The Lundgren-Monin-Novikov Hierarchy: Kinetic Equations for Turbulence

We present an overview of recent works on the statistical description of turbulent flows in terms of probability density functions (PDFs) in the framework of the Lundgren-Monin-Novikov (LMN) hierarchy. Within this framework, evolution equations for the PDFs are derived from the basic equations of fluid motion. The closure problem arises either in terms of a coupling to multi-point PDFs or in terms of conditional averages entering the evolution equations as unknown functions. We mainly focus on the latter case and use data from direct numerical simulations (DNS) to specify the unclosed terms. Apart from giving an introduction into the basic analytical techniques, applications to two-dimensional vorticity statistics, to the single-point velocity and vorticity statistics of three-dimensional turbulence, to the temperature statistics of Rayleigh-B\'enard convection and to Burgers turbulence are discussed.Comment: Accepted for publication in C. R. Acad. Sc

Lagrangian statistics in forced two-dimensional turbulence

We report on simulations of two-dimensional turbulence in the inverse energy cascade regime. Focusing on the statistics of Lagrangian tracer particles, scaling behavior of the probability density functions of velocity fluctuations is investigated. The results are compared to the three-dimensional case. In particular an analysis in terms of compensated cumulants reveals the transition from a strong non-Gaussian behavior with large tails to Gaussianity. The reported computation of correlation functions for the acceleration components sheds light on the underlying dynamics of the tracer particles.Comment: 8 figures, 1 tabl

Beam Dynamics Studies for SRF Photoinjectors

The SRF photoinjector combines the advantages of photo assisted production of high brightness, short electron pulses and high gradient, low loss continuous wave CW operation of a superconducting radiofrequency SRF cavity. The paper discusses beam dynamics considerations for ERL class applications of SRF photoinjectors. One case of particular interest is the design of the SRF photoinjector for BERLinPro, an ERL test facility demanding a high brightness beam with an emittance better than 1 mm mrad at 77 pC and average current of 100 m

Virtual Cathode Diagnostics with a Large Dynamic Range for a Continuous Wave SRF Photoinjector

In a SRF photoinjector the close relationship between the laser pulse and the generated electron bunch parameters requires continuous monitoring of some of the laser pulse parameters. A laser diagnostic system, called virtual cathode, is a key part of a system that controls the stability of the laser. One of the main challenges for the virtual cathode is to cover the large dynamic range of the photocathode laser between commissioning at 120 Hz and operation at 1.3 GHz repetition rate with constant laser pulse parameters. The design of the virtual cathode as well as first measurements with a photocathode drive laser for the SRF injector test facility GunLab of BERLinPro will be presente