PhD and MPhil Thesis Classes - Université Libre de Bruxelles

3.3 Charged Particle Motionasn s v s (x, t) =n∑vs(t)δe i s (3.13)i=1J(x, t) = ∑ sδe s v s (x, t)n s (x, t) (3.14)Charge conservation follows from the definitions (3.13) and (3.14) as well as fromthe first and second Maxwell equations∂ρ c∂t + ∇ · J = 0 (3.15)Thus, the electric and magnetic fields at any point x in physical space depend onthe instantaneous position of all particles.3.3 Charged Particle MotionUnderstanding of the motion of a set of charged particles in an electromagnetic field isthe subject of plasma physics. A single charged particle entering a region of space wherean electromagnetic field is present (produced by some unspecified external forces) willundergo a uniform acceleration in the direction of the field when the field is reducedto a constant electric field E. In the presence of a constant magnetic field B, the particlewill perform a helical motion, wrapping itself around a field line. If the fields aresimultaneously present, the motion is more complex and the particle does not remainattached to a single magnetic field line. It rather drifts through space in a directionperpendicular to both the electric and the magnetic fields. In reality fields are spatiallyinhomogeneous and non-stationary, which introduces extra drift motions and increasesthe complexity of the problem.In this section we study the aspects of the motion of the individual charged particlein electromagnetic fields.29