High-order Discretization of a Gyrokinetic Vlasov Model in Edge Plasma Geometry

We present a high-order spatial discretization of a continuum gyrokinetic Vlasov model in axisymmetric tokamak edge plasma geometries. Such models describe the phase space advection of plasma species distribution functions in the absence of collisions. The gyrokinetic model is posed in a four-dimensional phase space, upon which a grid is imposed when discretized. To mitigate the computational cost associated with high-dimensional grids, we employ a high-order discretization to reduce the grid size needed to achieve a given level of accuracy relative to lower-order methods. Strong anisotropy induced by the magnetic field motivates the use of mapped coordinate grids aligned with magnetic flux surfaces. The natural partitioning of the edge geometry by the separatrix between the closed and open field line regions leads to the consideration of multiple mapped blocks, in what is known as a mapped multiblock (MMB) approach. We describe the specialization of a more general formalism that we have developed for the construction of high-order, finite-volume discretizations on MMB grids, yielding the accurate evaluation of the gyrokinetic Vlasov operator, the metric factors resulting from the MMB coordinate mappings, and the interaction of blocks at adjacent boundaries. Our conservative formulation of the gyrokinetic Vlasov model incorporates the fact that the phase space velocity has zero divergence, which must be preserved discretely to avoid truncation error accumulation. We describe an approach for the discrete evaluation of the gyrokinetic phase space velocity that preserves the divergence-free property to machine precision

Experimental simulations of beam propagation over large distances in a compact linear Paul trap

The Paul Trap Simulator Experiment (PTSX) is a compact laboratory experiment that places the physicist in the frame of reference of a long, charged-particle bunch coasting through a kilometers-long magnetic alternating-gradient (AG) transport system. The transverse dynamics of particles in both systems are described by similar equations, including nonlinear space-charge effects. The time-dependent voltages applied to the PTSX quadrupole electrodes are equivalent to the axially oscillating magnetic fields applied in the AG system. Experiments concerning the quiescent propagation of intense beams over large distances can then be performed in a compact and flexible facility. An understanding and characterization of the conditions required for quiescent beam transport, minimum halo particle generation, and precise beam compression and manipulation techniques, are essential, as accelerators and transport systems demand that ever-increasing amounts of space charge be transported. Application areas include ion-beam-driven high energy density physics, high energy and nuclear physics accelerator systems, etc. One-component cesium plasmas have been trapped in PTSX that correspond to normalized beam intensities, s=omega(2)(p)(0)/2 omega(2)(q), up to 80% of the space-charge limit where self-electric forces balance the applied focusing force. Here, omega(p)(0)=[n(b)(0)e(b)(2)/m(b)epsilon(0)](1/2) is the on-axis plasma frequency, and omega(q) is the smooth-focusing frequency associated with the applied focusing field. Plasmas in PTSX with values of s that are 20% of the limit have been trapped for times corresponding to equivalent beam propagation over 10 km. Results are presented for experiments in which the amplitude of the quadrupole focusing lattice is modified as a function of time. It is found that instantaneous changes in lattice amplitude can be detrimental to transverse confinement of the charge bunch. (c) 2006 American Institute of Physics.close6

Experiments on transverse compression of a long charge bunch in a linear Paul trap

The transverse compression of a long charge bunch is investigated in the Paul trap simulator experiment ( PTSX), which is a linear Paul trap that simulates the nonlinear transverse dynamics of an intense charged particle beam propagating through an equivalent kilometers- long magnetic alternating- gradient ( AG) focusing system. Changing the voltage amplitude at fixed focusing frequency in the PTSX device corresponds to changing the field gradient of the quadrupole magnets with fixed axial periodicity in the AG transport system. In this work, we present experimental results on transverse compression of the charge bunch in which the amplitude of the applied oscillatory focusing voltage is changed instantaneously, and adiabatically. The experimental data are also compared with analytical estimates and 2D WARP particle- in- cell simulationsclose6

Transverse compression of an intense ion beam propagating through an alternating-gradient quadrupole lattice

The transverse compression and dynamics of an intense beam propagating through an alternating-gradient quadrupole lattice, plays an important role in many accelerator physics applications. Typically, the compression can be achieved by means of increasing the focusing strength of the lattice along the beam propagation direction. However, beam propagation through the lattice transition region inevitably leads to a certain level of beam mismatch and halo formation. In this work we present a detailed analysis of these phenomena using the envelope equations in the smooth-focusing approximation, which describe the average effects of an alternating-gradient lattice, and full particle-in-cell numerical simulations using the WARP code, taking into account the effects of the alternating-gradient quadrupole field. Simulations are presented for both space-charge–dominated beams, and beams with a moderate space-charge strength

Approximate kinetic quasiequilibrium distributions for intense beam propagation through a periodic focusing quadrupole lattice

The transverse dynamics of an intense charged particle beam propagating through a periodic quadrupole focusing lattice is described by the nonlinear Vlasov-Maxwell system of equations, where the propagation distances play the role of time. To determine matched-beam quasiequilibrium distribution functions, one needs to determine a dynamical invariant for the beam particles moving in the combined applied and self-generated fields. In this paper, a perturbative Hamiltonian transformation method is developed which is an expansion in the particle’s vacuum phase advance ϵ[over ¯]∼σ_{v}/2π, treated as a small parameter, which is used to transform away the fast particle orbit oscillations and obtain the average Hamiltonian accurate to order ϵ[over ¯]^{3}. The average Hamiltonian is an approximate invariant of the original system, and can be used to determine self-consistent beam quasiequilibrium solutions that are matched to the focusing channel. The equation determining the average self-field potential is derived for general boundary conditions by taking into account the average contribution of the charges induced on the boundary. It is shown for a cylindrical conducting boundary that the average self-field potential acquires an octupole component, which results in the average motion of some beam particles being nonintegrable and their trajectories chaotic. This chaotic behavior of the beam particles may significantly change the nature of the Landau damping (or growth) of collective excitations supported by an intense charged particle beam

New Spectral Method for Halo Particle Definition in Intense Mis-matched Beams

An advanced spectral analysis of a mis-matched charged particle beam propagating through a periodic focusing transport lattice is utilized in particle-in-cell (PIC) simulations. It is found that the betatron frequency distribution function of a mismatched space-charge-dominated beam has a bump-on-tail structure attributed to the beam halo particles. Based on this observation, a new spectral method for halo particle definition is proposed that provides the opportunity to carry out a quantitative analysis of halo particle production by a beam mismatch. In addition, it is shown that the spectral analysis of the mismatch relaxation process provides important insights into the emittance growth attributed to the halo formation and the core relaxation processes. Finally, the spectral method is applied to the problem of space-charge transport limits