Stability condition for the drive bunch in a collinear wakefield accelerator

The beam breakup instability of the drive bunch in the structure-based collinear wakefield accel- erator is considered and a stabilizing method is proposed. The method includes using the specially designed beam focusing channel, applying the energy chirp along the electron bunch, and keeping energy chirp constant during the drive bunch deceleration. A stability condition is derived that defines the limit on the accelerating field for the witness bunch.Comment: 10 pages, 6 figure

Interpolation of equation-of-state data

Aims. We use Hermite splines to interpolate pressure and its derivatives simultaneously, thereby preserving mathematical relations between the derivatives. The method therefore guarantees that thermodynamic identities are obeyed even between mesh points. In addition, our method enables an estimation of the precision of the interpolation by comparing the Hermite-spline results with those of frequent cubic (B-) spline interpolation. Methods. We have interpolated pressure as a function of temperature and density with quintic Hermite 2D-splines. The Hermite interpolation requires knowledge of pressure and its first and second derivatives at every mesh point. To obtain the partial derivatives at the mesh points, we used tabulated values if given or else thermodynamic equalities, or, if not available, values obtained by differentiating B-splines. Results. The results were obtained with the grid of the SAHA-S equation-of-state (EOS) tables. The maximum $lg P$ difference lies in the range from $10^{-9}$ to $10^{-4}$, and $\Gamma_1$ difference varies from $10^{-9}$ to $10^{-3}$. Specifically, for the points of a solar model, the maximum differences are one order of magnitude smaller than the aforementioned values. The poorest precision is found in the dissociation and ionization regions, occurring at $T \sim 1.5\cdot 10^3 - 10^5$ K. The best precision is achieved at higher temperatures, $T>10^5$ K. To discuss the significance of the interpolation errors we compare them with the corresponding difference between two different equation-of-state formalisms, SAHA-S and OPAL 2005. We find that the interpolation errors of the pressure are a few orders of magnitude less than the differences from between the physical formalisms, which is particularly true for the solar-model points.Comment: Accepted for publication in A&

Numerical Simulation of Physical and Chemical Processes in Fluidized Bed

The paper presents a numerical simulation of the furnace with a circulating fluidized bed. Numerical study carried out for the bottom of the combustion chamber with the varying heights of volume filling. The results contours of particulate matter concentration and of velocities, as well as a graphical representation of changes in the concentration of particles on the bed height are shown. Simulation performed in Eulerian - Eulerian representation on a 2D model

The Study of Dynamic Processes in the Boiler Furnace with Circulating Fluidized Bed

The paper presents a numerical simulation of the furnace with a circulating fluidized bed. Numerical study carried out on all volume of the combustion chamber. The results contours of particulate matter concentration and of velocities, as well as a graphical representation of changes in the concentration of particles on the bed height are shown. Simulation performed in Eulerian - Eulerian and Lagrange representation on a 3D model

Fatigue effect in ferroelectric crystals: Growth of the frozen domains

The model of the fatigue effect during cyclic switching caused by growth of the frozen domain area with charged domain walls has been proposed. It was claimed on the basis of the previous experimental results that for switching in increasing field the frozen domain area started to grow at the given sub-threshold field value and stopped at the threshold field. The influence of the shape and frequency of the field pulses used for cyclic switching has been considered. The uniaxial ferroelectric stoichiometric lithium tantalate single crystals produced by vapor transport equilibration with record low value of coercive field have been chosen as a model material for experimental verification of the model. The formation of the charged domain walls as a result of cyclic switching has been revealed by analysis of the domain images obtained by optical and Raman confocal microscopy. It has been shown that the fatigue degree is equal to the fraction of the frozen domain area. The experimental dependence of the switched charge on the cycle number has been successfully fitted by modified Kolmogorov-Avrami formula. The experimentally observed frequency independence of fatigue profile for rectangular pulses and frequency dependence for triangular pulses has been explained by proposed model. © 2012 American Institute of Physics

Geometric wakes in collimators and step transitions of arbitrary cross-sections: conformal mapping approach

In the present study, we extend the approach of the wake field conformal mapping technique to the case of the step transition and a collimator. We assume that all pipes have different arbitrary cross-sectional shapes. We derive simple analytical expressions for the lower and upper bounds of both longitudinal and transverse wake potentials. We test the derived expressions against well-known formulas in several representative examples. The proposed method can greatly simplify the optimization of collimating sections as well as become a useful tool in the exploration of transverse beam shaping ideas.Comment: 11 pages 5 figure