23 research outputs found
Collective Modes and Colored Noise as Beam-Halo Amplifiers
As illustrated herein, collective modes and colored noise conspire to produce beam halo with much larger amplitude than could be generated by either phenomenon separately. Collective modes are inherent to nonequilibrium beams with space charge. Colored noise arises from unavoidable machine transitions and/or errors that influence the internal space-charge force. Lowest-order radial eigenmodes calculated self-consistently for a direct-current, cylindrically symmetric, warm-fluid Kapchinskij-Vladimirskij equilibrium serve to model the collective modes. Even with weak space charge, small-amplitude collective modes, and weak noise strength, a pronounced halo is seen to develop if these phenomena act on the beam over a sufficiently long time, such as in a synchrotron or storage ring
Coherent Synchrotron Radiation: Theory and Experiments
Our understanding of the generation of coherent synchrotron radiation in magnetic bending systems and its impact on beam dynamics has grown considerably over the past few years. The search for understanding has brought a number of surprises, all related to the complexity of the fully self-consistent problem. Herein I survey the associated phenomenology, theory, and experiments while emphasizing important subtleties that have recently been uncovered. I conclude by speculating on courses of future investigations that may prove fruitful
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Physics goals for the planned next linear collider engineering test facility
The Next Linear Collider (NLC) Collaboration is planning to construct an Engineering Test Facility (ETF) at Fermilab. As presently envisioned, the ETF would comprise a fundamental unit of the NLC main linac to include X-band klystrons and modulators, a delay-line power-distribution system (DLDS), and NLC accelerating structures that serve as loads. The principal purpose of the ETF is to validate stable operation of the power-distribution system, first without beam, then with a beam having the NLC pulse structure. This paper concerns the possibility of configuring and using the ETF to accelerate beam with an NLC pulse structure, as well as of doing experiments to measure beam-induced wakefields in the rf structures and their influence back on the beam
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Mixing of regular and chaotic orbits in beams
Phase mixing of chaotic orbits exponentially distributes the orbits through their accessible phase space. This phenomenon, commonly called ''chaotic mixing'', stands in marked contrast to phase mixing of regular orbits which proceeds as a power law in time. It is inherently irreversible; hence, its associated e-folding time scale sets a condition on any process envisioned for emittance compensation. We numerically investigate phase mixing in the presence of space charge, distinguish between the evolution of regular and chaotic orbits, and discuss how phase mixing potentially influences macroscopic properties of high-brightness beams
Fluctuations Do Matter: Large Noise-Enhanced Halos in Charged-Particle Beams
The formation of beam halos has customarily been described in terms of a
particle-core model in which the space-charge field of the oscillating core
drives particles to large amplitudes. This model involves parametric resonance
and predicts a hard upper bound to the orbital amplitude of the halo particles.
We show that the presence of colored noise due to space-charge fluctuations
and/or machine imperfections can eject particles to much larger amplitudes than
would be inferred from parametric resonance alone.Comment: 13 pages total, including 5 figure
Chaotic Orbits in Thermal-Equilibrium Beams: Existence and Dynamical Implications
Phase mixing of chaotic orbits exponentially distributes these orbits through
their accessible phase space. This phenomenon, commonly called ``chaotic
mixing'', stands in marked contrast to phase mixing of regular orbits which
proceeds as a power law in time. It is operationally irreversible; hence, its
associated e-folding time scale sets a condition on any process envisioned for
emittance compensation. A key question is whether beams can support chaotic
orbits, and if so, under what conditions? We numerically investigate the
parameter space of three-dimensional thermal-equilibrium beams with space
charge, confined by linear external focusing forces, to determine whether the
associated potentials support chaotic orbits. We find that a large subset of
the parameter space does support chaos and, in turn, chaotic mixing. Details
and implications are enumerated.Comment: 39 pages, including 14 figure
Production of Enhanced Beam Halos via Collective Modes and Colored Noise
We investigate how collective modes and colored noise conspire to produce a
beam halo with much larger amplitude than could be generated by either
phenomenon separately. The collective modes are lowest-order radial eigenmodes
calculated self-consistently for a configuration corresponding to a
direct-current, cylindrically symmetric, warm-fluid Kapchinskij-Vladimirskij
equilibrium. The colored noise arises from unavoidable machine errors and
influences the internal space-charge force. Its presence quickly launches
statistically rare particles to ever-growing amplitudes by continually kicking
them back into phase with the collective-mode oscillations. The halo amplitude
is essentially the same for purely radial orbits as for orbits that are
initially purely azimuthal; orbital angular momentum has no statistically
significant impact. Factors that do have an impact include the amplitudes of
the collective modes and the strength and autocorrelation time of the colored
noise. The underlying dynamics ensues because the noise breaks the
Kolmogorov-Arnol'd-Moser tori that otherwise would confine the beam. These tori
are fragile; even very weak noise will eventually break them, though the time
scale for their disintegration depends on the noise strength. Both collective
modes and noise are therefore centrally important to the dynamics of halo
formation in real beams.Comment: For full resolution pictures please go to
http://www.nicadd.niu.edu/research/beams
On relaxation processes in collisionless mergers
We analyze N-body simulations of halo mergers to investigate the mechanisms
responsible for driving mixing in phase-space and the evolution to dynamical
equilibrium. We focus on mixing in energy and angular momentum and show that
mixing occurs in step-like fashion following pericenter passages of the halos.
This makes mixing during a merger unlike other well known mixing processes such
as phase mixing and chaotic mixing whose rates scale with local dynamical time.
We conclude that the mixing process that drives the system to equilibrium is
primarily a response to energy and angular momentum redistribution that occurs
due to impulsive tidal shocking and dynamical friction rather than a result of
chaotic mixing in a continuously changing potential. We also analyze the merger
remnants to determine the degree of mixing at various radii by monitoring
changes in radius, energy and angular momentum of particles. We confirm
previous findings that show that the majority of particles retain strong memory
of their original kinetic energies and angular momenta but do experience
changes in their potential energies owing to the tidal shocks they experience
during pericenter passages. Finally, we show that a significant fraction of
mass (~ 40%) in the merger remnant lies outside its formal virial radius and
that this matter is ejected roughly uniformly from all radii outside the inner
regions. This highlights the fact that mass, in its standard virial definition,
is not additive in mergers. We discuss the implications of these results for
our understanding of relaxation in collisionless dynamical systems.Comment: Version accepted for Publication in Astrophysical Journal, March 20,
2007, v685. Minor changes, latex, 14 figure
Chaos and the continuum limit in nonneutral plasmas and charged particle beams
This paper examines discreteness effects in nearly collisionless N-body
systems of charged particles interacting via an unscreened r^-2 force, allowing
for bulk potentials admitting both regular and chaotic orbits. Both for
ensembles and individual orbits, as N increases there is a smooth convergence
towards a continuum limit. Discreteness effects are well modeled by Gaussian
white noise with relaxation time t_R = const * (N/log L)t_D, with L the Coulomb
logarithm and t_D the dynamical time scale. Discreteness effects accelerate
emittance growth for initially localised clumps. However, even allowing for
discreteness effects one can distinguish between orbits which, in the continuum
limit, feel a regular potential, so that emittance grows as a power law in
time, and chaotic orbits, where emittance grows exponentially. For sufficiently
large N, one can distinguish two different `kinds' of chaos. Short range
microchaos, associated with close encounters between charges, is a generic
feature, yielding large positive Lyapunov exponents X_N which do not decrease
with increasing N even if the bulk potential is integrable. Alternatively,
there is the possibility of larger scale macrochaos, characterised by smaller
Lyapunov exponents X_S, which is present only if the bulk potential is chaotic.
Conventional computations of Lyapunov exponents probe X_N, leading to the
oxymoronic conclusion that N-body orbits which look nearly regular and have
sharply peaked Fourier spectra are `very chaotic.' However, the `range' of the
microchaos, set by the typical interparticle spacing, decreases as N increases,
so that, for large N, this microchaos, albeit very strong, is largely
irrelevant macroscopically. A more careful numerical analysis allows one to
estimate both X_N and X_S.Comment: 13 pages plus 17 figure