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

A new adiabatic theory permits the understanding of one-dimensional dynamics of particles interacting with a large-amplitude wave packet for bounce time short compared with the transit time. This theory differs from previous ones in that the Hamiltonian varies slowly not with the time, but with the coordinate. The resulting adiabatic invariant is not equal, even in lowest order, to the usual action. This theory predicts the basic features of the interaction observed in previous numerical studies.

Particle dynamics in a large-amplitude wave packet.

Nonlinear wave-wave couplings near the upper hybrid resonance are studied via particle-in-cell simulations. It is found that the decay of an electron Bernstein wave (EBW) depends on the ratio of the incident frequency and electron cyclotron frequency. For ratios less than two, parametric decay into a lower hybrid wave (or an ion Bernstein wave) and EBWs at a lower frequency is observed. For ratios larger than two, the daughter waves could be an electron cyclotron quasi-mode and another EBW or an ion wave and EBW. For sufficiently high incident power, the former process may dominate. Because of the electron cyclotron quasi-mode, electrons can be strongly heated by nonlinear Landau damping. As a result, the bulk of the incident power can be absorbed near plasma edge at high power. The increase in number of decay channels with frequency implies that the allowable power into the plasma must decrease with frequency.

Decays of electron Bernstein waves near plasma edge

In the injection of electron-Bernstein waves (EBW) into a plasma, proposed for plasma heating and current drive in over-dense plasma, conversion of the fundamental to its second harmonic is predicted analytically and observed in computations. The mechanism is traced to the existence of locations where one can have both wave number and frequency matching between the fundamental and its harmonic. Further, at such locations, the second harmonic commonly has minimal group velocity, and this allows the amplitude of the second harmonic to build to values exceeding that of the fundamental at power levels less than anticipated in experiments. The second-harmonic power can then be deposited at half-harmonic resonances of the original wave, often far from the desired location of energy deposition. Estimates for the power at which this is significant are given.

Second-harmonic generation of electron-bernstein waves in an inhomogeneous plasma.

It was shown recently that it may 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 was pointed out that algorithmic difficulties related to discretization errors may have to be overcome in order to take full advantage of the potential speedup. In this paper, we summarize the findings, the difficulties and their solutions, and review the applications of the technique that have been performed to date.

/pdf/simulating-relativistic-beam-and-plasma-systems-using-an-3u05ow31mf.pdf

Simulating relativistic beam and plasma systems using an optimal boosted frame

Trapped particles in stellarators and tokamaks can be either locally trapped in the ripple wells or toroidally trapped by the 1/R variation of the magnetic field strength. Transitioning particles make transitions back and forth between these two states. The transition probability gives the relative rate of toroidally trapped particles to become locally trapped. In this paper the transition probably is uniquely defined, and an improved analytical calculation of the transition probability is given. It is then calculated numerically by following the full guiding‐center dynamics. Comparison with the numerical results shows that the present calculation is more accurate than those previously presented.

John R. Cary

Papers

Particle dynamics in a large-amplitude wave packet.

Decays of electron Bernstein waves near plasma edge

Second-harmonic generation of electron-bernstein waves in an inhomogeneous plasma.

Simulating relativistic beam and plasma systems using an optimal boosted frame

Probability of orbit transition in asymmetric toroidal plasma