Blowup of certain analytic solutions of the Hall magnetohydrodynamic equations

Núñez, Manuel; Álvarez, Jorge; Rojo, Jesús
June 2008
Physics of Plasmas;Jun2008, Vol. 15 Issue 6, p062104
Academic Journal
A recent analytic solution of the Hall magnetohydrodynamics equations is analyzed. It is shown that its evolution in time depends upon a certain set of inequalities upon the initial values of the velocity and the magnetic field. For most of the cases, both magnitudes will blow up in a finite time. This shows that for keeping the original structure of the solution, energy must be introduced into the system until eventually it cannot hold any longer.


Related Articles

  • Helical shell models for MHD. Lessinnes, T.; Plunian, F.; Carati, D. // Theoretical & Computational Fluid Dynamics;Nov2009, Vol. 23 Issue 6, p439 

    A shell model for magnetohydrodynamics (MHD) is derived directly from the dynamical system driving the evolution of three helical modes interacting in a triad. The use of helical modes implies that two shell variables are required for the velocity as well as for the magnetic field. The advantage...

  • On the solutions of three-dimensional non-null magnetic reconnection. Al-Salti, Nasser; Hornig, Gunnar // Physics of Plasmas;Aug2009, Vol. 16 Issue 8, p082101 

    Here we present solutions of a stationary magnetohydrodynamic (MHD) model for three-dimensional (3D) magnetic reconnection in the absence of a null point. The solutions are found in the form of an expansion scheme with a localized nonideal region. A wide variety of both analytical and numerical...

  • Three-dimensional magnetohydrodynamical simulation of expanding magnetic flux ropes. Arnold, L.; Dreher, J.; Grauer, R.; Soltwisch, H.; Stein, H. // Physics of Plasmas;Apr2008, Vol. 15 Issue 4, p042106 

    Three-dimensional, time-dependent numerical simulations of the dynamics of magnetic flux ropes are presented. The simulations are targeted towards an experiment previously conducted at California Institute of Technology [P. M. Bellan and J. F. Hansen, Phys. Plasmas 5, 1991 (1998)] which aimed at...

  • Steady-State MHD Flows in Nozzles with an External Longitudinal Magnetic Field. Brushlinskii, K. V.; Zhdanova, N. S. // Fluid Dynamics;May/Jun2004, Vol. 39 Issue 3, p474 

    Steady-state MHD flows in channels of the nozzle type in the presence of an external longitudinal magnetic field can be divided into two significantly different classes. Subcritical flows, in which the Alfvén velocity calculated from the longitudinal magnetic field is less than the plasma...

  • Control of resistive wall modes in a cylindrical tokamak with radial and poloidal magnetic field sensors. Finn, John M. // Physics of Plasmas;Sep2004, Vol. 11 Issue 9, p4361 

    A simple cylindrical linear magnetohydrodynamic model is introduced to explain recent numerical results relating to stabilization of resistive wall modes by feedback. These older results indicate that feedback with sensors detecting the perturbed poloidal magnetic field is more effective than...

  • Flow of a two-fluid plasma carrying a pulsed current in a steady-state magnetic field. Ostrovskaya, G. V. // Technical Physics;Nov2008, Vol. 53 Issue 11, p1391 

    The problem of the motion of plasma carrying a pulsed current in a steady-state magnetic field is solved in terms of two-fluid magnetohydrodynamics. The initial directions of the force and current vectors are determined, and the relations that determine their time evolution are obtained. The...

  • Magnetic reconnection with pressure gradient effect in compressible electron magnetohydrodynamics. Huishan Cai; Ding Li // Physics of Plasmas;Apr2008, Vol. 15 Issue 4, p042101 

    The general dispersion relation of the tearing mode with charge separation and pressure gradient effects in the whistler frequency is analytically derived in the framework of electron magnetohydrodynamics (EMHD). It is shown that pressure gradient effect enhances the growth rate, and makes the...

  • Magnetohydrodynamic analysis of the interaction of magnetized plasma flow with a perfect-conducting object. Nishida, Hiroyuki; Abe, Takashi // Physics of Plasmas;May2010, Vol. 17 Issue 5, p052901 

    In this study, a supersonic and super-Alfvénic magnetized plasma flow past a perfect-conducting cylinder was simulated based on single-fluid ideal magnetohydrodynamics to clarify the piling-up process of the magnetic field frozen in the plasma flow. Therefore, the magnetic field is assumed to...

  • Anisotropic form of third-order moments and relationship to the cascade rate in axisymmetric magnetohydrodynamic turbulence. Podesta, J. J.; Forman, M. A.; Smith, C. W. // Physics of Plasmas;Sep2007, Vol. 14 Issue 9, p092305 

    Laws governing the behavior of statistical third-order moments in the inertial range are among the few rigorous results in the theory of statistically homogeneous incompressible magnetohydrodynamic turbulence. These fundamental laws apply to both isotropic and anisotropic turbulence. Assuming...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics