On the Integrable Chaplygin Type Hydrodynamic Systems and Their Geometric Structure

A class of spatially one-dimensional completely integrable Chaplygin hydrodynamic systems was studied within framework of Lie-algebraic approach. The Chaplygin hydrodynamic systems were considered as differential systems on the torus. It has been shown that the geometric structure of the systems under analysis has strong relationship with diffeomorphism group orbits on them. It has allowed to find a new infinite hierarchy of integrable Chaplygin like hydrodynamic systems

Integrability of Riemann-Type Hydrodynamical Systems and Dubrovin’s Integrability Classification of Perturbed KdV-Type Equations

Dubrovin’s work on the classification of perturbed KdV-type equations is reanalyzed in detail via the gradient-holonomic integrability scheme, which was devised and developed jointly with Maxim Pavlov and collaborators some time ago. As a consequence of the reanalysis, one can show that Dubrovin’s criterion inherits important parts of the gradient-holonomic scheme properties, especially the necessary condition of suitably ordered reduction expansions with certain types of polynomial coefficients. In addition, we also analyze a special case of a new infinite hierarchy of Riemann-type hydrodynamical systems using a gradient-holonomic approach that was suggested jointly with M. Pavlov and collaborators. An infinite hierarchy of conservation laws, bi-Hamiltonian structure and the corresponding Lax-type representation are constructed for these systems

Studies of a Target System for a 4-MW, 24-GeV Proton Beam

Local Contact: H. Haseroth We propose to perform a proof-of-principle test of a target station suitable for a Neutrino Factory or Muon Collider source using a 24-GeV proton beam incident on a target consisting of a free mercury jet that is inside a 15-T capture solenoid magnet. This test could be performed in the TT2A tunnel of the NTOF proton line (upstream of the spallation target). The tests would require only ≈ 100 fast-extracted pulses of full PS intensity, delivered in a pulse-on-demand mode of operation over about 10 shifts. The main piece of apparatus is the LN2-precooled, 15-T copper magnet of total volume slightly over 1 m 3 with a 15-cm-diameter warm bore. The principle diagnostic is a high-speed optical camera. The mercury jet is part of a closed mercury loop that includes an insert into the bore of the magnet