Beam Loss Control on the ESS Accumulator Rings*
C M Warsop
Rutherford Appleton Laboratory,
Oxfordshire, UK
Abstract. The requirements for beam loss control on the 1.334GeV accumulator rings of the European Spallation
Source are summarised. The main features of the beam loss collector system design are described, along with the
underlying aims. Use of a specially developed code to test the proposed system under most foreseeable loss conditions,
with machine errors, is described. Predicted collection efficiencies, in terms of localisation and surviving halo, are given.
Simulations indicate that the required uncontrolled loss levels of <1 W/m over most of the machine will be achievable.
INTRODUCTION
The ESS Accelerators [1] provide 5 MW of beam
power for a short pulse length, 50 Hz spallation target.
The ~ 1.0ms pulse from the linac is compressed to
~1 |is by two accumulator rings, operating in parallel
at 50 Hz. During the ~600 turn charge-exchange
injection, 2.34xl014 protons are accumulated in each
ring. The 1.334GeV H" linac provides a mean and
peak current of 70 and 114mA respectively, chopped
at 70% duty factor, at the revolution frequency of the
rings, 1.242 MHz. This allows lossless capture in the
ring RF system, maintaining a gap for extraction. After
fast extraction from each ring, beams are brought
together in the target transport line.
The need for low and controlled loss has dominated
the machine design. Key measures for loss control in
the rings include 3D collimation in the injection line,
highly optimised injection with 3D painting which
minimises proton foil traversals. The concern here is
control of lost protons, once they enter the acceptance
of the ring [2]. To allow hands on maintenance, loss
levels over most of the machine (uncontrolled loss)
should not exceed 1 W/m levels. To achieve this,
collimator systems localise most loss (controlled loss)
in dedicated, well shielded regions of the machine.
Expected and Possible Losses
Regular losses, occurring operationally, 24 hours a
day will dominate activation levels. There are
unavoidable losses associated with foil interactions,
expected at 0.01% levels, manifested as transverse
emittance growth and energy loss. Unexpected effects,
or non-optimal set up, may lead to some transverse
and longitudinal loss. Important examples requiring
precautions are possible space charge emittance
growth and extraction loss. Also important are fault
losses, where high loss levels trip off the beam. Up to
a full beam pulse may require efficient removal, and
fault scenarios may lead to loss in any plane. Highest
priorities are for control of foil related losses, and
transverse losses. For comprehensive protection,
provision is also made for general longitudinal losses.
1. LOSS COLLECTION SYSTEMS
Betatron and Momentum Tail System
The main betatron collimation system is placed
downstream from injection, in a dedicated, well
shielded, dispersionless straight. For each transverse
plane, the design is based on a standard two stage
betatron collimation configuration [3], with long
primary jaws followed by secondary jaws at relative
betatron phases of 90° and 163°. The latter is given by
ISO-//, with cos ju = ^(£pl£s). Painted emittance,
primary (^), secondary (es) and aperture acceptances
are 150, 260, 285 and 480 n mm mr, respectively. The
secondary collimation limit is chosen on the basis of
expected alignment, and also to protect the extraction
system. Additional protective collimation is included
at 20° and 32°. To enhance protection, jaws are double
(both sides of the beam). This configuration is efficient
over a wide range of loss modes. Placement of the
primary jaw 180° from the injection point provides
collimation of the low momentum tail generated at the
foil.
General Momentum System
This consists of single stage collimation placed at
the first dispersion peak after the betatron system. It is
provided as a precaution against error conditions, and
for removal of out-scatter from the betatron system.
Practical Features and Layout
To minimise the number of mechanical units, and
enclose conveniently the most active surfaces,
* Work here based on parts of the author's Ph.D. thesis [2]
CP642, High Intensity and High Brightness Hadron Beams: 20th ICFA Advanced Beam Dynamics Workshop on
High Intensity and High Brightness Hadron Beams, edited by W. Chou, Y. Mori, D. Neuffer, and J.-F. Ostiguy
© 2002 American Institute of Physics 0-7354-0097-0/02/$ 19.00
174
horizontal
single
horizontal and
and vertical
vertical jaws
jaws are
are combined
combined into
into aa single
box
is also
also
box construction.
construction. This
This tubular
tubular geometry
geometry is
horizontal
and
vertical
jaws
are
combined
into
a
single
beneficial
for
interception
of
secondary
particles
and
beneficial for interception of
box
construction.
This
tubular
geometry
is
also
protection
of
downstream
components.
Primary
jaws
protection of downstream
beneficial
for
interception
of
secondary
particles
and
are
of
copper
and
secondaries
of
graphite,
lengths
are
are of copper and secondaries of
protection
of
downstream
components.
Primary
jaws
~0.5
lengths).
~0.5 and
and 1.0
1.0 m
m respectively
respectively (three interaction lengths).
are of copper
and secondaries
of graphite,
lengths are
The
are
enclosed
in
concrete;
active handling
The straights
straights
are
enclosed
in
concrete;
~0.5 and 1.0 m respectively (three interaction lengths).
concepts
arestraights
included
for
fast
and installation.
concepts
included
fast removal
removal
Theare
arefor
enclosed
in concrete; active handling
Collimators are
are modeled
modeled as
as 3D
3D objects,
objects, including
including
Collimators
interactions with
with inner
inner faces,
faces, and
and appropriate
appropriatetreatment
treatment
interactions
Collimators are at
modeled
as 3D objects,
of out-scattering
out-scattering
at boundaries.
boundaries.
All including
important
All
important
interactions
with
inner
faces,
and
appropriate
treatment
processes:
ionisation
energy
loss,
straggling,
elastic
processes: ionisation energy loss, straggling, elastic
of inelastic
out-scattering
at
boundaries.
All
important
and
inelastic
nuclear
scattering,
and
multiple
elastic
nuclear scattering, and multiple elastic
processes: are
ionisation
energy
loss,have
straggling,
elastic
scattering,
included.
These
been checked
checked
scattering,
are
included.
These
have
been
and inelastic
nuclear
scattering,
and
multiple
elastic
published data
data for
for the
the relevant
relevant regimes.
regimes.
against published
concepts areare
included
removal and
Compromises
made
placement
of installation.
betatron
Compromises
are
madeforin
infast
placement
collimators
for
combination
of
horizontal
and
vertical
collimators
for
combination
of
horizontal
Compromises are made in placement of
betatron
jaws,
to
quadrupoles.
final
betatron
jaws, and
and
to protect
protect
quadrupoles.of The
final and
collimators
for combination
horizontal
vertical
system
consists
combined
horizontal
vertical
systemjaws,
consists
of protect
combined
and of
to
quadrupoles.
Theand
final
betatron
consists
of 90°.
combined
horizontal
and vertical
jaws
0°,
32°
The 163°
jaws at
atsystem
0°, 20°,
20°,
32° and
horizontal
and
at 0°, 20°, 32°
90°. The
163° horizontal
vertical
collimators
are
around
the finaland
verticaljaws
collimators
areandsplit
split
vertical
collimators
are split
around
the are
final
quadrupole
to achieve
achieve
near optimal
optimal
quadrupole
to
near
phases.
Phases
quadrupole
to
achieve
near
optimal
phases.
Phases
within about
about 10°
10° of ideal values. Simple collimatorare
within
within
about
10° of flat
idealin
Simple collimator
jaw
designs
are
selected,
flat
invalues.
the longitudinal
and
jaw designs are selected,
jaw designs are selected, flat in the longitudinal and
transverse direction.
direction. The
The latter
latter is strongly influenced
transverse
transverse direction. The latter is strongly influenced
by the
the by
rectangular
machine
apertures.
by
rectangular
machine
apertures.
A beam
in gap
the rectangular
machine
apertures.
A beam
in gap
kicker system
system
could
be
added
kicker
could
be
added
if
required.
kicker system could be added if required.
lossisand
and
machine
error
conditions.
Therefore
expected
machine
conditions.
The loss
aim
to ensure
thaterror
the design
works Therefore
for
most
loss
conditions
are
defined,
modelled,
andloss
loss
various
loss
conditions
are
defined,
modelled,
and
expected loss and machine error conditions. Therefore
distributions
around the
the
machinemodelled,
determined.
The
distributions
around
determined.
The
various loss conditions
are machine
defined,
and loss
of surviving
surviving
halos
alsodetermined.
analysed. Basic
Basic
extent
of
isis also
analysed.
distributions
around halos
the machine
The
extent ofis
halos with
is also
Basic
behaviour
issurviving
first assessed
assessed
with
no analysed.
errors, and
and
then
behaviour
first
no
errors,
then
behaviour
is afirst
assessed
withwith
no errors,
andrandom
then
over
a number
number
of runs
runs
with
standard
random
observed
over
of
standard
observed
over a number of runs with standard random
error
conditions.
conditions.
scattering, are included. These have been checked
against
published
data for
thethe
relevant
regimes.
aim
is to
to ensure
ensure
that
the
design
worksfor
formost
most
The aim
is
that
design
works
error conditions.
3.
RESULTS
3.3.SIMULATION
SIMULATION
RESULTS
SIMULATION RESULTS
Figure3.1
3.1Transverse
Transverse Collimation:
Collimation:
Figure
Single
Turn
Figure
3.1
Transverse
Collimation:Single
SingleTurn
Turn
Figure
1.1Betatron
Main Betatron
System
Layout
in Long
Straight
Figure 1.1
1.1
Main
System
Layout
in Long
Long
Straight
Figure
Main
Betatron System
Layout
in
Straight
2. MONTE CARLO CODE
2. MONTE
MONTE CARLO
CARLO CODE
CODE
2.
Approach and Aims
Approach and
and Aims
Aims
Approach
Full understanding and control of activation
on a
Fullhigh
understanding
andmachine
control would
of activation
activation
on
intensity proton
require complete
Full
understanding
and
control
of
on aa
high
intensity
proton
machine
would
require
complete
models
of
(i)
loss
mechanisms
(ii)
proton
loss
control
high intensity proton machine would require complete
(iii)
particle
cascades
and
resulting
distributions
models
of
(i)
loss
mechanisms
(ii)
proton
loss
control
models of (i) loss mechanisms (ii) proton loss control of
unstablecascades
nuclei. The
approach
here distributions
is to concentrate on
(iii) particle
particle
and
resulting
(iii)
cascades and
resulting
distributions of
of
(ii)nuclei.
and model
this realistically
with
some care. on
Loss
unstable
The
approach
here
is
to
concentrate
unstablemechanisms
nuclei. Theare
approach
here
is
to
concentrate
on
not well with
known,
therefore
simple
(ii)
and
model
this
realistically
some
care.
Loss
(ii) andmodels
model ofthis
realistically
some care. Lossand
forwith
all expected
mechanisms are
are loss
not modes,
well known,
known,
therefore planes
simple
mechanisms
not
well
therefore
simple
growth rates, are used. The aim here is to determine,
models
of
loss
modes,
for
all
expected
planes
and
modelsand
of loss
modes,
expected
and
ensure
controlforof,all proton
lossplanes
distributions:
growth
rates,
are
used.
The
aim
here
is
to
determine,
growth activation
rates, arelevels
used.may
Thebeaim
here isfrom
to determine,
calculated
these.
and ensure
ensure control
control of,
of, proton
proton loss
loss distributions:
distributions:
and
activation
levels
may
be
calculated
from
these.
activation levels may
be calculated
from these.
Outline
of Simulation
The Outline
code tracksof
protons
around the machine, using
Simulation
Outline
Simulation
a detailed
lattice of
model
with aperture geometries.
The code tracks
protons
the machine,
are made
everyaround
half metre
to see if ausing
particle
TheChecks
code tracks
protons
around
the machine,
using
has been
lost.model
Representative
randomgeometries.
magnet and
a detailed
lattice
with aperture
a detailed
lattice model
aperture
geometries.
Qwith
shifts
Checksalignment
are madeerrors,
everyand
half
metreare
toincluded.
see if a particle
Checks are made every half metre to see if a particle
has been lost. Representative random magnet and
has been lost. Representative random magnet and
alignment errors, and Q shifts are included.
alignment errors, and Q shifts are included.
175
Figure 3.2 Transverse Collimation: Multiple Turn
Figure
Figure 3.2
3.2 Transverse
TransverseCollimation:
Collimation:Multiple
MultipleTurn
Turn
Test 1: Basic Transverse Collimation
Test
Basic
Transverse
Collimation
Test
1:tests
Basic
Transverse
Collimation
These1:
checked
the basic optical
performance
ofThese
the system,checked
ensuring
design
compromises
were
the
basic
optical
These tests
testsA checked
the
basic
optical performance
performance
reasonable.
matched
beam
distribution
uniformly
of
the
ensuring
design compromises
were
ofspanning
the system,
system,
ensuring
compromises
were
the
480
π mm beam
mrdesign
transverse
horizontal
and
reasonable.
A
matched
distribution
uniformly
reasonable.
A matched
distribution
vertical acceptances
wasbeam
introduced
at the uniformly
primary
spanning
the 480
πnmm
transverse horizontal
and
spanning
480around
mm mr
mr
horizontal
jaw, andthe
taken
the transverse
machine one
turn. Theand
vertical
acceptances
was
introduced
at
the
primary
momentum
distribution
wasintroduced
uniform over
vertical
acceptances
was
at the
thenominal
primary
jaw,
and
taken
the
machine
one
The
±0.8%
The the
test machine
was then repeated,
jaw,
andacceptance.
taken around
around
one turn.
turn.but
The
momentum
distribution
was
uniform
over
the
nominal
over multiple
turns. Simulations
were over
also repeated
a
momentum
distribution
was uniform
the nominal
±0.8%
acceptance.
The
test was
then repeated,
number
of times with
randomly
generated
±0.8%
acceptance.
The
test was
then errors.
repeated, but
but
over multiple turns. Simulations were also repeated a
over Simulation
multiple turns.
Simulations
were
repeated a
results
for single
and also
multiple
number
of times with
randomly
generated
errors. turn
number
of times
randomly generated
collimation
in with
the horizontal
plane are errors.
shown in
Figures
3.1 andresults
3.2. These
normalised
transverse
Simulation
for show
single
and multiple
turn
-3
1/2 and multiple turn
Simulation
results
for 10
single
phase
spacein(axes
units
mplane
): input
andin
collimation
the inhorizontal
are beam
shown
Collimation in the horizontal plane are shown in
Figures 3.1 and 3.2. These show normalised transverse
Figures 3.1 and 3.2. These show
normalised transverse
phase space (axes in units 10-33 m1/2
): input beam and
phase space (axes in units 10" m1/2): input beam and
collimated
beam, with
with no
no errors.
errors. The
The circles
circles indicate
indicate
collimated beam,
collimated
beam,
with
no
errors.
The
circles
indicate
acceptances of
of 260,
260, 285
285 and
and 480
4807cmmmr.
The
acceptances
π mm mr. The
acceptances ofdistribution
260, 285of
480 π mmaround
mr. The
corresponding
distribution
ofand
lost particles
particles
around
the
corresponding
lost
the
corresponding
distribution
ofFigure
lost particles
around
the
whole
machine
is
shown
in
3.3,
starting
at
the
whole machine is shown in Figure 3.3, starting at the
whole machine
is shown
in Figure
3.3, schematically:
starting at the
primary
collimator.
The lattice
lattice
is shown
shown
primary collimator.
The
is
schematically:
primaryelements
collimator.
The
lattice
isdipoles,
shown schematically:
darker
are
the
main
indicating
the
darker elements are the main dipoles, indicating the
darker
elements
are the
main
dipoles,
indicating the
main
arcs
of
the
three
super
period
machine.
main arcs of the three super period machine.
main arcs of the three super period machine.
.
.
,
,
Extraction
Extraction
Extraction
*%a
Collimation
Collimation
Collimation
Injection
Injection
Injection
RF
RF
RF
resulting beam
beam loss
loss distributions
distributions for
for 10
10µm/turn
|im/turn
resulting
resulting
beam
loss
distributions
for
10
µm/turn
growth
rates
are
shown
in
Figure
3.4,
and
for
10
and 11
growth rates are shown in Figure 3.4, and for 10 and
growth
rates
are shown
in3 Figure
3.4,1.and
for are
10 and
1
jim/turn
in
cases
2
and
of
Table
These
for
the
µm/turn in cases 2 and 3 of Table 1. These are for the
µm/turn
in cases
2with
and 3nooferrors:
Table 1.
These results
are for were
the
horizontal
plane
vertical
horizontal plane with no errors: vertical results were
horizontal
with As
no would
errors: be
vertical
results
wereof
essentiallyplane
the same.
same.
expected,
spread
essentially
the
As would
be expected,
spread
of
essentially
thethe
same.
As would straight
be expected,
spread with
of
loss
down
collimation
increased
loss down the collimation straight increased with
loss
down
the rates.
collimation
straight
increased
slower
growth
Simulations
were
repeatedwith
with
slower
growth
rates. Simulations
were
repeated
with
slower
growth
rates.
Simulations
were
repeated
with
errors.
However,
worst
cases
with
errors
still
achieved
errors. However, worst cases with errors still achieved
errors.
worst cases with errors still achieved
overallHowever,
control >95%.
>95%.
overall
control
overall control >95%.
TABLE 1.1.Percentage
PercentageLoss
Lossin
inSections
SectionsofofMachine
Machine
TABLE
TABLE
1. Percentage
Loss in
Sections
of Machine
(All
results
without
errors,
except*
which
are‘worst
'worstcases’)
cases')
(All results without errors, except* which are
(All
without errors,
except*Momentum
which are ‘worst cases’)
Betatron
Betatron
caseresults
RestOf
Of
case
Betatron
Betatron
Momentum
Rest
nd
rd Momentum
st
case
Betatron
Betatron
Rest
Of
st Cell
nd & 3rd
2
Collimator
1
Machine
1 Cell
2 &
&33rd
Collimator
Machine
1st Cell
2nd Cell
Collimator
Machine
Region
Cell
Region
Cell
Region
1
37.7+0.4
59.6+0.8
2.4+0.1
0.3(0.4*)
(0.4*)±0.1
±0.1
59.6±0.8
37.7±0.4
2.4±0.1
0.3
112
59.6±0.8
37.7±0.4
2.4±0.1
0.3
(0.4*)
±0.1
23.6+0.4
75.0±0.8
l.OtO.l
0.4
(1.4*)
±0.1
75.0±0.8
23.6±0.4
1.0±0.1
0.4(1.4*)
(1.4*)±0.1
±0.1
223
75.0±0.8
23.6±0.4
1.0±0.1
0.4
43.3+0.4
53.5+0.8
2.5+0.1
0.7
(4.6*)
±0.1
3
53.5±0.8
43.3±0.4
2.5±0.1
0.7 (4.6*) ±0.1
3
Figure
3.3 Loss
Loss Distribution for
for Test 1:
1: Single Turn
Turn
Figure
Figure3.3
3.3 Loss Distribution
Distribution for Test
Test 1: Single
Single Turn
53.5±0.8
43.3±0.4
2.5±0.1
0.7 (4.6*) ±0.1
Test 3:
3: Injection
Injection and
andExtraction
ExtractionLosses
Losses
Test
Test
3: Injection
and Extraction
Losses
These
results are
are without machine
machine errors: their
their
These
These results
results are without
without machine errors:
errors: their
inclusion
had
small
effect,
the
most
significant
being
inclusion
being
inclusion had
had small
small effect,
effect, the
the most
most significant
significant being
an increase
increase in surviving
surviving halo. The
The first figure
figure shows
shows
an
an increase in
in surviving halo.
halo. The first
first figure shows
the
cuts made
by the
jaw system:
in aa single
turn most
the
most
thecuts
cuts made
made by
by the
the jaw
jaw system:
system: in
in a single
single turn
turn most
beam
is confined
confined well
well within
within the
the machine
machine acceptance,
acceptance,
beam
is
beam is confined well within the machine acceptance,
except
that
escaping
due
to
out-scatter.
The 99%
99%
except
except that
that escaping
escaping due
due to
to out-scatter.
out-scatter. The
The 99%
surviving
single-turn
halos,
without
and
with
errors,
surviving
errors,
surviving single-turn
single-turn halos,
halos, without
without and
and with
with errors,
were
344
and
374
±3
n
mm
mr.
Corresponding
were
344
and
374
±3
π
mm
mr.
Corresponding
were 344 and 374 ±3 π mm mr. Corresponding
numbers
for
collimation
were 261
261 and
and 281
281
numbers
multi-turn
281
numbers for
for multi-turn
multi-turn collimation
collimation were
were
261
and
±3
n
mm
mr.
The
single
turn
loss
distribution
is
given
±3
±3ππmm
mmmr.
mr. The
The single
single turn
turn loss distribution is given
in
1,
case
1:
in
the
worst
case with
with errors,
errors, <1%
<1%
inin Table
Table
Table 1,
1, case
case 1:
1: in
in the
the worst
worst case
escaped
the
collimator
regions.
escaped
escaped the
the collimator
collimator regions.
regions.
Approximate simulations
simulations of
of the
the injection
injection process
process
Approximate
Approximate
simulations of
the injection
process
confirmed
foil
associated
losses
at
<0.01%,
and
confirmed foil
foil associated
associated losses
losses atat <0.01%,
<0.01%, and
and
confirmed
indicated
effective
loss
control.
Similarly,
efficiency
indicated effective
effective loss
loss control.
control. Similarly,
Similarly, efficiency
efficiency
indicated
of the
the general
general momentum
momentum system
system was
was satisfactory.
satisfactory.
of
of
the general
momentum system
was satisfactory.
Simulations also
also showed
showed that
that if unexpected
unexpected halo
halo
Simulations
Simulations
also showed
that ifif unexpected
halo
survives
until
extraction,
use
of
correction
elements
survives
until
extraction,
use
of
correction
elements
survives until extraction, use of correction elements
shouldallow
allowits
itscontrolled
controlledremoval.
removal.
should
allow
its
controlled
removal.
should
Test4:
4:Collector
CollectorOptions
OptionsStudied
Studied
Test
4:
Collector
Options
Studied
Test
Simulations, including
includingtransverse
transverseand
andlongitudinal
longitudinal
Simulations,
including
transverse
and
longitudinal
Simulations,
angles
on
collimator
jaws,
showed
significant
angles on
on collimator
collimator jaws,
jaws, showed
showed significant
significant
angles
enhancements
in
loss
control.
However,
improvements
enhancements in
in loss
loss control.
control. However,
However,improvements
improvements
enhancements
did not
not justify
justify the
the increased
increased complexity.
complexity.Similarly,
Similarly,
did
not
justify
the
increased
complexity.
Similarly,
simulations using
using higher
higheratomic
atomicmass
massprimaries
primariesalso
also
simulations
using
higher
atomic
mass
primaries
also
simulations
improved localisation
localisation of
ofloss,
loss,but
butnot
nottoto
toaaalevel
levelthat
that
improved
localisation
of
loss,
but
not
level
that
improved
theincreased
increasedinherent
inherentradiation
radiationhazard.
hazard.
justified the
the
increased
inherent
radiation
hazard.
justified
Ikw
4.CONCLUSIONS
CONCLUSIONS
4.
CONCLUSIONS
4.
Studies indicate
indicate that
thatloss
losscontrol
controltoto
to≥95%
>95%levels
levels
Studies
Studies
indicate
that
loss
control
≥95%
levels
shouldbe
bepossible.
possible.Larger
Largerhalos
halosobserved
observedwhen
whenerrors
errors
should
should
be
possible.
Larger
halos
observed
when
errors
were included
included showed
showed the
the importance
importance ofof
of large
large
were
were
included
showed
the
importance
large
machine acceptances.
acceptances. Simulated
Simulated loss
loss distributions
distributions
machine
machine
acceptances.
Simulated
loss
distributions
suggesteduncontrolled
uncontrolledloss
losslevels
levelspeaking
peakingatatat0.1
0.1W/m
W/m
suggested
suggested
uncontrolled
loss
levels
peaking
0.1
W/m
for
for aaa111kW
kWtotal
totalloss.
loss.
kW
total
loss.
Figure
10 µm/turn
(am/turn
Figure3.4
3.4 Loss
Loss Distribution
Distribution for Test 2: Growth 10
Tests
Test 2:
2: Transverse
Transverse Growth Rate Tests
Test
These tested
tested the
the operation
operation of the betatron system
These
system
foraarange
range of
of transverse
transverse beam
beam growth rates,
for
rates, equivalent
equivalent
1-1033 µm/turn
µm/turn at
at the
the primary
primary jaws.
jaws. A beam on
toto 1-10
|im/turn
on aa
single matched
matched emittance
emittance contour
contour was
was introduced at
at
single
the primary
primary collimator,
collimator, transported
transported around
the
around the
the
machine, and
and the
the emittance
emittance then
then incremented on
machine,
on each
each
turn. The
The process
process continued
continued over ~100’s
~100’s
of turns
turns
turn.
~100's of
turns until
until
until
most beam
beam was
was removed.
removed. Growth
Growth rates
rates were
were tested
tested in
most
in
in
one plane
plane at
at aa time:
time: in
in orthogonal
orthogonal
planes
one
in
orthogonal planes
planes beam
beam
beam
uniformly populated
populated the
the collimated
collimated acceptance.
acceptance.
uniformly
acceptance. The
The
The
REFERENCES
REFERENCES
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Technical
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ISBN
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89336-299-1,May
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May
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CC M
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Warsop,
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Thesis,
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Sheffield,
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