Journal of the Physical Society of Japan
Vol. 76, No. 9, September, 2007, 093501#2007 The Physical Society of JapanLETTERSDensity Enhancement of Muon Beams
with Tapered Glass Tubes
Takao M. K OJIMA1 , Dai T OMONO2 , Tokihiro I KEDA1 , Katsuhiko I SHIDA2 ,Yoshio I WAI1 , Masahiko I WASAKI2 , Yasuyuki M ATSUDA2 ,Teiichiro M ATSUZAKI2 , and Yasunori Y AMAZAKI1;3
1

Atomic Physics Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198
2RIKEN Nishina Center, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-01983Graduate School of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902(Received June 14, 2007; accepted July 19, 2007; published September 10, 2007)

We have demonstrated that the beam density of 54 MeV/c muons can be increased almost by a factorof two when a tapered glass tube is inserted coaxially along the muon beam. The observations arecompared with a multiple Coulomb scattering calculation, which reproduces the observation reasonably.
This technique opens a new and simple way to increase the muon intensity eﬀectively.
KEYWORDS: muon, beam density, glass capillary, enhancement, tapered glass tube
DOI: 10.1143/JPSJ.76.093501

mylar foil

light guidecollimator (40mmφ)
scintillator
PMT

beam port

glass tube

detector4

signal [mV]Spin polarized muons have been used for several decades
for material science study.1) Muons implanted into a sample
are quickly thermalized and then localized at characteristic
sites. These muons interact with the local magnetic ﬁeld,
resulting in muon spin precession and/or depolarization.
This makes spin polarized muons very sensitive andversatile microscopic probes to study magnetic properties
in various materials. One of the obstacles of this technique isthat the size of the polarized muon beam from accelerator
facilities is relatively large; typically a few tens of mm infull width at half maximum (FWHM) at the focal point.
However, most of intriguing samples, such as newly
synthesized chemical compounds and biological samples,are often much smaller in size than the beam diameter.
Usually a collimator is installed in front of the sample,
masking the muons which do not hit the sample. Thismethod suppresses the noise but does not increase thenumber of muons which hit the sample. Any method toincrease beam density on the sample will be of great interestand importance to the application of polarized muon beams.
Nebiki et al. injected 2 MeV Heþ ions into a tapered glass
capillary with inlet and outlet diameters of 0.8 mm and 0.8mm, respectively, and reported that the transmission eﬃciency was much larger than that expected from the inlet-to-outlet
area ratio.2) Ikeda et al. also demonstrated that a slow highlycharged ions (8 keV Ar8þ ) were guided through a similar
tapered capillary with beam density enhancement of a factorof about 10 while keeping their initial charge.3,4) With these
new ﬁndings in mind, we have studied the behavior of54 MeV/c muon beams with tapered glass tubes having aninlet diameter of 46 mm and an outlet diameter of 3 – 20 mm.
The experiment was performed at Port 2 of RIKEN-RAL
Muon Facility at Rutherford Appleton Laboratory, U.K.5)
Figure 1 schematically shows the experimental setup.
Muons with speciﬁed momentum are transported to thebeam port, and extracted into atmosphere through a thin
Mylar foil and an aluminum collimator of inner diameter
40 mm and length 85 mm. Beam divergence is 2 instandard deviation. The beam has a pulsed structure with arepetition rate of 50 Hz, each pulse consists of two bunchesof 70 ns FWHM separated by 320 ns. Typical beam intensity

3YX

2
10-40

Gauss fit
FWHM=39.0-20020

Gauss fit
FWHM=42.8

40-2002040position [mm]Fig. 1. (Color online) Top: a schematic view of the experimental setup(not to scale). Bottom: the beam proﬁle of 54 MeV/c mþ measured with a5 mm scintillator positioned 403 mm downstream from the collimator.

is about 104 muons per pulse for 54 MeV/c mþ . Positron/
electron contamination is negligible. The bottom of Fig. 1
shows the beam proﬁle of 54 MeV/c mþ at 403 mm downstream from the end of the collimator. Considering the sizeof the muon beam, we used tapered glass tubes with an inlet
diameter, Din , of 46 mm. The tubes were made of Pyrex.
The lengths of the tubes, L, were 100 – 400 mm, the outlet
diameters, Dout , were 3 – 20 mm, and the thickness was
2 mm. A beam momentum of 54 MeV/c was used because
muon loss in air of 400 mm is negligible, while muons stop
completely in a 2 mm glass wall, so that it does not interferewith the muon intensity observation. We prepared plastic
scintillation counters (EJ212) with thickness of 0.5 mm anddiameters, Dsci , of 5, 10, and 20 mm. One of the scintillators
was placed 3 mm downstream of the tube to monitor themuon intensity. The pulsed muon signal from the photomultiplier tube (PMT) was averaged over 128 beam pulses
with a digital storage oscilloscope.
Muon signal intensities, Vwith and Vwithout were measured
with and without the glass tube, respectively, keeping allother experimental conditions the same. The muon signal
enhancement factor, , is deﬁned as093501-1

LETTERS

J. Phys. Soc. Jpn., Vol. 76, No. 9T. M. KOJIMA et al.

taper angle θ [degree]

signal enhancement η3.5

2.5

taper angle θ [degree]

2μ+− Dsci=20mmμ+ Dsci=20mmμ+ Dsci=10mmμ Dsci= 5mm

54 MeV/c
L=400mm

3.02.52.0exp. μ+− Dsci=20mmexp. μ+ Dsci=20mm
exp. μ Dsci=Dout

1.5
sim. μ+ Dsci=20mm
sim. μ+ Dsci=Dout

1.005101520outlet diameter Dout [mm]101520Fig. 2. (Color online) The signal enhancement factor  as a function ofoutlet diameter Dout for 54 MeV/c muons with L ¼ 400 mm tubes for
Dsci ¼ 5, 10, and 20 mm. The error bar includes statistical and systematicerrors (see text). Data points with ‘‘T’’ shape error bar are the mean ofmultiple measurements and those with ‘‘|’’ shape error bar are measured
only once. Error bars of m data are omitted for clarity.

Vwith =Vwithout
Vwith =Vwithout, dDoutfor Dsci  Dout ;for Dsci > Dout ;

(1a)
(1b)

where the suﬃx ‘‘d  Dout ’’ stands for the muon signal
integrated within the area of Dout using muon beam proﬁle.
Figure 2 shows  as a function of Dout for Dsci ¼ 5, 10,
and 20 mm, and L ¼ 400 mm. The error bars were evaluatedfrom the deviation of the measured values to be about 5%.
Taking this fact into account, we also included error bars of
5% for data points measured only once. In addition, for alldata points, we added a systematic error of a few percent due
to the ﬁnite resolution of the oscilloscope. It is worth notingthat the signal enhancement for m was almost identical tothat of mþ .
Because the energy deposition of each muon to thescintillator depends on its kinetic energy and pass length in
the scintillator,  does not directly correspond to the density
enhancement of the muon beam. Energy and angular
distributions of muons at the position of the scintillator
were calculated with a Monte Carlo simulation, and a pair of
average deposition energies "with and "without was evaluatedfor each experimental condition. The number of muons Nwith
and Nwithout are proportional to Vwith ="with and Vwithout ="without , respectively. In the simulation; 1) the energy loss isscaled from proton data using a semi-empirical formula, 2)
the energy straggling is given by the Vavilov distribution,and 3) the angular distribution is given by the Moliere
expression for multiple scattering.6) For simplicity, a parallelmuon beam is generated having a 4% momentum dispersion
and the Gaussian position distribution shown in Fig. 1. Thebeam density enhancement factor, , is given as
Nwith =Nwithout
for Dsci  Dout ;(2a)¼Nwith =Nwithout, dDout for Dsci > Dout :(2b)Figure 3 shows  as a function of Dout for Dsci ¼ 20 mm
and Dsci ¼ Dout together with the results of the numericalFig. 3. (Color online) The beam density enhancement  for 54 MeV/cmuons as a function of Dout for Dsci ¼ 20 mm and Dsci ¼ Dout . The solidand dashed lines show the results of the simulation for Dsci ¼ 20 mm andDsci ¼ Dout , respectively.

simulation. As seen in the ﬁgure, beam density enhancements were observed for all the conditions studied, andfurthermore the simulation successfully reproduced the overall behavior of the experimental results. This enhancement
occurs because a certain fraction of muons incident on
the inner wall is reﬂected via small angle scattering andtransported to the outlet of the tube. For Dsci ¼ 20 mm, increases from 1:5 to 2:3 as Dout decreases from 20 to3 mm, whereas  stays almost constant for Dsci ¼ Dout . Thisdiﬀerence is due to muons with large angle at the outlet of
the tube. Since the counter is placed 3 mm downstream fromthe outlet, such muons miss the counter if Dsci ¼ Dout .
Although we do not know the real reason why the observed for Dsci ¼ Dout ¼ 5 mm was much smaller than the resultof the simulation, one possibility is slight misalignmentof the 5 mm scitillator from the tube axis.
Figure 4 shows  as a function of L with Dout ¼ Dsci ¼
20 mm and its Monte Carlo simulation. It is clearly seen that increases monotonically with L. When the length L varies
from 100 to 400 mm, the taper angle,  ¼ tan1 ½ðDin Dout Þ=2L, changes from 7.4 to 1.9 . As the incident angle

taper angle θ [degree]
20 10

density enhancement ξ5outlet diameter Dout [mm]

¼2

2.0

1.0



2.5

2.5

1.50

3

3.0

density enhancement ξ31.65 454 MeV/c μ+

3 2.5

21.5

Dout=Dsci=20mm

1.4
1.2
1.0experiment
simulation

0.80100

200300400500tube length L [mm]Fig. 4. (Color online) The beam density enhancement  for 54 MeV/c mþas a function of the tube length L for Dout ¼ Dsci ¼ 20 mm. The solid line
shows the simulation.

093501-2

J. Phys. Soc. Jpn., Vol. 76, No. 9LETTERS

with respect to the inner wall increases, the probability ofmuons coming back to the inner side of the tube by a small
angle scattering decreases steeply.
We simulated the density enhancement under vacuum
condition for 27 – 81 MeV/c. The simulation shows theenhancement factor is about 2 and almost constant all overthe momentum region, including commonly used surface
muon of 27 MeV/c. The simulation also suggests that thedensity enhancement factor improves further when the tube
is made of heavy material like copper, lead, or gold.
Preparations in this direction are in progress.
In summary, we have observed a beam density enhancement of around two with tapered glass tubes for 54
MeV/c mþ and also m beams in atmosphere. This enhancement is considered to be due to scattering of muons at thesurface of the inner wall with small incident angles. A
computer simulation with a multiple Coulomb scatteringmodel reproduces the behavior of the experimental ﬁndings.
The simulation also suggests that a similar density enhancement is expected for a broad momentum range of muons
with a tapered tube placed in vacuum, and that theenhancement increases when a heavier material is usedfor the tube.

T. M. KOJIMA et al.

Acknowledgment
The authors deeply appreciate the help of Mr. Seigo
Sugahara, Advanced Development and Supporting Center,RIKEN in preparing various tapered tubes. This work waspartly supported by a Grant of Special Projects for Basic
Science of RIKEN ‘‘Development and Applications ofExotic Quantum Beams’’.

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