An exact solution of the space charge problem for the motion of a spherically symmetric beam in a homogeneous electric field

Sadovnikov B.I., Zhavoronkov A.A.

Perepelkin E.E., Inozemtseva N.G., Zhavoronkov A.A.

Kaplan A.E., Dubetsky B.Y., Shkolnikov P.L.

We predict that Coulomb explosion of a nanoscale cluster, which is ionized by high-intensity laser radiation and has a naturally occurring spatial density profile, will invariably produce shock waves. In most typical situations, two shocks, a leading and a trailing one, form a shock shell that eventually encompasses the entire cluster. Being the first example of shock waves on the nanometer scale, this phenomenon promises interesting effects and applications, including high-rate nuclear reactions inside each individual cluster.

Smirnov V.L.

The review is devoted to accelerators of the cyclotron type. Systematization of cyclotrons and description of their basic structural units are presented, and theoretical basics of cyclotron physics are given. The numerical modeling techniques used to design cyclotrons are described, which include the methods for beam dynamics analysis and the algorithms applied for their software implementation. A survey of existing program codes intended for the analysis of particle dynamics in cyclotron facilities is presented.

Rubina L.I., Ul’yanov O.N.

A system of equations for the motion of an ionized ideal gas is considered. An algorithm for the reduction of this system of nonlinear partial differential equations (PDEs) to systems of ordinary differential equations (ODEs) is presented. It is shown that the independent variable ψ in the systems of ODEs is determined from the relation ψ = t + xf1(ψ) + yf2(ψ) + zf3(ψ) after choosing (setting or finding) the functions fi(ψ), i = 1, 2, 3. These functions are either found from the conditions of the problem posed for the original system of PDEs or are given arbitrarily to obtain a specific system of ODEs. For the problem on the motion of an ionized gas near a body, we write a system of ODEs and discuss the issue of instability, which is observed in a number of cases. We also consider a problem of the motion of flows (particles) in a given direction, which is of significant interest in some areas of physics. We find the functions fi(ψ), i = 1, 2, 3, that provide the motion of a flow of the ionized gas in a given direction and reduce the system of PDEs to a system of ODEs.