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

Halo formation is an important issue in intense charged particle beams because the loss of halo particles can lead to radio activation of the accelerator. Halo formation can be described by a particle-core model in a continuous focusing channel. We explore the properties of such halo formation by numerical calculations of the equations of motion and from simulations using the object-oriented particle-in-cell code OOPIC, which was modified to allow for external focusing.

/pdf/halo-formation-in-an-intense-charged-particle-beam-6lnfnb1wmr.pdf

Halo formation in an intense charged particle beam

The truncated power series technique (differential algebra or DA) is a powerful tool for non-linear map analysis of accelerators. The most natural language for numerical DA's is C++, since it is object oriented and has operator overloading. Traditional C++, though, can be inefficient for scientific programming due to creation of many temporaries and extra loops in overloaded operators. The recent expression templates technique allows a user to combine the elegance of the object oriented approach with the speed of procedural languages. The way it was created, it is not directly applicable for DA. We created a set of classes whose structure will be suitable for implementing DA vectors and maps. Classes realizing the expression templates technique are separated from the client classes, which allows their reuse for different mathematical concepts. Speed tests on the KCC compiler showed that new C++ classes for DA have the same speed as hand-coded C.

/pdf/expression-templates-for-truncated-power-series-3fuljq4z6v.pdf

Expression templates for truncated power series

Electron and proton trapping and acceleration by an electron bubble in laser interaction with plasma are investigated by using three-dimensional particle-in-cell simulations. A nanowire is used to initialize the wave-breaking. Protons can be efficiently accelerated if the plasma consists mainly of heavier ions such as tritium.

Electron and Ion Acceleration in the Bubble Regime

Speed-limited particle-in-cell (SLPIC) simulation 1 is a new method for particle-based plasma modeling of systems wherein the timestep constraints needed for numerical stability are significantly more restrictive than is necessary to model the kinetic physics of interest. SLPIC effectively 'slows down' fast particles whose kinetics do not play a central role in the system dynamics, permitting larger simulation timesteps to be stably used and circumventing the need to resolve fast-timescale phenomena (e.g., electron plasma oscillations) that are irrelevant to slower kinetic processes. SLPIC is a relatively minor modification of conventional particle-in-cell techniques, and is compatible with the field solvers, boundary conditions, and general numerical approaches used by standard PIC; it has been shown to be more efficient than PIC methods in finding steady-state solutions for 1D collisionless sheath problems. In this presentation, we'll give a brief overview of how SLPIC differs from traditional PIC methods, and will explore the use of SLPIC techniques in Tech-X's VSim code to more rapidly and efficiently study the free expansion of plasma into vacuum 2.

Modeling Plasma Expansion Into Vacuum With Speed-Limited Particle-Incell (Slpic) Simulation

Integrating the Relativistic Lorentz Force Law for plasma simulations is an area of current research (*, **, ***). In particular, recent research indicates that interaction with highly-relativistic laser fields is particularly problematic for current integration techniques (****). Here is presented a special-purpose integrator yielding improved accuracy for highly-relativistic laser-particle interactions. This integrator has been implemented in the particle-in-cell code VSim, and the authors present an accuracy and performance comparison with several particle push methods.

John R. Cary

Papers

Halo formation in an intense charged particle beam

Expression templates for truncated power series

Electron and Ion Acceleration in the Bubble Regime

Modeling Plasma Expansion Into Vacuum With Speed-Limited Particle-Incell (Slpic) Simulation

Integrating the Lorentz Force Law for Highly-Relativistic Particle-in-Cell Simulations