249 research outputs found
Beam-Breakup Instability Theory for Energy Recovery Linacs
Here we will derive the general theory of the beam-breakup instability in
recirculating linear accelerators, in which the bunches do not have to be at
the same RF phase during each recirculation turn. This is important for the
description of energy recovery linacs (ERLs) where bunches are recirculated at
a decelerating phase of the RF wave and for other recirculator arrangements
where different RF phases are of an advantage. Furthermore it can be used for
the analysis of phase errors of recirculated bunches. It is shown how the
threshold current for a given linac can be computed and a remarkable agreement
with tracking data is demonstrated. The general formulas are then analyzed for
several analytically solvable cases, which show: (a) Why different higher order
modes (HOM) in one cavity do not couple so that the most dangerous modes can be
considered individually. (b) How different HOM frequencies have to be in order
to consider them separately. (c) That no optics can cause the HOMs of two
cavities to cancel. (d) How an optics can avoid the addition of the
instabilities of two cavities. (e) How a HOM in a multiple-turn recirculator
interferes with itself. Furthermore, a simple method to compute the orbit
deviations produced by cavity misalignments has also been introduced. It is
shown that the BBU instability always occurs before the orbit excursion becomes
very large.Comment: 12 pages, 6 figure
Spin, Statistics, and Reflections, II. Lorentz Invariance
The analysis of the relation between modular PCT-symmetry -- a
consequence of the Unruh effect -- and Pauli's spin-statistics relation is
continued. The result in the predecessor to this article is extended to the
Lorentz symmetric situation. A model \G_L of the universal covering
\widetilde{L_+^\uparrow}\cong SL(2,\complex) of the restricted Lorentz group
is modelled as a reflection group at the classical level. Based
on this picture, a representation of \G_L is constructed from pairs of
modular PCT-conjugations, and this representation can easily be verified to
satisfy the spin-statistics relation
Uniformly Accelerated Observer in Moyal Spacetime
In Minkowski space, an accelerated reference frame may be defined as one that
is related to an inertial frame by a sequence of instantaneous Lorentz
transformations. Such an accelerated observer sees a causal horizon, and the
quantum vacuum of the inertial observer appears thermal to the accelerated
observer, also known as the Unruh effect. We argue that an accelerating frame
may be similarly defined (i.e. as a sequence of instantaneous Lorentz
transformations) in noncommutative Moyal spacetime, and discuss the twisted
quantum field theory appropriate for such an accelerated observer. Our analysis
shows that there are several new features in the case of noncommutative
spacetime: chiral massless fields in dimensions have a qualitatively
different behavior compared to massive fields. In addition, the vacuum of the
inertial observer is no longer an equilibrium thermal state of the accelerating
observer, and the Bose-Einstein distribution acquires -dependent
corrections.Comment: 19 pages. Typos correcte
Endomorphism Semigroups and Lightlike Translations
Certain criteria are demonstrated for a spatial derivation of a von Neumann
algebra to generate a one-parameter semigroup of endomorphisms of that algebra.
These are then used to establish a converse to recent results of Borchers and
of Wiesbrock on certain one-parameter semigroups of endomorphisms of von
Neumann algebras (specifically, Type III_1 factors) that appear as lightlike
translations in the theory of algebras of local observables.Comment: 9 pages, Late
Schwarzschild black hole with global monopole charge
We derive the metric for a Schwarzschild black hole with global monopole
charge by relaxing asymptotic flatness of the Schwarzschild field. We then
study the effect of global monopole charge on particle orbits and the Hawking
radiation. It turns out that existence, boundedness and stability of circular
orbits scale up by , and the perihelion shift and the
light bending by , while the Hawking temperature scales
down by the Schwarzschild values. Here is the
global charge.Comment: 12 pages, LaTeX versio
Coupled-Bunch Beam Breakup due to Resistive-Wall Wake
The coupled-bunch beam breakup problem excited by the resistive wall wake is
formulated. An approximate analytic method of finding the asymptotic behavior
of the transverse bunch displacement is developed and solved.Comment: 8 page
Diamonds's Temperature: Unruh effect for bounded trajectories and thermal time hypothesis
We study the Unruh effect for an observer with a finite lifetime, using the
thermal time hypothesis. The thermal time hypothesis maintains that: (i) time
is the physical quantity determined by the flow defined by a state over an
observable algebra, and (ii) when this flow is proportional to a geometric flow
in spacetime, temperature is the ratio between flow parameter and proper time.
An eternal accelerated Unruh observer has access to the local algebra
associated to a Rindler wedge. The flow defined by the Minkowski vacuum of a
field theory over this algebra is proportional to a flow in spacetime and the
associated temperature is the Unruh temperature. An observer with a finite
lifetime has access to the local observable algebra associated to a finite
spacetime region called a "diamond". The flow defined by the Minkowski vacuum
of a (four dimensional, conformally invariant) quantum field theory over this
algebra is also proportional to a flow in spacetime. The associated temperature
generalizes the Unruh temperature to finite lifetime observers.
Furthermore, this temperature does not vanish even in the limit in which the
acceleration is zero. The temperature associated to an inertial observer with
lifetime T, which we denote as "diamond's temperature", is 2hbar/(pi k_b
T).This temperature is related to the fact that a finite lifetime observer does
not have access to all the degrees of freedom of the quantum field theory.Comment: One reference correcte
A New Approach to Spin and Statistics
We give an algebraic proof of the spin-statistics connection for the
parabosonic and parafermionic quantum topological charges of a theory of local
observables with a modular PCT-symmetry. The argument avoids the use of the
spinor calculus and also works in 1+2 dimensions. It is expected to be a
progress towards a general spin-statistics theorem including also
(1+2)-dimensional theories with braid group statistics.Comment: LATEX, 15 pages, no figure
On local boundary CFT and non-local CFT on the boundary
The holographic relation between local boundary conformal quantum field
theories (BCFT) and their non-local boundary restrictions is reviewed, and
non-vacuum BCFT's, whose existence was conjectured previously, are constructed.Comment: 16 pages. Contribution to "Rigorous Quantum Field Theory", Symposium
in honour of J. Bros, Paris, July 2004. Based on joint work math-ph/0405067
with R. Long
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