Space Charge Simulations of First-Turn Experiments on the
University of Maryland Electron Ring (UMER)
R.A. Kishek*, S. Bernal, Y. Cui, T.F. Godlove, I. Haber, J. Harris, Y. Huo, H. Li,
P.G. O’Shea, B. Quinn, M. Reiser, M. Walter and Y. Zou
Institute for Research in Electronics and Applied Physics, Univ. of Maryland, College Park, MD 20742-3511, USA
Abstract. Emerging particle accelerators require beam brightness and intensity surpassing traditional limits, bringing
beams into the realm of nonneutral plasmas where particles interact primarily via long-range collective forces. Therefore
the understanding of collective interactions is crucial for successful development of such applications as spallation
neutron sources, high energy colliders, heavy ion inertial fusion, intense light sources, and free electron lasers. The
University of Maryland Electron Ring (UMER), currently just completed, is designed to be a scaled model (3.6-m
diameter) for exploring the dynamics of such intense beams. Using a 10 keV electron beam, other parameters are scaled
to mimic those of much larger ion accelerators, except at much lower cost. An adjustable current in the 0.1-100 mA
range provides a range of intensities unprecedented for a circular machine. Since UMER is primarily designed to serve
as a research platform for beam physics, it is equipped with a vast array of diagnostics providing 6-D phase space
measurements for effective comparison against computer codes. Simulations using the WARP code are presented which
model recent experiments on transverse and longitudinal beam evolution during the first-turn of UMER.
Keywords:
PACS:
Space-charge-dominated beams, Circular Accelerators, Beam Dynamics
29.27.Bd; 52.58.Hm; 41.75.Lx
activation of the machine, and more significantly,
contributing to electron cloud effects by the excitation
of unwanted electrons from the beam pipe.
1. INTRODUCTION
Emerging particle accelerators require beam
brightness and intensity surpassing traditional limits,
bringing beams into the realm of nonneutral plasmas
where particles interact primarily via long-range
collective forces. The challenge for building these
next-generation accelerators is to preserve beam
quality, over possibly kilometers from the source to
the target, despite all the different mechanisms for
beam degradation introduced by these collective
interactions. As the space charge intensity increases,
single-particle effects give way to long-range
collective interactions between particles and the beam
self-potential as a whole [1]. In other words, the beam
becomes a nonneutral plasma and is therefore
susceptible to a complex array of plasma modes and
instabilities [2].
The approach taken at the University of Maryland
is to implement scaled experiments using modest-cost
nonrelativistic electron beams to simulate higherenergy ion beams. The University of Maryland
Electron Ring (UMER) [3-5], currently just closed and
in the process of multi-turn commissioning, provides a
long-path platform for exploring the dynamics of such
intense beams. The ring configuration permits the
investigation of dispersion, resonances, and other
effects that would occur in rings, in addition to those
occurring in a straight lattice. Using a 10 keV electron
beam, other parameters are scaled to model those of
much larger ion accelerators, except at much lower
cost. An adjustable current in the 0.1-100 mA range
provides a range of intensities unprecedented for a
circular machine. By design, UMER provides a lowcost,
well-diagnosed
research
platform
for
investigating beam dynamics.
Whereas the list of challenges to successful intense
accelerator development are many, a few beam
dynamics issues stand out. In particular, emittance
growth can limit the achievable spot size at the target,
collective instabilities can lead to beam breakup, and
halo formation can lead to emittance growth,
UMER is augmented with a separate setup, the
Long Solenoid Experiment (LSE) [6-7] for
CP773, High Intensity and High Brightness Hadron Beams, edited by I. Hofmann, J.-M. Lagniel, and R. W. Hasse
© 2005 American Institute of Physics 0-7354-0258-2/05/$22.50
147
investigating the longitudinal beam dynamics and the
evolution of energy spread due to Coulomb collisions
in a straight geometry.
Longitudinally, the UMER beam consists of a
single pulse whose length can be varied from 50-100
ns. Since the circulation time for a 10 keV electron
round the 11.52-m UMER circumference is 200 ns,
only a single pulse is injected at any one time, at a
repetition rate of 10-60 Hz. The pulsed injection
system has been redesigned to reduce the number of
pulsed elements to a single dipole surrounding a wide
glass gap. To achieve the required fast switching time,
the dipole was specially designed with a low number
of conductors to minimize its inductance. Due to
space limitations, this configuration forces us to use a
single quadrupole for both arms of the Y-shape,
sharing it between injection and circulation. The
design has been analyzed and simulated in detail [8]
and is currently undergoing final experimental testing
[9].
This publication will briefly review the UMER
design then outline some of the recent experimental
and computational results. For convenience, the
results are divided into three categories: source
physics, transverse dynamics, and longitudinal
dynamics. An outline of the future plans concludes
our discussion.
2. UMER DESIGN
3. THE UMER SOURCE
All beams are born space-charge-dominated at the
source.
Whereas subsequent acceleration and
emittance growth will reduce the beam intensity,
previous experience has shown that any irregularities
at the source can be ‘frozen-in’ and preserved for a
relatively long time downstream [10]. Imperfections
in the particle distribution at the source, a hot spot for
instance, may subsequently resurface in the form of
unwanted halo, or seed instabilities. On the other
hand, like most realistic sources, the UMER electron
gun presents a considerable challenge to simulation.
In UMER the biggest challenge stems from the
presence of a fine grid close to the cathode, used for
applying a pulse to extract the beam. The grid-cathode
distance is 0.15 mm, which is roughly of the order of
the grid wire thickness, and much less than the 2.5 cm
distance from the cathode to the anode. As we found
out, this significantly affects the beam dynamics near
the cathode, since the grid-cathode potential difference
is of the order of only 60 V. A significant outcome is
a hollowed velocity distribution, first measured
experimentally with a pepper-pot [11]. Introducing
that distribution into 2-1/2 D simulations using the
WARP code [12] of the remainder of the injector was
seen to significantly improve agreement with the
measured data [13]. The attribution of this hollowed
velocity to the cathode grid was not confirmed,
however, until we were able to perform detailed 3-D
WARP simulations of the gun structure, including that
cathode-grid gap and the grid wires [14].
Figure 1: Photograph of UMER as of Oct. 2004.
The design of UMER, photographed in Fig. 1, was
discussed in detail in ref. [4]. The beam currently
drifts at 10 keV through a 36-cell FODO lattice per
turn, each cell containing a single 10° bend. Three
induction gaps will provide longitudinal focusing, and,
in a future stage, be used to accelerate the beam to 50
keV.
At the present β of 0.2, the beam is
nonrelativistic and has a similar velocity to heavy ion
machines or proton linacs. A current in the range 0.1
to 100 mA ensures that the (generalized) perveance
covers a wide range of intensities in regions of
relevance for the proton and ion machines. The beam
intensity can be quantified in a number of ways, for
example using the dimensionless intensity parameter,
χ, defined in ref. [3-4] as the ratio of the space-charge
force to the external focusing force at the beam radius.
The tune depression is expressed in terms of χ as
ν
k
=
= 1 − χ , and the plasma wavenumber kp as
ν 0 k0
kp
= 2 χ . With a zero-current phase advance per
k0
period of σ0 = 76°, a measured (4*rms) emittance of εn
= 12-15 µm and beam radius a = 0.3 - 1 cm, χ in
UMER can be made to vary from 0.2 to the extremely
space charge dominated 0.96.
148
photos indicated a number of problems [Fig. 2a].
First, the beam suffers from an rms mismatch (each of
these photos is taken inside a diagnostic chamber
spaced at the same location relative to the lattice
period, so the beam should have the same shape in all
the photos). Second, there is some visible rotation of
the beam ellipse, a result that can happen when the
quadrupole symmetry is broken, for example by
random rotations in some of the magnets. On some of
the pictures, one can notice an evolving beam halo.
4. TRANSVERSE DYNAMICS
Although we had most of the mechanical parts at
the start of construction, we decided to follow a
phased commissioning plan whereby we gradually
install and commission additional sections of the ring.
This provided us with additional data using our end
diagnostic chamber, as well as provided us with more
experience in handling the beam [15]. Although we
were able to transport the beam over half of the first
turn with no significant problems, the phosphor screen
(a)
(b)
Figure 2: Photographs of the UMER beam transport through the first 24 lattice periods (photos every 2 periods) (a) before and
(b) after applying successive corrections for dipole errors, normal quadrupole errors, and skew quadrupole errors (adapted from
Ref. 16).
In order to preserve the beam quality, a crucial step
for multi-turn operation, we have developed automated
computer control programs and algorithms which: (a)
steer the beam to the center of the lattice using a 2quadrupole scan algorithm; (b) locally match the beam
using the phosphor-screen measurements along the
first turn; and (c) correct for beam rotation errors using
the measurements and a novel skew quad corrector
element [16]. The control program reads in data from
the Phosphor Screens (integrated over one 100 ns
beam bunch), processes it to compute beam size and
centroid location, then calculates appropriate magnet
corrections and applies them to the next bunch using
electronic control of the power supplies. Figure 2
displays phosphor-screen images of the UMER beam
taken before and after these corrections for quadrupole
skewness and mismatch to illustrate the effects. The
beam rotation angle is reduced from a peak of ± 30° to
± 10°, while the beam size mismatch is reduced from a
variance of 0.44 mm2 down to 0.235 mm2 (for a beam
with a 5 mm radius).
149
based on a parallel-plate retarding-voltage concept,
except it introduces a collimating cylinder which
improves the energy resolution by two orders of
magnitude, without significantly impacting the
temporal resolution [19]. This device has been used to
measure the energy spread close to the LSE source and
further downstream, after transport through a 1.5 meter
long solenoid [6-7]. The results indicate a general
agreement between experimental measurements of
energy spread and predictions from the collisional
Boersch effect and longitudinal-longitudinal effect.
Some deviations from the theory deserve further study
and are pending publication [20].
5. LONGITUDINAL DYNAMICS
Longitudinally, we are in the process of designing
the induction gap pulsers [17], which will generate the
ear fields needed to keep the beam ends confined
during multi-turn operation. To understand the effect
of errors in the pulse shape, we would like to introduce
perturbations to the beam. This we can accomplish by
(a) using the induction gaps; (b) using the cathode grid
mentioned in section 3; or (c) using photoemission
from a 5-ns laser pulse directed at the cathode. The
laser method is the most flexible of the three, as it
allows us to arbitrarily vary the relative intensities of
the main beam and the perturbation, and also to
combine longitudinal and transverse perturbations (by
including masks in front of the laser) [18]. Fig. 3
shows a typical laser-induced perturbation (in this case
highly nonlinear) superimposed over a rectangular
main beam pulse. Observing its evolution over the
first turn of UMER, we see the current pulse split into
a forward-traveling “fast” wave, and a backwardtraveling “slow” wave. By measuring the rate of
separation of those pulses, we get an accurate
measurement of the sound speed which agrees nicely
with the theoretical predictions [1], for sufficiently
small initial perturbations. This experiment has been
simulated using the WARP code and the actual
experimental measurement of the initial pulse. The
simulation agree well with the experiment.
6. FUTURE PLANS
As of the time of writing (Dec. 2004), we have
closed the ring mechanically and propagated the beam
pulse past the injection Y-section, registering a second
pulse on the first beam position monitor, and have thus
entered the multi-turn commissioning stage. The
pulser for the pulsed injection magnet is undergoing
the finishing touches, after which we will go for much
more than a single turn. At the extreme space charge
limit of UMER, our goal is to circulate for 10 turns.
Noting that we can vary the beam current and
emittance at the source using various means, we are
starting commissioning with lower currents and
working our way up. Our ultimate goal for lower
intensities is to circulate 100 turns. Note however that
our least intense beam still contain significant space
charge, with a tune depression k/ko of 0.82, resulting
in a space charge tune shift of 1.4.
Once commissioned, we intend to use UMER to
study a wide variety of the phenomena and challenges
that arise in intense beam accelerators, including but
not limited to: halo formation, emittance growth due to
errors and misalignments, longitudinal beam capture,
introduction of perturbations and instabilities,
anisotropic beams, resonances, etc. All this is possible
due to flexibility of the UMER design, due to the fact
that it is a machine dedicated to beam physics
research, and due to the plethora of detailed beam
diagnostics. For example we can introduce lattice
errors in a controlled way and examine their effects.
We can also change the initial distribution of the beam
by means of apertures as well as the laser. For studies
of resonances, we can vary the initial current and
emittance to generate a drifting beam either close or
far away from resonance. We can also examine
resonance crossing due to emittance growth, and
eventually in a future phase of the project, due to
acceleration.
Figure 3: Oscilloscope trace of beam current vs. time from
UMER showing a typical 5 ns laser-induced perturbation (in
this case highly nonlinear) superimposed over a 100 ns
rectangular thermionic main beam.
Aside from UMER, we have a separate experiment,
the 2-m straight Long Solenoid Experiment (LSE),
dedicated for studies of longitudinal dynamics. This
experiment has been recently used for a dual purpose:
(a) to develop and test a compact, high spatial and
temporal resolution energy analyzer; and (b) to
investigate the evolution of beam energy spread. The
energy analyzer used is a third-generation design
150
Nuclear Instruments and Methods A, accepted for
publication (2004).
As is clear from the above review, the scaled
experiments at the University of Maryland provide an
efficient way to learn about interesting and significant
beam dynamics issues at moderate to high intensities.
The experimental results obtained during construction
of the ring are very promising, and we look forward to
the multi-turn operation regime and even longer path
lengths.
ACKNOWLEDGMENTS
We are indebted to many in the accelerator
community for their support and interest, especially to
I. Hofmann, T. Wangler, C.L. Bohn, G. Franchetti, and
others interested in collaborating with us. We are also
grateful to Dave Grote, Alex Friedman, and Jean-Luc
Vay for their excellent support of the WARP code.
This project is fully funded by the US Dept. of
Energy grant numbers DEFG02-94ER40855 and
DEFG02-92ER54178.
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