The departure of particle distributions from the Maxwellian is commonly observed in space plasmas. These non-Maxwellian distributions which are typical for plasmas that are not in thermal equilibrium, can be modeled with κ-distribution. Kinetic simulations of quasi-parallel collisionless shocks show that proton distribution is a composite of thermal, suprathermal, and non-thermal parts. By using particle-in-cell shock simulations, we show that κ-distribution adequately fits thermal and suprathermal parts together, as a single continuous distribution in early proton spectra. We derive suprathermal proton distribution directly from the generalized entropy of non-extensive statistical mechanics, and show that thermal and suprathermal populations are both naturally embedded in κ-distribution. We find that the index κ of the distribution increases with the distance from the shock, following the decrease in suprathermal part. The non-equilibrium plasma distribution which is continuously being enriched with suprathermal particles at the reforming shock barrier, reaches the thermal equilibrium in the far downstream. The suprathermal part completely fades there, and the shape of proton distribution becomes a Maxwellian from which directly emerges a power-law.

在空间等离子体中通常观察到粒子分布与麦克斯韦分布的偏离。这些非麦克斯韦分布对于不处于热平衡状态的等离子体来说是典型的，可以用κ 分布建模。准平行无碰撞冲击的动力学模拟表明，质子分布是热、超热和非热部分的复合体。通过使用细胞内粒子冲击模拟，我们表明κ 分布充分地将热和超热部分拟合在一起，作为早期质子光谱中的单个连续分布。我们直接从非广延统计力学的广义熵推导出超热质子分布，并表明热和超热种群都自然嵌入在κ -分布。我们发现，随着超热部分的减少，分布的指数κ随着距激波的距离增加而增加。在重整冲击屏障处不断富含超热粒子的非平衡等离子体分布在远下游达到热平衡。那里的超热部分完全消失，质子分布的形状变成麦克斯韦，从中直接出现幂律。