Dynamical bunching and density peaks in expanding Coulomb clouds

Abstract

Expansion dynamics of single-species, non-neutral clouds, such as electron bunches used in ultrafast electron microscopy, show novel behavior due to high acceleration of particles in the cloud interior. This often leads to electron bunching and dynamical formation of a density shock in the outer regions of the bunch. We develop analytic fluid models to capture these effects, and the analytic predictions are validated by PIC and N-particle simulations. In the space-charge dominated regime, two and three dimensional systems with Gaussian initial densities show bunching and a strong shock response, while one dimensional systems do not; moreover these effects can be tuned using the initial particle density profile and velocity chirp.

Density shocks in the relativistic expansion of highly charged one component plasmas

“…Specifically, we showed that a density shock, seen in Coulomb explosion studies [5-8, 20, 27, 34], was present in the analytic density evolution of initially Gaussian distributions under both cylindrical and spherical symmetries but absent under planar symmetry unless an appropriate initial chirp in phase space is present. Moreover, such a shock is absent in nonrelativistic dynamics of uniform systems with cold initial conditions suggesting that uniform distribution evolution is unique in this regard [19]. We noted in our previous work that the density evolution seen in PIC simulations using an electromagnetic (EM) solver and relativistic particle pusher, which should capture all relativistic effects if the initial field is accurate, do not significantly differ from our analytic description for the densities analyzed there [19].…”

“…sets the timescale for the relativistic expansion of high density charge clouds; as was found in the non-relativistic cases [19]. In addition to the plasma frequency, we find it advantageous to define the related 1D-number density as…”

“…However, for electron injectors utilizing photoemission the initial conditions of the bunch is often Gaussian, or at the very least non-uniform, and it has long been known that charge redistribution from the * zerbe@msu.edu † duxbury@msu.edu non-uniform to the uniform bunch is one of the major sources of emittance growth [17] suggesting that uniform distributions are at best an idealization that miss much of the physics present in the typical situation. However, we have recently shown that dynamics similar to Wangler's charge redistribution for freely expanding bunches leads to an opportunity of "Coulomb cooling" -a mechanism we believe employs the intense Coulomb fields to carry off heat from non-neutral plasmas [18,19]. Our analysis is directed at a better understanding of the relativistic expansion dynamics of uniform and non-uniform systems to study mechanisms of emittance growth near the particle source but also with the goal of understanding and optimizing Coulomb cooling.…”

“…Here we concentrate on characterizing the relativistic density dynamics for both uniform and non-uniform initial conditions. Numerous works within the UEM literature have already looked at various aspects of the evolution of nonuniform distributions [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Reed presented a fluid model that described the dynamics of non-uniform bunch expansion under the assumptions that the bunch could be treated as having planar symmetry in the non-relativistic regime [27].…”

“…Moreover, such a shock is absent in nonrelativistic dynamics of uniform systems with cold initial conditions suggesting that uniform distribution evolution is unique in this regard [19]. We noted in our previous work that the density evolution seen in PIC simulations using an electromagnetic (EM) solver and relativistic particle pusher, which should capture all relativistic effects if the initial field is accurate, do not significantly differ from our analytic description for the densities analyzed there [19]. Moreover, we have seen that the PIC simulations using an EM solver do not significantly differ from those using an electrostatic (ES) solver with relativistic particle pusher for much higher densities than those examined in our previous work, or in the work described here.…”