In the field of beam physics, two frontier topics have taken center stage due to their potential to enable new approaches to discovery in a wide swath of science. These areas are: advanced, high gradient acceleration techniques, and x-ray free electron lasers (XFELs). Further, there is intense interest in the marriage of these two fields, with the goal of producing a very compact XFEL. In this context, recent advances in high gradient radio-frequency cryogenic copper structure research have opened the door to the use of surface electric fields between 250 and 500 MV m−1. Such an approach is foreseen to enable a new generation of photoinjectors with six-dimensional beam brightness beyond the current state-of-the-art by well over an order of magnitude. This advance is an essential ingredient enabling an ultra-compact XFEL (UC-XFEL). In addition, one may accelerate these bright beams to GeV scale in less than 10 m. Such an injector, when combined with inverse free electron laser-based bunching techniques can produce multi-kA beams with unprecedented beam quality, quantified by 50 nm-rad normalized emittances. The emittance, we note, is the effective area in transverse phase space (x, p x /m e c) or (y, p y /m e c) occupied by the beam distribution, and it is relevant to achievable beam sizes as well as setting a limit on FEL wavelength. These beams, when injected into innovative, short-period (1–10 mm) undulators uniquely enable UC-XFELs having footprints consistent with university-scale laboratories. We describe the architecture and predicted performance of this novel light source, which promises photon production per pulse of a few percent of existing XFEL sources. We review implementation issues including collective beam effects, compact x-ray optics systems, and other relevant technical challenges. To illustrate the potential of such a light source to fundamentally change the current paradigm of XFELs with their limited access, we examine possible applications in biology, chemistry, materials, atomic physics, industry, and medicine—including the imaging of virus particles—which may profit from this new model of performing XFEL science.

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A numerical approach for the solution of Maxwell's equations is presented. Based on a finite difference Yee lattice the method transforms each of the four Maxwell equations into an equivalent matrix expression that can be subsequently treated by matrix mathematics and suitable numerical methods for solving matrix problems. The algorithm, although derived from integral equations, can be considered to be a special case of finite difference formalisms. A large variety of two and three-dimensional field problems can be solved by computer programs based on this approach: electro statics and magnetostatics, low-frequency eddy currents in solid and laminated iron cores, high-frequency modes in resonators, waves on dielectric or metallic waveguides, transient fields of antennas and waveguide transitions, transient fields of free-moving bunches of charged particles etc.

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Two-plane focusing of sheet electron beams will be an essential technology for an emerging class of high-power, 100 to 300 GHz rf sources [Carlsten et al., IEEE Trans. Plasma Sci. 33, 85 (2005)]. In these devices, the beam has a unique asymmetry in which the transport is emittance dominated in the sheet's thin dimension and space-charge dominated in the sheet's wide dimension. Previous work has studied the stability of the transport of beams in the emittance-dominated regime for both wiggler and periodic permanent magnet (PPM) configurations with single-plane focusing, and has found that bigger envelope scalloping occurs for equilibrium transport, as compared to space-charge dominated beams [Carlsten et al., this issue, Phys. Rev. ST Accel. Beams 8, 062001 (2005)]. In this paper, we describe the differences in transport stability when two-plane focusing is included. Two-plane wiggler focusing degrades the transport stability slightly, whereas two-plane PPM focusing greatly compromises the transport. On the other hand, single-plane PPM focusing can be augmented with external quadrupole fields to provide weak focusing in the sheet's wide dimension, which has stability comparable to two-plane wiggler transport.