There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Controlling chaos

http://ab-initio.mit.edu/~oskooi/papers/Oskooi10.pdf

Meep: A flexible free-software package for electromagnetic simulations by the FDTD method

Laser-driven accelerators, in which particles are accelerated by the electric field of a plasma wave (the wakefield) driven by an intense laser, have demonstrated accelerating electric fields of hundreds of GV m-1 (refs 1–3) These fields are thousands of times greater than those achievable in conventional radio-frequency accelerators, spurring interest in laser accelerators4,5 as compact next-generation sources of energetic electrons and radiation To date, however, acceleration distances have been severely limited by the lack of a controllable method for extending the propagation distance of the focused laser pulse The ensuing short acceleration distance results in low-energy beams with 100 per cent electron energy spread1,2,3, which limits potential applications Here we demonstrate a laser accelerator that produces electron beams with an energy spread of a few per cent, low emittance and increased energy (more than 109 electrons above 80 MeV) Our technique involves the use of a preformed plasma density channel to guide a relativistically intense laser, resulting in a longer propagation distance The results open the way for compact and tunable high-brightness sources of electrons and radiation

https://escholarship.org/content/qt9c55r46s/qt9c55r46s.pdf?t=lnras5

High-quality electron beams from a laser wakefield accelerator using plasma-channel guiding

Summary form only given. Fundamental processes in atoms, molecules, as well as condensed matter are triggered or mediated by the motion of electrons inside or between atoms. Electronic dynamics on atomic length scales tends to unfold within tens to thousands of attoseconds (1 attosecond [as] = 10-18 s). Recent breakthroughs in laser science are now opening the door to watching and controlling these hitherto inaccessible microscopic dynamics. The key to accessing the attosecond time domain is the control of the electric field of (visible) light, which varies its strength and direction within less than a femtosecond (1 femtosecond = 1000 attoseconds). Atoms exposed to a few oscillations cycles of intense laser light are able to emit a single extreme ultraviolet (XUV) burst lasting less than one femtosecond. Full control of the evolution of the electromagnetic field in laser pulses comprising a few wave cycles have recently allowed the reproducible generation and measurement of isolated sub-femtosecond XUV pulses, demonstrating the control of microscopic processes (electron motion and photon emission) on an attosecond time scale. These tools have enabled us to visualize the oscillating electric field of visible light with an attosecond "oscilloscope", to control single-electron and probe multi-electron dynamics in atoms, molecules and solids. Recent experiments hold promise for the development of an attosecond X-ray source, which may pave the way towards 4D electron imaging with sub-atomic resolution in space and time.

Attosecond Physics

Based on the particle-in-cell (PIC) plasma simulation method, the speed-limited PIC (SLPIC) method delivers faster kinetic plasma simulation in cases where the particle distributions evolve slowly compared with the maximum stable PIC timestep. SLPIC thus offers more feasible, fully kinetic simulation in regimes that historically have required fluid approaches, such as magnetohydrodynamic (MHD), two-fluid, or Boltzmann electron treatments. In particular, SLPIC allows an explicit time advance with steps much larger than the inverse plasma frequency, avoiding the instability explicit PIC faces with large timesteps. SLPIC avoids this instability by slowing down fast particles (e.g., electrons) in a way that is rigorously underpinned by an approximate Vlasov equation; unlike MHD, two-fluid, and Boltzmann electron approaches, SLPIC does not fundamentally neglect any first-principles plasma physics, although the choices of grid cell size, timestep, and number of macroparticles per cell naturally limit the physical phenomena that can be accurately represented. SLPIC can be implemented with minor modifications of a standard PIC code and does not require an implicit time advance. It enables large timesteps in first-principles kinetic plasma simulation of appropriately slow phenomena, and it can handle many of the same complications as PIC, such as boundary conditions and collisions. In an argon plasma sheath test problem, a SLPIC simulation achieved a speed-up of a factor of 160 over the corresponding PIC simulation, without loss of accuracy.

Speeding Up Simulations By Slowing Down Particles: Speed-Limited Particle-In-Cell Simulation

Magnetic fields with translational symmetry, axisymmetry, and helical symmetry are integrable. That is, they have good flux surfaces. The current closure condition, that ∮dl/B is a flux surface quantity, also holds. It is possible to construct magnetic fields with broken symmetry, which have nearly integrable magnetic fields. It is shown that for nearly integrable nonsymmetric fields, the current closure condition need not hold.

Magnetic field integrability and the current closure condition

dxhdf5: A software package for importing HDF5 physics data into OpenDX☆

A simple analytical decay law for correlation functions of periodic, area-preserving maps is obtained. This law is compared with numerical experiments on the standard map. The agreement between experiment and theory is good when islands are absent, but poor when islands are present. When islands are present, the correlations have a long, slowly decaying tail.

Long-time correlations of periodic, area-preserving maps

Recent developments have shown that one can get around the difficulties of finding the eigenvalues and eigenmodes of the large systems studied with high performance computation by using broadly filtered diagonalization [G. R. Werner and J. R. Cary, J. Compo Phys. 227, 5200 (2008)]. This method can be used in conjunction with any time-domain computation, in particular those that scale very well up to 10000s of processors and beyond. Here we present results that show that this method accurately obtains both modes and frequencies of electromagnetic cavities, even when frequencies are nearly degenerate. The application was to a well-characterized Kaon separator cavity, the A15. The computations are shown to have a precision to a few parts in 10{sup 5}. Because the computed frequency differed from the measured frequency by more than this amount, a careful validation study to determine all sources of difference was undertaken. Ultimately, more precise measurements of the cavity showed that the computations were correct, with remaining differences accounted for by uncertainties in cavity dimensions and atmospheric and thermal conditions. Thus, not only was the method validated, but it was shown to have the ability to predict differences in cavity dimensions from fabrication specifications.

http://iopscience.iop.org/article/10.1088/1742-6596/180/1/012003/pdf

John R. Cary

Papers

Speeding Up Simulations By Slowing Down Particles: Speed-Limited Particle-In-Cell Simulation

Magnetic field integrability and the current closure condition

dxhdf5: A software package for importing HDF5 physics data into OpenDX☆

Long-time correlations of periodic, area-preserving maps

Validation of broadly filtered diagonalization method for extracting frequencies and modes from high-performance computations