerating energy from 3.8
to 14.5 MeV/ A for ions having a mass to charge ratio smaller than 4. The harmonic
number hAVp is 2. To improve the extraction efficiency and beam quality, a flat-
top acceleration system was installed in collaboration with the Center for Nuclear
Study (CNS), Graduate School of Science, University of Tokyo, in 2001 [13] and has
been used in routine operations. The flat-top acceleration voltage is generated by a
superposition of the fundamental frequency (12—24 MHz) and 3rd-harmonic (36—72
MHz) frequency. This system reduces the momentum and time spreads of the beam

and improves the transmission, not only for the AVF but also for the RRC.

2.2 Ring Cyclotron

The RRC has K = 540 MeV. It consists of four sectors with an angle of 50° and two
Dees with an angle of 235° (Fig. 1.3). The pole gap is 80 mm and the maximum flux
density is 1.67 Tesla. The beam pre-accelerated by the AVF cyclotron is transported

through the beam line 4 m above the median plane of the RRC and levelled down

¢>o . ¢o

    
     

3:
>4
.................................................. F‘I............
psi: :0
l I 0
01 1O
0). l
Q1 1
1 i
I fly
1
I
i
1

Figure 2.2: Dependence of acceleration voltage on the relative phase (15.

22

into the medium plane at a slope of 45° by a couple of 45° bending magnets, a
quadrupole doublets and a quadrupole singlet. Each of Dees can generate 275 kV
at. maximum. The Dee voltage has a radial distribution for the purpose of phase
compression described in Sec. 1.2.6, and Vat/Vin,- = 1.6 for the frequencies operated
at the present experiments. RF is tunable from 18 to 45 MHz and the operational
RF is twice that of the AVF. The harmonic number hRRC is 5 in the case of the
AVF injection, thus particles are not accelerated at the highest voltage (Fig. 2.2).
However, the quadratic relation in Eq. (1.11) is applied also in this case, because the

dependence of acceleration voltage on the relative phase c5 is expressed as

V(cfi) = V0(sin(¢0—¢)+sin(q§o+¢))
= 2VOSinq$0cosq§,

where

235°
(190 = 2 X hRRC CE.“ 600 .

 

The injection radius is 0.89 m on the average, while the extraction radius is 3.56 m.
The velocity gain is 4, which is equivalent to the ratio of the extraction to injection
radii. Since the ratio of the AVF extraction radius to the RRC injection radius is 4/ 5,
while hAVF/hRRC = 2 / 5, the beam exists only in alternate RF buckets as shown in Fig.
2.3. Thus the beam bunches in neighboring turns are extracted at different times by
1 / frf (cf. Fig. 4.6). This configuration is useful to diagnose single turn extraction. An
example is presented in Sec. 4.3. The beam accelerated up to the extraction radius is
peeled off by an EDC and extracted from the RRC through a couple of MDCs. Two
bending magnets, EBMl and EBM2, guide the extracted beam to the transport line.
The accelerator parameters of the AVF and the RRC in the present experiments are

summarized in Table 2.2.

23

 

Figure 2.3: Beam configuration in the RRC in the case of the AVF injection.

Table 2.2: Accelerator parameters.

 

 

 

 

 

 

Beam AVF RF RRC RF Harmonics Intensity
135-MeV/A I4N7+ 16.30 MHz 32.6 MHz 5 50 enA
95-MeV/A 40Ar17+ 14.05 MHz 28.1 MHz 5 50 enA
110—MeV/A 22Ne10+ 15.05 MHz 30.1 MHz 5 100 enA

 

2.3 Beam Transport

The beam extracted from the RRC is transported to the target in the E4 experimental
area through the transport system shown in Fig. 2.4. The transport system consists of
six dipoles (EBMI, EBM2, DAAl, DMAl, DAD4, DMD4), nine quadrupole triplets
(QA01, QA02, QAll, QD12, QD13, QD14, QD15, QD16, Q4A1), a quadrupole septe—
nary (TWISTER), a set of two dipoles (WDl, WD2) and a quadrupole doublet (WQl,
WQ2). The TWISTER, WDl, WD2, WQl and WQ2 are the parts of the spectrom-
eter SMART described later. A removable charge stripping foil (STRIP in Fig. 2.4)
can be inserted between QA01 and QA02. This foil was used for the purpose of
measuring the dependence of time-of—flight on the momentum of the beam in the
experiment using the 22Ne beam. Details are described later in Sec. 3.5.

A typical beam envelope calculated by using the computer code TRANSPORT [14]

is shown in Fig. 2.5. The transfer matrix from the EDC to the target is

24

H120 NHQO

$7- 8: -.

mom i.

8T-.- - B: -

SEE «on
G Hg ’/
N93 /

N03 as,

HOB ADS Nam

nu
DU

U
m EMEB

2
mm .330

nun—o vane made .350 ~
, Ba 8.. . D
#043

mom (

Figure 2.4: Transport line components from the RRC to F2 of SMART together with

the extraction components of the RRC.

25

Beam Envelope from RRC to Target

 

: f—‘T Y T _l' V '7 '7 TV I T I U ' l V Y ' T l ' V V V I V V V I '— V V I'— V I 1 V V V I V Y fiT:
4 T Horizontal ‘.
Z Vertical

 

 

 

 

Length [m]

Figure 2.5: A Typical beam envelope from the RRC to the target of scattering cham-
ber in E4 experimental area.

 

 

1% 0.8089 —0.0430 0 0 0 —3.1035 :1:
a’ 18.857 1.9009 0 0 0 —22.837 a
y' 0 0 —0.1378 —0.1151 0 0 y
= , (2.1)
b’ 0 0 9.7494 0.8878 0 0
1' —0.2214 —0.8719 0 0 1 —7.7312 1
(5', 0 0 0 0 0 1 5

 

 

 

 

where r and y denote horizontal and vertical positions in cm, a and b horizontal and

vertical angles in mrad, and 6 = (Sp/p in ‘70, respectively.

26

Incident

 

 

Scattered ’7
pa<rticles + _
x i

——#J

 

 

 

     

Collomator l
Faraday cup

 

 

Figure 2.6: Side view of the SMART scattering chamber.

2.4 Target and Collimator

Figure 2.6 shows a schematic view of the scattering chamber. It is a cylindrical
chamber with an inner diameter of 510 mm and equipped with a turning table. Since
the beam injection angle is rotated by the beam swinger system described in the next
section, the Faraday cup is installed on the turning table. The target is rotated so
that the thickness viewed by the incident beam is kept constant. To keep the count
rate of detectors reasonable, elastically scattered particles are measured instead of
direct measurement of the beam. The scattering angle 6 must be sufliciently small
in order to obtain a good signal-to-noise ratio (elastic to non-elastic scattering ratio),
but can not be ~0° to separate scattered particles from the beam. In the present
experiments, 6 2 2° was chosen (cf. Fig. A.1). Usually the beam on target has a
distribution with width of a few mm. To make the most of the momentum resolving
power of the SMART, a gold strip target with 1-mm width and 1-pm thickness was
used in the energy resolution measurement of HPGe, while an ordinary gold foil target
with 0.25-1im thickness was used in the longitudinal emittance measurements in order

to reduce the energy-loss straggling.

27

To keep the higher order effects other than (.L'|(5) small, a 5.5-mm thick tantalum
collimator with an aperture of 5 mm in diameter was set 420-mm downstream from
the target, which corresponds to the 12-mrad angular acceptance. Due to the finite
mass of the target, the angular acceptance also contributes to the energy spread.
The energy dependence on the scattering angle dE / d6 and the energy spread AEang
due to the angular acceptance of the collimator are calculated according to the two-
body kinematics and summarized in Table 2.3. Also the energy spread AEstmggje
due to the energy-loss straggling in the target, together with target thickness, and
their quadratic sum AEtoml are presented. They are comparable to the resolution of
SMART and sufficiently smaller than the beam energy spread.

Table 2.3: Energy spreads due to the angular acceptance of the collimator AEa,ng and
the energy-loss straggling in the target AEstraggle (F WHM)

 

 

 

 

 

 

I4N ”Ne 40Ar units

Beam energy T 1890 2420 3800 [MeV]
dE/d6 10.1 20.0 56.6 :MeV/rad]

AEang 0.12 0.24 0.68 [MeV]

Target thickness 1 0.25 0.25 [pm]

AEsmggle 0.13 0.09 0.16 [MeV]

ABM 0.18 0.33 0.84 [MeV]

AEtotal /T 0.95 1.36 2.21 x10'4

 

 

 

 

2.5 Magnetic Spectrometer SMART

The magnetic spectrometer SMART [12] is composed of the beam twister, the beam
swinger, and the magnetic analyzer consisting of QQD—QD magnet series (Fig. 2.7).
Different from ordinary spectrometer systems, the scattering angle is changed by
rotating the beam swinger while the analyzer is fixed on the ground. The twister is
used to keep the beam emittance irrespective of the scattering angle. The analyzer has

two focal planes, F1 and F2, each of which serves as the large—acceptance and high-

28

resolution spectrometer, respectively. The typical optics properties of the SMART

are summarized in Table 2.4.

The first order transfer matrix from the target to F2 calculated by using RAY-

—0.8337
16.078

TRACEiS
Fcr.’- ”0.5212 —0.0007 0
(1' 18.8574 1.9009 0
y' = 0 0
b’ 0 0
_6’_ _ 0 0 0

 

 

 

0

0
-—0.0578
—0.0946

0

—7.5131 1 ”:1:-

—38.0819 0.
0 y
0 b
1 _ _ 5_

 

 

 

where .1: and y denote horizontal and vertical positions in cm, a and 0 horizontal and

vertical angles in mrad, and 6 = 6 in %, respectively. The momentum resolution
P P

in Table 2.4 is calculated by assuming a. beam width of 1 mm on the target. The most

important matrix element in Eq. (2.2) is (.116), which is experimentally determined

to be —-7.7 cm/% in the present experiments. Other terms, including higher order

matrix elements, have negligible contributions due to the small acceptance of the

collimator.

Table 2.4: Typical optical characteristics of the SMART.

 

 

 

 

 

Focal plane F1 F2
Magnet arrangement Q-Q-D Q-Q-D-Q—D
Momentum dispersion 3.4 m 7.5 m
Momentum resolution p/(Sp 3000 13000
Momentum acceptance Ap/ p 15 % 4%
Angular acceptance 20 msr 10 msr

 

 

29

D1

 

detector
system

 

Fl Q3 F2 ‘

D2 ‘

 

 

 

close-up view of the detector system

 

 

o ' - ‘9 . //
tw13ter fr: 4‘ \‘f/{I/y

~\
§ \

§

L_l_l
O 10 20 cm

 

 

 

 

Figure 2.7: Arrangement of SMART and the detector system.

30

2.6 Detector Systems

Two types of detector systems were used for the present experiments: (1) the system
for the energy resolution measurement, composed of a HPGe detector and brass and
scintillator active slits, which are used for defining the particle momentum as shown in
Fig. 2.8, and (2) the system for the longitudinal emittance measurements, composed
of a silicon position sensitive detector (Si-PSD) and a pair of plastic scintillators

detecting the position and timing of particles, respectively (Fig. 2.9).

2.6.1 Energy Resolution Measurement

In the energy resolution measurement, momentum-analyzed particles were brought
to the atmosphere through a 16-,um aramid window, collimated by the slits and
detected by the HPGe detector. The brass slit with a thickness of 10 mm was set
20—mm downstream from the vacuum window to protect HPGe against undesirable
irradiation. The aperture size was 3 mmwx 12 mm“. Behind the brass slit, the

active slit made of plastic scintillator with a thickness of 0.1 mm and an aperture

   

 

 

<—active slit
brass slit

 

 

 

 

L1_.u_1_l_1_1_1_1_l

Figure 2.8: Setup of the HPGe detector and the slits for the energy resolution mea—
surement.

31

of 1 mmwx 10 mmH was located. According to Eq. (2.2), the l-mm aperture width
corresponds to a relative momentum width of 1.3x 10‘4. The active slit was attached
to a photo multiplier tube (PMT) via a light guide. A carbon aramid foil with a
thickness of 9 11m was used for light shield. Using the active slit, particles scattered
from the edge of the brass slit were vetoed, which, otherwise, cause a tail of peak in
the spectrum.

The HPGe detector (EURISYS MEASURES: EGM 3800-30-R) consisted of a Be
entrance window of 300-11m thickness and a semi-planar HPGe crystal with 30-mm
thickness and 70—mm sensitive diameter. The crystal was mounted 5-mm behind from
the entrance window in a cryostat. This detector was specially fabricated for the mea-
surement of intermediate energy protons by Kobayashi group at Tohoku University
and was kindly loaned to us for this experiment. Although the feedback capacitor
of the preamplifier was modified to allow the measurement up to ~ 4-GeV particles,
the thick Be window is not appropriate for heavy ion detection and must be care—
fully treated in the analysis. Also the HPGe detector was set either perpendicular or
inclining by 43° to the particle path (Fig. 2.8), expecting to see the influence of the
electric field direction on the charge collection, which may be deteriorated by the high
density of electron-hole pairs as described in Sec. 1.3.4. The difference of energy-loss
straggling in the air between the vacuum window and the detector, 44 mm and 65
mm for normal and inclined injections, respectively, must be taken into consideration
in the analysis. The detector was operated at the liquid nitrogen temperature with a

bias voltage of —4000 V.

2.6.2 Longitudinal Emittance Measurements

In the longitudinal emittance measurements, momentum-analyzed particles were brought
to the atmosphere through a 50-nm Kapton vacuum window (See Fig. 2.9). Two plas—

tic scintillators, J 1 (front) and J2 (rear), measured the arrival time of the particles.

32

‘l

—— Si-PSD

E>=if<1 l
PMT J 1 J2 PMT

Plastic Scinti.

i L1_1_1_L_L.L_1_1_1_l
j 0 10 cm

Figure 2.9: Setup of Si—PSD and the plastic scintillators for the longitudinal emittance
measurements.

 

 

 

 

 

 

They have sensitive areas of 65 mmx 55 mm and a thickness of 0.5 mm. The PMTs
were shielded by iron tubes in order to prevent the reduction of signals due to stray
field produced by the second dipole magnet of the spectrometer. Since the PMT and
the light guide were attached to the opposite side for each scintillator, the averaged

time

___ tJl + tJ2
'3V 2

becomes almost position-independent. The time resolution, on the other hand, is

estimated from the spread of time difference between J1 and J2,

15616 = tJl — in.

After correcting the position dependence, (Stdig = 212 and 218 ps (FWHM) have
been obtained from the data of 3800-MeV 40Ar and 2420-MeV 22Ne, respectively. By

assuming 6tJ1 = (5th, (5tav is related to (Stdig as

(St _ 6&3, +6t32 : 6rd”;

_ 2 2 ’

 

33

which results in 106 and 109 ps (F WHM) for 40Ar and 22Ne, respectively.

A silicon position sensitive detector (Si-PSD), Hamamatsu S2461, was used to
measure the horizontal positions of the particles at F2. The Si-PSD is a strip detector
consisting of 48 p-type silicon strips and an n—type silicon base with 250-11m thickness.
Each strip is 48 mm in length and 0.9 mm in width and implanted on the silicon
base at intervals of 1 mm. An aluminum electrode is mounted on each strip and
connected to an external resistive divider network system giving discrete readouts. A
simplified equivalent circuit along with the layout of the strips is shown in Fig. 2.10.
The operating voltage of -60 V was applied to the Si-PSD in order to obtain full

depletion. Two output signals from Si-PSD, Qleft and Qrigm, can be expressed as

 

7'1 + Rf:
Qleft = Q m
(2.3)
L—.1:
T2 ‘1' R L
Qright : Q m 1

where L is the length of Si-PSD, Q is the charge produced by an incident particle
injected at the distance 1: from the left end of the range, R is an impedance of the

circuit of Si—PSD and TI and r2 are input impedances of preamplifiers. Equation (2.3)

 

 

 

 

 

  
  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 -l
L
X resistive divider 48 47 ' ' ' 3 2 l
network —— —— — _ M r
Z, R ]
Q-‘°" > Q_right
['1 r2
T KM“\/\. NLA./\/~
MP“ N‘VT'NW 48 mm
r1...
-' ' Al electrode i
I H p-type Si
n-type Si
n-lmplantation r —‘ ~—— —— L__l ___1I
If 48 mm A

Figure 2.10: A simplified equivalent circuit and the layout of Si-PSD.

34

can be written as

Qleft = A]: + B
Qright = A(L—:r) "I" C .

(2.4)

The parameters B and C are obtained by using a pulse generator and a dedicated

calibrator (See sec.3.4.). Then the position x is given by

’L‘ = Qleft - B
‘ (Qleft—B) + (Q,,g,,,_c) L- (2.5)

 

2.7 Data Acquisition

A schematic diagram of the data acquisition systems for the energy resolution mea-
surement and the longitudinal emittance measurements are shown in Figs. 2.11 and
2.12, respectively. In the case of the energy resolution measurement, data were stored
in HSM (CES High Speed Memory 8170) via FERA bus and FERA driver (LeCroy
4301). In the case of the longitudinal emittance measurements, on the other hand,
data were read via CAMAC at each event without buffering. In both cases, data
were stored and analyzed on a personal computer running a free-Unix clone, Linux.

Details of the data acquisition system can be found in Ref. [15].

2.7 .1 Energy Resolution Measurement

The signal from HPGe detector was fed to a spectroscopy amplifier (ORTEC 671)
and formed to a Gaussian with shaping time of 6 nsec. The unipolar output (UNI in
Fig. 2.11) has a pulse height in proportion to the energy deposited in the HPGe. It
was digitized by an ORTEC AD413A analog-to—digital converter (ADC) with a 13-bit
resolution and subsequently fed to HSM to make energy spectra. The bipolar output

(B1) was used for monitoring signals. The logic signal output, counter & rate meter

35

 
   
 

Active

Slit AMP

Counting Room

 

 

 

 

 

 

 

 

 

 

 

Date Acquisition Software
Counting Room start I “Op 0
‘ Output HSM OVFL
Register
stop
Fl 6.6 0.6
vcto OUT veto
sum
756 756 G G
Lo ic Uni Logic Unit '
level I level 2
Counting Room
m” TAC
Fm Logic Dela 4303
TPC
60 ns 60 ns Delay
4120*

 

 

Counting Room

 

 

 

 

 

43009

HIPO
REQ BUSY
CLR 4301 WAX
FERA wsr
0“ DRIVE

 

- HSM

DAQ ON

 

OVFL

Figure 2.11: Data acquisition system for the energy resolution measurement.

Q_lctt Pn-r .. ., SA671 uenuator 1/4 %
Q_right Pm SA671 AttenuatorlM

 

 

 

60119

W

levelZ

level 1 veto

 

 

756
:[Logic Unit

 

 

756
Logic Unit

 

 

 

 

 

 

 

RRC Cavity

Figure 2.12: Data acquisition system for the longitudinal emittance measurements.

36

(CRM), was fed to a. logic unit (Phillips Scientific 756) and a gate generator (LeCroy
222) to make the gate for ADC. The signal from the active slit was amplified by 10,
discriminated by a constant-fraction discriminator (ORTEC CF8000) and fed to an
ORTEC 567 time—to—amplitude converter (TAC). The TAC output was converted by
AD413A and used for a veto.

2.7 .2 Longitudinal Emittance Measurements

The signals from plastic scintillators, J 1 and J 2, were amplified by Phillips Scien-
tific 776 and fed to a constant fraction discriminator (CF D), Tennelec 454, in the
experimental area. The CF D outputs were transmitted to the counting room and
discriminated again by a discriminator (LeCroy 821). The outputs were subsequently
sent to a time-to—digital converter (TDC), KAIZU 3781A, in order to obtain the infor-
mation of particle arrival time. The outputs from the discriminator were also used to
make a coincidence signal between J1 and J 2, which triggered the data acquisition.
The signals from J1 and J2 were also sent to an ADC (LeCroy 2449W). The Si-PSD
signals, Q19“ and Qright, were transmitted to shaping amplifiers (ORTEC 671) via a
preamplifier and subsequently fed to an ADC (HOSHIN C008). It should be noted
that the RF signal fed to TDC represents the injection phase and is different from
the one fed to the RRC cavities, the phase of which is shifted by a phase shifter (Fig.

2.12).

37

Chapter 3

Analysis

3.1 Energy Calibration of HPGe

The output of HPGe was calibrated by using the standard 7—sources, 60Co, 22Na and
137Cs. Figure 3.1 shows the energy spectra for these sources. The background 7 ray
from 40K, as seen in Fig. 3.1, was also used for calibration. The energies of gamma
rays and corresponding ADC channels are listed in Table 3.1. The regression line

obtained by the least. squares method is
Energy [keV] = —4.03 -l— 0.923 X ADC [channel] . (3.1)

The energy resolution at 1332.5-keV was 14.2 keV (F VVHM) in this calibration. This
is reasonably good for measuring energies as large as ~ 2 GeV, although the resolution

is generally 2 keV in ordinary 7-1‘ay spectroscopies. The resolution at 1890 MeV is

6E 1.333 14.2
— = = 2. -4
E V 1890 1332.5 8X10

expected to be

 

38

 

6000

5000

 

 

 

4000 M

3000

 

Counts/Channel

2000

1000

 

 

1500i
1000 :— —

500E— {

i E = —4.03+cht0.923 [keV] ‘

O . . . . l i 1 . . l . . i . l i . . .
0 500 1000 1500 2000

ADC [Channel]

Energy [keV]

 

 

 

Figure 3.1: Energy spectra from 137Cs, 22Na and 60Co sources which are used for the
energy calibration of ADC channels. The peak from the background, 40K, was also
observed.

if estimated in the same manner as See. 1.3.2. The gain of spectroscopy amplifier for
the energy resolution measurement was determined to be 4.4 in such a way that 1890

MeV corresponded to 6000 channels, while the gain was 1500 in the 7-ray calibration.

39

Table 3.1: Energies of 7 rays emitted by 60Co, 22Na, 137Cs and 40Kr, and the corre-
sponding ADC channels.

ADC [Channel] 558.4 721.1 1274.9 1385.5 1447.8 1587.8
Energy [keV] 511.0 651.7 1173.3 1274.5 1332.5 1460.9
Source 22Na 137Cs GOCO ”Na 6000 40K

 

 

 

 

 

 

40

 

1400 -n.,.fi.r-..2,..,2
f
b

A I

 

 

 

 

1200’ 1
I . . l
3 1000_ Active Slit OFF 1
E, 800’ 1
U , 4
} . .- , , 1
8 600’ , ActiveShtON 1
o I l
U 400 1
200: r
1
0 2 - -
5940 5960 5960 6000 6020
ADC [Channel]

Figure 3.2: Energy spectra for all events (unshaded) and for events without signals
from the active slit (shaded).

3.2 Veto by Active Slit

Figure 3.2 shows typical energy spectra detected by the HPGe at normal injection.
The unshaded one is the spectrum for all events without using the information from
the active slit. Two peaks are observed; one at higher energy is formed from particles
passing through the 1-mm aperture of active slit, while one at lower energy is from
particles which pass through the aperture of brass slit but not the active slit, thus lose
some energies in the 0.1-mm scintillator. The shaded one is the spectrum obtained by
rejecting events having signals from the active slit. It is clearly seen that the particles
penetrating the 0.1-mm scintillator are completely eliminated. The lower energy peak
in the unshaded spectrum has a slightly larger width than the one at higher energy,
due to the larger aperture of brass slit (3 mm) and the energy—loss straggling in the
scintillator, but the difference is not significant because the resolution of HPGe has

the largest contribution.

41

 

 

 

 

 

 

 

 

 

 

 

 

 

      

 

 

   

 

400 ' ' T ' T ' T ' ' I ' ' ' V I r r T '
B L J
1:: 300’ 2
r:
as
.1: . .
Q 200 ~ -
m . .
4-3 r
‘3 i
8 » 1
0* c c c t ] t : 1 : J, : : : 1 I : . .2
100 T ,
: t=1.466+ch.2.573.10-2 :
,... 80 — -
'0 I I
c: . .
V 60 r 1
0 . .
.E 40 L _‘
5n : I
20} €
0’.#Em....1.-..11111
o 1000 2000 3000 4000

TDC (Channel)

Figure 3.3: Typical time spectrum used for time calibration (upper panel). Pulses
from a time calibrator had a 10 ns interval over 100 ns range. The regression line is
shown in the lower panel.

3.3 Time Calibration

The time calibration was performed by using pulses generated by a time calibrator
(ORTEC 462). Each of TDCs reading J1, J2 and RF signals was calibrated individ-
ually. Figure 3.3 shows one of typical time spectra for pulses having a 10 ns interval

over 100 ns range and the regression line obtained by the least squares method.

3.4 Position Calibration

Each of ADC channels of Si—PSD signals, Q18“ and Qright, was calibrated by using a
pulse generator. One of typical spectra and a regression line obtained by the least

squares method are shown in Fig. 3.4. Then B and C in Eq. (2.5) were determined

42

 

r v v v v r v v v v v v v v v
4
125 *- _.
4
q

 

 

 

 

l-
l.
5 i ‘
C3 100 _- j
‘3 C
,2 .
U 75 :- 'j
\ .- .
3 I :
G 50 r 1
:1 , .
o . .
o ’ 4
25 j “1
I 1
a F55 l - l - ‘ '

 

 

 
 
     

PSD-Left

ALJLL

 

 

amplitude (arb. units)
Co)
I

01ert=1.583-10‘3 itch+9.09-10’2 :
. . . l . i l . . . . '

J A l L L A A

 

0 ' ‘
0 1000 2000 3000 4000
ADC (Channel)

Figure 3.4: Spectrum used for calibration of Left ADC (upper panel). The regression
line is shown in the lower panel.

in the following way. Equation (2.4) is reduced to

Qleft — B = Qright _ C

a: L—rz: ’

(3.2)

which is a straight line containing the point (B, C) in (Qleft, Qright) plot. Thus (B, C)
is given by the intersecting point of Qleft-Qright correlation lines for different ac. These
correlation lines were obtained by using a pulse generator and a dedicated position
calibrator for Si—PSD. The result is shown in Fig. 3.5. However, Eq. (2.4) is correct
only in the ideal case. Since the real detector has stray capacitance, which makes
the time constant RC position-dependent, signals are not linear functions of a: due to
the ballistic deficit in shaping circuits. In the present case, fortunately, the discrete
structure of the spectrum (Fig. 3.6) definitely gives us information on the absolute
position. A third order polynomial giving the correct position a: was determined by

the least squares method. In the following analysis, random numbers in [0,1] were

43

 

 

 

 

 

 

 

 

6. "1""1'"'1""1"*'1"",
I ersm=1 x 0,8,, + 7.329-10-8 ;
’9? 5; th,=15.34xo,,g—2.2a4 ;
:3 4» +0.1508
' _ -1
,2 [ (B-C)’; Z
3 _ (0.16, 0.16)
.... 3_ 3_....,....1....‘_
5 * .
Q, : 0.27 "‘
2:— b —
~ 0.1— —
. 1 j .
1— 0.01.1.1....11.1.-i
0.0 0.1 0.2 0.3:
0 1. 1112111. 1 . . l . 1. 1111.11... .
0 1 2 3 4 5 8

Q1611 (arb. units)

Figure 3.5: Qleft-Qright plot for different :1: generated by the dedicated position cali-
brator. The inset is a closeup around the intersecting point.

added to r for removing spurious structure of the spectra.

3.5 Time of Flight Correction

The flight time of particle traveling from the RRC to the detector depends on the par-
ticle momentum. This effect must be corrected to obtain the longitudinal emittance

of the RRC. The time-of-fiight (ToF) is given by

L LE
t=—=—+,
1) pc2

where L is the flight path length, E is the total energy and p is the momentum of a

particle. The ToF difference (it is related to the momentum difference 6p via

[L0 8 E E0 6L
(it = —— — —— 6
.c28p(7))+p0623pl p
F 1 1 6L 6])
- ——.‘+— .—. 3.3
”iii Leap/P01 0P0 ( )

44

 

 

 

2500 + t V V I Y Y T I V V Y I Y I Y ‘I’ I

2000:
1500

1000

Counts

500

‘Vrl'j'er‘r‘l‘v'

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ill - "

2° 7:: = —27.14+56.26xr
—6.337xrz+4.274x7'3

 

 

 

 

 

 

:1: [mm]
C
1
1

ALL L‘AL All.

p
P
—10— —
.
h

-2o£— —:
r 1 1 . . i l . . i l . . . l . . .
0.0 0.2 0.4 0.6 0.8 1.0

r=(o...-B>/1<Q....-B)+(amt-0)]

 

 

 

Figure 3.6: Spectrum of .z/ L calculated by using Eq. (2.5) (upper panel). Discrete
peaks reflecting the strip structure are clearly seen. The lower panel shows the regres-
sion curve to deduce the correct position determined by the least squares method.

L0 is the length of the reference orbit. From the first quadrupole of QA02 (Fig. 2.4)

 

L
to SMART -F 2, L0 = 89.5 m. The transfer matrix element 83/]? = (l|6) can be esti-
0
mated, e.g., by using TRANSPORT, where R56 = —(l|6). In the code cosv INFINITY

[16], even the correction coefficient Bt/(aT/To) is directly given by —ME(5, 6) . While
the first term in Eq. (3.3) is independent of the transport condition, the second term
is very sensitive to the choice of transport parameters and changes even its sign easily.
It was determined for each case of 40Ar and 22Ne in the following way.

In the case of 40Ar beam, data were obtained displacing the phase of the RRC
Dee voltages relative to the injection phase in step of 2° (198 ps for 28.1-MHz RF).
Since the RF signal fed to TDC represents the injection phase (Sec. 2.7.2), the time
difference between the RF and the detector does not change if the acceleration is truly

isochronous, but it does change due to the phase compression described in Sec. 1.2.6.

According to Eq. (1.13), the shift by the phase compression is proportional to the
injection phase with respect to the RF, Aqu,-. (1|6) has been artificially determined so
as to satisfy this relation. Figure 3.7 shows the time spectra corrected only by the first
term in Eq. (3.3) It is seen that time spectra at Again,- = +4° to —2° do not shift while
time spectra at Arbinj = —4° and —6° do significantly. On the other hand, by assuming
(1|6) = —35.5 cm/%, the corrected time spectra shift approximately in proportion to
their injection phases as shown in Fig. 3.8. This hypothetical value is consistent with a
transfer matrix element (1 [(1) = —32.6 cm/% calculated by TRANSPORT. Substituting
L0 = 89.5 m and 70 = 1.1021 as well as (ll6) = —35.5 cm/% into Eq. (3.3), ToF

correction is obtained as

5
6t : [—584.8—281.7];I—) [ns] . (3.4)
0

In the case of 22Ne. beam, the dependence of ToF on the particle momentum was
determined by slightly degrading the momentum with the charge stripper (Fig. 2.4).
The shift in (t, (5) plot directly gives the coefficient in Eq. (3.3). The used stripper was
a. carbon foil with a thickness of 9 mg/cmz. Figure 3.9 shows the correlation spectra,
h2(t, 6) and h1(t, (5), detected at F2 with (right panel) and without the stripper (left
panel), respectively. The displacements, to and (50, were determined so as to minimize

the chi squares defined by
x2 = 217110.. (Sn—1120.40, 6,-6.9 1".
i j

The obtained values are to = 0.525 ns and 60 = —1.021 x 10‘3, resulting in the TOP

46

Without Artificial Correction

Counts/Channel

I

f” 1.

rJ

l

5:

on.

£113

5

 

 

 

<

-17
M [In]

Figure 3.7: Time spectra with the first-term correction only. The injection phase
with respect to the RF phase of the RRC, A4510, is displaced in step of 2°.

With Artificial Correction

Cantu/Channel

 

 

 

-17
6t [ns]

Figure 3.8: Same as Fig. 3.7 but with the correction assuming (1|6) = —35.5 cm/%.

correction to be

(it = ——514.206—p [ns] . (3.5)
P0

47

w/o stripper

 

stfipper

 

-10‘3

610/10

'1’
o'
._
X

N.
I

 

 

 

 

 

 

 

residual

l

 

610/10
- 1 0‘3

—2x10'3

 

 

 

 

 

200

Count.
Figure 3.9: The correlation between the time and momentum of particles detected at
F2 without the stripper (left) and with the stripper (right).

48

 

Figure 3.10: Beam spot on a ZnS scintillation target at the target position with (right
panel) and without the stripper foil (left panel). Ticks on the target are marked in 5

mm step.

To justify the above procedure, the beam spot on the target should not move

irrespective of the momentum, which is achieved by an achromatic transport. The

calculated transfer matrix from the stripper to the target is

 

 

"$1 - 0.3620 0.1745
(1' — 1.5762 2.0025
11’ _ 0 0
b’ — 0 0
l’ —0.31 15 0.0805

. 6’ 0 0

 

0
0
0.4601

0 0 0.8351
0 0 4.9694
—0.0785 0 0

—1.1680 2.3725 0 0

0
0

0
0

1 1.6120
0 1

 

 

 

(3.6)

(zld) is not zero but sufficiently small. It was experimentally verified by using a ZnS

scintillation target (Fig. 3.10).

49

Chapter 4

Results and Discussions

4.1 Energy Resolution of HPGe

Figure 4.1 shows typical energy spectra with the active slit at normal and 43° injec-
tions. The peak widths determined by a Gaussian peak fitting are 1.52 MeV and 1.80
MeV (FWHM), which correspond to relative energy spreads of (SE / E = 8.0x 10‘4 and
9.5x 10‘4 for the normal and 43° injections, respectively. Subtracting the estimated

energy—loss straggling in the 300-,um Be window and the air between the exit vacuum

 

 

  
      

   
    

 

 

 

 

 

 

_ r r I I I r ff 7 [f1 1 1 r1 7 I I .1 1000 _ 1 I r r l r T r I I r r 1 r I r r r r _‘
600 h- Normal 5 800 r —.
3 - : 3 . 43 degrees -
g . ‘i I -
g . . g 600 _— —_
U 400 — — o - -
} ~ 4 5 : I
‘5 I 73 400 — —
:1 . :1 ; 3
O O
U 200 — .9 U : :
: 200 _— E
o l J L l l l A l l l L 1 ‘4‘ q o I. l l l AMI l I l l l l h
5960 5970 5980 5990 6000 5940 5950 5960 5970 5980
ADC [Channel] ADC [Channel]

Figure 4.1: Energy spectra with the active slit at normal and 43° injections, respec-
tively.

50

Table 4.1: Peak width in observed energy spectra, the contributions from energy-loss
straggling and the intrinsic energy resolution of HPGe at normal and 43° injections
for 1890-MeV 14N.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Injection Peak Straggling Beam Intrinsic Unit
Angle Width Be Air Spread Resolution
Normal 1.52 0.72 0.24 0.47 1.23 MeV
8.0 3.8 1.3 2.5 6.5 x10-4
43° 1.80 0.88 0.30 0.47 1.47 MeV
9.5 4.7 1.6 2.5 7.7 x10”4
(FWHM)

window and the Be window, the intrinsic energy resolution of HPGe becomes 1.23
MeV and 1.47 MeV (FWHM) for the normal and 43° injections, respectively. The
energy-loss straggling in the vacuum window and the light shield is negligibly small.

The results are summarized in Table 4.1.

Note that the present HPGe detector is not optimized for our purpose. For exam-
ple, the use of smaller Ge crystal decreases the leakage current and the capacitance,
which results in the lower electronics noise, and allows the use of small and thin Be
window, say 25 um, resulting in the smaller energy-loss straggling. Since the intrinsic
resolution achieved in the present experiment is already at a level of practical use, it
is concluded that HPGe is promising as an energy detector for longitudinal emittance
measurements.

The energy resolution at 43° was slightly worse than that at normal injection,
contrary to our expectation that the inclined electric field with respect to the particle
path will improve the charge collection, leading to the improvement of energy reso—
lution. There are two possible reasons: One is that, because the HPGe detector was
not precisely set on the beam axis (Fig. 2.8), particles were injected near the edge
of crystal where the electric field can be weak. A weak electric field deteriorates the
charge collection and accordingly the energy resolution. The other is an underesti-

mation of energy-loss straggling in the Be window, which mainly contributes to the

51

systematic error of energy resolution. This is also suggested even from the data for
normal injection, as the observed resolution 6.5x 10‘4 is significantly worse than the
one expected from the 7-source data described in Sec. 3.1. The present estimation of
energy-loss straggling has some ambiguities since the data in this energy region are
rare. The error may be removed by directly measuring the energy-loss straggling in

a Be foil with the spectrometer.

4.2 Longitudinal Emittance of 40Ar Beam
— case of single turn extraction ——

Figure 4.2 shows the longitudinal emittances of 3800-MeV 40Ar. (It is the extraction
time relative to the RF of the RRC, instead of the injection time, and is corrected
for ToF according to Eq. (3.4). The injection phase Agbinj is displaced relative to
the RF of the RRC in step of 2° (198 ps for 28.1-MHz RF). Like in Fig. 1.7, it
is clearly seen that there is a quadratic correlation between (it and (ST/T, which
is expected from Eq. (1.11). A sinusoidal curve corresponding to the RF of 28.1
MHz is displayed for eye-guide. The correlation is, however, smeared by fairly large
spread of distribution. The time and energy spreads are approximately 700 ps and
1.3x10‘3 (FWHM), respectively. The energy resolution expected from (z|6) of the
spectrometer, 2.5x 10’4, can be deteriorated by several times due to the beam spread
on the target, ~5 mm. The time resolution for the scintillators, on the other hand,
was confirmed to be 100 ps in the present experiment (Sec. 2.6.2). The other source
of time spread is not clear. It is unlikely that the beam in acceleration has such a
time spread. The investigation of this spread is critical for the longitudinal emittance
measurement. A smaller time spread will be particularly helpful to see the steep
correlations more clearly.

Figure 4.2 includes not only the sinusoidal correlation but also the effect of phase

52

A¢|nl=_2 deg

21(10-3

Adw=0 deg

2x 1 o"

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

O O
h 5.
b 1} .
O c
n H
I I
o o
3? 3?
N N
1 1
n I)
I l
O O
'x' A A A 1 A 1 n A l 1 'x- 1 I A A 1 A l A 1 A A
+19 ~18 -17 -16 +19 -18 -17 -16
1 at [nsec] I a: [nose]
7° A¢w=-4 deg 1:: MM=+2 deg
31‘ 3:
N N
O O
h s
5 a
0 9
n n
I I
O O
'1? 37
N N
1 I
F) I"
l I
O O
'; 1 l I A A A l A A A A "x‘ A_
+19 -18 -17 -16 +19 --18 7 -16
1 at [11959] I a: [nose]
A =—6 de "
To fin] 9 1°
3? 3?
N N
o o
s. s.
h b
O Q
n Fl
I I
.9 9
X X
N N
1 1
I" n
I I
o o
v— . A 1 l A 1 A l A A A A V; A l I
5—19 —15 —17 —16 +19
1 6t [nose] 1

 

 

-18 -17 -16
6t [nsec]

Figure 4.2: Longitudinal emittances of 3800-MeV 40Ar. The injection phase Adm,-
displaced relative to the RF of the RRC in step of 2°.

53

compression discussed in Sec. 1.2.6 (upper panel in Fig. 4.3). The effect is directly
seen by taking the extraction time relative to the injection (middle panel in Fig. 4.3).
The projected spectra corresponding to the lower panel of Fig. 4.3 are presented in
Fig. 4.4. The shifts of spectra are deduced from Gaussian peak-fitting and plotted as
a function of Aqbinj in Fig. 4.5. According to Eq. (1.13), where Vat/Vim- = 1.6 for the
RRC, they are expected to lie on the solid line in Fig. 4.5. It is approximately the
case, but the deviation indicates a higher order effect, the origin of which is a future

problem.

54

 

I ' I ' I ' I ' I ' I 1 I

Phase s
Compress 1

I

   
 
 

1 .000

I

0.998

T/T0

0.998 r-

  

Extracted beam
{1119(3th bCBme-“MW

0.994

  
  

 

 

 

0.992 I A I . I x I A I A I A I
—6 —4 -2 0 2 4 6

A¢mz Rel. Phase, RF-rExt. [deg]

 

1.000 -

0.998

T/ To

0.998

0.994

 

0.992
0.8 l
0.8
0.4 i
0.2 ’

 

 

Rel. Intensity [arb. units]

 

0.0“l
-6-4-20246

mom—Mm, : Rel. Phase, Inj. -* Ext. [deg]
Figure 4.3: Schematic illustration of phase compression effect for the case of narrow-

bunched beam. The extraction time is either relative to the RF of the RRC (upper
panel) or relative to the injection (lower panel).

55

 

1500}- '”’3 A¢mf'
1000E- "
500 —

lllllljlllll

p-—_—_-.-
1.

 

1500:
1000:
500:

 

1500:

H
010
CO
CO

 

Counts/0.25 ps

1500;
1000 E-
500:

 

1500:
1000:
500:

 

 

1500i-
iooog-
500 :-

 

 

 

I
l
l
I
I
I
I
I
1|

—18 -17 -16
Relative Time, Inj. -> Extr. [ns]

Figure 4.4: Projected spectra of the extraction time relative to the injection. The
phase of the RF with respect to the injection, Aqbinj, is shifted in step of 2°.

 

56

 

   
 

 

 

 

I I ' I ' I ' I I I ' ' ' I ' ' ' I ' 1 1 T v
. I>
,_, ’\ Effect of Phase Compression ?
247.0 - . .
‘3 (X21 ) 2 .5?
Ago -1 ..
E": 13.1

I V.“ so
..—'. SE.

a .
. - 17.2 :I‘U
0) O D
m

5 .9
E E
1" .2
g -l7.4 ‘ _2 a

\

. I . . . I . . . I . . . I . mg I F. . I ‘3 g
-6 -4 -z o 2 4 9:,

Act”: Inj. Phase relative to RRC RF [deg]

Figure 4.5: Shifts of time spectra deduced from F ig.4.4 plotted as a function of

Agbinj. The solid line is a prediction from Eq. (1.13). The dashed curve is a third
order polynomial for eye-guide.

57

4.3 Longitudinal Emittance of 22Ne Beam
— case of multi-turn extraction —

The tuning of cyclotrons for the single—turn extraction is not always achieved at
RIKEN. In fact, it is sometimes the case that two or three turns are extracted for
experiments not requiring a high-quality beam, like ones using a secondary beam.
As a case of multi-turn extraction, the longitudinal emittance of 2420-MeV 22Ne is
discussed in this section.

The time structure of the extracted beam relative to the injection time is shown
in the upper panel of Fig. 4.6. Two peaks are observed separated by 33.2 us, one of
which would disappear for the case of single—turn extraction. As described in Sec.
2.2, adjacent turns are extracted at different times from the main one by 33.2 us
because hAVF/hRRC = 2/ 5 and frf = 30.10 and 15.05 MI-lz for the RRC and AVF,
respectively. Note that the main turn is extracted at an interval of 66.4 ns. The
longitudinal emittances for the main and adjacent turns are presented in the middle
panel of Fig. 4.6. There are two loci for the adjacent turn, suggesting a mixture of
two turns. Together with the main turn, all of the three turns have different (ST-6t
correlations from each other. A possible explanation of this is illustrated in Fig. 4.7.
It is assumed that the beam is not injected at the phase of highest voltage and the
phase spread is relatively large. A part of the beam distribution is peeled off by the
extraction devices at the N—l turn, the main part at the N turn and the remaining at
the N +1 turn. They are extracted at different phases and accordingly with different
(ST-(St correlations. This idea is supported by the data obtained with the lower Dee
voltage by 2x 10"3 relative to the nominal value. They are shown in the lower panel
of Fig. 4.6. Here the beam in the N—l turn is not extracted and a smaller part of the
beam is extracted in the main turn, as expected from the lower panel of Fig. 4.7. This

illustration, however, does not explain the data quantitatively and a further study

58

 

 

 

L 7 I I
i - ,, . . -
2000+: 133.3 ris ‘
V, l.“{;£0!,\11lz)
0.
§ 1500 main turn H
\ r
m r
T5 000; a
:1 1 .
8 I adjacent
500); turn H
0L L l l I
‘40 —20 0 20 40
t [ns]

' adjacent turn, AV/V=O main turn, AV/V=0

 

   

 

 

 

 

 

 

 

 

 

 

 

 

'1 n
I I
O O
3? 3?
1’ V
k h
h I}
O ‘0
"’ n
I I
O O
3? 3?
N N
o 22 I 0 A 18 010 A 12 J 14 A 16
' [Its] ‘ 1 [ns]
adjacent turn, AV/V=—2x10"3 moin turn. AV/V=—2x10'3
p, n
I I
O O
'1? 3?
1’ V'
s. 5.
b h
‘0 Q
'9 n
I I
‘3 ‘3
X X
N N
o 22 A 0 I 18 010 A 12 I 14 I 1 6
' {It} t [ns]

Figure 4.6: Time spectrum (upper panel), the longitudinal emittances for the main
and adjacent turns at the nominal Dee voltage (middle panels) and at a slightly
lowered Dee voltage (lower panels). Straight lines are for eye-guide.

59

 

Extraction
Window

Loss in
Ext. Devices

 

 

' AV/V = —2-10‘3

  

2 ?/ Extraction
Window
0. " . Loss in
. ........................................................ Ext, Devices

 

 

 

Phase [deg]

Figure 4.7: Schematic illustration of (ST-cit correlations for neighboring turns at the
nominal Dee voltage (upper panel) and at a slightly lowered Dee voltage (lower panel).

60

must be made.

61

Chapter 5

Conclusions

It is important to measure the longitudinal emittance of the beam coming from the
RRC for successful operations of the new facility, RIBF. A compact and convenient
energy detector is desired for routine operations, thus the use of a HPGe detector
was proposed and the feasibility of its use with energetic heavy ions was studied. The
energy resolution of a HPGe detector for a high-energy heavy ion, 135-MeV/ A 14N,
has been measured using a magnetic spectrometer for defining the particle energies.
A reasonably good resolution, (SE/E = 6.5X10‘4 (F WHM), has been observed by
a HPGe detector with the crystal size as large as $70 mm in diameter and 30 mm
in thickness. As a better resolution is expected for smaller crystals, the HPGe is
promising as an energy detector for longitudinal emittance measurements.

Using the same magnetic spectrometer, the longitudinal emittances have been
measured for the 3800-MeV 40Ar beam, as a case of the single-turn extraction, and
for the 2420-MeV 22Ne beam, as a case of the multi-turn extraction. For the 40Ar
beam, by displacing the RF phase of the RRC from —6° to +4° in step of 2°, a
quadratic correlation reflecting the sinusoidal RF voltage as well as the effect of
phase compression have been observed. The time spread, however, was larger than

expected from the detector resolution and acceleration mechanism. Its origin should

62

be investigated to observe the correlation more clearly. For the 22Ne beam, it was
found from the time structure of the beam that several turns were extracted. Besides,
the longitudinal emittance had a structure suggesting a mixture of different turns.
An illustrative explanation has been proposed for identifying each turn. Data with a
different Dee voltage are consistent with this idea. However, a further study must be
made to obtain a quantitative understanding.

In conclusion, it has been demonstrated that the measurement of longitudinal
emittance provides rich information on the acceleration condition and will be very

helpful for the beam tuning of the present and new facilities.

63

Chapter 6

Future Prospects

Aiming at a. higher energy resolution, a new HPGe detector with a small crystal and
a. thin Be window had been ordered to Princeton Gammatech, Inc. (Fig. 6.1). The
specification is summarized in Table 6.1. The experiment of 22Ne in October, 2003,
was originally proposed to test the resolution of this detector, but, unfortunately, the
product was not delivered in time for the experiment. This is going to be performed
in this December.

Another test experiment for longitudinal emittance measurement without using
a magnetic spectrometer is planned to be performed in the near future. A large
scattering chamber, which allows an elastic measurement at 6 = 2°, has been designed
and is under construction.

Since the energy-loss straggling is not negligible even with the plastic scintillator
as thin as 100 pm, the use of a micro-channel plate (MCP) combined with a thin foil
for secondary electron production may be examined. Also the improvement of time
resolution is critical to see steep correlations more clearly (Sec. 4.2).

After the completion, the system using these detectors will be installed near the
exit of the RRC, where the correction of ToF is not required. It will be used for

tuning the beam to the present and new facilities as well as for a further study of the

64

Table 6.1: Specifications of Ge detector (Princeton Gammatech: IGP1010185 Model).

 

 

 

 

 

 

 

 

 

 

 

 

Crystal Diameter Thickness Be End Cap
Type Window Length
Planar Ge $10 mm 10 mm 50.8 nm 200 mm
Preamplifier Gain Energy Vacuum Dewar
Type Range Flange Volume
Resistive Feedback 1 / 60 2 2 GeV CF $70 mm 7.5 f
l
/:::\
I
l
l
Ge crysto/

 

———<——>«>—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 6.1: Overview of the newly fabricated HPGe detector.

65

beam from the RRC. Particularly important for the operation of the new facility is a
study of 60-MeV/ A beams, which are obtained by using the LINAC as the injector,

instead of the AVF cyclotron, but were not available in the present experiments.

66

Appendix A

Angular Distribution of Elastic

Scattering

The knowledge on the elastic scattering cross section is important for designing ex-
periments without using a magnetic spectrometer, but data for heavy ions are scarce.
The angular distribution of elastic scattering of 14N on 197Au target at E /A = 135
MeV / A has been obtained in the present experiment. The result of the cross section
in the laboratory frame is presented in Fig. A.1. It is remarkable that the cross section
varies exponentially and the distribution is much steeper than that of the Coulomb
scattering from a point charge (Rutherford scattering). Since the cross section be-
comes very small at backward angles, it will be appropriate to make measurements
at (9 = 2°~3° in this energy region. The counting rate dY/dt is related to the cross

section do #1018}, by

dY (10
TI; -— InmAQlaba (A.I)

where 1 denotes the beam intensity, n the thickness of target and A121,“, the detector

solid angle.

67

197Au(14N,14N)197Au elastic

 

  
    

 

 

 

 

 

 

 

dO/dfl , : E3135 MeV/u
(b/sr) ' ‘
102
101
100 . . . g .. . . . ' i .
__._ exp I f g '

10-1 Ruth 4f 3 ' - \

2 3 4 5 ' 6

Glen (deg)

Figure A.1: Angular distribution of 197Au(14N,14 N)197Au elastic scattering at E /A =
135 MeV/ A compared with Rutherford scattering. The exponential line is for eye-

guide.

68

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70

   

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