Detector Backgrounds for a High Energy Muon Collider

O. Benary^\*^, S. Kahn^§^, and I. Stumer^§^

^§^Brookhaven National Laboratory, Upton, NY 11973

^\*^Tel-Aviv University, Ramat-Aviv, Tel-Aviv 69978, Isreal

**Abstract.** The potentially large background produced from the decay
products of muons could affect the quality of the physics in a high
energy muon collider. This paper examines the kinds of background
present and their expected rate. The results are based on a simulation
of muon colliders with center of mass energies of 100 GeV, 500 GeV and 4
TeV.

# INTRODUCTION

How well the background can be controlled will determine the kind of
physics that can be done in a muon collider. Most backgrounds are
associated with the products of the decaying muons that get into the
detector region. A 2 TeV/c muon beam with 210^12^ μ per bunch will
produce 210^5^ decays per meter. The number of decays per length scales
with 1/γ because of the Lorentz contraction. The electrons produced from
muon decays will not have the designed momentum of the collider ring and
will either interact with the wall of the beam chamber producing
electromagnetic showers or produce bremsstrahlung in regions of large
transverse magnetic field. The design of a detector for a muon collider
will be constrained by the necessity to reduce the electromagnetic
background.

Detector backgrounds have been studied for a potential muon collider at
three different energies:

-   A 50  50 GeV/c Higgs factory collider.

-   A 250 250 GeV/c muon collider at the same energy as the phase 1
    NLC.

-   A 2  2 TeV/c muon collider at an energy not accessible to an
    electron collider.

Results of these studies have been reported elsewhere \[1-2\]. No
explicit investigation has been done for backgrounds in muon colliders
with$\sqrt{s}$ between 10 TeV and 100 TeV. This paper will review what
has been learned about muon collider background in the studies that have
been previously performed. Extrapolation to higher energies may not be
straight forward since the shielding geometry and the beam final focus
elements have been optimized at each energy to reduce backgrounds. The
effort to minimize the backgrounds will have a strong influence on both
the design of the detector and the design of the magnets in the *final
focus* of the intersection region (IR).

**BACKGROUNDS**

The following classes of backgrounds have been investigated for a muon
collider:

-   Muon Decay Background.

-   Beam Halo Background.

-   Beam-Beam Interactions.

Most of the work to date has been devoted to the backgrounds associated
to muon decays. The backgrounds associated to muon decays include:

-   Electron showers.

-   Synchrotron Radiation and pair production.

-   Photonuclear interactions producing hadrons.

-   Bethe-Heitler muon production.

These will be discussed thoroughly in the following sections. Beam halo
backgrounds come from accelerator sources. The beam scraping system will
be designed to reduce halo, however even a small residual muon halo can
produce a large background in the detector.

The backgrounds associated with the muon decay have been studied with a
GEANT simulation of a detector that would be appropriate for a muon
collider. Figure 1 shows a sketch of the geometry of such a detector
along with the final focus magnets of the collider ring. The detector
geometry includes the following features:

-   Conical tungsten shield over the beam extending to 20^o^ in both
    forward and backward directions. The shield prevents most of the
    electromagnetic showers from penetrating into the detector region.

-   Expanding shield inner cone beyond minimum aperture position (1.1
    meters from IP for 2  2 TeV collider) is 4 of the beam size.

-   Between IP and minimum aperture point the inner radius is an inverse
    cone with an angle equal to but opposite sign of the previously
    mentioned angle of expansion after the minimum aperture point. These
    cones are designed so that the detector does not *see* any surface
    where incident decay electrons could have interacted.

-   The open space between the IP and the beginning of the tungsten
    shield is small. It is only 3 cm for the 2  2 TeV collider.

-   The inner surface of each shield is shaped in a sawtooth manner.
    These steps and slopes collimate the electrons in the beam and
    maximize the absorption of the electromagnetic showers from the
    electrons that graze the cone surface. This reduces the funneling of
    low energy electrons down the beam pipe. Figure 2 shows the geometry
    of the inner surface of the tungsten shield.

-   An 8 T dipole magnet with collimator inside is placed upstream of
    the first quadrupole magnet to sweep decay electrons away before the
    final collimation.

> **Table 1:** Parameters describing the geometry of the intersection
> region for the muon colliders studied at three energies.

  ---------------------------- ------------- --------------- -------------
  ***Parameter***              ***50 50     ***250250      ***2 2
                               GeV***        GeV***          TeV***

  Shield Angle                 20^o^         20^o^           20^o^

  Open Space to IP             6 cm          3 cm            3 cm

  Min Aperture Point from IP   80 cm         1.1 m           1.1 m

  R~iris~ at Min Aperture      0.8 cm        0.5 cm          0.5 cm

  Distance to 1^st^ Quad       7 m           8 m             6.5 m
  ---------------------------- ------------- --------------- -------------

![](media/image1.png)

**Figure 1.** Sketch of the IP region and 130 meters of the final focus
magnet system. This sketch shows the geometry of the detector used in
the GEANT simulation of the 2 × 2 TeV Muon Collider.

**Muon Decay Background**

The electromagnetic showers produced from the muon decay electrons
interacting with the beam chamber wall are mostly contained in the
tungsten shielding. A small residual flux of soft photons does reach the
detector region. Electrons in the showers are trapped at small radius by
the 2-4 T detector solenoid field. This is shown in table 2. Table 2
also shows fluences for protons, neutrons, and pions. Hadrons are
produced in \~1% of the interactions in an electromagnetic shower. These
hadrons are produced as a result of photonuclear processes:

-   Giant Dipole Resonance in the energy region 5 \< E~~ \< 30 MeV.

-   Quasi-Deuteron Region in the energy region 30 \< E~~ \< 30 MeV.

-   Baryon Resonance Production in the energy region 150 MeV \< E~~ \<
    2 GeV.

-   Vector Dominance in the energy region E~~\> 2 GeV.

The GEANT program used in these simulations has been modified to include
these processes. Hadron production is also possible at the highest
energies through leptoproduction. This process has been ignored in the
studies so far, however they certainly would be important at very high
energy muon colliders. The MICAP option in GEANT for hadron showering
package was used since it handles neutrons down to thermal energies. Low
energy neutrons can be bothersome since they live a long time. They can
bounce around entering the same detector element several times giving
extraneous signals. In order to alleviate this problem,
borated-polyethelene is placed where possible around the tungsten
shielding and the calorimeter to soak up as many neutrons as possible.
This reduces the neutron flux substantially.

![](media/image2.wmf)**FIGURE 2:** Absorber and collimation system on
the inside surface of the tungsten shield. This system is designed to
reduce electrons in the beam pipe in the vicinity of the IP.

Shown in Table 2a, b are the radial particle fluxes in *cm^2^/crossing*
for two bunches of 10^12^  each at different radii for the 50  50 GeV
and 2  2 TeV machines. The rates are shown for , n, p, , e, and .
The energy thresholds used to define the particle fluxes are E~~\> 25
keV, E~n~\> 40 keV, E~p~ \> 10 MeV, E~~ \> 10 MeV. The fluxes between 5
cm and 20 cm are what a vertex detector would see. A central tracker
might be located at 50-100 cm and the calorimeter would start at 150 cm.
The fluxes shown in Table 2 can be interpreted as occupancy in a 300 m
 300 m silicon pad detector that might be used as a vertex detector.
If one assumes that the probability that low energy photons and neutrons
interact in the silicon pad detector is 0.003 and 0.0001, respectively,
hits and occupancy rates can be calculated. Table 3A and B show the
background hits and occupancy for the 50 × 50 GeV and 2 × 2 TeV
colliders, respectively. Figure 3 shows the occupancy for all three
energies studied. The left-hand part of Figure 3 shows the occupancies
for all particles while the right-hand part shows the occupancies for
the charge particles only. The total occupancy is above 1% at small
radii, mostly due to photon conversions. The charge particle occupancy
is equal or below 1% at all the radii in the figure. One can reduce the
occupancy rates by using smaller pixel sizes or using new innovated
detector ideas.

**TABLE 2A. Flux per crossing for two 50 GeV beams of 10^12^  per
bunch.**

  ------------ ---------- ---------- ---------- ---------- ---------- ------------
  **Radius**   ****      **n**      **p**      ****      **e**      ****

  **5 cm**     4300       32                               3.8        0.15

  **10 cm**    1100       36                    0.24       0.3        0.07

  **15 cm**    480        75                    0.11                  0.03

  **20 cm**    270        98                    0.09                  0.007

  **50 cm**    40         37         0.05       0.015                 0.0004

  **100 cm**   9          18         0.005                            0.0002

  **150 cm**   4          9          0.02                             2.110^-5^
  ------------ ---------- ---------- ---------- ---------- ---------- ------------

**TABLE 2B. Flux per crossing for two 2 TeV beams of 10^12^  per
bunch.**

  ------------ ---------- --------- ---------- ---------- ---------- ----------
  **Radius**   ****      **n**     **p**      ****      **e**      ****

  **5 cm**     2700       120       0.05       0.9        2.3        1.7

  **10 cm**    750        110       0.20       0.4                  0.7

  **15 cm**    350        100       0.13       0.4                  0.4

  **20 cm**    210        100       0.13       0.3                  0.1

  **50 cm**    70         120       0.08       0.05                 0.02

  **100 cm**   31         50        0.04       0.003                0.008

  **150 cm**                                                         0.003
  ------------ ---------- --------- ---------- ---------- ---------- ----------

**TABLE 3A. Background hits and occupancy for 50 × 50 GeV μ collider.
*Hit* rates are quoted for two beams with bunches of 10^12^ μ's each.
*Occupancy* is quoted for two beams with 4 × 10^12^ μ's each and that
the silicon detector has 300 × 300 μm pads.**

+---------+---------+---------+---------+---------+---------+---------+
| **R     | **γ**   | **n**   | **Ch    | *       | **      | **Ch    |
| adius** |         |         | arged** | *Hits** | Total** | arged** |
|         | **c     | **c     |         |         |         |         |
| **cm**  | m^−2^** | m^−2^** | **c     | **c     | **Occu  | **Occu  |
|         |         |         | m^−2^** | m^−2^** | pancy** | pancy** |
+---------+---------+---------+---------+---------+---------+---------+
| **5**   | 13      | 0.03    | 4       | 17      | 6.1%    | 1.4%    |
+---------+---------+---------+---------+---------+---------+---------+
| **10**  | 3.3     | 0.04    | 0.6     | 4       | 1.4%    | 0.2%    |
+---------+---------+---------+---------+---------+---------+---------+
| **15**  | 1.4     | 0.07    | 0.14    | 1.6     | 0.6%    | 0.05%   |
+---------+---------+---------+---------+---------+---------+---------+
| **20**  | 0.8     | 0.1     | 0.10    | 1.0     | 0.4%    | 0.04%   |
+---------+---------+---------+---------+---------+---------+---------+
| **50**  | 0.1     | 0.03    | 0.065   | 0.2     | 0.07%   | 0.02%   |
+---------+---------+---------+---------+---------+---------+---------+
| **100** | 0.03    | 0.02    | 0.005   | 0.06    | 0.02%   | 0.002%  |
+---------+---------+---------+---------+---------+---------+---------+
| **150** | 0.01    | 0.01    | 0.02    | 0.04    | 0.014%  | 0.007%  |
+---------+---------+---------+---------+---------+---------+---------+

**TABLE 3B. Background hits and occupancy for 2× 2 TeV μ collider. *Hit*
rates are quoted for two beams with bunches of 10^12^ μ's each.
*Occupancy* is quoted for two beams with 2 × 10^12^ μ's each and that
the silicon detector has 300 × 300 μm pads.**

+---------+---------+---------+---------+---------+---------+---------+
| **R     | **γ**   | **n**   | **ch    | *       | **      | **Ch    |
| adius** |         |         | arged** | *Hits** | Total** | arged** |
|         | **c     | **c     |         |         |         |         |
| **cm**  | m^−2^** | m^−2^** | **c     | **c     | **Occu  | **Occu  |
|         |         |         | m^−2^** | m^−2^** | pancy** | pancy** |
+---------+---------+---------+---------+---------+---------+---------+
| **5**   | 8.1     | 0.012   | 5.0     | 13.1    | 2.4%    | 0.9%    |
+---------+---------+---------+---------+---------+---------+---------+
| **10**  | 2.3     | 0.011   | 1.3     | 3.6     | 0.65%   | 0.23%   |
+---------+---------+---------+---------+---------+---------+---------+
| **15**  | 1.1     | 0.010   | 0.93    | 2.0     | 0.36%   | 0.17%   |
+---------+---------+---------+---------+---------+---------+---------+
| **20**  | 0.6     | 0.010   | 0.53    | 1.1     | 0.20%   | 0.10%   |
+---------+---------+---------+---------+---------+---------+---------+
| **50**  | 0.2     | 0.012   | 0.15    | 0.36    | 0.06%   | 0.03%   |
+---------+---------+---------+---------+---------+---------+---------+
| **100** | 0.1     | 0.005   | 0.05    | 0.16    | 0.03%   | 0.01%   |
+---------+---------+---------+---------+---------+---------+---------+

The lifetime of a vertex detector in a high radiation environment is of
concern. The radiation damage to a silicon vertex detector at 5 cm from
the beam can be estimated. Table 4 shows the hits/cm^2^/yr (1 year =
10^7^ sec) and expected lifetime of the device under normal operating
conditions. An acceptable number of hits for the silicon vertex detector
lifetime is 1.510^14^.

**TABLE 4. Radiation damage by neutrons on a silicon vertex detector
situated at 5 cm from the beam. It is assumed that the machine is
operating 10^7^ sec/year at 15 Hz with 1000 turns per machine fill. The
neutrons counted are those with E~kin~\>100 keV.**

+-------------+-------------+-------------+-------------+-------------+
| **Energy**  | **/bunch** | **Neutr     | **Hits/c    | *           |
|             |             | ons/cm^2^** | m^2^/year** | *Lifetime** |
|             |             |             |             |             |
|             |             | **Per       |             | **(years)** |
|             |             | crossing**  |             |             |
+-------------+-------------+-------------+-------------+-------------+
| **5050     | 410^12^    | 30          | 1.810^13^  | 8           |
| GeV**       |             |             |             |             |
+-------------+-------------+-------------+-------------+-------------+
| **250250   | 410^12^    | 50          | 310^13^    | 5           |
| GeV**       |             |             |             |             |
+-------------+-------------+-------------+-------------+-------------+
| **22 TeV** | 210^12^    | 100         | 310^13^    | 5           |
+-------------+-------------+-------------+-------------+-------------+

![](media/image3.png){width="5.794444444444444in"
height="2.6597222222222223in"}**FIGURE 3: Occupancy for 300 m 300 m
silicon pads, as a function of the radius for the three energies
studied. Left-hand figure shows the total occupancy while the right-hand
figure shows the occupancy for charged particles only.**

**Bethe-Heitler Muons**

A significant flux of muons with high energy come from  pair production
in electromagnetic showers. These Bethe-Heitler muons will be a concern
at high energy colliders. Figure 4 shows the spectrum of Bethe-Heitler
muons in the final focus region for the 22 TeV collider. This figure is
obtained by convoluting the energy spectrum from the decay of 2 TeV
muons (\<E~electron~\> = 670 GeV) with the  pair production cross
section. Figure 5 displays the trajectories of typical Bethe-Heitler
muons from the last 130 m section of beam pipe before the detector in
the 22 TeV collider. The most serious effect of these muons is that
they may make deeply inelastic collisions in the electromagnetic or
hadronic calorimeter. A large deposit of energy in a single cell in the
vicinity of other jets can cause severe fluctuations in the global
parameters such as transverse energy or missing transverse energy. This
is a more serious problem for the higher energy muon colliders.

Table 5 gives the attributes of the Bethe-Heitler muons found at the
three energies. In the 250×250 GeV and 2×2 TeV cases there is massive
lead shielding around the final focus quadrupoles to reduce the
Bethe-Heitler muons as much as possible. In the higher energy cases 1%
of these muons reach the calorimeter. In the 2×2 TeV case the B-H muons
have 〈p~μ~〉 = 15.4 GeV/c and deposit 2.9 GeV in the calorimeter on
average. This sits on top of a uniform pedestal of 100 GeV to 100 TeV of
deposited energy from all other sources. The size of the pedestal is
dependent on the calorimeter technology used. Since calorimeters based
on scintillator technology will have a higher pedestal of deposited
energy, they may not be a desirable choice. The high neutron background
in the calorimeter favors the use of liquid argon as the active
calorimeter medium. The B-H muons cause large local fluctuations in the
energy deposited in a cell. These energy spikes can (1) cause false
triggers when event selection is based on transverse or overall energy
balance, (2) generate false jets, and (3) give incorrect energy of real
jets. False jet generation can be eliminated with longitudinal energy
balance. Errors in energy of real jets can be a more serious problem.
They can be reduced to some extent with radial energy distribution cuts.

Figure 6 shows the energy deposition for B-H muons in calorimeter cells
segmented in ∆φ and ∆cosθ for the 2×2 TeV muon collider. In this study
the lead shield around the final focus quadrupoles is not included. The
left-hand figure has no timing cut, where as the right-hand plot has a 1
ns timing in synch with the particles from the beam IP. The figure shows
that B-H muons in the central (barrel) part of the calorimeter are
eliminated. Figure 7 illustrates the paths of muons from the IP and B-H
muons arriving at the central and the forward calorimeters. A B-H muon,
which was in time with the muon beam at its production point at 100 m
away, would go directly to the calorimeter, whereas a muon heading to
the IP would travel 100 m *plus* an additional time for the transit of a
particle created at the IP to reach the calorimeter.

![](media/image4.jpeg){width="5.809722222222222in" height="3.4875in"}

**FIGURE 4. Bethe-Heitler muon spectrum at generation.**

![](media/image5.jpeg){width="5.554861111111111in"
height="4.106944444444444in"}

**FIGURE 5. Trajectories of Bethe-Heitler muons from sources in the
shielding around the beampipe in the last 130 m from the IP for the 2×2
TeV collider. The outer edge of the calorimeter is approximately 4 m**

**TABLE 5: Attributes of Bethe-Heitler muons at the energies of the
three muon colliders studied. This table gives the parameters at the
source of the muon pairs and in the calorimeter. It is assumed that lead
shielding surrounds the final focus quadrupoles for the 250×250 GeV and
2×**2 TeV colliders.

  --------------------- ------------- ----------------- -----------------
  Collider Energy       50×50 GeV     250×250 GeV       2×2 TeV

  Source Length         20 m          33 m              130 m

   (p\>1GeV/c) per     9.6×10^-6^    8.3×10^-5^        5.4×10^-4^
  electron                                              

  Beam  per bunch      4×10^12^      2×10^12^          2×10^12^

  B-H  per bunch       6100          17500             28000
  crossing                                              

  〈p~μ~〉~initial~     4.4           9.5               22
  GeV/c                                                 

  μ's entering          25            160               220
  calorimeter                                           

  〈p~μ~〉 in           1.8           6.3               15.4
  calorimeter, GeV/c                                    

  〈E~dep~〉, GeV       0.4           1.3               2.9

  Total E~dep~ by all   10            210               640
  μ's                                                   

  E~dep~ pedestal, GeV  1             25                50

  Fluctuation in        1             15                55
  E~dep~, GeV                                           

  E~⊥~ pedestal, GeV    0.5           15                15

  Fluctuation in E~⊥~   0.5           8                 40
  ,GeV                                                  
  --------------------- ------------- ----------------- -----------------

The difference in time-of-flight between signal muon path and the B-H
muon path would exceed 1 ns which can be used to remove the background.
The situation is not the same for the forward and backward calorimeters.
The time difference between the path of a forward-going B-H muon
reaching the forward calorimeter and path for a beam muon *plus*
produced particle to reach the forward calorimeter is very small. The
timing cut will only eliminate the B-H muons in the backward calorimeter
in this case. Thus the timing cut can only eliminate half of the B-H
muon background in the forward and backward calorimeters.

**Pair Production**

Although coherent beam-beam electron pair production (beamsstrahlung) is
small \[3\] incoherent pair production from processes like
μ^+^μ^−^→μ^+^μ^−^e^+^e^−^ is significant in the 2×2 TeV collider. The
cross section for such processes is estimated to be 10 mb \[4\]

![](media/image6.wmf)

> **FIGURE 6. Energy deposition from Bethe-Heitler muons into a
> calorimeter at a 22 TeV muon collider. The calorimeter cells are
> segmented in cells with 0.1 and cos≈ 0.05. The right-hand plot
> has a timing cut of 1 ns.**

![](media/image7.png){width="5.0in" height="2.282638888888889in"}

> **FIGURE 7. Sketch illustrating the paths of signal muons from the IP
> and Bethe-Heitler muons generated by an electromagnetic shower in the
> beam chamber wall 100 meters upstream. The difference in path length
> between the signal muons and the B-H muons is large enough to
> distinguish by a 1 ns difference in time-of-flight in the central
> calorimeter. In the forward calorimeter a 1ns difference in
> time-of-flight is not sufficient to be distinguished the signal muon
> from the B-H background. This sketch is *not* to scale.**

which would mean approximately 3×10^4^ electron pair per beam crossing.
Although these electrons do not have significant transverse momentum
initially they can be deflected into the detector by the oncoming beam.
This potential background was examined with a simple tracking program to
follow electrons created on the axis (the worse case) as they are
deflected away from the opposing bunch. After they are past that bunch
the electrons are trapped in spiral orbits in the detector magnetic
field. Figure 8 shows the trajectories of the electron tracks for
initial momentum in the range of 3.8 to 3000 MeV/c in a 4 tesla solenoid
field. The study was done for a 2 tesla and 4 tesla detector solenoid
field. In the 2 tesla case electrons with P~init~ \< 30 MeV/c do not
make it out to the 10 cm detector plane, while those with P~init~ \> 100
MeV/c have an initial angle that keeps them within the nose shield.
Approximately 10% of the electron tracks are between these limits and
pass through the detector plane at 10 cm. This gives an electron track
fluence \< 10 tracks/cm^2^. For a detector plane at 5 cm there would be
an electron track fluence of 30 tracks/cm^2^. If the detector solenoid
field is 4 tesla, no electron tracks reach 10 cm and the fluence at 5 cm
is reduced by a factor of 2.

![](media/image8.jpeg){width="5.7875in" height="3.6979166666666665in"}

**FIGURE 8. Trajectories of inelastic electron pair tracks with initial
momentum between 3.8 and 3000 MeV/c. These tracks are in a 4 T solenoid
field.**

**Beam Halo Background**

Beam halo background is the background from the tails of the beam that
can get into the detector. Since muons can traverse long distances
without interacting, any source of beam loss in the ring can potentially
deflect some muons into detector. This is generally not as serious a
problem in hadron or electron colliding rings. Since each beam has
2×10^12^ muons, a small beam halo that could get into the detector would
be very troublesome. Halo calculations are hard to do since they depend
on a detailed model of the ring, the injection system and the injected
beam profile. In addition imperfections in the building of the
accelerator can contribute. Beam halo can have two components: (1) that
which is associated to the initial filling of the ring which will die
out in a small number of turns and (2) that which is generated or
regenerated in the ring and can persist throughout the fill. The former
is not of as great concern since the physics data from the first few
turns can be ignored.

A collimation system\[5\] in the ring is designed to scrape the beam at
a position in the ring 180° away from the IP. This system would scrape
the beam at 3 σ in x and y.

Studies with very limited statistics have been performed tracking muons
with x, x′, y, or y′ greater than 3.5, 4, 4.5, 5 beam σ around a 2 TeV
lattice. In this study muons were tracked through finite sized magnets,
not lumped elements. Muons were allowed pass through material with
multiple scattering corrections. With samples of 200 μ's no beam halo
tracks appeared in the detector region. These samples are too small to
make significant conclusions. Much more work in this area needs to be
done.

**CONCLUSIONS**

The highest energy muon collider that physics backgrounds have been
studied is the 2×2 TeV machine. It is not easy to make meaningful
extrapolations to 100 TeV com muon colliders. It is likely that certain
backgrounds such as hadron production and Bethe-Heitler muons will
increase with energy. It can be assumed that a very high energy muon
collider in the range of 10-100 TeV in the center of mass will not be
the first machine built. One will learn much better how to estimate and
control these physics backgrounds by building lower energy machines such
as the 4 TeV center of mass machine that was studied at SNOWMASS '96.

# Acknowledgments

This research was supported by the U. S. Department of Energy under
Contract No.

DE-ACO2-98CH10886.

**REFERENCES**

1\. *μ^+^μ^^ Collider: A Feasibility Study.* BNL-52503, FNAL Conf
96/092, LBNL-38946 (1996).

2\. Ankenbrandt, C. M. *et al.*, "Status of Muon Collider Research and
Development and Future Plans", *Phys. Rev. Special Topics --AB 081001*
(1999).

3.  P. Chen, *Beam-Beam Interactions in Muon Colliders,* Nucl. Phys. B
    (Proc. Suppl.) **51A**, 179 (1996).

4.  I. Ginzburg, *The e^+^e^−^ Pair Production at μ^+^μ^−^ Collider,*
    Nucl. Phys. B (Proc. Suppl.) **51A**, 186, (1996).

```{=html}
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5.  A. Drozhdin *et al., Scraping Beam Halo in μ^+^μ^−^ Colliders,* AIP
    Conf. Proc. **441**, p 242 (1998),

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