Simulation of an Axial Vircator

An algorithm of particle-in-cell simulations is described and tested to aid further the actual design of simple vircators working on axially symmetric modes. The methods of correction of the numerical solution, have been chosen and jointly tested, allow the stable simulation of the fast nonlinear multiflow dynamics of virtual cathode formation and evolution, as well as the fields generated by the virtual cathode. The selected combination of the correction methods can be straightforwardly generalized to the case of axially nonsymmetric modes, while the parameters of these correction methods can be widely used to improve an agreement between the simulation predictions and the experimental data.Comment: 9 pages, 3 figure

To the positive miscut influence on the crystal collimation efficiency

The paper concerns the crystal based collimation suggested to upgrade the Large Hadron Collider collimation system. The issue of collimation efficiency dependence on the muscut angle characterizing nonparallelity of the channeling planes and crystal surface is mainly addressed. It is shown for the first time that even the preferable positive miscut could severely deteriorate the channeling collimation efficiency in the crystal collimation UA9 experiment. We demonstrate that the positive miscut influence can increase the nuclear reaction rate in the perfectly aligned crystal collimator by a factor of 4.5. We also discuss the possible miscut influence on the future LHC crystal collimation system performance as well as suggest simple estimates for the beam diffusion step, average impact parameter of particle collisions with the collimator and angular divergence of the colliding particle beam portion.Comment: 14 pages, 9 figure

THE SMALLEST SINGULAR VALUE OF INHOMOGENEOUS SQUARE RANDOM MATRICES

We show that for an $n\times n$ random matrix $A$ with independent uniformly anti-concentrated entries, such that $\mathbb{E} ||A||^2_{HS}\leq K n^2$, the smallest singular value $\sigma_n(A)$ of $A$ satisfies $$P\left( \sigma_n(A)\leq \frac{\varepsilon}{\sqrt{n}} \right) \leq C\varepsilon+2e^{-cn},\quad \varepsilon \ge 0.$$ This extends earlier results of Rudelson and Vershynin, and Rebrova and Tikhomirov by removing the assumption of mean zero and identical distribution of the entries across the matrix, as well as the recent result of Livshyts, where the matrix was required to have i.i.d. rows. Our model covers "inhomogeneus" matrices allowing different variances of the entries, as long as the sum of the second moments is of order $O(n^2)$. In the past advances, the assumption of i.i.d. rows was required due to lack of Littlewood--Offord--type inequalities for weighted sums of non-i.i.d. random variables. Here, we overcome this problem by introducing the Randomized Least Common Denominator (RLCD) which allows to study anti-concentration properties of weighted sums of independent but not identically distributed variables. We construct efficient nets on the sphere with lattice structure, and show that the lattice points typically have large RLCD. This allows us to derive strong anti-concentration properties for the distance between a fixed column of $A$ and the linear span of the remaining columns, and prove the main result

Two-dimensional model of intrinsic magnetic flux losses in helical flux compression generators

Helical Flux Compression Generators (HFCG) are used for generation of mega-amper current and high magnetic fields. We propose the two dimensional HFCG filament model based on the new description of the stator and armature contact point. The model developed enables one to quantitatively describe the intrinsic magnetic flux losses and predict the results of experiments with various types of HFCGs. We present the effective resistance calculations based on the non-linear magnetic diffusion effect describing HFCG performance under the strong conductor heating by currents.Comment: 29 pages,18 figure