557 research outputs found
Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver
Due to discretization effects and truncation to finite domains, many
electromagnetic simulations present non-physical modifications of Maxwell's
equations in space that may generate spurious signals affecting the overall
accuracy of the result. Such modifications for instance occur when Perfectly
Matched Layers (PMLs) are used at simulation domain boundaries to simulate open
media. Another example is the use of arbitrary order Maxwell solver with domain
decomposition technique that may under some condition involve stencil
truncations at subdomain boundaries, resulting in small spurious errors that do
eventually build up. In each case, a careful evaluation of the characteristics
and magnitude of the errors resulting from these approximations, and their
impact at any frequency and angle, requires detailed analytical and numerical
studies. To this end, we present a general analytical approach that enables the
evaluation of numerical discretization errors of fully three-dimensional
arbitrary order finite-difference Maxwell solver, with arbitrary modification
of the local stencil in the simulation domain. The analytical model is
validated against simulations of domain decomposition technique and PMLs, when
these are used with very high-order Maxwell solver, as well as in the infinite
order limit of pseudo-spectral solvers. Results confirm that the new analytical
approach enables exact predictions in each case. It also confirms that the
domain decomposition technique can be used with very high-order Maxwell solver
and a reasonably low number of guard cells with negligible effects on the whole
accuracy of the simulation.Comment: 33 pages, 14 figure
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
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Noninvariance of Space and Time Scale Ranges under a Lorentz Transformation and the Implications for the Numerical Study of Relativistic Systems
We present an analysis which shows that the ranges of space and time scales spanned by a system are not invariant under the Lorentz transformation. This implies the existence of a frame of reference which minimizes an aggregate measure of the range of space and time scales. Such a frame is derived for example cases: free electron laser, laser-plasma accelerator, and particle beam interacting with electron clouds. Implications for experimental, theoretical and numerical studies are discussed. The most immediate relevance is the reduction by orders of magnitude in computer simulation run times for such systems
An efficient and portable SIMD algorithm for charge/current deposition in Particle-In-Cell codes
In current computer architectures, data movement (from die to network) is by
far the most energy consuming part of an algorithm (10pJ/word on-die to
10,000pJ/word on the network). To increase memory locality at the hardware
level and reduce energy consumption related to data movement, future exascale
computers tend to use more and more cores on each compute nodes ("fat nodes")
that will have a reduced clock speed to allow for efficient cooling. To
compensate for frequency decrease, machine vendors are making use of long SIMD
instruction registers that are able to process multiple data with one
arithmetic operator in one clock cycle. SIMD register length is expected to
double every four years. As a consequence, Particle-In-Cell (PIC) codes will
have to achieve good vectorization to fully take advantage of these upcoming
architectures. In this paper, we present a new algorithm that allows for
efficient and portable SIMD vectorization of current/charge deposition routines
that are, along with the field gathering routines, among the most time
consuming parts of the PIC algorithm. Our new algorithm uses a particular data
structure that takes into account memory alignement constraints and avoids
gather/scatter instructions that can significantly affect vectorization
performances on current CPUs. The new algorithm was successfully implemented in
the 3D skeleton PIC code PICSAR and tested on Haswell Xeon processors (AVX2-256
bits wide data registers). Results show a factor of to
speed-up in double precision for particle shape factor of order to . The
new algorithm can be applied as is on future KNL (Knights Landing)
architectures that will include AVX-512 instruction sets with 512 bits register
lengths (8 doubles/16 singles).Comment: 36 pages, 5 figure
The compatible conversion system
Compatible conversion system centralizes the solution of general problems arising from the use of direct access mass storage. It also provides a simple stable interface for the conversion of production programs to process on third generation computer system
Optimization of laser-plasma injector via beam loading effects using ionization-induced injection
Simulations of ionization induced injection in a laser driven plasma
wakefield show that high-quality electron injectors in the 50-200 MeV range can
be achieved in a gas cell with a tailored density profile. Using the PIC code
Warp with parameters close to existing experimental conditions, we show that
the concentration of in a hydrogen plasma with a tailored
density profile is an efficient parameter to tune electron beam properties
through the control of the interplay between beam loading effects and varying
accelerating field in the density profile. For a given laser plasma
configuration, with moderate normalized laser amplitude, and maximum
electron plasma density, , the
optimum concentration results in a robust configuration to generate electrons
at 150~MeV with a rms energy spread of 4\% and a spectral charge density of
1.8~pC/MeV.Comment: 13 pages, 10 figure
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
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