Charged Particle Transport in a Collisionless Magnetized Plasma

Abstract

Here we start with the non-relativistic Boltzmann equation (2.1),

$$\displaystyle\begin{array}{rcl} \frac{\partial f} {\partial t} +\boldsymbol{ v} \cdot \nabla _{\boldsymbol{r}}f + \frac{\boldsymbol{F}} {m} \cdot \nabla _{\boldsymbol{v}}f = \left (\frac{\delta f} {\delta t} \right )_{s} + S.& &{}\end{array}$$

(4.1)

Note that, here, this equation has been implicitly separated into mean and fluctuating parts, with the fluctuating components being treated as scattering terms and have been relegated to the right-hand side. The particle source term is denoted by S. The force term in the Boltzmann equation (2.1) can be quite general. Here we restrict ourselves to $\boldsymbol{F} = q\left (\boldsymbol{E} +\boldsymbol{ v} \times \boldsymbol{ B}/c_{s}\right )$; the electromagnetic force on a particle with mass m and charge q, where c _s is the speed of light.