Within the framework of a Hilbert space theory, we develop a maximum-``power variational principle (MPVP) applicable to classical spontaneous electromagnetic radiation from relativistic electron beams or other prescribed classical current sources. A
simple proof is summarized for the case of three-dimensional fields propagating in vacuum, and specialization to the important case of paraxial optics is also discussed. The techniques have been developed to model undulator radiation from relativistic electron beams, but are more broadly applicable to synchrotron or other radiation problems, and may generalize to certain structured media. We illustrate applications with a simple, mostly analytic example involving spontaneous undulator radiation (requiring a few additional approximations), as well as a mostly numerical example involving x-ray generation via high harmonic generation in sequenced undulators
The Constitutionally mandated task of assigning Congressional seats to the various U.S. States proportional to their represented populations (according to their numbers) has engendered much contention, but rather less consensus. Using the same princi
ples of entropic inference that underlie the foundations of information theory and statistical thermodynamics, and also enjoy fruitful application in image processing, spectral analysis, machine learning, econometrics, bioinformatics, and a growing number of other fields, we motivate and explore a method for Congressional apportionment based on minimizing relative entropy (also known as Kullback-Leibler divergence), or, equivalently, maximizing Shannon entropy. In terms of communication theory, we might say that the entropic apportionment gives each constituent as equal a voice as possible. If we view representational weight as a finite resource to be distributed amongst the represented population, the entropic measure is identical with the Theil index long employed in economics to measure inequality in the distribution of wealth or income, or in ecology to measure the distribution of biomass or reproductive fitness. Besides Congressional apportionment, the method is also directly applicable to other multi-regional or multi-constituency legislatures, to party-list proportional voting systems used in various parliamentary elections, and similar settings, where the task is to allocate a discrete number of seats or other resources, and the primary goal is one of maximal proportionality or equity. In addition, the same entropic figure-of-merit can be used in parallel to compare different choices for the total number of representatives, and then subsequently to assess different Congressional district sizes, after seats are assigned and proposed district boundaries drawn.
Ultra-fast stochastic cooling would be desirable in certain applications, for example, in order to boost final luminosity in a muon collider or neutrino factory, where short particle lifetimes severely limit the total time available to reduce beam ph
ase space. But fast cooling requires very high-bandwidth amplifiers so as to limit the incoherent heating effects from neighboring particles. A method of transit-time optical stochastic cooling has been proposed which would employ high-gain, high-bandwidth, solid-state lasers to amplify the spontaneous radiation from the charged particle bunch in a strong-field magnetic wiggler. This amplified light is then fed back onto the same bunch inside a second wiggler, with appropriate phase delay to effect cooling. But before amplification, the usable signal from any one particle is quite small, on average much less than one photon per pass, suggesting that the radiation should be treated quantum mechanically, and raising doubts as to whether this weak signal even contains sufficient phase information necessary for cooling, and whether it can be reliably amplified to provide the expected cooling on each pass. A careful examination of the dynamics, where the radiation and amplification processes are treated quantum mechanically, indicates that fast cooling is in principle possible, with cooling rates which essentially agree with classical calculations, provided that the effects of the unavoidable amplifier noise are included. Thus, quantum mechanical uncertainties do not present any insurmountable obstacles to optical cooling, but do establish a lower limit on cooling rates and achievable emittances.
Within the framework of Hilbert space theory, we derive a maximum-power variational principle applicable to classical spontaneous radiation from prescribed harmonic current sources. Results are first derived in the paraxial limit, then appropriately
generalized to non-paraxial situations. The techniques were developed within the context of undulator radiation from relativistic electron beams, but are more broadly applicable.
A modified version of the Plasma Beat-Wave Accelerator scheme is introduced and analyzed, which is based on autoresonant phase-locking of the nonlinear Langmuir wave to the slowly chirped beat frequency of the driving lasers via adiabatic passage thr
ough resonance. This new scheme is designed to overcome some of the well-known limitations of previous approaches, namely relativistic detuning and nonlinear modulation or other non-uniformity or non-stationarity in the driven Langmuir wave amplitude, and sensitivity to frequency mismatch due to measurement uncertainties and density fluctuations and inhomogeneities.
