The natural Hamiltonian systems (systems with separable Hamiltonians) are considered. The variety of explicit three-stage symplectic schemes is described. A classification of the third-order accurate schemes is given. All fourth-order schemes are found (there are seven of them). It is proved that there are no fifth-order schemes. The schemes with improved properties, such as invertibility and optimality with respect to the phase error, are listed. Numerical results that demonstrate the properties of these schemes are presented, and their comparative analysis with respect to the accuracy–efficiency criterion is given. The disbalance of total energy is used as the accuracy criterion.

The paper discusses devices with a Disk Explosive Magnetic flux compression Generator (DEMG), which are similar to the ALT-1,2 experimental devices and are intended for testing the possibility of producing 1-3 TPa (10-30 Mbar) pressures and the possibility of measuring Hugoniots of different materials at such pressures. It is expected that two-layer, cylindrical liners, Al+Fe and/or Al+W, will be used, driven by 4-5 MG magnetic fields to ~ 20 km/s velocities. The paper presents and discusses simulated characteristics of these devices, in which currents, energies and powers delivered to the liner load can reach ~ 70 MA, ~ 40 MJ and ~ 20 TW and exceed those in the ALT-1,2 devices by a factor of ~2, ~ 4 and ~ 7, respectively.

Described here is the cluster dynamics method (CDM) which is one of the variants of particle method intended for simulation of the processes associated with large deformations and continuity violation of the material. The basic advantage of CDM is the possibility to choose the base cluster and allows the simulation of the processes in a wide range of spatial scales (from micrometer to tens of centimeters). Described here is the construction procedure for cluster interaction potentials corresponding to real equations of state of material by the example of typical metals. Numerical simulation of shock wave arrival at profiled plate surface and high-velocity target penetration was carried out using CDM. The computational results are compared with experimental data and other computational results. The results show that CDM can be used for full-scale simulation of large deformation and dynamic fracture of materials at impulse loading at characteristic rates of relative deformation of 10(3)-10(6) s(-1).

The plane one-dimensional problem of the diffusion of a megagauss field into a metal wall is solved taking into account heat conduction and radiation transfer. At the interface, the magnetic field is assumed to be constant, and in this sense, the problem is close to the self-similar diffusion problem with parameters dependent on the self-similar variable x/\(\sqrt t \). It is shown that if heat conduction and radiation transfer are taken into account, in megagauss fields (in the examined formulation for fields B > 1.6 MGs) there is no loss of conductivity of the material evaporated by the magnetic field because of the formation of a plasma layer at the interface with a temperature in the electronvolt range. However, the role of the plasma layer in the structure of the skin layer remains insignificant up to fields B ≈ 10 MGs.

A very high-current liner implosion experiment was conducted, using an explosive magnetic-compression generator (EMG) to deliver a peak current of 102 /spl plusmn/ 3 MA, to implode a 4.0-mm-thick aluminum liner. Analysis of experimental data showed that the inner surface of the liner had attained a velocity of between 6.8-8.4 km/s, consistent with detailed numerical calculations. Both calculations and data were consistent with a final liner state that was still substantially solid at target impact time and had a total kinetic energy of over 20 MJ.

3D gas-dynamic techniques is used to study turbulence in the gravitational field at a plane interface of two incompressible fluids with density difference n=3. The case is considered, where the acceleration changes its sign at a certain time. The computed data is compared to the computations by the phenomenological kappa-epsilon model and relevant available experimental data.

The problem on magnetohydrodynamic (MHD) flow of a solitary vortex across a magnetic field in a volume confined by rigid walls is solved numerically for large Reynolds numbers (including magnetic Reynolds numbers) and small Alfven-Mach numbers M A . In this case, the MHD problem is reduced to that of two-dimensional hydrodynamic turbulence. It is shown that sound is not generated by a turbulent medium for small values of M A ; consequently, this kinetic energy dissipation channel is closed in this case. Calculations show that, in contrast to 3D turbulence, kinetic energy dissipation for 2D turbulence occurs, as expected, over time periods on the order of L 2 / v ( L is the characteristic size of the system and v is the kinematic viscosity). In our calculations with numerical viscosity v ∼ v Δ x (Δ x is the unit cell size), this corresponds to time values on the order of ∼( L /Δ x )( L/v ). In the kinetic energy spectra for a turbulent flow in a bounded region in the inertial interval (lying between the energy-carrying and viscosity regions), the values of E ( k ) decrease with increasing wave numbers k at a higher rate than in proportion to k −3 . The volume distribution of vorticity becomes narrower with time (the characteristic values of curl v decrease) and is blurred; for large time periods, the distribution approximately retains its shape as well as asymmetry with respect to positive and negative values, which is associated with the asymmetry of the initial conditions.

To study dynamic strength of materials according to the initial liner perturbation growth in Rayleigh-Taylor instability development, three-layer liner systems driven by azimuthal magnetic field pressure have been suggested. This paper demonstrates that 0.4 m diameter disk EMG ensuring currents up to /spl sim/70 MA can be used for this purpose. In the three-layer liner systems, the liner shock-free loading to more than 1 Mbar pressures is therewith possible, with the pressures rising for times longer than 1/spl mu/s or longer than 0.3/spl mu/s in different systems. Here the shock loading of the liners under study is possible up to 3-4 Mbar pressures. Examples of 2D computations of the initial perturbation growth in the liners under study at shock-free and shock pressures up to 1 Mbar, strain rates up to 10/sup 8/sec/sup -1/, and strains up to 200 % are given.

The liner magnetic implosion experiments typically employ liners having the shape of a right circular cylinder. This paper considers the feasibility to use axially symmetric liners of a more complex (concave) shape. According to computations, the liner linear mass can decrease many-fold during concave liner implosion with an appropriate selection of the initial curvature (in plane r-z). These liners can be considered as variable (decreasing) mass liners. The above feature is interesting in that it allows a considerable increase in the rate of the liner convergence toward the axis as compared to a cylindrical liner of the same initial thickness and the same initial radius. As for the liner velocity at a fixed speed of operation of current source, its increase is desirable in a number of practical applications of liner high-velocity magnetic implosion (generation of megabar pressures, X-ray pulse, etc.).

MHD plasma flow transverse to a magnetic field in a bounded domain, initially set in a form of a sole vortex, is solved numerically. This problem is of interest for dynamic magnetized plasma systems such as the MAGO/MTF system. For plasma subsequent compression issues in those systems, it is important to know how long the hydrodynamic motion persists in them. This can affect convective plasma cooling and result in impurities entering into the plasma due to wall washing by this flow. A case of large Reynolds numbers (and large magnetic Reynolds) and small Alfven-Mach number MA is considered, i.e. it is assumed that the initial relaxation due to magnetosonic shock waves has already occurred. In this case the MM problem reduces to a problem of 2D hydrodynamic turbulence. Calculations showed that, as it should be for 2D turbulence and in contrast to the case of the 3D turbulence, kinetic energy dissipation proceeds very slowly at small M/sub A/, for times /spl sim/L/sup 2//v (L is the characteristic system size, v is kinematic viscosity). When MA is not small, the kinetic energy dissipation is caused by emission of magnetosonic waves and their subsequent nonlinear (shock-wave) damping.

Devices for producing 10-30 Mbar pressures in cylindrical targets of /spl sim/1 cm radius would be unique tools to study material properties under extreme conditions for a variety of research and application purposes. The paper presents results of theoretical and computational studies demonstrating the feasibility of this. The multi-module disk EMG themselves and especially those with an electrically exploded opening switch developed by VNIIEF are shown to be able to ensure the required acceleration of solid impacting liners, e.g., two-layered liners made of aluminum (on the outside) and molybdenum or tungsten (inside), up to 15-20 km/s velocities. The impacting liners optimal in their match to two considered energy sources have radii from /spl sim/7 cm to /spl sim/3 cm for targets of /spl sim/1 cm radius. Results of 2D magnetohydrodynamic liner compression computations are also presented, according to which the 2D effects of the liner interaction with end components may not lead to considerable violations of the desired 1D pattern of the liner impact on the target.

A joint US/Russian Advanced Liner Technology experiment ALT-1 was conducted to simulate the anticipated performance of the Atlas capacitor bank. A disk-explosive magnetic generator and foil opening switch were used to produce an electrical current waveform that reached a peak value of 32.5 MA and that imploded an aluminum liner to an inner surface velocity of 12 km/s.

Relatively soft X-rays (quantum energy about 0.3 keV) may be produced by acceleration of a plasma liner up to a velocity of /spl sim/300 km/s followed by stagnation in a pinch. This means that if the plasma acceleration distance is several cm, the time of plasma motion must be about 0.1 of a microsecond. This results in a difficulty, associated with the problem of plasma stability and the liner having very small thickness and very small tolerance on initial thickness and density. Besides, quick energy input into the load requires complicated fast opening switches, which need to be experimentally tested. For experiments with explosive magnetic generators (EMG) it is reasonable to develop simpler systems to reach mass velocities about 300 km/sec. The work by A.M Buyko et al. (1995) theoretically considers one of these systems, where a liner mass during its magnetic deceleration significantly decreases and the velocity increases, i.e., a variable mass liner (VML). The same work suggests two experimental designs to test a new concept: full-scale experiment, including X-rays generation and a model experiment, including testing of the initial stage of VML formation (v

The reaction of reinforced-concrete blast chambers to internal explosive loading has been investigated experimentally and numerically. The high resistance of the concrete within the reinforcing cage to shock-wave loading has been demonstrated, together with its substantial contribution to the load-carrying capacity of the chamber. It is noted that the disintegration of the chamber wall begins with the appearance of residual deformation of the inner shell. The loading of the chamber wall in the experiments is shown to be impulsive. A method of estimating the load-carrying capacity of chambers similar to those tested is proposed.