SS -156 2271

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DESIGN FOR A MUON SHIELD IN THE NEUTRINO BEAM USING MAGNETIZED IRON

Y. W. Kang National Accelerator Laboratory

ABSTRACT

The well-collimated high -energy muon beam at the end of the decay tunnel

encourages an introduction of the magnetic deflection in the muon shielding. It is

suggested that high-energy muons be deflected by a magnetic field while the remaining

muons are ranged out. With this setup we could improve the neutrino flux at the

bubble chamber as much by 60% over the present design, at no increase in cost.

The present study (at 200 GeV only) indicates that a magnetized iron shield is

highly promising and a further study is useful.

1. INTRODUCTION

In recent studies magnetized-iron shielding has been suggested to reduce the

cost of muon shielding in the high -energy neutrino beam and also to increase the neu­

trino flux at a detector. Some proposals have been made by March, la and March and

Frisch, lb and a preliminary experiment at BNL has been carried out to test the

feasibility of magnetized -iron shielding. tc

We consider the possibility that the 300-m long shield in the present deSign2 be

replaced by a 15-m long magnetized-iron shield with 18-kG field, and a further con­

tinuation of 85 -rn long shielding, including iron up to 40 m downstream. This method

is based on the fact that the high -energy muons at the end of the decay tunnel are well

collimated and relatively few, so that we could bend them out, while the slower muons

which are produced by secondary processes are ranged out by further shielding. The

decay tunnel downstream is enveloped by thin cylinders of iron and heavy concrete so

that all the muons hitting the tunnel wall may be ranged out. This setup will improve

the present neutrino flux at the bubble chamber by as much as 6!Y'/o It will also pro­

vide an adequate shielding thickness for a low-energy neutrino beam (down to one GeVl,

which may be produced by 100-GeV primary protons if such an operation is found to

be profitable.

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55-156 -2­

We calculate the mean energy loss of muons, muon flux, and angular distribution

at the end of the decay tunnel, muon deflections after passage through a magnetic field,

the coulomb scattering, and the numbers of muons which scatter with large angles in

the iron shielding. Then the shape of a muon shielding is discussed on the basis of

these calculations.

n. THE MUON-SHIELDING CONFIGURATION

The most important thing in the introduction of a magnetic deflection in the muon

shielding is that all the muons are deflected away from a detector uniformly and a sit­

uation does not occur where some muons hit the detector because of the magnetic field.

Only an ill-collimated beam or poor magnet design could produce such a situation.

The muon beam at the end of the decay tunnel in the present design is highly collimated,

partly due to a long decay tunnel (see Fig. 1). The divergence averages 0.3 mrad

around the center of the beam line and only 1.1 mrad at 0.75 m from the center as

seen in Fig. 2. This condition allows the introduction of a magnetic field in the muon

shielding to be promising.

Our basic approach is that all the muons within the radius of one meter at the

end of the decay tunnel are deflected by a block of magnetized iron; muons of lower

energy due to other processes like inelastic scattering are ranged out, while the other

muons hitting the tunnel wall downstream are also ranged out. In order to range out

the muons hitting the tunnel wall we envelop the tunnel with thin iron or heavy concrete

cylinders, according to the calculations of the ray traces. There are some uncertatn­

ties in muon range, due to uncertainties in cross sections of inelastic scattering, 1b

trident production, 3 etc. Therefore, we are rather conservative in the muon­

shielding design. In addition it is very important that we suppress the radiation level 5

outside the bubble chamber to a value lower than the maximum tolerance level (6 x 10

muons/ m 2/puISe) and thus provide a safe working condition at the bubble-chamber in­

stallation.

Foramagneticfieldof18 kG, for example, a 1S-mlongmagnetized-iron shield is

required at a distance of 122.5 m from the bubble chamber for 2 OO-GeV muons to clear the

5 m high bubble chamber. The lower energy muons will be deflected more, as given in

Fig. 4. The deflection by the magnetic field is found to be much greater than that by the cou­

lomb scattering (see Figs. 4 and 5) so that the coulomb scattering is not a serious problem.

However, the coulomb scattering effect was considered to determine the shape of iron shield

Since the fl.+ I~ - ratio atthe end of the decay tunnel is highly asymmetrical, it is much better

to bend muons with larger number down into the earth. However, we will also worry about

their destinations. With respect to the muon deflections it should be remembered that

the bubble-chamber magnet itself can deflect incoming muons out to some extent.

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It is imperative to continue the shielding behind the magnetized-iron block

because there are many processes which deflect muons in the wrong direction so that

they may hit the bubble chamber. Some of these processes are inelastic scattering,

trident production, coulomb scattering, initial angular distribution, etc. We esti ­

mated an iron thickness for this shielding against possible inelastic scattering pro­

cess. The physical quantities required in this calculation are the number of muons

of energy greater than 100 GeV, deflection angles in the magnetic field, the length of

magnetized iron, and the cross section of inelastic scattering. We used Figs. 4,5, 9

and 6 and 1.4 x 10 muons for the number of muons greater than 100 GeV. The 4D-m

long iron shield downstream will stop all inelastically scattered muons which would

otherwise hit the sensitive volume of the bubble chamber. Certainly this is a problem

into which we have to look carefully.

We have also considered locating the magnetized-iron block behind the iron

shield. The length of the magnetized iron can be a little reduced but the size increases

laterally. Hence we will r equtre more magnetized iron than the configuration in

Fig. 7. The worst thing is that as a result of coulomb scattering and interactions we

now have an ill-collimated muon beam. 1c

Since the number of secondary events like inelastic scattering is proportional to

the length of a magnetized iron, the higher the magnetic field the better efficiency in

magnetic deflection we obtain.

The coil insulation is susceptible to radiation damage and a careful schedule of

maintenance will be required. If the magnetized iron can be located behind a hadron

shielding of 10m the radiation hazard could be greatly reduced at some sacrifices of

the muon collimation.

Ill. CALCLLA nONS

A. The Mean Energy Loss of 200-GeV Muons

The mean energy loss of muons (ionization loss only) was calculated numerically 4

in the range of 0.1 to 200 GeV on the basis of work by Barkas and Joseph5 The 2/g 2/gvalue is 2.29 MeV-cm (Fe) for 200-GeV muons and 2.36 MeV-cm (Fe) for

6 2/g300-GeV muons. Perkins obtained 2.26 MeV-cm for the mean energy loss by

integrating Sternheimer's ionization loss formula. The two values are different by

about 4%.

B. The Muon Flux Greater than 100 GeV at the End of the Decay Tunnel

The high-energy muon flux at the end of the decay tunnel is estimated by the

ray traces (NUFLUX computer program)7 and simple calculations. The CKP particle

production formula is used to calculate high-energy pion yield above 100 GeV. For

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75 x 1013 incident protons the muon flux of energy greater than 150 GeV is 4.1 x 102!pulse 6 2!pulse

muons!m inside the radius 0.75 m and 1.1 x 10 muons!m in the re­

gion of the radius of 0.75 to 1,5 m if the radius of the tunnel is 1.5 m . The muon flux 9 2/pulse

greater than 100 GeV is 1.4 x 10 muons!m inside the radius 0.75 m and 7 2/pulse

3.3 x 10 muons!m in the zone from radius 0.75 to 1.5 m , The mean muon

angle with respect to the proton beam is 0.3 mrad at the central region, 1.1 mr ad at

0.75 m from the center, and 2.3 mrad at 1.5 m from the center. The muon flux and

angular distributions are given in Figs. 1 and 2.

C. The Muon Deflection in the Magnetic Field

The muon deflection D after a passage in a magnetic field B(kG)and a recess of

R (ml i s given by

D [(1 - t ) In (1 - t) - t ] +R ~ meters,

where Pine = the incident momentum of muons in GeV/ c

II = the mean energy loss of a muon in GeV/m

J=.L P.

inc

L = the length of the magnetic field in meters

R = the recess, in meters

1 . In (1 - t) r-ad ians (See Fig. 3 and Appendix I)

The muon deflections after a passage through the m.a.gnet.Lz e d iron are given for

various values of parameters in Fig. 4.

D. The Coulomb Scattering

When the muons pass through the iron shield they are deviated by the multiple

coulomb scattering. The r ms projected lateral displacement at the exit of the shield

is given by8

J<x2 > ={~~ [1-t

2+2t 1/2

Inrt)]}

where K = 12.2 x 10- 3 GeV2!m

for iron

II = the mean energy loss of muons

p = the incident muon momentum in GeV/ c

= II YiP

Y the length of a shield in meters

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The rms projected lateral displacements are given for various values of param­

meters in Fig. 5.

E. The Cross Section of Muon Inelastic Scattering

A muon deflected by the magnetic field may be inelastically scattered back into

the detector. It is important, therefore, to know the number of inelastically scattered

particles in the magnetized iron shielding.

Assuming that muons are the same kind of particles as electrons, the cross

section of deep inelastic scattering is given by9

2 8 cos "2 .48

sm "2

2 2for momentum-transfer squared greater than 0.7 GeV /c . Here E and E' are the energies

of an incident and scattered muon, respectively, e is the scattering angle, and c 1/137. Thes

numbers of scattered muons in iron are given as a function of the scattering angles in Fig. 6.

IV. CONCLUSION

In Table I we compare various modes of shielding for 200-GeV muons. The

magnetized iron shield is not so cheap but the neutrino flux improvement is substan­

tial. The pure iron shielding of 140 m is not so bad, but needless to say, a pure

uranium shielding or any combined shielding of uranium and iron seems to be very

expensive at the present cost I$600 to $700/ ton).

In conclusion, we considered a magnetized iron shield within the present de­

sign cost. The basic approach is to deflect high-energy muons greater than 100 GeV

out and to range lower energy muons out. The neutrino flux improvement is substan­

tial and this kirrl of approach seems to be promising. No extension to 400 GeV has

yet been cons id er ed.

Table 1. Modes of Muon Shielding for 200-GeV Muons.

Mode of Shielding Cost Relative Shieldi~ Length (m ) $ Millions Neutrino Fluxa Cost

Iron (100 m) plus Earth 270 0.6 1.0 $BO/ton

Iron 140 1.0 1.4 $80/ton

Magnetized iron plus iron 100 0.6 1.6 $375/ton for

magnetized iron, $8 olton remainder

Uranium 70 3.0 to 3.5 1. 7 $600 to $700/ton

aThe NUFLUX computer program was used to compute the neutrino fluxes. The neutrino energy cutoff is 3 GeV.

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APPENDIX 1.

Suppose that a muon of incident momentum Pine and of incident angle y. is de­

flected by an angle ~ ~ 2 - ~ 1 after a passage L meters in the magnetic field B kG. 0

ISee Fig. 3.) For a muon momentum P in the magnetic field

where 13 is the mean energy loss of muons. Hence

x

13JJ + (~~) .Pine - P 0 2 • dx

o

We also have (2)

(3)

where p is the radius of curvature of a muon trajectory. From (1), (21. and (3)

J[1+(~) 2]dx 00.03 B

~ 2dx

For most cases of interest the angles with the normal are very small.

Hence ~ «1dx

Thus

~(dx 2 Pine - I3x ) ~ 0.03 B .

The solutions for ~ and y are

Lof 0.03 Bdx Pine )in _ L Pine - I3x ( Pine 13

o

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0.03 B P. mc

y [ (1 - t) in (1 - t ) - t J

where

From the following relation

the deflection D by the magnetic field is given by

0.03 B P. D

mc [(1 - t) in (1 - t) - t] + R ~ meters.

REFERENCES

l a . R. H. March, Magnetized Iron Muon Shields, National Accelerator Laboratory

1969 Summer Study Report SS-B, Vol. 1.

b. R. H. March and D. H. Frisch, Problems of Magnetic Shielding for Neutrino

Beams Requtr ing Detailed Study. National Accelerator Laboratory 1969 Summer

Study Report SS - 27, Vol. 1.

c. T. Toohig, Report on a Crude Experiment to Test a Magnetized Iron Muon Shield

for the Slow-Extracted Proton Beam (SEB) at the AGS, National Acceleratory Labora­

tory 1969 Summer Study Report SS-55, Vol. 1.

2y. W. Kang and F. A. Ne z r i ck , Neutrino Beam Design, National Accelerator Labora­

tory 1969 Summer Study Report SS-146, Vol. 1.

3M. J. Tannenbaum, private communtcatton . The total cross section of trident pro­3t 2

duction is 0.5 X 10- cm in carbon at the incident energy 100 to 200 GeV.

4R. H. Thomas, Lawrence Radiation Laboratory UCID-I00I0, W. H. Barkas , Nuclear

Research Emulsions, Vol. 1. , Chap. 9 Academic Press, New York, 1963.

Sp. H. Joseph, Cornell University CLNC-S2, 1969.

6D. H. Perkins, Utization Studies for a 300-GeV Proton Synchrotron 11, 11969.

7The NUFLUX neutrino program used at NAL is a variation of the CERN program.

We wish to thank D. W. Venus for the private communication of the CERN program.

B20a-BeV Accelerator Design Studies, Xli-3D, 1965.

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9 L. N. Hand, Large Momentum Transfer Muon and Electron Scattering at NAL,

National Accelerator Labor-ator-y 1969 Summer Study Repor-t 8S-48, Vol. IV.

I09:,---r----r_--~--r_--~--~-___,

-, ," -,, 10

" -, -,

-,UI

-0C -,0 \. ... 107 a,

C eu "0

0 C

rt)

-0 )(

10 10 <,

>eu (!)

" UI C 0 ~

~

105

104L..-_---IL...-_---'__.......I.__.....L__--L__..L._~...

60 80 100 120 140 160 180 200

Muon Energy, GeV Fig. 1. The muon flux distribution at the end of the decay tunnel assuming that the

number of the incident protons is 5 X 1013 per pulse.

SS-156-9­

3

"0 2 c ~

E

o o 0.5 1.0 1.5

Tunnel Radius (rn)

Fig. 2. The muon angular distribution at the end of the decay tunnel.

L = Magnetic Field Length

R = Recess

D = Deflection

Pine = Incident Particle Momentum

Y • Y = Incident and Outgoing 1 2 Angles

~----L------1j------~------:----R -,r----l-

_:L. Y2

D t

-y

L, Fig. 3. Description of the parameters in the magnetic deflection.

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I rl-. iii iii i

Field = 18 K gauss Recess = 107.5 m

,... o­0,

en... Ql.. Ql

E c ­0.. o Ql--Ql C

I

I

15m

I ,...

0,

,61,

60 120100

Incident Muon

80 iii

160140

Energy. GeV

, ,

180 i

200 '

'J1 'J1,... '" o-

Fig. 4. The muon deflection after a passage in the magnetic field and a recess.

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E-..: c CD E CD 0 10'0 Q. If)

0

CD" -0 CD·0 ~

a. 102

0

-~

CD

0 -I

fJ)

~ a::

I03~__L.....__"""_~"'-_--I__-I--J

o 40 80 120 160 200

Muon Energy (GeV)

Fig. 5. The coulomb scattering in the iron.

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Muon Inelastic Scattering

Scattered Muon Energy

A: 0.25 EinctoO.8Einc

If 8: 0.5 Einc to 0.8 E inc

.~ 10-7 C: 0.75 Einc to 0.8 Einc E o C\I C\I <,

"C

~ ~ 10 o o Vl UJ l: o :::J ~­ E· =IOOGeV o Inc =50GeV ~

eu .0 =40GeV E =30GeV :::J

Z

Fig. 6. The numbers of inelastically scattered muons are given as a function of the scattered angle for the given energy range of scattered muons,

Return Yoke

p<~COil ,-,

I \ Area of IncidentI Muon Beam \ '_ ... '

Cross Section of Deflecting Magnet

Decay Tu nnel i ..'.......: :r-',>. : zzTl7~lZrn nczraTa ..,

- ..• • ••• -L' • • /. -. -••~ -. ", i> > A - ..

:.~.-~ .~ .. r// / / / / / / / / / ///1. / ../-,

0­ ...w, -.--.-----.--.~I+H-H~ w,

. . . . .' . " . . .. . .. 4m

Magnetized -Iron Soil Iron Shield B.C. 18 kG Transverse

3 Fiducial .. VolumeField2

tr: tr: ... eno 0­

Fig. 7. The muon shielding configuration.