scholarly journals Mathematical Theory of One-dimensional Isothermal Blast Waves in a Magnetic Field

1979 ◽  
Vol 32 (5) ◽  
pp. 491 ◽  
Author(s):  
I Lerche
Keyword(s):  
Magnetic Field ◽  
Fluid Flow ◽  
Critical Point ◽  
Blast Wave ◽  
Supernova Remnants ◽  
Magnetic Energy ◽  
Flow Speed ◽  
Blast Waves ◽  
One Dimensional ◽  
Self Similar

An investigation is made of the self-similar flow behind a one-dimensional blast wave from a planar explosion (situated on z = 0) in a medium whose density and magnetic field vary with distance as Z-W ahead of the blast front, with the assumption that the flow is isothermal. It is found that; if OJ OJ > 0 the governing equation possesses a set of movable critical points. For a weak, but nonzero, magnetic field it is shown that the value of the smallest critical point does not lie in the physical domain z > O. The post-shock fluid flow then cannot intersect the critical point, and is smoothly continuous. It is shown that to be physically acceptable, the fluid flow speed must pass through the origin. It is also shown that OJ must be less than t for the magnetic energy swept up by the blast wave to remain finite. The overall conclusion from the investigation is that the behaviour of isothermal blast waves in the presence of an ambient magnetic field differs substantially from the behaviour calculated for no magnetic field. These results point to the inadequacy of previous attempts to apply the theory of self-similar flows to evolving supernova remnants without making any allowance for the dynamical influence of magnetic field pressure.

scholarly journals Mathematical Theory of Cylindrical Isothermal Blast Waves in a Magnetic Field

1981 ◽  
Vol 34 (3) ◽  
pp. 279 ◽  
Author(s):  
I Lerche
Keyword(s):  
Magnetic Field ◽  
Supernova Remnants ◽  
Magnetic Pressure ◽  
Blast Waves ◽  
Physical Domain ◽  
Fluid Flow Velocity ◽  
Magnetic Tension ◽  
Self Similar ◽  
The Magnetic Field ◽  
Similar Flows

An investigation is made of the self-similar flow behind a cylindrical blast wave from a line explosion (situated on r = 0, using conventional cylindrical coordinates r, 4>, z) in a medium whose density and magnetic field both vary as r -w ahead of the blast front, with the assumption that the flow is isothermal. The magnetic field can have components in both the azimuthal B(jJ and longitudinal B, directions. It is found that: (i) For B(jJ =f:. 0 =f:. B, a continuous single-valued solution with a velocity field representing outflow of material away from the line of explosion does not exist for OJ OJ > 0 the governing equation possesses a set of movable critical points. In this case it is shown that the fluid flow velocity is bracketed between two curves and that the asymptotes of the velocity curve on the shock are intersected by, or are tangent to, the two curves. Thus a solution always exists in the physical domain r ~ o. The overall conclusion from the investigation is that the behaviour of isothermal blast waves in the presence of an ambient magnetic field differs substantially from the behaviour calculated for no magnetic field. These results have an impact upon previous applications of the theory of self-similar flows to evolving supernova remnants without allowance for the dynamical influence of magnetic pressure and magnetic tension.

scholarly journals Magnetic relaxation and the Taylor conjecture

2015 ◽  
Vol 81 (6) ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Magnetic Field ◽  
Initial Phase ◽  
Magnetic Relaxation ◽  
Magnetic Energy ◽  
Magnetic Pressure ◽  
Second Phase ◽  
One Dimensional ◽  
Induction Equation ◽  
Two Phases ◽  
The Magnetic Field

A one-dimensional model of magnetic relaxation in a pressureless low-resistivity plasma is considered. The initial two-component magnetic field $\boldsymbol{b}(\boldsymbol{x},t)$ is strongly helical, with non-uniform helicity density. The magnetic pressure gradient drives a velocity field that is dissipated by viscosity. Relaxation occurs in two phases. The first is a rapid initial phase in which the magnetic energy drops sharply and the magnetic pressure becomes approximately uniform; the helicity density is redistributed during this phase but remains non-uniform, and although the total helicity remains relatively constant, a Taylor state is not established. The second phase is one of slow diffusion, in which the velocity is weak, though still driven by persistent weak non-uniformity of magnetic pressure; during this phase, magnetic energy and helicity decay slowly and at constant ratio through the combined effects of pressure equalisation and finite resistivity. The density field, initially uniform, develops rapidly (in association with the magnetic field) during the initial phase, and continues to evolve, developing sharp maxima, throughout the diffusive stage. Finally it is proved that, if the resistivity is zero, the spatial mean $\langle (\boldsymbol{b}\boldsymbol{\cdot }\boldsymbol{{\rm\nabla}}\times \boldsymbol{b})/b^{2}\rangle$ is an invariant of the governing one-dimensional induction equation.

Formation of the SN1987A Ring due to magnetic pressure

1997 ◽  
Vol 180 ◽  
pp. 473-473
Author(s):  
M. Mori ◽  
H. Washimi ◽  
S. Shibata
Keyword(s):  
Magnetic Field ◽  
Radio Emission ◽  
Blast Wave ◽  
Magnetic Energy ◽  
Minimum Energy ◽  
Magnetic Pressure ◽  
Interaction Region ◽  
Stellar Winds ◽  
Fast Wind ◽  
The Magnetic Field

Several weeks after the explosion of supernova (SN) SN1987A, the UV flash of the SN illuminated a ring-like structure in the circumstellar material at about 0.65 ly from the SN. The interaction between the stellar winds from the SN progenitor is considered to be the candidate for the formation of the circumstellar structure. In the case that the stellar winds are spherically symmetric, the interaction should result in a shell-like structure. However, Washimi, Shibata & Mori (1996) show that the magnetic field in the winds causes an anisotropy which leads to the formation of a ring-like structure. When the fast wind of the blue supergiant phase of the progenitor sweeps up the surrounding slow wind of the red-supergiant phase, the magnetic field as well as the wind material are piled up in the interaction region. Since the magnetic energy increases in proportion to the square of the amplitude, the magnetic field exhibits its effect prominently at the interaction region; due to the magnetic pressure force the material at lower latitudes is compressed into a ring-like structure. It is suggested that this magnetic process can also explain the newly observed pair of rings of the SN1987A nebula. We note that the idea of a magnetic field effect is consistent with the radio observation of a supernova remnant, detected by Staveley-Smith et al. (1992) at about 1200 days after the explosion. This radio emission is explained by the collision of the supernova blast wave with the shocked blue wind. This position corresponds to the averaged expansion speed of the supernova ejecta ∼ 0.08 ly which is consistent with the estimation by Shigeyama and Nomoto (1990). The estimated magnetic-energy density by the minimum-energy argument is ∼ 4 × 10–8f–4/7N m–2, where f is the fractional volume of the radiating acceleration region, suggesting a magnetic field of a few milli-Gauss or more (Chevalier 1992). This field intensity is consistent with an intensity of ≈ 2 · 10–4 Gauss obtained between the reverse shock and the contact surface shown, if one takes into account a further enhancement of the field due to the sweeping-up process by the supernova blast wave. When the SN ejector collides with the ring at the end of this century or at the beginning of the next one, we can also expect more intense radio emission at rather middle and high latitudes where the magnetic intensity is greater, rather than at the equator where the ring-like structure is located.

Parametric investigation of self-similar decay laws in MHD turbulent flows

1999 ◽  
Vol 61 (3) ◽  
pp. 507-541 ◽  
Author(s):  
S. GALTIER ◽  
E. ZIENICKE ◽  
H. POLITANO ◽  
A. POUQUET
Keyword(s):  
Magnetic Field ◽  
Turbulent Flows ◽  
Magnetic Energy ◽  
Nauk Sssr ◽  
Mhd Turbulence ◽  
Integral Scale ◽  
Self Similar ◽  
Grid Points ◽  
The One ◽  
The Magnetic Field

An investigation of the decay laws of energy and of higher moments of the Elsässer fields z±=v±b in the self-similar regime of magnetohydrodynamic (MHD) turbulence is presented, using phenomenological models as well as two-dimensional numerical simulations with periodic boundary conditions and up to 20482 grid points. The results are compared with the generalization of the parameter-free model derived by Galtier et al. [Phys. Rev. Lett.79, 2807 (1997)], which takes into account the slowing down of the dynamics due to the propagation of Alfvén waves. The new model developed here allows for a study in terms of one parameter governing the wavenumber dependence of the energy spectrum at scales of the order of (and larger than) the integral scale of the flow. The one-dimensional compressible case is also dealt with in two of its simplest configurations. Computations are performed for a standard Laplacian diffusion as well as with a hyperdiffusive algorithm. The results are sensitive to the amount of correlation between the velocity and the magnetic field, but rather insensitive to all other parameters such as the initial ratio of kinetic to magnetic energy or the presence or absence of a uniform component of the magnetic field. In all cases, the decay is significantly slower than for neutral fluids in a way that favours for MHD flows the phenomenology of Iroshnikov [Soviet Astron.7, 566 (1963)] and Kraichnan [Phys. Fluids8, 1385 (1965)] as opposed to that of Kolmogorov [Dokl. Akad. Nauk. SSSR31, 538 (1941)]. The temporal evolution of q-moments of the generalized vorticities 〈[mid ]ω±[mid ]q〉 =〈[mid ]ω±j[mid ]q〉 up to order q=10 is also given, and is compared with the prediction of the model. Less agreement obtains as q grows – a fact probably due to intermittency and the development of coherent structures in the form of eddies, and of vorticity and current sheets.

Self-similar resistive decay of a current sheet in a compressible plasma

1979 ◽  
Vol 22 (2) ◽  
pp. 289-302 ◽  
Author(s):  
Keith B. Kirkland ◽  
Bengt U. ö. Sonnerup
Keyword(s):  
Magnetic Field ◽  
Current Sheet ◽  
Interplanetary Space ◽  
Magnetic Energy ◽  
Flow Direction ◽  
Inertia Effects ◽  
Compressible Plasma ◽  
Earth Magnetic Field ◽  
Self Similar ◽  
A Current

Self-similar solutions of the magnetogasynamic equations are derived which describe the resistive decay of a plane current sheet in a compressible plasma. Such current sheets are thought to provide the magnetic energy storage in solar flares. They also occur at the boundaries between regions containing different magnetic-field directions in interplanetary space, and at the interface between the solar wing and the earth' magnetic field. It is shown that the resistive decay of a current sheet in a compressible plasma must involve plasma motion. The convective effects associated with this motion are incorporated in the analysis; the inertia effects are not. The electrical and thermal conductivities are taken to be constant, but the analysis may easily be generalized to include realistic temperature and magnetic field dependences of these quantities. Radiative and viscous terms are not included. The ordinary differential equations resulting from the similarity hypothesis are solved numerically, yielding curves of the plasma density, temperature, and velocity, as well as of the magnetic and induced electric fields, as functions of the similarity variable. The non-dimensional groups of importance are: y, the ratio of specific heats at constant pressure and constant volume; Kx, the ratio of thermal to resistive diffusivity; β∞, the ratio of plasma pressure to magnetic pressure at large distances from the current sheet. The first of these ratios is kept constant and equal to 5/3, corresponding to a monoatomic gas. The behaviour of the solution when the other two ratios are varied is investigated. The plasma velocity at large distances from the current sheet does not vanish in these solutions. It is always directed toward the sheet. However, when the diffusivity ratio K∞ is small, plasma flow away from the centre of the sheet also occurs in two narrow regions, one on each side of the centre. As a result of the reversals in the flow direction, the density then displays a relative minimum at the centre of the sheet with two outward travelling maxima adjacent to it. The plasma temperature at the centre of the sheet becomes very large for small K∞ and β∞ The expansion of the sheet becomes explosive and inertia effects can no longer be neglected. The physical meaning of these results is discussed and directions for further research are outlined.

A TWO-DIMENSIONAL BLAST WAVE IN RELATIVISTIC MAGNETOHYDRODYNAMICS

1994 ◽  
Vol 04 (01) ◽  
pp. 57-69 ◽  
Author(s):  
MAURICE H.P.M. VAN PUTTEN
Keyword(s):  
Magnetic Field ◽  
Shock Front ◽  
Rarefaction Wave ◽  
Blast Wave ◽  
High Pressures ◽  
Early Time ◽  
Blast Waves ◽  
Mhd Waves ◽  
The Core ◽  
Relativistic Magnetohydrodynamics

The blast wave produced by a star-like object in a magnetic field is studied numerically in the approximation of ideal, fully relativistic magnetohydrodynamics (MHD). Waves of this type are observed to evolve along three episodes. At early time an outgoing shock front and an ingoing rarefaction wave is established. The ingoing rarefaction wave steepens, and gives rise to dust formation in the core. The steep rarefaction wave front becomes an ingoing shock. An annular region of high magnetic pressure about the equatorial plane deforms this shock front radially, whereby it becomes prolate along the axis of symmetry. The core is subsequently refilled as this shock front converges. Subsequent collapse in the center gives rise to high pressures, familiar from the well-known converging shock problem in nonrelativistic hydrodynamics, and high densities unique to the relativistic description. The results are compared with spherical blast waves in relativistic hydrodynamics, where a similar three episodes can be found and where collapse of the interior shock at the center constitutes a fluid singularity. It remains an open question whether such fluid singularity persists in the full MHD problem. The computations employ the covariant equations of constraint-free MHD in divergence form introduced in earlier work. The magnetic field is kept divergence free to within machine round-off error.

scholarly journals Modelling decadal secular variation with only magnetic diffusion

2019 ◽  
Vol 219 (Supplement_1) ◽  
pp. S58-S82 ◽  
Author(s):  
Maurits C Metman ◽  
Philip W Livermore ◽  
Jonathan E Mound ◽  
Ciarán D Beggan
Keyword(s):  
Magnetic Field ◽  
Fluid Flow ◽  
Standard Deviation ◽  
Secular Variation ◽  
Magnetic Energy ◽  
Time Windows ◽  
Liquid Core ◽  
Global Scale ◽  
Magnetic Diffusion ◽  
Magnetic Structures

SUMMARY Secular variation (SV) of Earth’s internal magnetic field is the sum of two contributions, one resulting from core fluid flow and the other from magnetic diffusion. Based on the millenial diffusive timescale of global-scale structures, magnetic diffusion is widely perceived to be too weak to significantly contribute to decadal SV, and indeed is entirely neglected in the commonly adopted end-member of frozen-flux. Such an argument however lacks consideration of radially fine-scaled magnetic structures in the outermost part of the liquid core, whose diffusive timescale is much shorter. Here we consider the opposite end-member model to frozen flux, that of purely diffusive evolution associated with the total absence of fluid flow. Our work is based on a variational formulation, where we seek an optimized full-sphere initial magnetic field structure whose diffusive evolution best fits, over various time windows, a time-dependent magnetic field model. We present models that are regularized based on their magnetic energy, and consider how well they can fit the COV-OBS.x1 ensemble mean using a global error bound based on the standard deviation of the ensemble. With these regularized models, over time periods of up to 30 yr, it is possible to fit COV-OBS.x1 within one standard deviation at all times. For time windows up to 102 yr we show that our models can fit COV-OBS.x1 when adopting a time-averaged global uncertainty. Our modelling is sensitive only to magnetic structures in approximately the top 10 per cent of the liquid core, and show an increased surface area of reversed flux at depth. The diffusive models recover fundamental characteristics of field evolution including the historical westward drift, the recent acceleration of the North Magnetic Pole and reversed-flux emergence. Based on a global time-averaged residual, our diffusive models fit the evolution of the geomagnetic field comparably, and sometimes better than, frozen-flux models within short time windows.

scholarly journals Impact of dust in the decay of blast waves produced by a nuclear explosion

2020 ◽  
Vol 476 (2238) ◽  
pp. 20200105 ◽  
Author(s):  
Meera Chadha ◽  
J. Jena
Keyword(s):  
Radiation Effects ◽  
Nuclear Explosion ◽  
Blast Waves ◽  
Dust Particles ◽  
One Dimensional ◽  
Self Similar ◽  
The One ◽  
Similar Solutions ◽  
The Impact ◽  
Relaxing Gas

In this paper, we have studied the impact created by the introduction of up to 5% dust particles in enhancing the decay of blast waves produced by a nuclear explosion. A mathematical model is designed and modified using appropriate assumptions, the most important being treating a nuclear explosion as a point source of energy. A system of partial differential equations describing the one-dimensional, adiabatic, unsteady flow of a relaxing gas with dust particles and radiation effects is considered. The symmetric nature of an explosion is captured using the Lie group invariance and self-similar solutions obtained for the gas undergoing strong shocks. The enhancements in decay caused by varying the quantity of dust are studied. The energy released and the damage radius are found to decrease with time with an increase in the dust parameters.

Sign in / Sign up

Export Citation Format

Share Document