In this paper, we use power series method to study the propagation of cylindrical shock waves produced on account of a strong explosion in a non‐ideal gas under the influence of azimuthal magnetic field. Here, the density is assumed to be uniform and magnetic pressure is assumed to vary according to power law with distance from the symmetry axis in the undisturbed medium. Using power series method, we obtain approximate analytic solutions in the form of a power series in (a₀/V )², where a₀ and V are the velocities of sound in the undisturbed medium and shock front, respectively. The first‐order and second‐order approximate solutions to the considered problem are discussed with the help of the said method. We construct solutions for the first‐order approximation in closed form. Distributions of the flow variables such as fluid velocity, density, pressure, and magnetic pressure for the first‐order approximation are analyzed graphically behind the shock front. Also, the effects of non‐ideal parameter and shock Cowling number on the flow variables are discussed. It is observed that an increase in the value of non‐ideal parameter causes fluid velocity to increase, and density, pressure, and magnetic pressure to decrease. Increase in the shock Cowling number causes decrease in density and pressure, whereas increase in fluid velocity and magnetic pressure behind the shock. Also, it is found that numerical results obtained in the absence of magnetic field recover the existing results in the literature. Further, these results are found to be in good agreement with those obtained by the Runge‐Kutta method of fourth‐order.

中文翻译：

---

冲击波在非理想气体中在磁场作用下的传播

在本文中，我们使用幂级数方法研究了在方位磁场的影响下，非理想气体中发生强烈爆炸而产生的圆柱状冲击波的传播。在此，假定密度是均匀的，并且假定磁压力根据幂定律随未受扰介质中距对称轴的距离而变化。使用幂级数的方法，我们得到在幂级数的形式近似解析解（一个₀ / V）²，其中一个₀和V分别是未受扰动的介质和冲击前的声速。借助所述方法讨论了所考虑问题的一阶和二阶近似解。我们以封闭形式构造一阶近似的解。一阶近似值的流量变量（如流体速度，密度，压力和电磁压力）的分布在冲击波前的后面以图形方式分析。此外，还讨论了非理想参数和激振整流罩数对流量变量的影响。可以看到，非理想参数值的增加会导致流体速度增加，而密度，压力和磁压降低。激振整流罩数的增加导致密度和压力的降低，反之，则冲击后的流体速度和电磁压力会增加。而且，发现在没有磁场的情况下获得的数值结果恢复了文献中的现有结果。此外，发现这些结果与通过四阶Runge-Kutta方法获得的结果非常一致。