**1. Introduction**

The study of propagation of strong shock waves has always been given undivided attention by various research groups in the field of science. In particular, it is useful in nuclear science, plasma physics, geophysics, astrophysics, explosions, etc. Shocks are ubiquitary and quite useful in the generation of energy. Radially converging shocks are used to create a hot spot at the center in Inertial Confinement Fusion (ICF). The heat generated in the process is used to activate nuclear fission. After World War II, it becomes extremely important to understand explosion dynamics. Motivated by this, Sedov [1] first coined the idea of a similarity solution for the point explosion problem in an ideal medium. Soon, this solution became famous as the "Sedov Similarity Solution" among researchers due to its importance in blast wave theory. Taylor [2] found the analytical first approximate solution for the problem. These results of Sedov and Taylor showed a way to estimate the effects of nuclear or supernova explosions. Later, Sakurai [3,4] used this first approximate solution to find self-similar solutions to the problem. Murata [5] and Donato [6] obtained the exact solutions to blast wave problems in gas dynamics. Murata [5] assumed that change in density ahead of shock front is governed

by the exponent of distance from the point (or axis) of ignition. The density ahead of the leading shock was assumed to vary as the power of the radial distance from the center of explosion in his study. Book [7] used Sedov formulas to find similarity solution of the point explosion problem. Lalicata and Torrisi [8] used the similarity method for reacting flow. Propagation of shock waves generated by sudden explosions within the presence of a magnetic field is very important because this phenomenon is well marked in the disassembled nature of the absorption of energy. Anisimov and Spiner [9] and Lerche [10] presented the theory of blast waves in magnetogasdynamics. A first comprehensive study on the effect of magnetic field on the exploding shocks was presented by Lerche [11] in 1979. There is an abrupt change in the entropy across an exploding shock and it releases a very high energy in the process. It is well known that after the explosion, the front of the blast wave is circumscribed by the surfaces of the shocks and propagates with decreasing velocity. Furthermore, a very high energy is released in the process. It raises the temperature of the surrounding. Therefore, the assumption of an ideal medium is not valid anymore, and one must consider the effect of non-deal medium on the blast waves. The gas particles are ionized due to the presence of high temperature at the center. These ionized gas particles generate the magnetic field. Therefore, the inclusion of a magnetic field on the study of blast waves is essential for capturing the physics of the process well. It has many applications in oceanography, astrophysics, aerodynamics, and atmospheric sciences.

Many research groups have worked afterwards on the topic to better understand the dynamics of shock waves in a magnetic field. Among the recent research on the topic, we wish to mention the work of Arora et al. [12], Siddiqui et al. [13], Singh et al. [14,15], and Pandey et al. [16]. Menon and Sharma [17] studied the flattening and steepening of the characteristics wave fronts in an ideal medium with magnetic field. Arora et al. [18] found a similar solution to the propagation of shocks in a non-ideal medium. Relaxation effects were also included in the study. Later, Siddiqui et al. [19] used asymptotic expansion of flow variables to find the solution to nonlinear waves far from the origin. The relaxation of gas particles has been taken into account in the study. Evolutionary behavior of weak shocks in real gas is presented by Arora and Siddiqui [20]. Despite there being vast literature available on imploding shocks in real gas, the behavior of shock front after ignition is still an open problem. In the present work, we have analyzed the flow variables after a blast in ignition by using the Sakurai analytical approach. The medium is considered to be real gases. Effects of a magnetic field have also been taken into account.

This paper is summarized as follows: Section 1 contains a brief introduction to the topic and historical background of earlier studies. Section 2 presents the fundamental equations governing the conservation laws. Rankine–Hugoniot (RH) jump conditions are also presented in this section. In Section 3, we introduce the new independent variables and transform the fundamental equations in the form of non-dimensional functions using the similarity analysis. In Section 4, power series solutions in terms of (*C*/*U*)<sup>2</sup> have been presented for the problem. In Section 5, the first approximation solutions are obtained which correspond to Taylor's series solution. In Section 6, a brief conclusion is given about the whole study of this paper. Based on the study, we have concluded that the density and magnetic pressure of the particle decreases behind the leading shock. Charged particles are transported away by the magnetic field, and this gives an increase in the velocity of blast wind.
