Starting from one dimensional Kappa distribution for electrons, we have systematically developed the combined Kappa-Cairns distribution. We have found the effective bounds of both nonthermal parameters κ $\kappa $ and β e $\beta _{e}$ for the combined Kappa-Cairns distribution. This distribution can generate more highly energetic particles in comparison with both Kappa and Cairns distributions. We have investigated ion acoustic solitary structures in a collisionless magnetized plasma composed of negatively charged static dust grains, adiabatic warm ions and a population of highly energetic electrons generated from the combined Kappa-Cairns distribution. Sagdeev pseudo-potential technique has been considered to investigate the arbitrary amplitude steady state solitary structures including double layers and supersolitons. We have developed a computational scheme to draw the existence domains showing the nature of existence of different solitary structures. Different solitary structures of both positive and negative polarities have been observed for different values of κ $\kappa $ and β e $\beta _{e}$ . We have seen two important transitions of solitary structures for negative polarity, viz., soliton before the formation of double layer → double layer → supersoliton → soliton after the formation of double layer, and soliton before the formation of supersoliton → supersoliton → soliton. For the second case, we have a supersoliton structure without the formation of double layer and this case is completely new one for magnetized plasma. Different solitary structures supported by the system have been investigated with the help of compositional parameter spaces and the phase portraits of the dynamical systems describing different solitary structures.

中文翻译：

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Kappa 和 Cairns 分布电子对无碰撞磁化尘埃等离子体中离子声学孤立结构的综合影响

从电子的一维 Kappa 分布开始，我们系统地开发了组合 Kappa-Cairns 分布。我们已经找到了组合 Kappa-Cairns 分布的非热参数 κ $\kappa $ 和 β e $\beta _{e}$ 的有效边界。与 Kappa 和凯恩斯分布相比，这种分布可以产生更高能的粒子。我们研究了无碰撞磁化等离子体中的离子声学孤立结构，该等离子体由带负电荷的静态尘埃颗粒、绝热热离子和由 Kappa-Cairns 组合分布产生的高能电子群组成。Sagdeev 赝势技术已被考虑用于研究包括双层和超孤子在内的任意振幅稳态孤立结构。我们开发了一个计算方案来绘制存在域，显示不同孤立结构的存在性质。对于 κ $\kappa $ 和 β e $\beta _{e}$ 的不同值，已经观察到不同的正极性和负极性的孤立结构。我们已经看到了负极性孤子结构的两个重要转变，即双电层形成前的孤子→双电层→超孤子→双电层形成后的孤子，以及超孤子形成前的孤子→超孤子→孤子。对于第二种情况，我们有一个没有形成双层的超孤子结构，这种情况对于磁化等离子体来说是全新的。