153,077 research outputs found
Study of Beam Diagnostics with Trapped Modes in Third Harmonic Superconducting Cavities at FLASH
Off-axis beams passing through an accelerating cavity excite dipole modes
among other higher order modes (HOMs). These modes have linear dependence on
the transverse beam offset from the cavity axis. Therefore they can be used to
monitor the beam position within the cavity. The fifth dipole passband of the
third harmonic superconducting cavities at FLASH has modes trapped within each
cavity and do not propagate through the adjacent beam pipes, while most other
cavity modes do. This could enable the beam position measurement in individual
cavities. This paper investigates the possibility to use the fifth dipole band
for beam alignment in the third harmonic cavity module. Simulations and
measurements both with and without beam-excitations are presented. Various
analysis methods are used and compared. A good correlation of HOM signals to
the beam position is observed.Comment: 2nd International Particle Accelerator Conference (IPAC '11), San
Sebastian, Spain, Sep 4-9, 201
The Picard group of the loop space of the Riemann sphere
The loop space of the Riemann sphere consisting of all C^k or Sobolev W^{k,p}
maps from the circle S^1 to the sphere is an infinite dimensional complex
manifold. We compute the Picard group of holomorphic line bundles on this loop
space as an infinite dimensional complex Lie group with Lie algebra the first
Dolbeault group. The group of Mobius transformations G and its loop group LG
act on this loop space. We prove that an element of the Picard group is
LG-fixed if it is G-fixed; thus completely answer the question by Millson and
Zombro about G-equivariant projective embedding of the loop space of the
Riemann sphere.Comment: International Journal of Mathematic
Bott - Borel - Weil Construction For Quantum Supergroup Uq(gl(m|n))
The finite dimensional irreducible representations of the quantum supergroup
are constructed geometrically using techniques from the Bott -
Borel - Weil theory and vector coherent states.Comment: Latex, 22 page
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