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

Zerbe, Brandon S.; Duxbury, P. M.

doi:10.1103/physrevaccelbeams.22.114402

Cited by 4 publications

(7 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(23). Moreover our previous work on the forces present in laminar flow Coulomb explosion problems 3,38,39 can be straightforwardly extended to the forces in the sample perspective for particle configurations exhibiting laminar flow.…”

Section: Discussionmentioning

confidence: 98%

“…Consider the 3D charge density ρ q (x, y, z; t). Assuming planar symmetry, this distribution may be decomposed 3,38,39 ρ q (x, y, z; t) = Σ tot ρ(x; t)…”

Section: Statistical Dynamics From Initial Populations a Expected 1d ...mentioning

confidence: 99%

“…The sample perspective benefits greatly from the Lagrangian description of fluid dynamics. Previous work describing Coulomb explosion 2,3,38,39 has successfully employed the Lagrangian description to describe the density evolution from a population perspective.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exact solutions to planar emittance growth problems

Zerbe,

Duxbury

2020

Preprint

View full text Add to dashboard Cite

This paper is the first in a series which develops the theory of emittance dynamics based on simple statistical reasoning. Emittance is a central quantity used to characterize the quality of electron microscopes, photon sources and particle beams.Emittance growth in high intensity charged particle beams is a particularly challenging non-equilibrium statistical physics problem in which effects such as disorderedinduced heating and charge reorganization can lead to very rapid degradation of emittance and beam quality. The concepts of free energy and entropy have been utilized to improve conceptual understanding of emittance dynamics. Here we develop a theory based on the second order cumulant of particle distributions and use this formulation to exactly solve several one dimensional problems. These solutions are important extensions of the existing results for the free expansion dynamics of pancake bunches used in ultrafast electron microscopy, which at short times are known to expand quadratically with time 1-3 . Here we show that the squared emittance of a strictly planar expanding bunch increases as a quadratic polynomial of time.We compare theories based on individual particle trajectories with theories based on distributions and expand the foundations of theories based on individual particle trajectories, which we call the "sample picture". Our later work uses this formulation to derive generalized envelope equations which capture emittance growth effects in two and three dimensional systems.

show abstract

Section: Discussionmentioning

confidence: 98%

“…Consider the 3D charge density ρ q (x, y, z; t). Assuming planar symmetry, this distribution may be decomposed 3,38,39 ρ q (x, y, z; t) = Σ tot ρ(x; t)…”

Section: Statistical Dynamics From Initial Populations a Expected 1d ...mentioning

confidence: 99%

See 1 more Smart Citation

Exact solutions to planar emittance growth problems

Zerbe,

Duxbury

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…This effect is also seen in the field of ultrafast electron diffraction (UED), where laser-driven photoemission creates a pancake-shaped bunch (r >> z) at the cathode surface. In this system, a transverse ring-like density perturbation appears at the expanding edge, resulting in a hollowed transverse profile [10,11]. As in the case with the BTF ion beam, the hollow xy profile is only visible for a slice through the longitudinal core, while the fullyprojected profile is uniform.…”

Section: Self-field-driven Core Hollowing In Charged Particle Bunchesmentioning

confidence: 89%

Rapid charge redistribution leading to core hollowing in a high-intensity ion beam

Ruisard,

Aleksandrov

2020

Preprint

View full text Add to dashboard Cite

Recently, the first direct measurement of a full 6D accelerator beam distribution was reported [1]. That work observed a correlation between energy and transverse coordinates, for which the energy distribution becomes hollowed and double-peaked near the transverse core. In this article, a similar structure is shown to emerge in expansion of an initially uncorrelated, high density bunched beam as the result of velocity perturbation from nonlinear space charge forces. This hollowing is obscured when the 6D phase space is projected onto one-and two-dimensional axes. This phenomenon has not been widely recognized in accelerator systems, but parallels can be drawn to observations of laser-ionized nanoclusters and electron sources for diffraction. While this effect provides insight into the origin of the measured core correlation, it does not provide a complete description. A better reproduction of the measured structure can be obtained via self-consistent simulation through the radio-frequency quadrupole.

show abstract

“…Uniformly charged ellipsoids can be spatially and temporally (re)compressed by linear electromagnetic fields to the limit that their emittance allows [32]. For more realistic non-uniform ellipsoidal charge distributions, the self-electric field will not be linear in space, which can result in shock waves in the distribution [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

General formulation of Coulomb explosion dynamics of highly symmetric charge distributions

Zandi¹,

Veen²

2022

J. Phys. Commun.

View full text Add to dashboard Cite

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 Newton’s equation of motion with the Lorentz force. We develop a kinetic theory to include the stochastic force due to random motions of electrons in 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.

show abstract

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

Cited by 4 publications

References 48 publications

Exact solutions to planar emittance growth problems

Exact solutions to planar emittance growth problems

Rapid charge redistribution leading to core hollowing in a high-intensity ion beam

General formulation of Coulomb explosion dynamics of highly symmetric charge distributions

Contact Info

Product

Resources

About