Blast waves propagation in magnetogasdynamics: power series method

2020 ◽  
Vol 75 (12) ◽  
pp. 1039-1050
Author(s):  
Munesh Devi ◽  
Rajan Arora ◽  
Deepika Singh
Keyword(s):  
Magnetic Field ◽  
Shock Waves ◽  
Power Series ◽  
Shock Front ◽  
Closed Form ◽  
Analytic Solutions ◽  
Blast Waves ◽  
Series Method ◽  
Power Series Method ◽  
The Magnetic Field

AbstractBlast waves are produced when there is a sudden deposition of a substantial amount of energy into a confined region. It is an area of pressure moving supersonically outward from the source of the explosion. Immediately after the blast, the fore-end of the blast wave is headed by the shock waves, propagating in the outward direction. As the considered problem is highly nonlinear, to find out its solution is a tough task. However, few techniques are available in literature that may give us an approximate analytic solution. Here, the blast wave problem in magnetogasdynamics involving cylindrical shock waves of moderate strength is considered, and approximate analytic solutions with the help of the power series method (or Sakurai’s approach [1]) are found. The magnetic field is supposed to be directed orthogonally to the motion of the gas particles in an ideal medium with infinite electrical conductivity. The density is assumed to be uniform in the undisturbed medium. Using power series method, we obtain approximate analytic solutions in the form of a power series in ${\left({a}_{0}/U\right)}^{2}$, where a0 and U are the velocities of sound in an undisturbed medium and shock front, respectively. We construct solutions for the first-order approximation in closed form. Numerical computations have been performed to determine the flow-field in an ideal magnetogasdynamics. The numerical results obtained in the absence of magnetic field recover the existing results in the literature. Also, these results are found to be in good agreement with those obtained by the Runge–Kutta method of fourth-order. Further, the flow variables are illustrated through figures behind the shock front under the effect of the magnetic field. The interesting fact about the present work is that the solutions to the problem are obtained in the closed form.

scholarly journals Relativistic Particle Acceleration in Plerions

1994 ◽  
Vol 142 ◽  
pp. 797-806
Author(s):  
Jonathan Arons ◽  
Marco Tavani
Keyword(s):  
Magnetic Field ◽  
Particle Acceleration ◽  
Shock Waves ◽  
Shock Front ◽  
Heavy Ions ◽  
Surface Brightness ◽  
Crab Nebula ◽  
Electrons And Positrons ◽  
The Crab Nebula ◽  
The Magnetic Field

AbstractWe discuss recent research on the structure and particle acceleration properties of relativistic shock waves in which the magnetic field is transverse to the flow direction in the upstream medium, and whose composition is either pure electrons and positrons or primarily electrons and positrons with an admixture of heavy ions. Particle-in-cell simulation techniques as well as analytic theory have been used to show that such shocks in pure pair plasmas are fully thermalized—the downstream particle spectra are relativistic Maxwellians at the temperature expected from the jump conditions. On the other hand, shocks containing heavy ions which are a minority constituent by number but which carry most of the energy density in the upstream medium do put ~20% of the flow energy into a nonthermal population of pairs downstream, whose distribution in energy space is N(E) ∝ E−2, where N(E)dE is the number of particles with energy between E and E + dE.The mechanism of thermalization and particle acceleration is found to be synchrotron maser activity in the shock front, stimulated by the quasi-coherent gyration of the whole particle population as the plasma flowing into the shock reflects from the magnetic field in the shock front. The synchrotron maser modes radiated by the heavy ions are absorbed by the pairs at their (relativistic) cyclotron frequencies, allowing the maximum energy achievable by the pairs to be γ±m±c2 = mic2γ1/Zi, where γ1 is the Lorentz factor of the upstream flow and Zi, is the atomic number of the ions. The shock’s spatial structure is shown to contain a series of “overshoots” in the magnetic field, regions where the gyrating heavy ions compress the magnetic field to levels in excess of the eventual downstream value.This shock model is applied to an interpretation of the structure of the inner regions of the Crab Nebula, in particular to the “wisps,” surface brightness enhancements near the pulsar. We argue that these surface brightness enhancements are the regions of magnetic overshoot, which appear brighter because the small Larmor radius pairs are compressed and radiate more efficiently in the regions of more intense magnetic field. This interpretation suggests that the structure of the shock terminating the pulsar’s wind in the Crab Nebula is spatially resolved, and allows one to measure γ1, and a number of other properties of the pulsar’s wind. We also discuss applications of the shock theory to the termination shocks of the winds from rotation-powered pulsars embedded in compact binaries. We show that this model adequately accounts for (and indeed predicted) the recently discovered X-ray flux from PSR 1957+20, and we discuss several other applications to other examples of these systems.Subject headings: acceleration of particles — ISM: individual (Crab Nebula) — relativity — shock waves

scholarly journals Propagation of Blast waves in a Non-Ideal Magnetogasdynamics

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 458 ◽  
Author(s):  
Astha Chauhan ◽  
Rajan Arora ◽  
Mohd Siddiqui
Keyword(s):  
Magnetic Field ◽  
Gas Dynamics ◽  
Approximate Analytical Solution ◽  
Ideal Gas ◽  
Specific Conductance ◽  
Blast Waves ◽  
Highly Nonlinear ◽  
Vast Literature ◽  
Flow Variables ◽  
The Magnetic Field

Blast waves are generated when an area grows abruptly with a supersonic speed, as in explosions. This problem is quite interesting, as a large amount of energy is released in the process. In contrast to the situation of imploding shocks in ideal gas, where a vast literature is available on the effect of magnetic fields, very little is known about blast waves propagating in a magnetic field. As this problem is highly nonlinear, there are very few techniques that may provide even an approximate analytical solution. We have considered a problem on planar and radially symmetric blast waves to find an approximate solution analytically using Sakurai’s technique. A magnetic field has been taken in the transverse direction. Gas particles are supposed to be propagating orthogonally to the magnetic field in a non-deal medium. We have further assumed that specific conductance of the medium is infinite. Using Sakurai’s approach, we have constructed the solution in a power series of ( C / U ) 2 , where C is the velocity of sound in an ideal gas and U is the velocity of shock front. A comparison of obtained results in the absence of a magnetic field within the published work of Sakurai has been made to generate the confidence in our results. Our results match well with the results reported by Sakurai for gas dynamics. The flow variables are computed behind the leading shock and are shown graphically. It is very interesting that the solution of the problem is obtained in closed form.

The Scope of the Power Series Method

2013 ◽  
Vol 86 (1) ◽  
pp. 56-62
Author(s):  
Richard Beals
Keyword(s):  
Power Series ◽  
Series Method ◽  
Power Series Method
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