Magnetic field quantization is an important issue for degenerate environments such as neutron stars, radio pulsars and magnetars etc., due to the fact that these stars have a magnetic field higher than the quantum critical field strength of the order of $4.4\times 10^{13}~\text{G}$ , accordingly, the cyclotron energy may be equal to or even much more than the Fermi energy of degenerate particles. We shall formulate here the exotic physics of strongly magnetized neutron stars, known as pulsars, specifically focusing on the outcomes of the quantized magnetic pressure. In this scenario, while following the modified quantum hydrodynamic model, we shall investigate both linear and nonlinear fast magnetosonic waves in a strongly magnetized, weakly ionized degenerate plasma consisting of neutrons and an electron–ion plasma in the atmosphere of a pulsar. Here, linear analysis depicts that sufficiently long, fast magnetosonic waves may exist in a weakly dispersive pulsar having finite phase speed at cutoff. To investigate one-dimensional nonlinear fast magnetosonic waves, a neutron density expression as a function of both the electron magnetic and neutron degenerate pressures, is derived with the aid of Riemann’s wave solution. Consequently, a modified Korteweg–de Vries equation is derived, having a rarefractive solitary wave solution. It is found that the basic properties such as amplitude, width and phase speed of the fast magnetoacoustic waves are significantly altered by the electron magnetic and the neutron degenerate pressures. The results of this theoretical investigation may be useful for understanding the formation and features of the solitary structures in astrophysical compact objects such as pulsars, magnetars and white dwarfs etc.

中文翻译：

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脉冲星中的磁场量化

磁场量子化对于中子星、射电脉冲星和磁星等简并环境来说是一个重要问题，因为这些恒星的磁场高于量子临界场强的数量级。 $4.4\乘以 10^{13}~\text{G}$ 因此，回旋加速器的能量可能等于甚至远大于简并粒子的费米能量。我们将在这里制定被称为脉冲星的强磁化中子星的奇异物理学，特别关注量子化磁压的结果。在这种情况下，在遵循改进的量子流体动力学模型的同时，我们将研究脉冲星大气中由中子和电子离子等离子体组成的强磁化、弱电离简并等离子体中的线性和非线性快磁声波。在这里，线性分析描述了足够长、快速的磁声波可能存在于一个弱色散脉冲星中，该脉冲星在截止时具有有限的相速度。为了研究一维非线性快磁声波，借助黎曼波解导出作为电子磁压和中子简并压力的函数的中子密度表达式。因此，导出了一个修正的 Korteweg-de Vries 方程，它具有一个稀薄的孤立波解。研究发现，快磁声波的振幅、宽度和相速等基本性质受到电子磁和中子简并压力的显着改变。这一理论研究的结果可能有助于理解脉冲星、磁星和白矮星等天体物理致密天体中孤立结构的形成和特征。具有稀折射孤波解。研究发现，快磁声波的振幅、宽度和相速等基本性质受到电子磁和中子简并压力的显着改变。这一理论研究的结果可能有助于理解脉冲星、磁星和白矮星等天体物理致密天体中孤立结构的形成和特征。具有稀折射孤波解。研究发现，快磁声波的振幅、宽度和相速等基本性质受到电子磁和中子简并压力的显着改变。这一理论研究的结果可能有助于理解脉冲星、磁星和白矮星等天体物理致密天体中孤立结构的形成和特征。