arXiv subjects

Vladimir S. Semenov

Publications and source records attributed to Vladimir S. Semenov.

4 recordsLinked to original sources

arXiv2001

Euler potentials for the MHD Kamchatnov-Hopf soliton solution

In the MHD description of plasma phenomena the concept of magnetic helicity turns out to be very useful. We present here an example of introducing Euler potentials into a topological MHD soliton which has non-trivial helicity. The MHD soliton solution (Kamchatnov, 1982) is based on the Hopf invariant of the mapping of a 3D sphere into a 2D sphere; it can have arbitrary helicity depending on control parameters. It is shown how to define Euler potentials globally. The singular curve of the Euler potential plays the key role in computing helicity. With the introduction of Euler potentials, the helicity can be calculated as an integral over the surface bounded by this singular curve. A special programme for visualization is worked out. Helicity coordinates are introduced which can be useful for numerical simulations where helicity control is needed.

physics.plasm-ph↗

arXiv2001

Rate of steady-state reconnection in an incompressible plasma

The reconnection rate is obtained for the simplest case of 2D symmetric reconnection in an incompressible plasma. In the short note (Erkaev et al., Phys. Rev. Lett.,84, 1455 (2000)), the reconnection rate is found by matching the outer Petschek solution and the inner diffusion region solution. Here the details of the numerical simulation of the diffusion region are presented and the asymptotic procedure which is used for deriving the reconnection rate is described. The reconnection rate is obtained as a decreasing function of the diffusion region length. For a sufficiently large diffusion region scale, the reconnection rate becomes close to that obtained in the Sweet-Parker solution with the inverse square root dependence on the magnetic Reynolds number, determined for the global size of the current sheet. On the other hand, for a small diffusion region length scale, the reconnection rate turns out to be very similar to that obtained in the Petschek model with a logarithmic dependence on the magnetic Reynolds number. This means that the Petschek regime seems to be possible only in the case of a strongly localized conductivity corresponding to a small scale of the diffusion region.

physics.plasm-ph↗

arXiv2001

Energy confinement for a relativistic magnetic flux tube in the ergosphere of a Kerr black hole

In the MHD description of plasma phenomena the concept of magnetic field lines frozen into the plasma turns out to be very useful. We present here a method of introducing Lagrangian coordinates into relativistic MHD equations in general relativity, which enables a convenient mathematical formulation for the behaviour of flux tubes. With the introduction of these Lagrangian, so--called ``frozen--in'' coordinates, the relativistic MHD equations reduce to a set of nonlinear 1D string equations, and the plasma may therefore be regarded as a gas of nonlinear strings corresponding to flux tubes. Numerical simulation shows that if such a tube/string falls into a Kerr black hole, then the leading portion loses angular momentum and energy as the string brakes, and to compensate for this loss, momentum and energy is radiated to infinity to conserve energy and momentum for the tube. Inside the ergosphere the energy of the leading part turns out to be negative after some time, and the rest of the tube then gets energy from the hole. In our simulations most of the compensated positive energy is also localized inside the ergosphere because the inward speed of the plasma is approximately equal to the velocity of the MHD wave which transports energy outside. Therefore, an additional physical process has to be included which can remove energy from the ergophere. Magnetic reconnection seems fills this role releasing Maxwellian stresses and producing a relativistic jet.

astro-ph↗

arXiv1999

Reconnection rate for the steady-state Petschek model

Reconnection rate is found for the canonical simplest case of steady-state two-dimensional symmetric reconnection in an incompressible plasma by matching of outer Petschek solution and internal diffusion region solution. The reconnection rate obtained naturally incorporates both Sweet-Parker and Petschek regimes, the latter seems to be possible only for the case with strongly localized resistivity.

physics.plasm-ph↗