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

Oscillatory modes of the Pierce system have been calculated. These modes are found to have growth rates comparable to the previously investigated purely growing modes. When these modes are included, it is found that the Pierce system is unstable for most values of ωp L/V0≳π.

Unstable oscillatory Pierce modes of neutralized electron beams

Divergence preservation in the ADI algorithms for electromagnetics

A modified Boris-like integration, in which the spatial coordinate is the independent variable, is derived. This spatial-Boris integration method is useful for beam simulations, in which the independent variable is often the distance along the beam. The new integration method is second order accurate, requires only one force calculation per particle per step, and preserves conserved quantities more accurately over long distances than a Runge-Kutta integration scheme. Results from the spatial-Boris integration method and a Runge-Kutta scheme are compared for two simulations: (i) a particle in a uniform solenoid field and (ii) a particle in a sinusoidally varying solenoid field. In the uniform solenoid case, the spatial-Boris scheme is shown to perfectly conserve for any step size quantities such as the gyroradius and the perpendicular momentum. The Runge-Kutta integrator produces damping in these conserved quantities. In the sinusoidally varying case, the conserved quantity of canonical angular momentum is used to measure the accuracy of the two schemes. For the sinusoidally varying field simulations, error analysis is used to determine the integration distance beyond which the spatial-Boris integration method is more efficient than a fourth-order Runge-Kutta scheme. For beam physics applications where statistical quantities such as beam emittance are important, these results imply the spatial-Boris scheme is 3 times more efficient.

http://raman.physics.berkeley.edu/papers/EfficiencyOfBoris-likeIntegration_PhysRevSTAB_5_094001.pdf

Efficiency of a Boris-like integration scheme with spatial stepping

High amplitude coherent electron‐trajectories have been seen in 3D particle‐in‐cell simulations of the colliding pulse injection scheme of laser‐wakefield accelerators in the bubble regime, and explained as a consequence of laser‐driven coherent betatron oscillation in our recent paper [K. Nemeth et al., Phys. Rev. Lett. 100, 095002 (2008)]. In the present paper we provide more details on the shape of the trajectories, their relationship to the phase velocity of the laser and indicate the dependence of the phenomenon on the accuracy of the numerical representation and choice of laser/plasma parameters.

Laser-Driven Coherent Betatron Oscillation in a Laser-Wakefield Cavity: Formation of Sinusoid Beam Shapes and Coherent Trajectories

An enhancement of the velocity diffusion over the quasilinear value is observed in the regime where the autocorrelation time is much smaller than the linear growth time or resonance broadening time. The diffusion enhancement occurs when the resonance broadening time is small compared with the linear growth time. These simulations are self consistent and have enough modes to be in the continuous spectrum limit. That is, even at the initial amplitudes the intermode spacing is sufficiently small that the resonance overlap parameter is large. A possible mechanism for the enhanced diffusion (spontaneous spectrum discretization) is discussed.

John R. Cary

Papers

Unstable oscillatory Pierce modes of neutralized electron beams

Divergence preservation in the ADI algorithms for electromagnetics

Efficiency of a Boris-like integration scheme with spatial stepping

Laser-Driven Coherent Betatron Oscillation in a Laser-Wakefield Cavity: Formation of Sinusoid Beam Shapes and Coherent Trajectories

Numerical observation of turbulence enhanced growth rates