International School of Radiation Damage and Protection
10th Course: Accelerator Radiation Protection
RADIATION PROTECTION AT HIGH
ENERGY PROTON ACCELERATORS
Marco Silari and Graham R. Stevenson
CERN
1211 Geneva 23, Switzerland
Marco Silari, CERN
RP at High Energy Proton Accelerators
1
Summary of the presentation
• Characteristics of hadron cascades
• Particularity of high-energy hadron accelerators
– accelerators, targets areas, experimental areas,
superconducting RF cavities
•
•
•
•
•
Prompt radiation
Muons
Potential exposure to secondary beams
Hazard of heavy ion beams
Radiation protection at future accelerators
Marco Silari, CERN
RP at High Energy Proton Accelerators
2
Hadron cascade
• The way in which the
radiological problems
associated with a proton
accelerator vary with energy
depends on two parameters:
– the multiplicity of the
production of secondary
particles which increases as
the proton energy increases,
and
– the increase in average
energy of these secondaries
which makes them capable
of producing further
inelastic interactions.
Marco Silari, CERN
RP at High Energy Proton Accelerators
3
Secondary particle production (1)
The fluence of
hadrons with
energy greater
than 40 MeV at
1 metre per
proton interacting
an a 5 cm long
copper target at
proton energies
of 7 (*), 23 (+),
225 (z) and
400 GeV (∇)
Marco Silari, CERN
RP at High Energy Proton Accelerators
4
Secondary particle production (2)
This increase in the fluence of secondary
hadrons will have as a direct consequence an
increase in the induced radioactivity in an object
installed close to a loss point such as an
extraction septum, target or vacuum chamber
for a given number of lost protons.
The length of the activated regions downstream
of such an interaction point also increases
dramatically with the energy of the proton
beam.
Marco Silari, CERN
RP at High Energy Proton Accelerators
5
Secondary particle production (3)
FLUKA simulation of
the star density
distribution per
interacting proton
in a 10 cm radius
iron cylinder,
0.5 cm thick, placed
around a thin
copper target
struck by protons
of different
energies
Marco Silari, CERN
RP at High Energy Proton Accelerators
6
Secondary particle production (4)
FLUKA simulations of
cascades in iron
showing contours of
star density
(10-3 stars cm-3) per
interacting proton in
a dump struck by
protons of different
energies
⇒ This behaviour
governs the
thickness of lateral
shielding required
for proton beamdumps
Marco Silari, CERN
RP at High Energy Proton Accelerators
7
Lateral shielding requirements
Lateral shield thickness in metres required to achieve 10 μSv h-1
alongside a beam dump for a proton beam intensity of 1012 s-1. N.B.
0.5 m of concrete must be added to all iron thicknesses.
Proton Energy
Concrete (ρ = 2.4 g cm-3)
Iron (ρ = 7.2 g cm-3)
3 GeV
6.56
2.78
10 GeV
7.02
2.97
30 GeV
7.44
3.15
100 GeV
7.91
3.35
300 GeV
8.34
3.53
1 TeV
8.81
3.72
(Data from Fassò et al., Shielding against high-energy radiation, LandoltBörnstein,1990).
Marco Silari, CERN
RP at High Energy Proton Accelerators
8
Energy dependence of hadronic activity (1)
Hadronic activity is e.g. the total number of stars produced in a
cascade or the number of neutrons produced having energies
between 1 and 10 MeV.
Let N(E) be one such measure of activity and consider the activity
N(nE) produced by a hadron of energy nE, where n is a multiplier
roughly identified with the average multiplicity of high-energy
secondaries (charged and neutral) produced in the first collision.
Unless it is a π0, a secondary with energy Ei produces a hadronic
activity N(Ei) , and
N (nE) = ∑i N ( Ei )
N (nE ) ≈ (1 − fπ 0 )nN ( E )
Marco Silari, CERN
fraction of the energy
lost to the hadronic
sector through π0 in a
single interaction
RP at High Energy Proton Accelerators
9
Energy dependence of hadronic activity (2)
If n and fπ0 can be regarded as constants independent of energy,
a solution to the iterative equation above is a power law:
with
N ( E ) = KE m
1− m =
ln (1 /(1 − fπ 0 ) )
ln n
In the energy range from several GeV to 1 TeV, fπ0 = 0.25 - 0.33
and n = 5 - 10.
n = 5, fπ0 = 0.25 ⇒ m = 0.82
fπ0 = 0.33 ⇒ m = 0.75.
A suitable average value of m ≈ 0.83
n = 10, fπ0 = 0.25 ⇒ m = 0.87
Marco Silari, CERN
RP at High Energy Proton Accelerators
10
Radiation areas in the SPS
Peculiarities:
• Spatial separation of problems
• Induced activity includes a lot
of spallation products ⇒ relevant
for the production of radioactive
waste
• With increasing energy the
extent of regions with an induced
activity hazard increases
H > 2 mSv/h
100 μSv/h < H < 2 mSv/h
7.5 μSv/h < H < 100 μSv/h
Marco Silari, CERN
RP at High Energy Proton Accelerators
11
Classification of radiation areas
AREA
Dose rate limit (μSv/h)
Average
Non
designated
Supervised
Simple
controlled
Limited stay
Maximum
≤ 0.15
≤ 0.5
≤ 2.5
≤ 7.5
≤ 25
≤ 100
≤
Consigne
2 mSv/h
High
radiation
> 2mSv/h
but
≤ 100 mSv/h
Prohibited
≥ 100 mSv/h
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Marco Silari, CERN
No film badge required
Public exposure < 1 mSv/year
No film badge required
Employees exposure < 1 mSv/year
Film badge required
Employees exposure cannot exceed
15 mSv/year
Film badge and personal dosimeter required
Work needs authorisation of RP or RSO
Film badge and personal dosimeter required
Strict access control enforced
Access needs authorisation of RP or RSO
Access protected by machine interlocks
Access needs authorisation of division
leader, Medical Service and RP group
Access monitored by RP group
RP at High Energy Proton Accelerators
12
CERN area monitors
Several types of
ionisation chambers
(air-, hydrogen or
argon-filled) and rem
counters are used to
monitor the radiation
fields in the
accelerator tunnels,
in the experimental
areas and in the
environment.
Marco Silari, CERN
RP at High Energy Proton Accelerators
13
CERN RP central data acquisition system
All installed
radiation monitors
can be read
remotely. Data are
stored in a
database for
future retrieval.
Monitor
parameters such as
alarm threshold
can only be
modified by
authorised
personnel.
Marco Silari, CERN
RP at High Energy Proton Accelerators
14
Controlled access to accelerator areas (1)
Access to primary beam areas
is supervised by the
Accelerator Control Room
Access is granted via a film
badge reader. Upon check that
the person is authorised to
access the area, the operator
frees a key and gives access
Marco Silari, CERN
RP at High Energy Proton Accelerators
15
Controlled access to accelerator areas (2)
Areas in the SPS can
either be under closed,
supervised
or free access
Marco Silari, CERN
RP at High Energy Proton Accelerators
16
Ring survey in the SPS
1.E+05
LSS2
1.E+04
Protons
1.E+03
Ions
1.E+02
1.E+01
Dose equivalent rate (µSv/h)
Dose equivalent rate (µSv/h)
1.E+05
LSS4
1.E+04
Ions
1.E+02
1.E+01
1.E+00
400
1.E+00
200
204
208
212
216
220
224
228
Protons
1.E+03
404
408
412
416
420
424
428
Position
232
Horizontal dispersion in meters
Position
5
4
3
2
1
0
-1
Position
Marco Silari, CERN
RP at High Energy Proton Accelerators
17
432
Electron emission in superconducting cavities
HIGH INTENSITY, LOW ENERGY
(~ 0.5 MeV) ELECTRONS
LOCATION OF MAXIMUM
ELECTRIC FIELD (IRIS)
LOW INTENSITY, HIGH ENERGY ELECTRONS
50 cm
Marco Silari, CERN
RP at High Energy Proton Accelerators
18
Stray radiation from SC RF cavities
Each cavity has its own
“history” and the conditioning
process can vary significantly
from unit to unit, as does the
intensity of the
bremsstrahlung radiation
10
140
B
120
100
6
80
60
4
40
Electric field (MV/m)
Gamma dose rate (mGy/h)
8
2
160
helium processing
without helium processing
140
20
0
0
0
5
10
15
20
Conditioning time (h)
Sharp increase in the radiation
emission when the electric field ⇒
is raised above a given threshold
Marco Silari, CERN
Gamma dose rate (mGy/h)
120
100
80
60
40
20
0
-20
0
2
4
6
8
Electric field (MV/m)
RP at High Energy Proton Accelerators
19
Induced radioactivity in LEP cavities
• The dose rate decreases by about a factor of 10 in 40 minutes,
due to the decay of short-lived radionuclides, followed by a much
slower decrease (another factor of 10 in about 48 hours).
• Stainless steel
• Short-lived:50Cr(γ,n)49Cr (half-life 42.1 min), 54Fe(γ,n)53Fe
(8.51 min), 54Fe(γ,n)53mFe (2.6 min), 92Mo(γ,n)91mMo (1.09 min)
and 92Mo(γ,n)91Mo (15.49 min)
• Long-lived: 48V, 51Cr, 52Mn, 54Mn, 56Ni,
60Co, 88Y, 92mNb, 95Nb, 99Mo
57Ni, 56Co, 57Co, 58Co,
• Copper:
• Short-lived:63Cu(γ,n)62Cu (half-life 9.74 min) and
63Cu(γ,3n)60Cu (23.2 min)
• Long-lived: 51Cr,
74As, 120Sb
Marco Silari, CERN
54Mn, 56Co, 57Co, 58Co, 60Co, 65Zn, 72Se, 75Se,
RP at High Energy Proton Accelerators
20
Radiation fields around proton accelerators:
neutrons
Neutrons
Protons
Charged particles
– muons
Neutron spectral fluence outside a 80 cm thick
concrete shield and a 40 cm thick iron shield
(leptons,
m=105 MeV,
τ=2.2 10-6 s)
– protons
– ...
Marco Silari, CERN
RP at High Energy Proton Accelerators
21
Neutrons outside shielding of highenergy proton accelerators
Fraction of ambient dose
equivalent below a given
energy, as a function of
energy, for the neutron
spectral fluences outside
a 80 cm thick concrete
shield (0) and a 40 cm
thick iron shield (*)
Marco Silari, CERN
RP at High Energy Proton Accelerators
22
Radiation fields around proton accelerators:
muons (1)
Muons arise from the decay of pions and kaons, either in particle
beams or in cascade induced by high energy hadrons. They can also
be produced in high-energy hadron-nucleus interactions
Decay lengths from pions and kaons are 55.9 m and 7.51 m times
the momentum (in GeV/c) of the parent, respectively
Muons are weakly interacting particles → they can only be stopped
by “ranging them out”. Muons mainly lose energy by ionisation, as
their cross-section for nuclear interaction is very low.
Usually muon shielding is only important at accelerators above
10 GeV. At lower energy the shielding necessary to reduce
radiation levels arising from nuclear cascade processes is in excess
of the ionisation range of muons that could contribute to the
radiation problem.
Marco Silari, CERN
RP at High Energy Proton Accelerators
23
Radiation fields around proton accelerators:
muons (2)
Muon shielding is therefore limited to the
forward direction. Typical thickness of
hadron dumps at high energy proton
accelerators is a few metres of iron
Muons from pion decay have a momentum
spectrum that extends from 57% of the
momentum of the parent pion to the pion
momentum itself. Secondary pion beams
generally have dumps of longitudinal
depth of 1-2 m Fe → decay muons will
penetrate the dumps for pion beams with
momentum > 2-3 GeV/c
A beam of 107 pions per pulse with momentum of 20 GeV/c travelling over a
distance of 50 m ⇒ ~ 5 x105 muons per pulse (5% of the parent beam) ⇒ for a
pulse repetition period of 2 s, taking an approximate fluence to dose equivalent
conversion factor equal to 40 fSv m2 and assuming that the muon beam is
averaged over a typical area for the human torso of 700 cm2 ⇒ 500 µSv/h
Marco Silari, CERN
RP at High Energy Proton Accelerators
24
Effect of straggling on the range of muons
Shield
Momentum
Most
10% go
1% go
0.1% go
Range
Range
Material
(GeV/c)
muons
beyond:
beyond:
beyond:
determined
determined
stop at:
(m)
(m)
(m)
from
from
(dE/dx)total
(dE/dx)ionisation
(m)
(m)
(m)
Iron
200
110
120
132
140
105
132
ρ = 7.2
400
190
205
220
228
175
260
Earth
50
110
120
130
135
105
110
ρ = 2.0
100
210
220
235
245
205
210
200
390
410
430
445
380
410
400
710
740
780
800
670
815
500
870
890
930
950
800
1010
g cm-3
g cm-3
Marco Silari, CERN
RP at High Energy Proton Accelerators
25
Muon shielding
Comparison of the longitudinal thickness in metres of iron shielding
required to achieve 10 μSv h-1 due to the hadron and muon components
of the cascade for a proton beam intensity of 1012 s-1.
Proton Energy
Hadron shield
5 GeV
10 GeV
3.4
4.6
30 GeV
100 GeV
Marco Silari, CERN
6.0
14.0
8.4
300 GeV
1 TeV
Muon shield
36.0
77.0
10.2
RP at High Energy Proton Accelerators
170.0
26
Experimental areas
Vertical longitudinal
cut through the beam
lines of the CERN SPS
North Experimental
Areas
Marco Silari, CERN
RP at High Energy Proton Accelerators
27
Narrow beam dosimetry
Since in the case of partial irradiation effective dose
is not an adequate risk indicator as it is unable to take
into account the incidence of deterministic effects,
both effective dose and organ dose in the exposed
tissue or organ have to be considered. The absorbed
dose in an organ is an estimator for deterministic
effects should the threshold for such effects be
reached. Where this threshold is not reached, the
effective dose can be used to estimate the
probability of stochastic effects.
Marco Silari, CERN
RP at High Energy Proton Accelerators
28
Effects of partial-body irradiation
Tissue and Effect
Testes
Temporary sterility
Permanent sterility
Threshold
(Gy)
Annual Limit (Sv)
Alone Whole-body
0.15
3.5
0.2
0.2
0.05
0.05
Ovaries
Sterility
2.5-6.0
0.2
0.05
Lens of the eye
Detectable opacities
Cataract
0.5-2.0
5.0
0.15
0.15
0.05
0.05
0.5
1.5
0.4
0.4
0.05
0.05
Bone Marrow
Depression of hematopoeises
Fatal aplasia
50 Gy for most organs will cause an effect in 1-5% of persons irradiated
70 Gy for most organs will cause an effect in 25-50% of persons irradiated
Marco Silari, CERN
RP at High Energy Proton Accelerators
29
Beam loss
Beam
Beam intensity to cause
Death
(5 Gy)
20 GeV protons
450 GeV protons
7 TeV protons
50 GeV electrons
5 X 1013
2 X 1012
1 X 1011
1 X 1012
Temporary Sterility
(0.15 Gy)
1.5 X 1011
1 X 1010
3 X 108
1.5 X 1010
An SPS beam of several hundred GeV (250 machine pulses per
hour) and 108 particles per pulse can give rise to a dose rate
at 1 metre of approximately 50 mGy/h or 250 mSv/h
Marco Silari, CERN
RP at High Energy Proton Accelerators
30
In-beam exposure (1)
Dose at the
surface ≈ 10-8
Gy per
incident
particle
FLUKA calculations of dose in a
1 mm radius cylinder around
proton beams of different
energies in tissue-equivalent
material: * 20 GeV,
{ 100 GeV, + 500 GeV,
2 TeV and × 7 TeV
Marco Silari, CERN
RP at High Energy Proton Accelerators
31
In-beam exposure (2)
Dose at the
surface ≈ 10-8
Gy per
incident
particle
Secondary electron
beams can be created
at proton accelerators
FLUKA calculations of dose in a
1 mm radius cylinder around
electron beams of different
energies in tissue-equivalent
material: * 20 GeV, { 50 GeV,
+ 100 GeV, 200 GeV and
× 500 GeV
Marco Silari, CERN
RP at High Energy Proton Accelerators
32
Minimum-ionizing particles
•
A minimum-ionizing particle loses energy at a rate of about
2 MeV/(g cm-2)
• For a uniform flux and without any cascading, and assuming
that the beam corresponds to an area of 2 X 2 mm2,
this corresponds to:
2
X
1.6
X
10-13 (J/MeV) X 1000 (g/kg)/4 X 10-2 cm2 = 8 X 10-9 Gy
• This corresponds well to the FLUKA calculations at the
surface
• This means that we shall cause a detectable opacity in the
lens of the eye with a single pulse of 108 particles
Marco Silari, CERN
RP at High Energy Proton Accelerators
33
Organ doses - Summary
We can now determine the number of pulses which
will cause damage for a beam intensity of 108
particles per machine pulse.
Damage
Required
Dose (Gy)
Machine
pulses
Testes – Temporary sterility
Bone marrow
Testes or Ovaries – Permanent
sterility
General organ damage
0.15
1
2
15
4
60
50
700
Marco Silari, CERN
RP at High Energy Proton Accelerators
34
Organ dose and effective dose for protons
Eye
Thyroid
Thymus
Breast
k = particle
energy in GeV
Lung
DT = AD + BD log k
E = AE + BE log k
(Gy or per primary particle)
aram
eter
s
1E-10
1E-12
0
100
200
300
400
Proton Energy (GeV)
ORGAN
Right eye
Thyroid
Thymus
Breast
Lung
BD
AD
-10
3.24 10
5.82 10-11
3.80 10-11
7.89 10-12
1.45 10-12
AE
-11
2.38 10
1.20 10-11
8.19 10-12
1.22 10-12
1.82 10-12
BE
-13
4.63 10
1.47 10-11
4.88 10-12
2.52 10-12
1.01 10-12
8.77 10-13
3.76 10-12
2.40 10-12
2.00 10-12
1.15 10-12
Thyroid
Thymus
Effective Dose (Sv per proton)
ing p
1E-11
fitt
Organ dose (Gy per proton)
1E-9
Breast
Lung
Eye
1E-11
1E-12
0
100
200
300
400
Proton Energy (GeV)
Marco Silari, CERN
RP at High Energy Proton Accelerators
35
Organ dose and effective dose for electrons
Eye
Thyroid
Thymus
Breast
Lung
1E-10
Thyroid
Thymus
1E-11
1E-12
0
100
200
300
Electron Energy (GeV)
400
Effective Dose (Sv per electron)
Organ dose (Gy per primary electron)
1E-9
Breast
Lung
Eye
1E-12
1E-13
0
100
200
300
400
Electron Energy (GeV)
Marco Silari, CERN
RP at High Energy Proton Accelerators
36
Breast
Thymus
Fraction of effective dose due to non-target organs
for protons, for four of the five target organs
investigated (the eye has no associated wT-value)
Lung
Thyroid
1
0.1
0
100
200
300
400
Proton Energy (GeV)
Same for electrons
Marco Silari, CERN
Fraction of the effective dose due to non-target organs
Fraction of the effective dose due to non-target organs
Organs contributing to effective dose
Breast
Thymus
Thyroid
Lung
1
0.1
0.01
1E-3
0
100
200
300
400
Electron Energy (GeV)
RP at High Energy Proton Accelerators
37
Lead-ion beams (1): thick target
As for proton beams, the transverse shielding of high-energy
heavy ion beams mainly involves the attenuation of the
secondary neutrons generated in the hadronic cascade. Most
of the available Monte-Carlo codes cannot be employed
directly because they do not transport ions with masses larger
than one atomic mass unit.
There is also a general lack of knowledge about the source
terms for neutron production from high-energy heavy ions.
Recent measurements at CERN have shown that the spectral
fluence of the secondary neutrons outside a thick shield is
similar for light (protons) and heavy (lead) ions stopped in a
thick target.
Marco Silari, CERN
RP at High Energy Proton Accelerators
38
Lead-ion beams (2): thick target
The approach of considering a high energy lead ion as an independent
grouping of free protons is sufficiently accurate for the purpose of
evaluating the ambient dose equivalent of secondary neutrons
outside thick shielding.
The neutron yield from lead beams dumped in a thick target appears
to depend on energy as
0 .8
Y ∝ E Pb
where EPb is the energy per nucleon of the lead ion beams.
The yield also appears to scale linearly with the mass number of
the projectile.
Marco Silari, CERN
RP at High Energy Proton Accelerators
39
Lead-ion beams (3): thin target
90° neutron yield from high energy protons and lead ions on a
thin lead target (neutron per primary particle per steradian)
Scaling factor
(A=208)
(sr-1)
Experimental
(FLUKA guess)
(sr-1)
40 GeV/c protons + π+
(3.199 ± 0.003) x 10-1
3.499 x 10-1
40 GeV/c lead ions
(3.666 ± 0.003) x 10-1 (a)
26.6
A0.80
158 GeV/c lead ions
(4.566 ± 0.003) x 10-1 (a)
41.1
A0.84
Beam
FLUKA
(a) The simulation results refer to a proton beam of the same
energy per nucleon.
Marco Silari, CERN
RP at High Energy Proton Accelerators
40
Lead-ion beams (4)
• As far as we know, the stray radiation caused by realistic heavy ions rises no faster
than with the number of nucleons in the projectile nucleus.
Therefore the dose rates caused by a secondary SPS lead beam are about 200 times
higher than a secondary proton beam of the same particle intensity.
• Thus a lead beam containing 106 ions is equivalent to a “normal” beam of 2 X 108
particles.
BUT
• The Bethe-Bloch formulation for ionization energy loss tells us that the rate of
energy loss varies as the square of the charge of the projectile nucleus.
• Thus the “minimum” energy loss rate of 2 MeV/g cm-2 becomes for a lead nucleus a
loss rate of
13.4 GeV/g cm-2
• And this is not all distributed in “small” events as can be seen from emulsion photomicrographs of cosmic-rays tracks.
Marco Silari, CERN
RP at High Energy Proton Accelerators
41
Relativistic lead-ions in emulsions
Marco Silari, CERN
RP at High Energy Proton Accelerators
42
Relativistic lead-ions in plastics
Marco Silari, CERN
RP at High Energy Proton Accelerators
43
Damage caused by lead-ions
• The original line of dislocation damage in plastics has a diameter of about
100 Angstroms, or 0.01 microns. This can be etched to give a visible cone of about
35 microns depth/diameter.
• There is complete physical destruction of the structure of the plastic over an
area of 10-12 cm2 or for a beam of 106 lead particles the surface area destroyed is
10-6 cm2.
• The lead tracks in emulsions have a core of about 20 microns in radius.
Thus each lead track leaves a solid line of developed silver grains of 10-5 cm2 crosssectional area.
• So a beam of 106 particles spread out uniformly can turn an emulsion of 10 cm2
cross-sectional area black.
• In a beam of 4 mm2 cross-section there is the power to physically destroy a
fraction of 2.5 X 10-5 of its cross-sectional area or to put 250 times more energy
into an emulsion than is necessary to make developable silver grains.
Marco Silari, CERN
RP at High Energy Proton Accelerators
44
PB - Damage to tissue
• Multiplying the biological damage factors determined before
simply by Z2Pb = 6700 we might cause a detectable opacity in the
lens of the eye with a single pulse of 1.5 X 104 lead of ions.
• The organ dose is at least 1.5 X 10-6 Gy per beam particle. Thus:
Damage
Required
Dose (Gy)
Testes – Temporary sterility
Bone marrow
Testes or Ovaries – Permanent sterility
General organ damage
0.15
1
4
50
Pb Intensity
3X104
2X105
8X105
1.5X107
The conclusion is that it is more than prudent to keep out of a lead
beam of 106 ions per burst!
Marco Silari, CERN
RP at High Energy Proton Accelerators
45
CERN Neutrinos to Gran Sasso
Marco Silari, CERN
RP at High Energy Proton Accelerators
46
CERN Neutrinos to Gran Sasso
Marco Silari, CERN
RP at High Energy Proton Accelerators
47
Radiation hazard from neutrinos (1)
Expected annual dose equivalent from natural and accelerator
neutrino sources (Short and Long Baseline neutrino experiments)
Solar neutrinos (Eν ~ 1 - 10 MeV)
Atmospheric neutrinos (Eν ~ 100 MeV - 2 GeV)
Neutrino experiments (Eν ~ 10 – 100 GeV):
Fermilab (NuMI)
SBL, 1 km distance
LBL, 730 km distance
CERN/Gran Sasso SBL
Gran Sasso
Marco Silari, CERN
Annual dose equivalent (µSv)
10-7
2 x 10-9
10
8.5 x 10-6
10
5 x 10-5
RP at High Energy Proton Accelerators
48
CERN Neutrino Factory
Marco Silari, CERN
RP at High Energy Proton Accelerators
49
Radiation hazard from neutrinos (2)
b
d
ν
θ∼1/γ
h
s
a
z
R
s2 = 2 R d - d2
θ ∼ 1/γ
sin φ = s / R
a≅2θs
h ≅ z tan φ
b≅a/φ
E CoM d (m) s (km)
φ
Marco Silari, CERN
φ
z (km) h (m)
-3
0.5 TeV
100
35
5.6 10
4.0 TeV
500
80
12.5 10
-3
θ
a (m) b (m)
10
56
424 10
10
125
53 10
RP at High Energy Proton Accelerators
-6
-6
30
5300
8.5
680
50
Radiation hazard from neutrinos (3)
Marco Silari, CERN
RP at High Energy Proton Accelerators
51
Radiation hazard from neutrinos (4)
Marco Silari, CERN
RP at High Energy Proton Accelerators
52