Obtaining 3-150 MeV Focused Particle Microbeams
Alexander D. Dymnikov
Louisiana Accelerator Center, The University of Louisiana at Lafayette, P.O. Box 44210, Lafayette, LA, 70504-4210, USA
Abstract. The number of nuclear microprobe setups is growing steadily and its potential in research fields such as biomedicine, material
science and geology is being established. The most existing microprobe lenses can focus a proton beam up to energy of 30 MeV. The
studies reported here deal with magnetic quadrupole systems such as Russian Separated Quadruplet for obtaining 3-150 MeV proton
microbeams. For a given magnetic field in the quarupole lenses optimal parameters of microprobes for different energies of protons are
obtained. The smallest beam spot size and appropriate geometry of the focusing and matching slit systems have been found for three
different emittances.
INTRODUCTION
High energy ion microprobes have developed into a very
powerful analytical tool in recent years.1"2 High depth and
lateral resolution ion beam analysis (IBA) techniques are
contributing to the evolution of the geometrical design of
nanostructures. The lateral resolution of microprobes is
increasing toward the submicron regime. Also very high
depth resolution IBA is finding increasing use in
investigations of ultra-thin films. The promising recent
developments are related to experiments with low current
(low emittance) ion beams, in which one exploits the
penetration in matter of each single ion. Low current ion
microprobes are used in material science for a wide range of
applications.
Focusing of ion beams of MeV energy is mostly
accomplished by quadrupole lenses. One of the most
popular quadruplet systems is the Russian Quadruplet (RQ).3
For the first mode of excitations, the RQ has negative
demagnification and for the second mode the
demagnification
becomes
positive.
The
positive
demagnification has a maximum when the drift space
between the middle lenses is approximately the same as the
object drift space. This type of RQ is called the Separated
Russian Quadruplet (SRQ). Many investigations of the
microprobes are based on the magnetic RQ but an
electrostatic version of the RQ is also used as the probeforming system.
The penetrating capability of microbeams is growing
with their energy. Many existing microprobes exploit 2-5
MeV beams but there are laboratories using heavy ions at
energies of some tens of MeV. The new microprobe facility
was installed at the Munich 15 MV tandem van de Graaf
Accelerator.4 It was designed to focus protons with energies
up to 30 MeV as well as heavy ions up to 200 MeV*q2/A to
a submicron beam spot. The unprecedented high-proton
energies and the availability of heavy ions can open new
perspectives in microprobe analysis. Increasing the proton
energies by factors of 10-50 has at least two advantages. On
the one hand, the projected range of the incident ions and
therefore the analyzing depth increases drastically.
Secondly, due to the reduced lateral straggling of highvelocity ions a good lateral resolution even in larger simple
depths is achieved.4 The studies reported here deal with
magnetic quadrupole systems such as Russian Separated
Quadruplet for obtaining 3-150 MeV proton microbeams.
For a given magnetic field on the poles of the quarupole
lenses optimal parameters of microprobes for different
energies of protons are obtained. The smallest beam spot
size and appropriate geometry of the focusing and matching
slit systems have been found.
NUMERICAL OPTIMIZATION
Notations and assumptions
The beam-shaping sy stem consists of the SRQ and two
collimating slits, placed in front of the focusing system and
separated by the distance /12. The half width of the slit is
denoted by r\ (the object slit) and r2 (the divergence slit).
The object distance (the d istance b etween t he object p lane
and the entrance plane of the first lens) is denoted by s0. The
following are assumed given: the total length lt=6 m of the
system (the d istance from t he o bject si it t o t he t arget), t he
working distance g=0.18 m (the distance from the last lens
to the position of the target), the magnetic field on the each
pole of quadrupole lenses is equal to 2.5 kgs. At this case the
lengths of quadrupole lenses are the functions of the beam
energy £, which is changed from 3 MeV to 150 MeV. The
minimum half width of the beam spot sizer on the target
was found for three different beam emittances em=r\ r2ll\2,
em^W9 m , em2 =3*10-10 m and em3 = 3*10'n m, or for
three beam currents, Il912 and 73. Since the beam current is
proportional to em2,12 =0.01 I\ and 73 =0.0001 /,.
The parameters and geometry of SRQ at
different energies
The calculated values of demagnification, focal distance
and spherical aberration of the investigated SRQ at different
energies E are shown in Fig. 1.
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
343
Ihe demagnification
The length of the outer lenses
\
\
^ou
200
f!50
30
'25
:
\
20
\
*100
'15
^\ ~^-—.
50
0
20
40
60
10
"—~-—.
80 100 120 140
Energy of protons
0
[MeV]
Ihe focal distance
20
40
Energy
60
80 100 120 140
of protons
[MeV ]
The length of the middle
lb
14
1 12
5 10
n
/
A 8
61
^
^
/^
lenses
^,^ •"""' •
f
20
40
60
80
100 120 140
Energy of pcotons
The spherical
[MeV]
0
20
x
/
£40
j. j.
3
^
^2.9
§2.8
"2.7
W
2.6
2.5
^
/
830
/
9D
0
20
40
60
80 100 120 140
The object
^
^^
TJ
60
of protons
[MeV]
aberration
70
I60
^50
40
Energy
80
100
Energy of protons
\
\
\ \>
\x
distance
\
\^
~^ -^
O 4
120 140
[MeV]
0
20
40
Energy
60
80 100 120 140
of protons
[MeV]
FIGURE 1. Parameters of SRQ as a function of energy E.
While the energy of protons changing from 3 MeV to 150
MeV the demagnification is decreasing from 248 to 41, the
focal distance is growing from 1.2 cm to 5.6 cm and the
biggest coefficient of spherical aberration is increasing from
17.2m to 75m.
The decrease of the demagnification and increase of the
focal length and the spherical aberration are due to the
increase of the lengths of the quadrupole lenses, which are
shown in Fig. 2 together with the decrease of the object
distance SQ.
Fig. 2 shows that the lengths of quadrupole lenses
become longer with the growth of E. But even for E =150
MeV the longest quadrupole lens has a reasonable length ~
33 cm for the chosen magnetic field induction on the poles
2.5 kgs. The middle lenses approximately two times shorter
than the outer ones, changing from 5 cm to 16 cm.
The object distance becomes smaller with the growth of
E due to longer lenses. The drift spaces between lenses
remain constant during all calculations.
FIGURE 2. The length of quadrupole lenses and the object
distance as a function of the proton beam energy E.
The geometry of the beam has been optimized to obtain the
minimum spot size on the target for a given emittance. The
shape of the beam envelope is optimal if the spot size on the
target has a minimum value for a given emittance. The beam
is defined by a set of two matching slits: object and
divergence slits. Thus, the shape of the beam envelope is a
function of r\ and /12, being r2 fixed for a given emittance
em. The optimal parameters r ls r2 and /12 determine the
optimal beam envelope or the optimal matching slits at every
emittance. The optimal probe forming system with a
magnetic SRQ comprises the optimal matching slits and the
optimal geometry of SRQ. For each emittance, the
parameters of the optimal probe forming system have been
found, some of which are shown in Figs. 3-5.
These results have been obtained by performing the
special program of optimizing analytical and numerical
calculations5"7.
344
v
200
•\\
175
1 150
£125
^100
75
50
35
30
'25
\ "^\
15
^_^
^—
0
20
40
60
———. ——
10
— -—
0
80 100 120 140
Energy of protons
20
/
65
4~£-
60
21 /
20
| 55
40
60
18
40
17
0
20
40
60
0
80 100 120 140
Energy of protons
\x
20
^x\
\
\\
40
60
80 100 120 140
40
60
80 100 120 140
Energy of protons
[MeV]
[MeV]
"\\
£50
45
80 100 120 140
Energy of protons
[MeV]
[MeV ]
4. /^>
2.5 \ \
2.25
I
2^
CM
H 1.75
\^
\
1.5
x
^- -^^
1.25
"^ -^i
0
20 40
Energy of protons
1.4
/
1.3
0
[MsV]
/
1.1
^
20
/
200
180
40
//
220
^
60
/
3
80 100 120 140
Ehergy of protons
[MeV]
FIGURE 3. Plots of the optimal rlt r2,712 and r as functions of the
beam energy E. em=3 fimxmrad.
[MeV]
^^^"
240
1
0
20
Energy of protons
260
//
^-^
1.2
1
0.5
60 80 100 120 140
20 40
60 80 100 120 140
Energy of protons
[MeV]
FIGURE 4. Plots of the optimal r\, r2, l\2 and r as functions of the
beam energy E. em~0.3 fimxmrad.
The size of the object diaphragm has the strongest influence
on the beam spot size for a given emittance and this is why
it is very important to use the optimal r, for obtaining the
smallest beam spot size. The optimal value of / J2 provides
the best distribution of density of the beam in the spot on the
target and allows avoiding tailing of the beam.
The radius of the divergence slit r2 for a given emittance em
is the function of r\ and /12,
345
From Figs. 3-5 it is possible to see the following.
7
The object slit
6
At each emittance the half-width of the object slit for E =
150 MeV is approximately five times smaller than this size
for E = 3 MeV. For all investigated cases it is changed from
220um (£=3 MeV, em=3*10'9 m) to 1.4 um (£=150 MeV,
em=3*10- n m).
JU
20
40
60
80 100 120 140
Energy of protons
7\
6.5
6
5.5
The divergence slit
[MeV]
The behavior of the size of the divergence slit as a function
of the beam energy differs for different emittances. For the
first emittance ew=3 ^imxmrad this size is approximately the
same (-65^im) for the energy range 30-150 MeV. For the
second emittance em=0.3 ^imxmrad this size has a maximum
(~22um) for 10 Mev protons. For the emittance em=0.03
fimxmrad the divergence slit becomes smaller with the
growth of the beam energy.
\
\
X
\s
\x
4.5
4
"^-^
^~^^
()
20 40
60
The distance between the object and divergence slits
80 100 120 140
Energy of protons
[MeV ]
The distance between the object and divergence slits is
slightly decreasing while emittance decreasing and it is
strongly decreasing with the growth of the beam energy.
J..U
\
-V
1.4
1.2
The minimum of the spot size
\
V
0.6
0.4
0.2
The minimum of the spot size is growing with the growth of
the beam energy but even for 150 MeV protons it is possible
to obtain rather small spot size ~50 nm.
^\^^
"^-—— •——— ==—_ ——
()
20 40
60
80 100 120 140
Energy of protons
Conclusion
[MeV ]
The results of this numerical investigation give the
possibility to e stimate the geometry of the i on microprobe
for very high beam energy up to 150 MeV and obtain
microbeams and nanobeams with a great penetration
capability.
50
REFERENCES
40
35
1.
0
20
40
60
80
100 120 140
Energy of protons
2.
[MeV]
FIGURE 5. Plots of the optimal r b r2, l\2 and r as functions
of the beam energy E. em-0. 03 jimxmrad.
3.
4.
Comparison of the minimum spot size and the optimal
slit parameters at different energies and at different
emittances.
5.
As the result of the optimization the minimum beam spot
size and appropriate optimal geometry of the matching slits
for three different emittances have been obtained as
functions of the beam energy. They are shown in Figs. 3-5.
Appropriate parameters and geometry of SRQ for all
considered cases are shown in Figs. 1-2.
346
6.
7.
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