关于德拜屏蔽的准确性
On the accuracy of the Debye shielding
摘要：
在等离子体物理中，德拜屏蔽的表达式通常是在假设等离子体粒子之间是弱耦合的，因此它们的动能远大于它们之间的势能，并且等离子体粒子的速度分布是麦克斯韦分布的情况下导出的。第一个假设还建立了等离子体参数ND，即具有德拜半径的球体内的粒子数应大于1，并决定了弱耦合和强耦合等离子体之间的差异。在这样的假设下，泊松方程可以线性化，并得到一个简单的解析表达式的静电势。然而，教科书很少讨论这种近似的准确性。在这项工作中，我们比较线性化的解决方案与精确的，数值计算得到的，并表明，线性化，低估了精确的解决方案，是相当不错的，甚至ND ~ 40。当粒子数很小时，或到试探电荷的距离过短时，我们给出了确定近似极限的定量判据。
英文摘要：
The expression for the Debye shielding in plasma physics is usually derived under the assumptions that the plasma particles are weakly coupled, so their kinetic energy is much larger than the potential energy between them, and that the velocity distributions of the plasma species are Maxwellian. The first assumption also establishes that the plasma parameter ND, the number of particles within a sphere with a Debye radius should be greater than 1, and determines the difference between weakly and strongly coupled plasmas. Under such assumptions, Poisson's equation can be linearised, and a simple analytic expression obtained for the electrostatic potential. However, textbooks rarely discuss the accuracy of this approximation. In this work we compare the linearised solution with the exact one, obtained numerically, and show that the linearisation, which underestimates the exact solution, is reasonably good even for ND ~ 40. We give quantitative criteria to set the limit of the approximation when the number of particles is very small, or the distance to the test charge too short.
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