General Formulation of Coulomb Explosion Dynamics of Highly Symmetric Charge Distributions
Abstract
We present a theoretical approach to study the dynamics of spherical, cylindrical and ellipsoidal charge distributions under their selfCoulomb 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 chargecurrent 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 Nbody simulations. We show that our method reproduces the wellknown 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2020
 DOI:
 10.48550/arXiv.2003.00611
 arXiv:
 arXiv:2003.00611
 Bibcode:
 2020arXiv200300611Z
 Keywords:

 Physics  Plasma Physics;
 Physics  Computational Physics
 EPrint:
 30 pages, 5 sections, 7 figures, 4 appendices A kinetic theory for the emittance of electron beams/pulses is presented for the first time