If D is C+ or D , then we prove that H1(D) is a Hermite regular coherent ring of weak global dimension 2 (the coherence was already proved in [4]). We show: there is a one-to-one equivalence between systems de ned by matrices with entries in H1(D) and coherent H1(D)-modules, coherent H1(D)-modules are stable by elementary algebraic operations, and thus, we can characterize the algebraic propert...

Frames which can be generated by the action of some operators (e.g. translation, dilation, modulation, ...) on a single element $f$ in a Hilbert space, called coherent frames. In this paper, we introduce a class of continuous frames in a Hilbert space $mathcal{H}$ which is indexed by some locally compact group $G$, equipped with its left Haar measure. These frames are obtained as the orbits of ...

We present a model describing high power stable broadband coherent synchrotron radiation (CSR) in the terahertz frequency region in an electron storage ring. The model includes distortion of bunch shape from the synchrotron radiation (SR), which enhances higher frequency coherent emission, and limits to stable emission due to an instability excited by the SR wakefield. It gives a quantitative e...

We introduce a refinement of the Gorenstein flat dimension for complexes over an associative ring—the flat-cotorsion —and prove that it, unlike dimension, behaves as one expects homological without extra assumptions on ring. Crucially, we show it coincides with where latter is finite, and right coherent rings—the setting known to behave expected.

We investigate influence on the storage ring beam dynamics of the coherent Synchrotron Radiation (SR) self fields produced by an electron bunch. We show that the maximum energy gain in the RF cavity must far exceed the energy loss of electrons due to the coherent SR.

In a synchrotron radiation source coherent infrared (IR) radiation is emitted when the bunch length is comparable to the wavelength of the emitted radiation. To generate coherent THz (far IR) radiation, the ANKA storage ring is operated regularly in a dedicated low-alpha optics. Different bunch lengths, corresponding to different spectral ranges of the THz spectrum and various electron beam ene...

Strong evidence for self-excited emission of coherent synchrotron radiation in the microwave spectral region was observed at the Synchrotron Ultraviolet Radiation Facility (SURF III) electron storage ring at the NIST. The microwave emission between 25 and 35 mm was dominated by intense bursts of radiation. The intensity enhancement during these bursts was on the order of 10 000 to 50 000 over t...