The basic relation which determines the motion of an individual charged particle of mass m and charge q in a combined electric and magnetic field is the equation

d

m— = qE + q(xB). (5.1)

dt

Here, v is the velocity vector of the particle at an arbitrary point in space and E and В are, respectively, the local electric field and magnetic flux density perceived by the particle; the magnetic flux density is commonly called the magnetic field. The last term in this equation is also known as the Lorentz force. We assume SI units so that the units of E are Newton/Coulomb while for В the units are Tesla; note that 1 Tesla (T) is defined as 1 Weber m"2 ( = 104 Gauss = 1 kg-s‘2-A’’).

While gravitational forces are of importance in stellar fusion, they are negligible compared to the externally generated magnetic field forces and the established electric fields associated with fusion energy devices of common interest; hence, gravitational force effects need not be included for our purposes.