1,122 research outputs found
Relations between some invariants of algebraic varieties in positive characteristic
We discuss relations between certain invariants of varieties in positive
characteristic, like the a-number and the height of the Artin-Mazur formal
group. We calculate the a-number for Fermat surfacesComment: 13 page
Cusps of Hilbert modular varieties
Motivated by a question of Hirzebruch on the possible topological types of
cusp cross-sections of Hilbert modular varieties, we give a necessary and
sufficient condition for a manifold M to be diffeomorphic to a cusp
cross-section of a Hilbert modular variety. Specialized to Hilbert modular
surfaces, this proves that every Sol 3-manifold is diffeomorphic to a cusp
cross-section of a (generalized) Hilbert modular surface. We also deduce an
obstruction to geometric bounding in this setting. Consequently, there exist
Sol 3-manifolds that cannot arise as a cusp cross-section of a 1-cusped
nonsingular Hilbert modular surface.Comment: To appear in Mathematical Proceedings Cambridge Philosophical Societ
New electron source concept for single-shot sub-100 fs electron diffraction in the 100 keV range
We present a method for producing sub-100 fs electron bunches that are
suitable for single-shot ultrafast electron diffraction experiments in the 100
keV energy range. A combination of analytical results and state-of-the-art
numerical simulations show that it is possible to create 100 keV, 0.1 pC, 20 fs
electron bunches with a spotsize smaller than 500 micron and a transverse
coherence length of 3 nm, using established technologies in a table-top set-up.
The system operates in the space-charge dominated regime to produce
energy-correlated bunches that are recompressed by established radio-frequency
techniques. With this approach we overcome the Coulomb expansion of the bunch,
providing an entirely new ultrafast electron diffraction source concept
Concept of a laser-plasma based electron source for sub-10 fs electron diffraction
We propose a new concept of an electron source for ultrafast electron
diffraction with sub-10~fs temporal resolution. Electrons are generated in a
laser-plasma accelerator, able to deliver femtosecond electron bunches at 5 MeV
energy with kHz repetition rate. The possibility of producing this electron
source is demonstrated using Particle-In-Cell simulations. We then use particle
tracking simulations to show that this electron beam can be transported and
manipulated in a realistic beamline, in order to reach parameters suitable for
electron diffraction. The beamline consists of realistic static magnetic optics
and introduces no temporal jitter. We demonstrate numerically that electron
bunches with 5~fs duration and containing 1.5~fC per bunch can be produced,
with a transverse coherence length exceeding 2~nm, as required for electron
diffraction
Compression of sub-relativistic space-charge-dominated electron bunches for single-shot femtosecond electron diffraction
We demonstrate compression of 95 keV, space-charge-dominated electron bunches
to sub-100 fs durations. These bunches have sufficient charge (200 fC) and are
of sufficient quality to capture a diffraction pattern with a single shot,
which we demonstrate by a diffraction experiment on a polycrystalline gold
foil. Compression is realized by means of velocity bunching as a result of a
velocity chirp, induced by the oscillatory longitudinal electric field of a 3
GHz radio-frequency cavity. The arrival time jitter is measured to be 80 fs
Multipole fringe fields
Abstract When creating an initial model of an accelerator, one usually has to resort to a hard edge model for the quadrupoles and higher order multipoles at the start of the project. Ordinarily, it is not until much later on that one has a field map for the given multipoles. This can be rather inconvenient when one is dealing with particularly thin elements or elements which are rather close together in a beamline as the hard edge model may be inadequate for the level of precision desired. For example, in the EMMA project, the two types of quadrupoles used are so close together that they are usually described by a single field map or via hard edge models. The first method has the desired accuracy but was not available at the start of the project and the second is known to be a rough approximation. In this paper, an analytic expression is derived and presented for fringe fields for a multipole of any order with a view to applying it to cases like EMMA. FRINGE FIELDS FOR DIPOLES In order to have fringe fields, given by a → B which satisfy Maxwell's equations, it is important to write all equations down explicitly. For Dipoles, it is sufficient to consider a two dimensional version of the equations Now, if we take B x = 0, we are left with together with which excludes all dependence on x. Further, we seek fringe fields which have a possible fall-off on axis given by the six parameter Enge function [1] with E(z) given by and all a i constants determined by models and/or experiment, or any function which decays sufficiently rapidly. Maxwell's equations (1) imply z . Both wave equations (for B y and B z ) can be easily solved to give Hence, if we ask that equations (1) be solved as well, we end up with If we further restrict ourselves to real magnetic fields, we obtain so B y and B z are given by twice the real and imaginary parts of the function e(z + iy) respectively. A possibility for having a magnetic field whose B y component fall off on axis is given by the six parameter Enge function [1] as which would force B z to have the form for some complex function E(z + iy). If we consider the simple case E(z + iy) = z + iy then equation
Application of laser-cooling to achieve an ultra-cold ion beam for FIB
A new type of ultra-cold ion source is under development which employs transverse laser cooling and compression of a thermal atomic rubidium beam followed by photo-ionization. The resulting ultra-cold plasma is focused to a nanometer-sized spot using an existing Focused Ion Beam column and this spot can be used for the fabrication of nano-structures. Simulations of a 10 cm long laser-cooling stage and of disorder-induced heating of the resulting ion beam, predict an achievable brightness for87Rb+ of order 107 A/m2 sr eV at an longitudinal energy spread of less than 1 eV and a current of tens of pA, which is substantially better than conventional ion sources. Experimental realization of the compact ion source has recently started with the development of an efficient high-flux atom source and a 2D laser cooler. Progress on these items will be reported
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