Abstract
The charge that a particle acquires in a plasma environment is certainly the most fundamental parameter of a dusty plasma. Here, the main charging currents to a dust particle, such as the widely used OML currents, are derived. From this, the particle charge under different conditions is determined. Further, the temporal evolution of dust charges and the interaction of dense dust clouds with the plasma are discussed.
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Notes
- 1.
The definite integral is given by
$$\displaystyle \begin{aligned} \int\limits_0^\infty x^n \mathrm{e}^{-ax^2} \mathrm{d} x = \frac{k!}{2 a^{k+1}}\quad \mbox{for odd}\quad n=2k+1\,. \end{aligned}$$ - 2.
Throughout this book, the thermal velocity of all species is defined as \(v_{\mathrm {th}} = \sqrt {8 k_{\mathrm {B}} T/(\pi m)}\) with the respective temperature T and mass m.
- 3.
The following integrals result in
$$\displaystyle \begin{aligned} \int\limits_v^\infty x \mathrm{e}^{-ax^2} \mathrm{d} x = \frac{1}{2 a} \mathrm{e}^{-av^2} \end{aligned}$$and
$$\displaystyle \begin{aligned} \int\limits_v^\infty x^3 \mathrm{e}^{-ax^2} \mathrm{d} x = \frac{1}{2 a^2} \left(1-av^2\right)\mathrm{e}^{-av^2}. \end{aligned}$$ - 4.
The error function is given by
$$\displaystyle \begin{aligned} \mbox{erf}(x) = \frac{2}{\sqrt{\pi}}\int\limits_0^x \exp(-y^2)\, \mathrm{d} y. \end{aligned}$$
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Melzer, A. (2019). Charging of Dust Particles. In: Physics of Dusty Plasmas. Lecture Notes in Physics, vol 962. Springer, Cham. https://doi.org/10.1007/978-3-030-20260-6_2
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