We present a theoretical approach to study the dynamics of spherical, cylindrical and ellipsoidal charge distributions under their self-Coulomb field and a stochastic force due to collisions and random motions of charged particles. The approach is based on finding the current density of the charge distribution from the charge-current continuity equation and determining the drift velocities of the particles. The latter can be used either to derive the Lagrangian of the system, or to write Newtons equation of motion with the Lorentz force. We develop a kinetic theory to include the stochastic force due to random motions of electrons into our model. To demonstrate the efficacy of our method, we apply it to various charge distributions and compare our results to N-body simulations. We show that our method reproduces the well-known emittance term in the envelope equation of uniform spherical and cylindrical charge distributions with correct coefficients. We use our model for the gravitational collapse of an ideal gas as well as the cyclotron dynamics of a cylindrical charge distribution in a uniform magnetic field and propose a method to measure the emittance of electron beams.
- Pub Date:
- March 2020
- Physics - Plasma Physics;
- Physics - Computational Physics
- 30 pages, 5 sections, 7 figures, 4 appendices A kinetic theory for the emittance of electron beams/pulses is presented for the first time