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

We present 2-D cylindrical particle-in-cell simulations of the E-157 beam wakefield experiment at SLAC, in which a 30 GeV electron beam passes through 1 m of preionized Li (lithium) plasma. Plasma electrons are blown out from the axis in the wake of the electron beam, driving a strong axial electric field, E z of order 1 GV/m, in the small region where the plasma electrons fall back to the cylin- drical axis. We also simulate wakefield accelerators with much higher plasma density and a 50 GeV drive beam. Electron impact ionization of the background neutral Li is found to be significant only for plasma densities of order 1017 cm-3 or larger. Other collisional processes are also considered.

Simulations of plasma wakefield

Improved Particle Statistics for Laser-Plasma Self-Injection Simulations

This work shows that halos in beams with space charge effects can be controlled by combining nonlinear focusing and collimation. The study relies on Particle-in-Cell (PIC) simulations for a one dimensional, continuous focusing model. The PIC simulation results show that nonlinear focusing leads to damping of the beam oscillations thereby reducing the mismatch. It has been well established previously that reduced mismatch leads to reduced halo formation. However, the nonlinear damping is accompanied by emittance growth causing the beam to spread in phase space. As a result, inducing nonlinear damping alone cannot help mitigate the halo. To compensate for this expansion in phase space, the beam is collimated in the simulation and further evolution of the beam shows that the halo is not regenerated. The focusing model used in the PIC simulation will be briefly discussed based on a systematic analysis that has already been done through canonical averaging using Lie transform perturbation theory. This analysis shows that by averaging over a lattice period for a specific arrangement of linear and nonlinear elements, one can reduce the focusing force to a form that is identical to that used in the PIC simulation in an averaged sense, thus providing an equivalence between the model and a realistic system.

Halo Mitigation Using Nonlinear Lattices

High-performance computations on Blue Gene/P at Argonne's Leadership Computing Facility have been used to determine phase shifts induced in injected RF diagnostics as a function of electron cloud density in the Main Injector. Inversion of the relationship between electron cloud parameters and induced phase shifts allows us to predict electron cloud density and evolution over many bunch periods. Long time-scale simulations using Blue Gene have allowed us to measure cloud evolution patterns under the influence of beam propagation with realistic physical parameterizations, such as elliptical beam pipe geometry, self-consistent electromagnetic fields, space charge, secondary electron emission, and the application of arbitrary external magnetic fields. Simultaneously, we are able to simulate the use of injected microwave diagnostic signals to measure electron cloud density, and the effectiveness of various mitigation techniques such as surface coating and the application of confining magnetic fields. These simulations provide a baseline for both RF electron cloud diagnostic design and accelerator fabrication in order to measure electron clouds and mitigate the adverse effects of such clouds on beam propagation.

/pdf/computation-of-electron-cloud-diagnostics-and-mitigation-in-4byrdpttw1.pdf

Computation of electron cloud diagnostics and mitigation in the main injector

The frequency extraction algorithm (Werner and Cary 2008 J. Comp. Phys. 227 5200) that enables a simple finite-difference time-domain algorithm to be transformed into an efficient eigenmode solver is applied to a realistic accelerator cavity modeled with embedded boundaries. Previously, the frequency extraction method was shown to be capable of distinguishing M degenerate modes by running M different simulations and to permit mode extraction with minimal post-processing effort that requires solving only a small eigenvalue problem. Realistic calculations for an accelerator cavity are presented in this paper to validate the method for realistic modeling scenarios and to illustrate the complexities of the computational validation process. The approach is able to extract frequencies that differ by corrected experimentally measured frequencies by about 1 part in 104, which is accounted for (in largest part) by machining errors. The extraction of frequencies and modes from accelerator cavities provides engineers and physicists with an understanding of potential cavity performance as it depends on the shape without incurring manufacture and measurement costs.

John R. Cary

Papers

Simulations of plasma wakefield

Improved Particle Statistics for Laser-Plasma Self-Injection Simulations

Halo Mitigation Using Nonlinear Lattices

Computation of electron cloud diagnostics and mitigation in the main injector

Validation of frequency extraction calculations from time-domain simulations of accelerator cavities