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

Crystallization of beams and non neutral plasmas is a fundamental process. A factor limiting the cooling of beams and non neutral plasmas is the energy exchange between the different degrees of freedom. To understand this problem, we study the crystallization of a strongly magnetized, non neutral plasma, where the exchange between perpendicular and parallel energy is small (in the limit of gyroradius small compared to Debye length). We introduce a microwave bath to transfer energy from the poorly cooled parallel degree of freedom to the well cooled (by synchrotron radiation) perpendicular degree of freedom. Results for the cooling of the parallel degree of freedom will be presented.

/pdf/cooling-of-non-neutral-plasma-by-energy-exchange-38zvors2y8.pdf

Cooling of non-neutral plasma by energy exchange

Cooling of Non-neutral Plasma by Energy Exchange

Numerical Simulations of A Crystallized Non-neutral Plasma

This paper briefly reviews the use of Lie transform perturbation theory applied to the dynamics of charged particle beams. Several details not provided here can be found in [1] and [2]. The work analyzes influences due to nonlinear components in external focusing of beams, a regime where the Courant-Snyder invariants are broken [3] for single particle dynamics. The Lie transform analysis is also used to analyze beams with space charge effects, which satisfy the Vlasov -Poisson system of equations. Equilibrium distributions may be obtained even in the nonlinear focusing regime, where simple solution such as the Kapchinskij-Vladimirskij [4] are no longer valid. The work utilizes results that were obtained earlier as part of the research activities of Prof. Allan Kaufman and members of his group.

Analyzing charged particle beams using lie transform perturbation theory

The optimal values of Q and (/spl omega/ - /spl Omega//sub r/) for cooling a pure electron plasma with a microwave bath have been calculated. An electron plasma which has no internal degree of freedom, cannot be cooled down below a heat bath temperature. However, the longitudinal cooling can be achieved by energy transfer from the poorly cooled parallel degree of freedom to the well cooled (by synchrotron radiation) perpendicular degree of freedom. To do this, we introduce a microwave bath to the electron plasma. A microwave tuned to a frequency below the gyrofrequency of the electron forces an electron moving towards the microwave to absorb a photon and then to move up one in Landau state. The electron loses longitudinal momentum in this process, so that the longitudinal energy can be reduced. On the basis that most of the electrons are in the ground or first excited state, we set up a transition equation and develop a FEM code. With an appropriate condition for B-field and intensity of the microwave, the cooling times for several values of Q and (/spl omega/ - /spl Omega//sub r/) are calculated and the optimal values are found. Applying the optimal values at appropriate times in a cooling process, the best cooling can be obtained. For an electron plasma magnetized with 10 T B-field, cooling to the solid state can occur within 2 hours. Without this optimization, times were always several hours, longer than the life time of the plasma in real system.

https://epaper.kek.jp/p03/papers/wpae040.pdf

John R. Cary

Papers

Cooling of non-neutral plasma by energy exchange

Cooling of Non-neutral Plasma by Energy Exchange

Numerical Simulations of A Crystallized Non-neutral Plasma

Analyzing charged particle beams using lie transform perturbation theory

Longitudinal cooling of a strongly magnetized electron plasma