Exact simulations of the trajectories of electrons accelerated from rest to relativistic velocities by radially polarized optical pulse: program and results

UnrestrictedA relativistic electron co-propagating with a slowly diverging focused 1-cycle, 1-Joule, 1-micron half-wave (111) radially- polarized optical pulse gains nearly 0.43 GeV energy while in a half focal region. In this thesis we describe a new computer program that extends this analytic result to compute the exact trajectory, and its consequences, of an electron initially at rest at any position near the focal region of the incident optical pulse. We have limited the "exact simulation" to try four families of pulse solutions (of Maxwell 's equations) which we have found to produce the highest final electron energy or highest amount of re-radiated light, varying the pulse parameters. The nature and statistics of the trajectories having different starting points show that (i) Nearly 100% of initially-at-rest non-interacting electrons struck in the focal volume of the (111) pulse mentioned above are accelerated to final energies between 0.10 and 0.27 GeV. (ii) The standard (111) pulse striking a large volume of initially-at-rest non-interacting electrons creates a cylindrical cavity completely empty of electrons. (iii) An electron struck by a standard (111) optical pulse radiates ~ 10 atto-joule, depending on its initial position in the focal region. (iv) We examined our simulation of radiated power from 2 electrons in the focal region and found the expected 4 factor from coherent scattering. We have extended our program to calculating the trajectory of initially-moving electrons. For 155 starting positions one micron apart on a line at 80 degrees to the axis of a standard (111) pulse, and having initial velocity 0.5c, the electron increase its energy by a average of 70 MeV