Goldstein-Kac telegraph processes with random speeds: Path probabilities, likelihoods, and reported Lévy flights.

The Goldstein-Kac telegraph process describes the one-dimensional motion of particles with constant speed undergoing random changes in direction. Despite its resemblance to numerous real-world phenomena, the singular nature of the resultant spatial distribution of each particle precludes the possibility of any a posteriori empirical validation of this random-walk model from data. Here we show that by simply allowing for random speeds, the ballistic terms are regularized and that the diffusion component can be well-approximated via the unscented transform. The result is a computationally efficient yet robust evaluation of the full particle path probabilities and, hence, the parameter likelihoods of this generalized telegraph process. We demonstrate how a population diffusing under such a model can lead to non-Gaussian asymptotic spatial distributions, thereby mimicking the behavior of an ensemble of Lévy walkers

Design of low level RF control for the TESLA superstructure

The superstructure is a viable option for the TESLA linear collider because of a high effective gradient and a reduced number of rf components. However, the high number and close proximity of passband modes impose challenging demands on the rf control system. The control problem is complicated by the fact that the cavity probe signal does not exactly reflect the actual accelerating voltage experienced by the beam due to the different coupling of the generator, pickup probe and beam to the FM passband modes. The digital control system developed for the standard 9-cell cavity is not adequate for operation of the superstructure. As discussed in this paper, an additional filter is needed to guarantee robustness and stability. Based on rf control simulations the filter characteristic is optimized

RF Parameters and Field Stability Requirements for the Cornell ERL

Abstract Cornell University, in collaboration with Jefferson Laboratory, has proposed the construction of a prototype energyrecovery linac (ERL) to study the energy recovery concept with high current, low emittance beams OVERVIEW The schematic of the injector RF system is shown in The main linac with energy recovery is based on five superconducting 9-cell cavities, each with its own field control system and klystron; see INJECTOR CAVITIES Buncher Cavity: The buncher cavity is a normal-conducting single-cell cavity made of copper. It is used to produce a correlated energy variation of about 10 keV along a σ gun = 12 ps, 500 keV bunch coming from the gun. This will shorten the bunch to σ inj = 2.3 ps in a drift space between the buncher cavity and first superconducting cavity. The RF properties [4] of the buncher cavity are listed in • offcrest, i.e. during zero-crossing. The RF power required to maintain a constant field in the cavity is then given b

Dynamic Lorentz force compensation with a fast piezoelectric tuner

Superconducting cavities are highly susceptible to small changes in resonance frequency due to their narrow bandwidth. At the proposed linac for the TESLA Linear Collider [1] the frequency changes resulting from mechanical deformations caused by Lorentz force detuning of the pulsed cavities will be of the order of the cavity bandwidth at the design operating gradient close to 25 MV/ m. The additional power required for field control is of the order of 10 % and will be intolerably high for the planned upgrade to 35 MV/m which appears to be feasible in the near future. While passive stiffening of the cavities is already applied to the present cavity design, the further reduction of the Lorentz force detuning constant is technically challenging. Therefore we propose an active scheme which reduces the timevarying Lorentz force detuning to much less than one cavity bandwidth. If successful, the scheme will improve the power efficiency of the TESLA linac significantly