Los Alamos Beam Halo Experiment: Comparing
Theory, Simulation, and Experiment
Thomas P. Wangler1 and Ji Qiang2
*Los Alamos National Laboratory, Los Alamos, NM 87544
Lawrence Berkeley National Laboratory, One Cyclotron Road, University of California,
Berkeley, CA 94720
2
Abstract. We compare macroparticle simulations with measurements from a proton
beam-halo experiment in a 52-quadrupole periodic-focusing channel. In the simulations,
three different initial distributions with the same Courant-Snyder parameters and
emittances, but different shapes, predict different mismatched-beam profiles in the
transport system. Input distributions with greater population in the tails produce larger
rates of emittance growth, a result that is qualitatively consistent with the particle-core
model of halo formation in mismatched beams. The simulations underestimate the
emittance growth rate for mismatched beams. Better agreement between simulations and
experiment for mismatched beams may require an input distribution that represents more
accurately the tails of the real input beam.
INTRODUCTION
We present the results of self-consistent macroparticle simulations including
space-charge forces, using the macroparticle simulation code IMPACT[1] for
comparison with experimental measurements of the beam profiles in a highcurrent proton beam. The measurements were made in a beam-transport channel
using a 6.7-MeV proton beam at the Low Energy Demonstration Accelerator
(LEDA) facility [2] at Los Alamos National Laboratory. A major goal of the
experiment was to validate the beam-dynamics simulations of beam halo, using
simulation codes such as IMPACT. Of particular importance was the validation of
the space-charge routine [3].
BEAM HALO EXPERIMENT
The LEDA facility consists of a 75-keV dc injector, a low-energy beam
transport (LEBT) system, and a 350-MHz radiofrequency quadrupole (RFQ),
which accelerates the proton beam to 6.7 MeV. A schematic diagram of the
LEDA beam-halo experiment transport system that follows the RFQ is given in
Fig. 1[4]. The transport system consists of 52 magnetic quadrupoles with
alternating polarity to provide strong periodic transverse focusing. Transverse
beam profiles were measured using beam-profile detectors[5] located in the
middle of the drift space after quadrupoles 4, 20, 22, 24, 26, 45, 47, 49 and 51.
The first four quadrupole gradients were independently adjusted to match the
CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli
© 2002 American Institute of Physics 0-7354-0102-0/02/$19.00
878
beam, by
by producing
producing equal
equal rms
rms sizes
sizes at
at the
the beam-profile
beam-profile detectors.
detectors. The
The gradients
gradients
beam,
were also
also adjusted
adjusted to
to produce
produce mismatches
mismatches in
in either
either aa breathing
breathing or
or aa quadrupole
quadrupole
were
mode. The
The beam
beam current
current was
was varied
varied over
over aa range
range from
from 16
16 to
to 100
100 mA.
mA. In
In this
this
mode.
paper we
we report
report results
results at
at 75-mA.
75-mA.
paper
Beam-profile diagnostic
52 quadrypofe
FODO
lattice
\
quadrupole
\
, , , B
\ s , ,
RFGRFQ6.7 MeV
4
20-26
45-51
FIGURE
FIGURE 1.
1. Block
Block diagram
diagram of
of the
the 52-quadrupole-magnet
52-quadrupole-magnet lattice
lattice showing
showing the
the nine
nine
locations
locations of
of beam-profile
beam-profile scanners.
scanners.
SIMULATIONS
SIMULATIONS
The
The lack
lack of
of detailed
detailed knowledge
knowledge of
of the
the initial
initial distribution
distribution in
in phase
phase space
space isis an
an
important
important issue.
issue. Our
Our approach
approach to
to the
the simulations
simulations has
has been
been to
to generate
generate three
three
different
different initial
initial distributions
distributions at
at the
the entrance
entrance of
of the
the beam-transport
beam-transport channel,
channel, all
all
with
with the
the same
same Courant-Snyder
Courant-Snyder ellipse
ellipse parameters
parameters and
and emittances;
emittances; the
the latter
latter were
were
deduced
deduced from
from the
the measurements.
measurements. The
The three
three input
input distributions
distributions are:
are: 1)
1) 6D
6D
Waterbag,
Waterbag, 2)
2) 6D
6D Gaussian,
Gaussian, and
and 3)
3) aa distribution
distribution called
called LEBT/RFQ,
LEBT/RFQ, generated
generated
from
from aa simulation
simulation through
through the
the LEBT
LEBT and
and RFQ,
RFQ, starting
starting at
at the
the plasma
plasma surface
surface atat
the
the exit
exit of
of the
the ion
ion source.
source. The
The particle
particle coordinates
coordinates of
of the
the LEBT/RFQ
LEBT/RFQ distribution
distribution
were
were scaled
scaled to
to produce
produce the
the correct
correct initial
initial Courant-Snyder
Courant-Snyder parameters
parameters and
and
emittances.
emittances.
The
The transverse
transverse phase-space
phase-space plots
plots of
of these
these distributions
distributions are
are shown
shown in
in Fig.
Fig. 2.2.
Figure
Figure 22 shows
shows qualitatively
qualitatively an
an increasing
increasing input
input beam
beam halo
halo as
as we
we progress
progress from
from
the
the Waterbag
Waterbag to
to the
the Gaussian
Gaussian to
to the
the LEBT/RFQ
LEBT/RFQ distribution.
distribution. For
For each
each of
of these
these
three
three initial
initial distributions
distributions we
we have
have simulated
simulated the
the beam
beam dynamics
dynamics through
through the
the
matched
beam
channel.
For
each
simulation,
we
have
used
about
matched beam channel. For each simulation, we have used about 2.8
2.8 million
million
macroparticles
macroparticles with
with aa computation
computation grid
grid of
of 65
65 X
X 65
65 XX 129.
129. Poisson’s
Poisson's equation
equation isis
solved
in
cylindrical
coordinates
with
transverse
perfect-conducting-wall
solved in cylindrical coordinates with transverse perfect-conducting-wall
boundary
boundary conditions
conditions and
and aa periodic
periodic boundary
boundary condition,
condition, longitudinally.
longitudinally.
All
All three
three distributions
distributions predict
predict aa nearly
nearly matched
matched transverse
transverse rms
rms beam
beam size,
size, in
in
good
good agreement
agreement with
with the
the matched-beam
matched-beam measurements.
measurements. The
The Waterbag
Waterbag
distribution
distribution generates
generates the
the best
best matched
matched solution
solution with
with aa nearly
nearly uniform
uniform rms
rms size
size
through
through the
the channel.
channel. The
The next
next best
best match
match corresponds
corresponds to
to the
the Gaussian
Gaussian
distribution.
distribution. The
The rms
rms beam
beam sizes
sizes from
from the
the simulation
simulation using
using the
the LEBT/RFQ
LEBT/RFQ
distribution
distribution fluctuate
fluctuate over
over aa range
range of
of about
about 10%
10%from
from the
the average
averagevalue,
value,which
whichisis
in
in best
best agreement
agreement with
with the
the measurements;
measurements; the
the matched
matched rms
rms sizes
sizes from
from
879
FIGURE 2. Transverse phase-space projections for three initial simulation distributions
at the entrance of the transport channel for the matched beam: 6D Waterbag (left), 6D
Gaussian (middle), and RFQ/LEBT (right). The upper plots show x-px phase space, and
the lower plots show y-py phase space.
measurements show a similar variation.
In addition to the rms sizes, we also measured the projected density
distributions, i.e. beam profiles in x and y at nine locations along the transport
channel. The density profiles from the simulations of the matched beam are
compared with measurements at the final detector in Fig. 3. In general, the
LEBT/RFQ simulation agrees best with the measured profiles, especially in the
core region. However, none of the distributions reproduce well the tails observed
FIGURE 3. Horizontal profiles from measurements (points) and simulations (curves) at
the final profile detector for 75-mA matched beam. The initial distributions for the
simulations are: 6D Waterbag (left), 6D Gaussian (center), and LEBT/RFQ (right).
The first four quadrupole magnets were also adjusted to produce breathingand quadrupole-mode rms mismatches. Figure 4 shows the comparison at the final
detector, for the LEBT/RFQ simulation and for a breathing-mode mismatch with
880
an initial rms beam size that is 50% larger than the matched case. Simulations for
all three initial distributions fail to reproduce the broad shoulders seen in Fig. 4,
which are induced in the measured beam profiles by the mismatches. The broader
shoulders for the real beam are evidence of a more rapid halo growth rate in the
real mismatched beam than in the simulations.
rti££lr
FIGURE 4. Horizontal profile from measurements (points) and the LEBT/RFQ
simulation (curve) at the final profile detector for a 75-mA breathing-mode mismatched
(by 50%) beam.
Figure 5 compares the rms emittance growth at the end of the channel
calculated from the measurements at 75 mA for the breathing-mode mismatched
beam (initial rms size 50% larger than the matched size) with those from the three
simulations. We find that the emittance-growth rates from simulations increase as
we progress from the 6D Waterbag to 6D Gaussian to the LEBT/RFQ
distribution, which means that the distributions with greater initial beam-halo had
more emittance growth. We interpret this as a result that would be expected from
the particle-core model [6], because the resonant particles that form the halo lie
outside the beam core. The emittance-growth rate calculated from measurements
is larger than those from any of the three simulations. Our interpretation is that the
initial distributions assumed for the simulations do not adequately populate the
tails, which include the resonant particles that are main source of the halo and
emittance growth.
CONCLUSIONS
Benchmarking
multiparticle
simulation
881
codes
against
experimental
measurements
measurements is a challenge, especially when the details of the initial 6D phasespace
space distribution are not known. We conclude that using only the known
Courant-Snyder parameters and the emittances as input parameters is not
sufficient
sufficient information
information for reliable simulations of beam halo formed in mismatched
beams.
beams. Using the IMPACT code, we have carried out simulations of the LEDA
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
WATERBAG
GAUSSIAN
LEBT/RFQ
MEASURED
Input
Input Particle
Particle Distribution
Distribution
FIGURE 5.
5. Emittance
Emittance growth
growth from
three simulations
FIGURE
from three
simulations and
and from
from the
the experiment,
experiment, for
for aa
50% breathing-mode
breathing-mode mismatch
mismatch at
at 75
mA.
50%
75 mA.
beam-halo experiment
experiment for
for the
the matched
matched case
case and
and for
50% breathing-mode
breathing-mode
beam-halo
for aa 50%
mismatch at
at 75
75 mA,
mA, using
using three
three different
different initial
particle distributions,
mismatch
initial particle
distributions, 6D
6D
Waterbag, 6D
6D Gaussian,
Gaussian, and
and LEBT/RFQ
LEBT/RFQ (generated
Waterbag,
(generated from
from simulation
simulation through
through the
the
LEBT and
and RFQ),
RFQ), all
all with
with the
the same
initial ellipse
LEBT
same initial
ellipse and
and emittance
emittance parameters
parameters
deduced from
from the
the measurements.
measurements. These
These three
three distributions
deduced
distributions differ
differ qualitatively
qualitatively
with respect
respect to
to their
their initial
initial halo,
halo, i.e.
i.e. initial
initial population
population of
with
of the
the outer
outer tails
tails of
of the
the
beam.
beam.
While all
all three
three initial
initial distributions
distributions give
While
give fair
fair agreement
agreement with
with the
the measured
measured
profiles for
for the
the matched
matched case,
case, the
the LEBT/RFQ
LEBT/RFQ initial
initial distribution
distribution does
does the
the best,
best, as
profiles
as
would be
be expected
expected since
since that
that distribution
distribution was
was formed
would
formed from
from aa more
more realistic
realistic
simulation of
of the
the real
real input
input beamline
beamline (LEBT
simulation
(LEBT and
and RFQ).
RFQ). However,
However, none
none of
of these
these
distributions
describe
very
well
the
observed
beam
profiles
of
the
mismatched
distributions describe very well the observed beam profiles of the mismatched
beams; the
the measured
measured mismatched
mismatched beam
beam profiles
profiles exhibit
beams;
exhibit structure
structure with
with pronounced
pronounced
shoulders
in
the
semilog
plots,
and
a
rapid
emittance
growth
rate,
shoulders in the semilog plots, and a rapid emittance growth rate, both
both of
of which
which
are
underestimated
by
all
three
simulations.
Our
interpretation
is
that
the
are underestimated by all three simulations. Our interpretation is that the higher
higher
emittance-growth rate
rate for
for the
the real
real beam
beam is
is caused
caused by
by aa higher
higher particle
particle density
emittance-growth
density in
in
the initial
initial halo,
halo, and
and consequently,
consequently, aa greater
population of
the
greater population
of the
the region
region of
of phase
phase
space that
that leads
leads to
to resonant
resonant halo
halo growth.
growth. We
We conclude
space
conclude that
that knowledge
knowledge of
of the
the
initial particle
particle distribution,
distribution, especially
especially the
the density
density in
tails, is
initial
in the
the tails,
is important
important for
for
accurate simulations
simulations of
of the
the beam
beam halo.
halo.
accurate
882
ACKNOWLEDGMENTS
We acknowledge the help of Dr. L. Young for providing an initial distribution
from LEBT/RFQ simulation. We thank the LEDA personnel for making the
experiment possible, and we acknowledge the work on the experiment by the rest
of the beam-halo scientific team, C. K. Alien, K. C. D. Chan, P. L. Colestock, K.
R. Crandall, R. W. Garnett, J. D. Gilpatrick, W. Lysenko, J. D. Schneider, M. E.
Schulze, R. L. Sheffield, and H. V. Smith. The simulation work was performed
by one of us (J.Q.) on the Cray T3E and IBM SP at the National Energy Research
Scientific Computing Center located at Lawrence Berkeley National Laboratory,
and the SGI Origin 2000 at the Advanced Computing Laboratory located at Los
Alamos National Laboratory. The simulation work was supported by U.S.
Department of Energy Office of Science, Division of High Energy and Nuclear
Physics, under the Advanced Computing for the 21st Century Accelerator Science
and Technology project, and the Los Alamos Accelerator Code Group.
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