This paper develops a model of rational bubbles where trade of an asset takes place through a chain of middlemen. We show that there exists a unique and robust equilibrium, and a bubble can occur due to information frictions in bilateral and decentralized markets. Under reasonable assumptions, the equilibrium price is increasing and accelerating during bubbles although the fundamental value is constant over time. Bubbles may be detrimental to the economy, but any announcement from the central bank has no effect on welfare with risk neutral agents. Middlemen are the source of financial fragility.

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Particle counting analysis (PCA) with a multi-stage scintillation detector shows a new perspective on angularly resolved spectral characterization of GeV-scale, multi-species ion beams produced by high-power lasers. The diagnosis provides a mass-dependent ion energy spectrum based on time-of-flight and pulse-height analysis of single particle events detected through repetitive experiments. With a novel arrangement of multiple scintillators with different ions stopping powers, PCA offers potential advantages over commonly used diagnostic instruments (CR-39, radiochromic films, Thomson parabola, etc .) in terms of coverage solid angle, detection efficiency for GeV-ions, and real-time analysis during the experiment. The basic detector unit was tested using 230-MeV proton beam from a synchrotron facility, where we demonstrated its potential ability to discriminate major ion species accelerated in laser–plasma experiments (i.e., protons, deuterons, carbon, and oxygen ions) with excellent energy and mass resolution. The proposed diagnostic concept would be essential for a better understanding of laser-driven particle acceleration, which paves the way toward all-optical compact accelerators for a range of applications.