BGK电子孤波的再研究
BGK Electron Solitary Waves Reexamined
摘要：
本文重新研究了电子Bernstein-Greene-Kruskal（BGK）孤立波（又称BGK相空间电子空穴）中俘获电子和通过电子的物理作用。结果表明，孤波势附近的电荷密度变化是俘获电子产生的负电荷与通过电子密度降低产生的正电荷的净平衡。BGK EH由电子密度增强以及密度耗尽组成，而不是像以前认为的那样只有密度耗尽。正核的屏蔽不是周围等离子体的热屏蔽，而是通过在势能槽内振荡的捕获电子来实现的。因此，BGK EH的总电荷为零。两个分离的EH不相互作用，也不需要负质量的概念。这些特征与非线性的强度无关。BGK EH不需要热屏蔽，因此它们的尺寸不限于大于德拜长度$λ_D$。我们的分析预测，可能存在小于$λ_D$的BGK EH。得到了BGK型弹性体的宽度（$δ$）-振幅（$ψ$）关系的一般不等式形式.对于具有势幅$\gg 1$的空心EH，我们证明了$δ\propto\sqrtψ$形式的宽度-振幅关系与钟形势是相同的。对于$ψ\ll 1$，宽度比$\sqrtψ$更快地接近零。
英文摘要：
This paper reexamines the physical roles of trapped and passing electrons in electron Bernstein-Greene-Kruskal (BGK) solitary waves, also called the BGK phase space electron holes (EH). It is shown that the charge density variation in the vicinity of the solitary potential is a net balance of the negative charge from trapped electrons and positive charge due to the decrease of the passing electron density. A BGK EH consists of electron density enhancements as well as a density depletion, instead of only the density depletion as previously thought. The shielding of the positive core is not a thermal screening by the ambient plasma, but achieved by trapped electrons oscillating inside the potential energy trough. The total charge of a BGK EH is therefore zero. Two separated EHs do not interact and the concept of negative mass is not needed. These features are independent of the strength of the nonlinearity. BGK EHs do not require thermal screening, and their size is thus not restricted to be greater than the Debye length $λ_D$. Our analysis predicts that BGK EHs smaller than $λ_D$ can exist. A width($δ$)-amplitude($ψ$) relation of an inequality form is obtained for BGK EHs in general. For empty-centered EHs with potential amplitude $\gg 1$, we show that the width-amplitude relation of the form $δ\propto\sqrtψ$ is common to bell-shaped potentials. For $ψ\ll 1$, the width approaches zero faster than $\sqrtψ$.
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