Sources of Halo and Beam Losses in a High Intensity
Sources of Halo and
BeamLinac
Losses in a High Intensity
Hadron
Hadron Linac
Nicolas Pichoff11
Nicolas Pichoff
CEA-DSM/DAPNIA/SACM, 91191 Gif-sur-Yvette cedex
CEA-DSM/DAPNIA/SACM,
91191 Gif-sur-Yvette cedex
Abstract. Different possible sources of emittance growth, halo formation and eventually beam losses in a high intensity
Abstract.
Different
possible sources of emittance growth, halo formation and eventually beam losses in a high intensity
hadron linac
are listed.
hadron linac are listed.
rotate with
with the
the same
same speed:
speed: There
There isis aa spread
spread inin
rotate
particles phase-advance.
phase-advance. InIn the
the presence
presence ofof spacespaceparticles
charge, the
the force
force in
in the
the beam
beam core
core isis “compensated”
"compensated"
charge,
by the
the space-charge
space-charge force
force reducing
reducing the
the particle
particle phase
phase
by
advances. Core
Core particles
particles are
arerotating
rotatingmore
moreslowly
slowlythan
than
advances.
these of
of the
the halo.
halo. When
Whenthe
thebeam
beamisismatched,
matched,particles
particles
these
leaving one
one area
area of
of the
the phase-space
phase-space are
are replaced
replaced by
by
leaving
others
others with
with the
the same
same Hamiltonian:
Hamiltonian: the
the emittance
emittance
pattern
pattern stays
stays the
the same,
same, no
no rms
rms emittance
emittance growth
growth isis
observed.
observed. When
When the
the beam
beam isis mismatched,
mismatched, particles
particles
leaving
leaving aa region
region are
are not
not replaced.
replaced. The
The emittance
emittance
pattern
pattern isis changed
changed and
and rms
rms emittance
emittance growth
growth isis
observed
observed (see.
(see. FIGURE
FIGURE 1).
1). Particle
Particleamplitude
amplitudeisisnot
not
amplified
amplified by
bymore
more than
thanthe
thebeam
beammismatch
mismatchfactor.
factor.
INTRODUCTION
Problem
in high
high
Problem of
of beam losses are of main interest in
power
power protons
protons or H"
H- linacs. They can activate the
structure,
structure, complicating
complicating considerably the maintenance
of
of the
the machine.
machine. This
This is a crucial point for many
projects
... running
projects like
like SNS, ESS, JHF, SPL, APT …
with protons
protons and/or
and/or H"
H- ions. Last years, aa big effort
with
effort has
has
been done
done in
in a large number of laboratories to
been
to
investigate to
to possible
possible causes of emittance growth
investigate
growth and
and
halo formation
formation able
able to cause beam losses. The main
halo
sources of
of halo
halo formation in a high beam-intensity
sources
linacs are
are listed
listed in
in this paper. I apologize if I did not
linacs
quote some
some of
of them;
them; it is either because I consider that
quote
that
they are
are probably
probably non-significant, or I simply
they
simply forgot
forgot
them. One
One can add that the only way to identify surely
them.
the main
main contributor
contributor of beam losses is the full scale
the
scale
experiment.
experiment.
2
0
BEAM MISMATCH
2
The main
main cause
cause of
of emittance
emittance growth
The
growth is
is known
known as
as
being the
the beam
beam mismatch.
mismatch. A
A beam
beam is
being
is matched
matched when
when
the beam
beam phase-space
phase-space distribution
distribution has
has the
the same
period
the
same period
as the
the external
external focusing
focusing force.
force. In
In aa mismatch
mismatch beam,
as
beam, the
the
non-linear forces,
forces, especially
especially the
the space-charge
non-linear
space-charge force,
force,
are responsible
responsible of
of this
this emittance
emittance growth
are
growth through
through 22
phenomena:
The
beam
filamentation
and
the
phenomena: The beam filamentation and the resonant
resonant
interaction between
between particle
particle individual
individual motion
interaction
motion and
and
beam core
core oscillation.
oscillation.
beam
2
0
2
Parametric
Parametric resonance
resonance with
withcore
core
In linear
linear forces,
forces, particles
particles are
moving in
In
are moving
in the
the phasephasespace
around
ellipses,
associated
to
the
space around ellipses, associated to the focusing
focusing
channel, defined
defined by
by the
the Courant-Snyder
Courant-Snyder parameters.
parameters.
channel,
All
the
particles
have
the
same
phase
advance
All the particles have the same phase advance per
per
meter, i.e.
i.e. they
they rotate
rotate around
around the
the concentric
concentric ellipses
meter,
ellipses
with the same angular speed. When the force is nonwith
the same angular speed. When the force is nonlinear, these ellipses transform into close curves
linear, these ellipses transform into close curves
corresponding to curves on with the motion
corresponding to curves on with the motion
Hamiltonian is constant. Moreover, the particles do not
The
The core
core oscillation
oscillation of
ofaamatched
matchedbeam
beamisisperiodic
periodic
with
the
same
period
as
the
external
with the same period as the external force.
force. InIn these
these
conditions,
conditions, avoiding
avoiding aa parametric
parametric resonance
resonance consists
consists
mainly in keeping the zero current phase-advance
mainly in keeping the zero current phase-advance
lower than 90° (avoiding the strong fourth order
lower than 90° (avoiding the strong fourth order
resonance). Nevertheless, the core oscillation of a
resonance). Nevertheless, the core oscillation of a
mismatched bunched beam is modulated by 3 other
mismatched bunched beam is modulated by 3 other
Hamiltonian is constant. Moreover, the particles do not
1
2
FIGURE
FIGURE 1.1. (x,
(x, x’)
x') phase-space
phase-space plot
plot ofofaamismatched
mismatchedbeam
beam
in
in non-linear
non-linear forces.
forces. External
External particles
particles are
are rotating
rotating faster
faster
than
than core
core particles.
particles.Apparent
Apparentemittance
emittancegrowth
growthoccurs.
occurs.
Beam Filamentation
Filamentation
Beam
1
2
[email protected]
[email protected]
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
111
frequency
modes
(mismatched
modes
[1]).
lower
modes
[1]).
lower
frequency
modes
(mismatched
lowerfrequency
frequencymodes
modes (mismatched
(mismatched modes
modes [1]).
[1]).
and
Unfortunately
and
unavoidably,
some
beam
particles
Unfortunately
Unfortunatelyand
andunavoidably,
unavoidably,some
somebeam
beamparticles
particles
oscillation
frequencies
twice
least
one
have
least
one
have
oscillation
frequencies
haveoscillation
oscillation frequencies
frequencies twice
twice atatat least
least one
one
mode.
Second
order
parametric
resonance
mismatched
mode.
Second
order
parametric
resonance
mismatched
mode.
Second
parametric
resonance
mismatched mode. Second order parametric resonance
can
give
large
amplitude
to
the
with
amplitude
to
the
with
the
core
can
withthe
thecore
core can
can give
give large
large amplitude
amplitude to
to the
the
concerned
[2].
concerned
particles
[2].
concernedparticles
particles[2].
[2].
ChargeExchange
Exchangewith
withResidual
ResidualGas
Gas
Charge
Exchange
with
Residual
Gas
Charge
Charge
Exchange
with
Residual
Gas
- --) can
Someparticle
particle(like
(likeHH
H")
canbebe
bestripped
strippedon
on
residual
Some
particle
(like
H
be
stripped
on
residual
Some
) )can
residual
Some
particle
(like
can
stripped
on
residual
gas.
From
the
stripping
cross
section
a
rate
of
beam
gas.
From
the
stripping
cross
section
a
rate
of
beam
gas.
From
the
stripping
cross
section
a
rate
of
gas. From the stripping cross section a rate of beam
beam
loss
can
be
estimated
depending
on
the
gas
loss
can
be
estimated
depending
on
the
gas
loss
can
be
estimated
depending
on
the
gas
loss can be estimated depending on the gas
composition,
pressureand
andthe
thebeam
beamenergy
energy(FIGURE
(FIGURE
composition,
pressure
and
the
beam
energy
(FIGURE
composition,
composition,pressure
pressure
and
the
beam
energy
(FIGURE
4,
from
[4]).
from
[4]).
4,4,
4,from
from[4]).
[4]).
Water vapour pressure (hPa) .
Water
(hPa) ..
Water vapour
vapour pressure
pressure (hPa)
1E-6
1E-6
1E-6
FIGURE
2.2.Trajectory
FIGURE2.
Trajectory(in(inred)
red)of
particlein
second
FIGURE
2.
Trajectory
red)
ofofaaaparticle
particle
ininaaaasecond
second
FIGURE
particle
in
second
order
parametric
orderparametric
parametricresonance
resonancewith
withaaamismatched
mismatchedmode.
mode.In
In
order
parametric
resonance
with
mismatched
mode.
In
order
mismatched
mode.
In
blue,
the
particle
position
ininaaa astroboscopic
stroboscopic
blue,
the
particleposition
positionin
stroboscopic(Poincaré)
(Poincaré)plot
plot
the
particle
stroboscopic
(Poincare)
plot
blue,
the
particle
(Poincaré)
plot
with
the
mode
periodicity.
Left:
(x,
with
themode
modeperiodicity.
periodicity.Left:
Left:(x,
(x,x’)
x’)phase-space
phase-spaceplot,
plot,
mode
periodicity.
Left:
(x,
x')
with
the
x’)
phase-space
plot,
Right:
(z,(z,
x)x)
plot.
Right:
plot.
Right:
(z,
x)
plot.
Right:
(z,
x)
plot.
INTERACTIONWITH
WITHRESIDUAL
RESIDUALGAS
GAS
INTERACTION
WITH
RESIDUAL
WITH
RESIDUAL
GAS
INTERACTION
GAS
hadronlinac
linaclinac
linacthe
theresidual
residualgas
gaspressure
pressure
InInaaa ahadron
hadron
linac
linac
the
linac
linac
the
residual
gas
pressure
In
residual
gas
pressure
-5 -5
-7-7 -8-8
7 -10-88
-55 hPa
varies
from
10
hPa
(close
to
the
source)
to
10
varies
from
10
(close
to
the
source)
to
10
from 10
10~ hPa
hPa (close
(close to the source)
source) to 10
10~-7-10
-10~
varies from
-10
-11
-11
11
-11
hPa
in
copper
structures
and
can
be
lower
than
10
hPa
in
copper
structures
and
can
be
lower
than
10
hPa in copper structures
structures and
and can be lower than 10
10"
hPa
in
superconducting
structures.
The
residual
gas
is
hPa
in
superconducting
structures.
The
residual
gas
is
hPa in
in superconducting
superconducting structures.
structures. The
The residual
residual gas
gas isis
mainlycomposed
composedofoflarge
largevariety
varietyofoflight
lightororheavy
heavy
mainly
mainly composed
composed of
of large
large variety
variety of
of light
light or
or heavy
heavy
gas.The
Thepartial
partialpressure
pressurefor
foreach
each varietyisisimportant.
important.
gas.
gas.
The
variety
gas.
The partial
partial pressure
pressure for
for each
each variety
variety is
is important.
important.
Scatteringon
onResidual
Residual Gas
Scattering
Scattering
on
Gas
Scattering
on Residual
Residual Gas
Gas
Bycolliding
collidinga aresidual
residualgas
gasatom,
atom,a abeam
beamparticle
particle
By
By gain
colliding
aa residual
gas
aa beam
particle
residual
gas atom,
atom,
beam The
particle
can
significant
transverse
momentum.
gain
can
gain a asignificant
transverse
momentum.
The gain
canprobability
gain
transverse
gain
gain aa significant
significant
transverse
momentum.
The
gain
given
the momentum.
differential The
nuclearprobability isis given
byby the
differential
nuclearprobability
is
differential
is given
given by
by
the
collisioncross-section
cross-section
andthe
depends
thenuclearparticle
collision
and
depends
onon the
particle
collision
cross-section
and
depends
on
the
particle
cross-section
and
on
energyand
andthe
theresidual
residualgas
gascomposition
compositionand
andpressure.
pressure.
energy
energy
and
the residual
gas
composition
and
and
and pressure.
pressure.
Particle
gaining
moretransverse
transverse
momentum
thanthe
the
Particle
gaining
more
momentum
than
Particle
gaining
more
transverse
momentum
than
the
gaining
more
transverse
momentum
than
the
beam
transverse
momentum
spread
populate
the
beam
beam transverse momentum spread populate the beam
beam
momentum
spread
populate
the
beam
transverse
momentum
spread
populatelarge,
the
beam
halo.transverse
themomentum
momentum
gain
sufficiently
large,
the
halo.
IfIfthe
gain
isissufficiently
the
halo.
If
the
momentum
gain
is
sufficiently
large,
the
halo.
If
the
momentum
gain
is
sufficiently
large,
the
particlecan
canbebedirectly
directly(after
(aftera aquarter
quarterofofbetatron
betatron
particle
particle
can
directly
aa quarter
of
can
directly
(after
quarter
ofofofbetatron
betatron
period)lost.
lost.be
Beam
tailat(after
at
given
position
linac
period)
Beam
tail
a agiven
position
a alinac
period)
lost.
Beam
tail
at
a
given
position
of
linac
lost.
Beam
tail
at
a
given
position
of
linac
can
be
easily
estimated
(FIGURE
3,
from
[3]).
They
can be easily estimated (FIGURE 3, from [3]).aaThey
can
begenerally
easily
estimated
(FIGURE
3,
from
[3]).
easilynot
estimated
(FIGURE
3,
from
[3]). They
They
aregenerally
notdense
densebut
but
populate
far
halo.
are
populate
far
halo.
are
far
are generally
generally not
not dense
dense but
but populate
populate
far halo.
halo.
r/r r/r
-8 -8
1E 00
1E 00
-8
1E -01
1E00
-01
1E
1E -02
1E-01
-02
1E
1E -03
1E-02
-03
1E
1E -04
1E-03
-04
1E
Beam density profile (a.u.)
Beam density profile (a.u.)
Beam density profile (a.u.)
0
1E -05
1E-04
-05
1E
1E -06
1E-05
-06
1E
1E -07
1E-06
-07
1E
1E -08
1E
-08
1E -07
1E -09
1E -09
1E -08
1E -10
1E -10
1E -09
1E -10
-6 -6
-6
-4 -4
-4
-2 -2
-2
r/r
00 0
0
0
2 2
4 4
2
4
1 /(r-r
40 )
1 /(r-r
0)
1 /(r-r 0 )
6 6
8 8
6
8
4
4
P = 10 - 5 h P a
P = 10 - 5 h P a
-6
P = -10
hPa
6
PP == 10
10 - 5hhPPaa
-7
P = -10
hPa
7
PP == 10
10 - 6hhPPaa
P = 10 - 8 h P a
P = 10 - 8- 7h P a
P = 10 h P a
P = 10 - 8 h P a
FIGURE3.3.Beam
Beamprofile
profileatatthe
theend
endofofa a20m
20mchannel
channelfor
for
FIGURE
different
Nitrogen
gas
pressure.
different Nitrogen
pressure.
FIGURE
3.
profile
at
FIGURE
3. Beam
Beamgas
profile
at the
the end
end of
of aa 20m
20m channel
channel for
for
different
different Nitrogen
Nitrogen gas
gas pressure.
pressure.
1E-7
1E-7
1E-7
1E-8
IE-8 - . _V ^
1E-8
1E-8
1E-9
1E-9
1E-9
1E-10
1E-10
1E-10
0 00
1010
µSiv/h
10
µSiv/h
µSiv/h
2020
µSiv/h
20
µSiv/h
µSiv/h
5050
µSiv/h
50
µSiv/h
µSiv/h
100
µSiv/h
100
µSiv/h
100
µSiv/h
200
µSiv/h
200
µSiv/h
200
µSiv/h
1W/m
1W/m
1W/m
200
200
200
200
400
400
400
400
600
800
600
800
600
800
600
800
Beam
energy
(MeV)
Beam
energy
(MeV)
Beam
energy
(MeV)
1000
1000
1000
1000
1200
1200
1200
1200
FIGURE4.4.
4.
Pressure
limit
for
structure
activation
(at
FIGURE
aaagiven
structure
activation
(at
FIGURE
4.Pressure
Pressurelimit
limitfor
for
agiven
given
structure
activation
(at
FIGURE
Pressure
limit
for
given
structure
activation
(at
feet
after
hours).
1111feet
feetafter
after3333hours).
hours).
feet
after
hours).
TransientSpace-Charge
Space-Charge
Compensation
Transient
Transient
Space-ChargeCompensation
Compensation
Transient
Space-Charge
Compensation
Atlow
low
energy,
because
the
high
ionization
cross
At
cross
At
low
energy,
because
of
the
high
ionization
cross
At
lowenergy,
energy,because
becauseofof
ofthe
thehigh
highionization
ionization
cross
section
combined
with
the
relatively
high
gas
pressure,
section
combined
with
the
relatively
high
gas
pressure,
section
section combined
combined with
with the
the relatively
relatively high
high gas
gas pressure,
pressure,
the beam
beam captures
captures particles
with opposite
charge
the
the
beam
captures
particles
with
opposite
charge
the
beam
captures particles
particleswith
with opposite
oppositecharge
charge
leadingtotoaaspace-charge
space-chargecompensation
compensation regime.
regime. The
The
leading
leading
leading to
to aa space-charge
space-charge compensation
compensation regime.
regime. The
The
effectofofthis
thiscompensation
compensationisisbenefic
beneficas,
as,atatstationary
stationary
effect
effect
effect of
of this
this compensation
compensation isis benefic
benefic as,
as, atat stationary
stationary
regime,ititreduces
reducesthe
thespace-charge
space-chargeforce
forcenon
nonlinearity
linearity
regime,
regime,
itit reduces
the
force
non
regime,
reducesemittance
the space-charge
space-charge
force
non linearity
linearity
andthe
theinduced
inducedemittance
growth. Nevertheless,
Nevertheless, the
the
and
growth.
and
the
induced
emittance
growth.
Nevertheless,
the
and
the
induced
emittance
growth.
Nevertheless,
the
main problem
problem arises
arises from
from the
the transient
transient regime
regime in
in
main
main
problem
arises
from
the
transient
regime
main
problem
arises
from
the
transient
regime
in
which the
the space-charge
space-charge force
force varies,
varies, inducing
inducing aain
which
which
the
space-charge
force
varies,
inducing
which
the
space-charge
force
varies,
inducing
transientmismatch
mismatchofofthe
thebeam
beamininthe
thechannel.
channel.Order
Orderaa
transient
transient
mismatch
of
the
beam
in
the
channel.
transient
mismatch
of
the
beam
in
the
channel.
Order
magnitude ofof the
the transient
transient time
time isis about
about 10
10Order
µs,
ofofmagnitude
µs,
of
magnitude
of
the
transient
time
is
about
10
of
magnitude
of
the
transient
time
is
about
10
negligible
in
case
of
cw
beam
but
concerning
1%
a
negligible in case of cw beam but concerning 1% ofofµs,
aus,
negligible
case
of
but
1%
negligible
inThis
case
of cw
cw beam
beam
but
concerning
1% of
of aa
1mspulse!
pulse!in
phenomena
has
bestudy
studycarefully
carefully
1ms
This
phenomena
has
totoconcerning
be
1ms
pulse!
This
phenomena
has
be
carefully
1ms
pulse!the
This
phenomena
has to
togrowth
be study
study
carefully
to
estimate
theinduced
induced
emittance
growth
and
beam
to
estimate
emittance
and
beam
to
estimate
the
induced
emittance
growth
and
beam
to
estimate
the
induced
emittance
growth
and
beam
losses.
losses.
losses.
losses.
EMITTANCEEXCHANGE
EXCHANGE
EMITTANCE
EMITTANCE
EMITTANCE EXCHANGE
EXCHANGE
Thespace-charge
space-chargeforce
forceinduces
inducesaacoupling
couplingbetween
between
The
The
force
aa coupling
between
The space-charge
space-charge
force induces
induces
coupling
between
transverse
and longitudinal
longitudinal
directions
(i.e.
the
transverse
and
directions
(i.e.
the
transverse
and
longitudinal
directions
(i.e.
the
longitudinal
force
depends
on
the
transverse
position,
transverse
and
longitudinal
directions
(i.e.
the
longitudinal force depends on the transverse position,
longitudinal
force
on
transverse
position,
andthe
thetransverse
transverse
forcedepends
depends
on
the longitudinal
longitudinal
longitudinal
force depends
depends
on the
theon
transverse
position,
and
force
the
and
the
force
depends
on
the
position).
Thiscoupling
coupling
induces
anexchange
exchange
between
and
the transverse
transverse
force
depends
on
the longitudinal
longitudinal
position).
This
induces
an
between
theparticles
particles
transverse
and
longitudinal
energies
for
position).
This
coupling
induces
an
between
position).
This
couplingand
induces
an exchange
exchange
between
the
transverse
longitudinal
energies
for
equal
phase-advances
[5].and
This
couldbe
bedangerous
dangerous
the
particles
transverse
longitudinal
energies
for
the
particles
transverse
and
longitudinal
energiesasas
for
equal
phase-advances
[5].
This
could
itchanged
changed
thematching
matching
conditions
(which
dependson
onas
phase-advances
[5].
This
be
equal
phase-advances
[5].
This could
could
be dangerous
dangerous
as
itequal
the
conditions
(which
depends
beamemittance
emittance
space-charge
drivenbeam)
beam)
and
ititthe
changed
the
conditions
(which
depends
on
changed
the matching
matching
conditionsdriven
(which
depends
on
the
beam
ininspace-charge
and
itcan
can
transfer
particles
fromthe
thelongitudinal
longitudinal
halo to
to
beam
emittance
in
driven
and
itthe
transfer
particles
from
halo
the
beam
emittance
in space-charge
space-charge
driven beam)
beam)
and
transverse
one.
ititthecan
transfer
particles
the
transverse
can
transferone.
particles from
from the
the longitudinal
longitudinal halo
halo to
to
the
the transverse
transverse one.
one.
112
the correction scheme has to be evaluated (as example,
for ESS [8]).
MAGNETIC STRIPPING
An electron can be stripped from a H" ion in a
magnetic field through an electro-quantum effect. The
probability per unit length to strip a H" ion in a
magnetic field B is:
CONCLUSION
Many phenomena can be responsible of emittance
growth, halo formation and beam losses in a linac. To
minimize the risk, precautions have to be taken already
from the design phase:
5
= 9.53-10 -£ r -exp (1)
This effect is more important at high energy and
depends exponentially on the magnetic field. As a
consequence, this limits the maximum magnetic field
and then quadrupole gradient at high energy.
o keep both transverse and longitudinal phase
advances below 90°, avoid the same transverse
and longitudinal phase advances,
o minimize the number of transitions, make them
smooth,
o take care to the residual gas,
o Estimate the safe element tolerances and associated
correction scheme,
o Avoid reduction of linac acceptance where
localized loses can take place,
o Estimate the mismatch of the pulse front-end and,
if needed, chop it at low energy.
INTRABEAM SCATTERING
The Coulomb collisions in beam induce energy
transfer between particles and directions. The effect of
this phenomenon has been estimated in high power
protons linacs in [6] and [7]. Because of the long timescale of this process compared to the beam life-time in
linac, its effect is marginal (about 10"11 of a 100 mA
beam in halo). Nevertheless, the effect varies with the
square of the beam current and the induced halo
extension can be large if the beam is far from energy
equipartition.
REFERENCES
1. Pichoff, N., "Envelope Modes of a Mismatched Bunched
Beam" , Internal note, DAPNIA/SEA 98/44, 1998.
TRANSPORT ERRORS
2. Lagniel, J.-M., N.I.M. A346, 46-53 (1994).
3. Pichoff, N. et al. Particle Accelerators,Vol. 63, pp211233.
A real accelerator is made of components that can
be badly aligned, powered, calculated or measured.
Some of these errors can be corrected using an
appropriate diagnostic-correction scheme, some
cannot. Multipolar terms in quadrupoles or cavities
contribute to the beam filamentation but generally at
second order compared to space-charge force.
Elements misalignment induces mainly a beam c.o.g.
transverse displacement, increasing the probability to
find a particle far from the beam axis. This error can
be compensated with steerers minimizing the beam
displacement in BPMs. Unfortunately fast errors like
vibrations cannot be easily compensated. The errors on
quadrupole gradients are even more difficult to
compensate. They induce residual mismatch that could
be estimated and corrected only from beam size
measurements, not easy with such high power beam.
The last important problem is the limited control of the
RE phase and field in the cavity. It induces c.o.g.
displacement in longitudinal phase-space, including
longitudinal emittance growth and displacement of the
beam final energy and phase.
4. Pichoff, N. et al., "Beam losses in ESS from H" stripping
on residual gas", ESS Linac Technical Note ESSLINTN-0202-01,2001.
5. Hoffman, L, "Emittance Coupling in high Intensity beam
applied to the SNS linac", in Particle Accelerator
Conference, edited by P. Lucas et S. Webber, Chicago,
2001, pp. 2902-2904.
6. Fedotov, A.V., Gluckstern, R.L., "Coulomb Scattering
within a Spherical Beam Bunch in High Current Linear
Accelerators", in Particle Accelerator Conference, edited
by A. Luccio et W. McKay, New-York, 1999, pp. 17551757.
7. Pichoff, N., "Mrabeam scattering on Halo Formation",
in Particle Accelerator Conference, edited by A. Luccio
et W. McKay, New-York, 1999, pp. 3277-3279.
8. The ESS Project, Vol. m - Technical Report, Edited by
F.H. Bohn et al., 2002. http://essnts.ess.kfa-iuelich.de/
An estimation of the effect of these errors has to be
calculated in the linac design step. The efficiency of
113