50 research outputs found
Successive approximations for charged particle motion
Single particle dynamics in electron microscopes, ion or electron
lithographic instruments, particle accelerators, and particle spectrographs is
described by weakly nonlinear ordinary differential equations. Therefore, the
linear part of the equation of motion is usually solved and the nonlinear
effects are then found in successive order by iteration methods. A Hamiltonian
nature of these equations can lead to simplified computations of particle
transport through an optical device when a suitable computational method is
used. Many ingenious microscopic and lithographic devices were found by H. Rose
and his group due to the simple structure of the eikonal method. In the area of
accelerator physics the eikonal method has never become popular. Here I will
therefore generalize the eikonal method and derive it from a Hamiltonian quite
familiar to the accelerator physics community. With the event of high energy
polarized electron beams and plans for high energy proton beams, nonlinear
effects in spin motion have become important in high energy accelerators. I
will introduce a successive approximation for the nonlinear effects in the
coupled spin and orbit motion of charged particles which resembles some of the
simplifications resulting from the eikonal method for the pure orbit motion
Orbit and Optics Improvement by Evaluating the Nonlinear BPM Response in CESR
We present an improved system for orbit and betatron phase measurement
utilizing nonlinear models of BPM pickup response. We first describe the
calculation of the BPM pickup signals as nonlinear functions of beam position
using Green's reciprocity theorem with a two-dimensional formalism. We then
describe the incorporation of these calculations in our beam position
measurements by inverting the nonlinear functions, giving us beam position as a
function of the pickup signals, and how this is also used to improve our
measurement of the betatron phase advance. Measurements are presented comparing
this system with the linearized pickup response used historically at CESR.Comment: 7 pages, 11 figure
Equilibrium ion distribution in the presence of clearing electrodes and its influence on electron dynamics
Here we compute the ion distribution produced by an electron beam when
ion-clearing electrodes are installed. This ion density is established as an
equilibrium between gas ionization and ion clearing. The transverse ion
distributions are shown to strongly peak in the beam's center, producing very
nonlinear forces on the electron beam. We will analyze perturbations to the
beam properties by these nonlinear fields. To obtain reasonable simulation
speeds, we develop fast algorithms that take advantage of adiabatic invariants
and scaling properties of Maxwell's equations and the Lorentz force.
Our results are very relevant for high current Energy Recovery Linacs, where
ions are produced relatively quickly, and where clearing gaps in the electron
beam cannot easily be used for ion elimination. The examples in this paper
therefore use parameters of the Cornell Energy Recovery Linac project. For
simplicity we only consider the case of a circular electron beam of changing
diameter. However, we parameterize this model to approximate non-round beams
well. We find suitable places for clearing electrodes and compute the
equilibrium ion density and its effect on electron-emittance growth and halo
development. We find that it is not sufficient to place clearing electrodes
only at the minimum of the electron beam potential where ions are accumulated
Transverse emittance dilution due to coupler kicks in linear accelerators
One of the main concerns in the design of low emittance linear accelerators
(linacs) is the preservation of beam emittance. Here we discuss one possible
source of emittance dilution, the coupler kick, due to transverse
electromagnetic fields in the accelerating cavities of the linac caused by the
power coupler geometry. In addition to emittance growth, the coupler kick also
produces orbit distortions. It is common wisdom that emittance growth from
coupler kicks can be strongly reduced by using two couplers per cavity mounted
opposite each other or by having the couplers of successive cavities
alternation from above to below the beam pipe so as to cancel each individual
kick. We therefore analyze consequences of alternate coupler placements.
We show here that for sufficiently large Q values, alternating the coupler
location from before to after the cavity leads to a cancellation of the orbit
distortion but not of the emittance growth, whereas alternating the coupler
location from before and above to behind and below the cavity cancels the
emittance growth but not the orbit distortion. These compensations hold even
when each cavity is individually detuned, e.g. by microphonics. Another
effective method for reducing coupler kicks that is studied is the optimization
of the phase of the coupler kick. This technique is independent of the coupler
geometry but relies on operating on crest. A final technique studied is
symmetrization of the cavity geometry in the coupler region with the addition
of a stub opposite the coupler, which reduces the amplitude of the off axis
fields and is thus effective for off crest acceleration as well.
We show applications of these techniques to the energy recovery linac (ERL)
planned at Cornell University
Synchro-Betatron Stop-Bands due to a Single Crab Cavity
We analyze the stop-band due to crab cavities for horizontal tunes that are
either close to integers or close to half integers. The latter case is relevant
for today's electron/positron colliders. We compare this stop-band to that
created by dispersion in an accelerating cavity and show that a single typical
crab cavity creates larger stop-bands than a typical dispersion at an
accelerating cavity.
We furthermore analyze whether it is beneficial to place the crab cavity at a
position where the dispersion and its slope vanish. We find that this choice is
worth while if the horizontal tune is close to a half integer, but not if it is
close to an integer. Furthermore we find that stop-bands can be avoided when
the horizontal tune is located at a favorable side of the integer or the half
integer.
While we are here concerned with the installation of a single crab cavity in
a storage ring, we show that the stop-bands can be weakened, although not
eliminated, significantly when two crab cavities per ring are chosen suitably.Comment: 7 pages, 9 figure
Compensation of wake-field-driven energy spread in Energy Recovery Linacs
Energy Recovery Linacs provide high-energy beams, but decelerate those beams
before dumping them, so that their energy is available for the acceleration of
new particles. During this deceleration, any relative energy spread that is
created at high energy is amplified by the ratio between high energy and dump
energy. Therefore, Energy Recovery Linacs are sensitive to energy spread
acquired at high energy, e.g. from wake fields. One can compensate the
time-correlated energy spread due to wakes via energy-dependent time-of-flight
terms in appropriate sections of an Energy Recovery Linac, and via
high-frequency cavities. We show that nonlinear time-of-flight terms can only
eliminate odd orders in the correlation between time and energy, if these terms
are created by a beam transport within the linac that is common for
accelerating and decelerating beams. If these two beams are separated, so that
different beam transport sections can be used to produce time-of-flight terms
suitable for each, also even-order terms in the energy spread can be
eliminated. As an example, we investigate the potential of using this method
for the Cornell x-ray Energy Recovery Linac. Via quadratic time-of-flight
terms, the energy spread can be reduced by 66%. Alternatively, since the energy
spread from the dominantly resistive wake fields of the analysed accelerator is
approximately harmonic in time, a high-frequency cavity could diminish the
energy spread by 81%. This approach would require bunch-lengthening and
recompression in separate sections for accelerating and decelerating beams.
Such sections have therefore been included in Cornell's x-ray Energy Recovery
Linac design