Using kernel-based statistical distance to study the dynamics of charged particle beams in particle-based simulation codes.

Measures of discrepancy between probability distributions (statistical distance) are widely used in the fields of artificial intelligence and machine learning. We describe how certain measures of statistical distance can be implemented as numerical diagnostics for simulations involving charged-particle beams. Related measures of statistical dependence are also described.

Extracting dynamical frequencies from invariants of motion in finite-dimensional nonlinear integrable systems.

Integrable dynamical systems play an important role in many areas of science, including accelerator and plasma physics. An integrable dynamical system with n degrees of freedom possesses n nontrivial integrals of motion, and can be solved, in principle, by covering the phase space with one or more charts in which the dynamics can be described using action-angle coordinates. To obtain the frequencies of motion, both the transformation to action-angle coordinates and its inverse must be known in explicit form.

Spectral Galerkin solver for intense beam Vlasov equilibria in nonlinear constant focusing channels.

A numerical method is described for producing stationary solutions of the Vlasov-Poisson system describing a relativistic charged-particle beam in a constant focusing accelerator channel, confined transversely by a general (linear or nonlinear) focusing potential. The method utilizes a variant of the spectral Galerkin algorithm to solve a nonlinear partial differential equation (PDE) in two degrees of freedom for the beam space charge potential in equilibrium. Numerical convergence with an increasing number of computed spectral modes is investigated for several benchmark problems.

Space-charge driven emittance growth in a 3D mismatched anisotropic beam.

We investigate the phenomenon of space-charge driven emittance growth in a three-dimensional mismatched anisotropic charged particle beam with relevance to high-intensity linear accelerators. The final emittance growth can be understood as a superposition of the contributions from the mismatch-induced halo formation and from the anisotropy-induced energy exchange. The averaged emittance growth per degree of freedom is bounded from above by the so-called "free energy limit" extended by the contributions from energy exchange.

Computation of the Lyapunov spectrum for continuous-time dynamical systems and discrete maps.

In this paper, we describe in detail a method of computing Lyapunov exponents for a continuous-time dynamical system and extend the method to discrete maps. Using this method, a partial Lyapunov spectrum can be computed using fewer equations as compared to the computation of the full spectrum, there is no difficulty in evaluating degenerate Lyapunov spectra, the equations are straightforward to generalize to higher dimensions, and the minimal set of dynamical variables is used. Explicit proofs and other details not given in previous work are included here.

Collective resonance model of energy exchange in 3D nonequipartitioned beams.

Energy exchange between the longitudinal and transverse degrees of freedom of nonequipartitioned bunched beams (non-neutral plasmas) is investigated by means of 3D simulation. It is found that collective instability may lead to energy transfer in the direction of equipartition, without full progression to it, in certain bounded regions of parameter space where internal resonance conditions are satisfied, in good agreement with stability charts from an earlier derived 2D Vlasov analysis. Nonequipartitioned stable equilibria, however, exist in relatively wide regimes of parameter space.