Simulation of beam-induced plasma in gas-filled rf cavities

Processes occurring in a radio-frequency (rf) cavity, filled with high pressure gas and interacting with proton beams, have been studied via advanced numerical simulations. Simulations support the experimental program on the hydrogen gas-filled rf cavity in the Mucool Test Area (MTA) at Fermilab, and broader research on the design of muon cooling devices. SPACE, a 3D electromagnetic particle-in-cell (EM-PIC) code with atomic physics support, was used in simulation studies. Plasma dynamics in the rf cavity, including the process of neutral gas ionization by proton beams, plasma loading of the rf cavity, and atomic processes in plasma such as electron-ion and ion-ion recombination and electron attachment to dopant molecules, have been studied. Through comparison with experiments in the MTA, simulations quantified several uncertain values of plasma properties such as effective recombination rates and the attachment time of electrons to dopant molecules. Simulations have achieved very good agreement with experiments on plasma loading and related processes. The experimentally validated code SPACE is capable of predictive simulations of muon cooling devices.Comment: 10 pp. arXiv admin note: text overlap with arXiv:1709.0528

Dynamical systems associated with particle flow models : theory and numerical methods

A new class of integro - partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of infinite-dimensional dynamical systems models) on the Newtonian equations of motion of a many-particle system incorporating widely used inelastic particle-particle force formulas. By using Taylor series expansions, these models can be approximated by a system of partial differential equations of the Navier-Stokes type. Solutions of the new models for granular flows down inclined planes and in vibrating beds are compared with known experimental and analytical results and good agreement is obtained. Theorems on the existence and uniqueness of a solution to the granular flow dynamical system are proved in the Faedo-Galerkin method framework. A class of one-dimensional models describing the dynamics of thin granular layers and some related problems of fluid mechanics was studied from the Liouville-Lax integrability theory point of view. The integrability structures for these dynamical systems were constructed using Cartan\u27s calculus of differential forms, Grassman algebras over jet-manifolds associated with the granular flow dynamical systems, the gradientholonomic algorithm and generalized Hamiltonian methods. By proving the exact integrability of the systems, the quasi-periodicity of the solutions was explained as well as the observed regularity of the numerical solutions. A numerical algorithm based on the idea of higher and lower modes separation in the theory of approximate inertial manifolds for dissipative evolutionary equations is developed in a finite-difference framework. The method is applied to the granular flow dynamical system. Numerical calculations show that this method has several advantages compared to standard finite-difference schemes. A numerical solution to the granular flow in a hopper is obtained using the finite difference scheme in curvilinear coordinates. By making coefficients in the governing equations functionally dependent on the gradient of the velocity field, we were able to model the influence of the stationary friction phenomena in solids and reproduce in this way experimentally observable results. Some analytical and numerical solutions to the dynamical system describing granular flows in vibrating beds are also presented. We found that even in the simplest case where we neglect the arching phenomena and surface waves, these solutions exhibit some of the typical features that have been observed in simulation and experimental studies of vibrating beds. The approximate analytical solutions to the governing system of equations were found to share several important features with actual granular flows. Using this approach we showed the existence of the typical dynamical structures of chaotic motion. By employing Melnikov theory the bifurcation parameter values were estimated analytically. The vortex solutions we obtained for the perturbed motion and the solutions corresponding to the vortex disintegration agree qualitatively with the dynamics obtained numerically

A Comparison Study of Two Methods for Elliptic Boundary Value Problems

In this paper, we perform a comparison study of two methods (the embedded boundary method and several versions of the mixed finite element method) to solve an elliptic boundary value problem

Second Order Upwind Lagrangian Particle Method for Euler Equations

AbstractA new second order upwind Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is suitable for the simulation of complex free surface / multiphase flows. The main contributions of our method, which is different from SPH in all other aspects, are (a) significant improvement of approximation of differential operators based on a polynomial fit via weighted least squares approximation and the convergence of prescribed order, (b) an upwind second-order particle-based algorithm with limiter, providing accuracy and long term stability, and (c) accurate resolution of states at free interfaces. Numerical verification tests demonstrating the convergence order for fixed domain and free surface problems are presented