Modeling laser wakefield accelerators in a Lorentz boosted frame

Modeling of laser-plasma wakefield accelerators in an optimal frame of reference \cite{VayPRL07} is shown to produce orders of magnitude speed-up of calculations from first principles. Obtaining these speedups requires mitigation of a high-frequency instability that otherwise limits effectiveness in addition to solutions for handling data input and output in a relativistically boosted frame of reference. The observed high-frequency instability is mitigated using methods including an electromagnetic solver with tunable coefficients, its extension to accomodate Perfectly Matched Layers and Friedman's damping algorithms, as well as an efficient large bandwidth digital filter. It is shown that choosing the frame of the wake as the frame of reference allows for higher levels of filtering and damping than is possible in other frames for the same accuracy. Detailed testing also revealed serendipitously the existence of a singular time step at which the instability level is minimized, independently of numerical dispersion, thus indicating that the observed instability may not be due primarily to Numerical Cerenkov as has been conjectured. The techniques developed for Cerenkov mitigation prove nonetheless to be very efficient at controlling the instability. Using these techniques, agreement at the percentage level is demonstrated between simulations using different frames of reference, with speedups reaching two orders of magnitude for a 0.1 GeV class stages. The method then allows direct and efficient full-scale modeling of deeply depleted laser-plasma stages of 10 GeV-1 TeV for the first time, verifying the scaling of plasma accelerators to very high energies. Over 4, 5 and 6 orders of magnitude speedup is achieved for the modeling of 10 GeV, 100 GeV and 1 TeV class stages, respectively

Speeding up simulations of relativistic systems using an optimal boosted frame

It can be computationally advantageous to perform computer simulations in a Lorentz boosted frame for a certain class of systems. However, even if the computer model relies on a covariant set of equations, it has been pointed out that algorithmic difficulties related to discretization errors may have to be overcome in order to take full advantage of the potential speedup. We summarize the findings, the difficulties and their solutions, and show that the technique enables simulations important to several areas of accelerator physics that are otherwise problematic, including self-consistent modeling in three-dimensions of laser wakefield accelerator stages at energies of 10 GeV and above.Comment: To be published in the proceedings of DPF-2009, Detroit, MI, July 2009, eConf C09072

Three dimensional simulations of space charge dominated heavy ion beams with applications to inertial fusion energy

Heavy ion fusion requires injection, transport and acceleration of high current beams. Detailed simulation of such beams requires fully self-consistent space charge fields and three dimensions. WARP3D, developed for this purpose, is a particle-in-cell plasma simulation code optimized to work within the framework of an accelerator`s lattice of accelerating, focusing, and bending elements. The code has been used to study several test problems and for simulations and design of experiments. Two applications are drift compression experiments on the MBE-4 facility at LBL and design of the electrostatic quadrupole injector for the proposed ILSE facility. With aggressive drift compression on MBE-4, anomalous emittance growth was observed. Simulations carried out to examine possible causes showed that essentially all the emittance growth is result of external forces on the beam and not of internal beam space-charge fields. Dominant external forces are the dodecapole component of focusing fields, the image forces on the surrounding pipe and conductors, and the octopole fields that result from the structure of the quadrupole focusing elements. Goal of the design of the electrostatic quadrupole injector is to produce a beam of as low emittance as possible. The simulations show that the dominant effects that increase the emittance are the nonlinear octopole fields and the energy effect (fields in the axial direction that are off-axis). Injectors were designed that minimized the beam envelope in order to reduce the effect of the nonlinear fields. Alterations to the quadrupole structure that reduce the nonlinear fields further were examined. Comparisons were done with a scaled experiment resulted in very good agreement

Thermal noise of folding mirrors

Current gravitational wave detectors rely on the use of Michelson interferometers. One crucial limitation of their sensitivity is the thermal noise of their optical components. Thus, for example fluctuational deformations of the mirror surface are probed by a laser beam being reflected from the mirrors at normal incidence. Thermal noise models are well evolved for that case but mainly restricted to single reflections. In this work we present the effect of two consecutive reflections under a non-normal incidence onto mirror thermal noise. This situation is inherent to detectors using a geometrical folding scheme such as GEO\,600. We revise in detail the conventional direct noise analysis scheme to the situation of non-normal incidence allowing for a modified weighting funtion of mirror fluctuations. An application of these results to the GEO\,600 folding mirror for Brownian, thermoelastic and thermorefractive noise yields an increase of displacement noise amplitude by 20\% for most noise processes. The amplitude of thermoelastic substrate noise is increased by a factor 4 due to the modified weighting function. Thus the consideration of the correct weighting scheme can drastically alter the noise predictions and demands special care in any thermal noise design process

Modeling the longitudinal wall impedance instability in heavy ion beams using an R-C pic code

The effects of the longitudinal wall impedance instability in a heavy ion beam are of great interest for heavy ion fusion drivers. We are studying this instability using the R-Z thread of the WARP PIC code. We describe the code and our model of the impedance due to the accelerating modules of the induction LINAC as a resistive wall. We present computer simulations which illustrate this instability. 2 refs., 2 figs., 1 tab

Renormalization approach to many-particle systems

This paper presents a renormalization approach to many-particle systems. By starting from a bare Hamiltonian ${\cal H}= {\cal H}_0 +{\cal H}_1$ with an unperturbed part ${\cal H}_0$ and a perturbation ${\cal H}_1$,we define an effective Hamiltonian which has a band-diagonal shape with respect to the eigenbasis of ${\cal H}_0$. This means that all transition matrix elements are suppressed which have energy differences larger than a given cutoff $\lambda$ that is smaller than the cutoff $\Lambda$ of the original Hamiltonian. This property resembles a recent flow equation approach on the basis of continuous unitary transformations. For demonstration of the method we discuss an exact solvable model, as well as the Anderson-lattice model where the well-known quasiparticle behavior of heavy fermions is derived.Comment: 11 pages, final version, to be published in Phys. Rev.

Effects of Hyperbolic Rotation in Minkowski Space on the Modeling of Plasma Accelerators in a Lorentz Boosted Frame

Laser driven plasma accelerators promise much shorter particle accelerators but their development requires detailed simulations that challenge or exceed current capabilities. We report the first direct simulations of stages up to 1 TeV from simulations using a Lorentz boosted calculation frame resulting in a million times speedup, thanks to a frame boost as high as gamma=1300. Effects of the hyperbolic rotation in Minkowski space resulting from the frame boost on the laser propagation in the plasma is shown to be key in the mitigation of a numerical instability that was limiting previous attempts

Short-Pulse, Compressed Ion Beams at the Neutralized Drift Compression Experiment

We have commenced experiments with intense short pulses of ion beams on the Neutralized Drift Compression Experiment (NDCX-II) at Lawrence Berkeley National Laboratory, with 1-mm beam spot size within 2.5 ns full-width at half maximum. The ion kinetic energy is 1.2 MeV. To enable the short pulse duration and mm-scale focal spot radius, the beam is neutralized in a 1.5-meter-long drift compression section following the last accelerator cell. A short-focal-length solenoid focuses the beam in the presence of the volumetric plasma that is near the target. In the accelerator, the line-charge density increases due to the velocity ramp imparted on the beam bunch. The scientific topics to be explored are warm dense matter, the dynamics of radiation damage in materials, and intense beam and beam-plasma physics including select topics of relevance to the development of heavy-ion drivers for inertial fusion energy. Below the transition to melting, the short beam pulses offer an opportunity to study the multi-scale dynamics of radiation-induced damage in materials with pump-probe experiments, and to stabilize novel metastable phases of materials when short-pulse heating is followed by rapid quenching. First experiments used a lithium ion source; a new plasma-based helium ion source shows much greater charge delivered to the target.Comment: 4 pages, 2 figures, 1 table. Submitted to the proceedings for the Ninth International Conference on Inertial Fusion Sciences and Applications, IFSA 201