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Register a new userCoherent Synchrotron Radiation in Whispering Gallery Modes: Theory and Evidence
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Authors
Robert L. Warnock
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Theory predicts that Coherent Synchrotron Radiation (CSR) in electron storage rings should appear in whispering gallery modes. In an idealized model these are resonances of the vacuum chamber that are characterized by their high frequencies and concentration of the field near the outer wall of the chamber. The resonant modes imply a series of sharp peaks in the frequency spectrum of CSR, and very long wake fields which lead to interbunch communication. Theory and experimental evidence for this behavior will be reviewed.
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We report on high resolution measurements of resonances in the spectrum of coherent synchrotron radiation (CSR) at the Canadian Light Source (CLS). The resonances permeate the spectrum at wavenumber intervals of $0.074 ~textrm{cm}^{-1}$, and are highly stable under changes in the machine setup (energy, bucket filling pattern, CSR in bursting or continuous mode). Analogous resonances were predicted long ago in an idealized theory as eigenmodes of a smooth toroidal vacuum chamber driven by a bunched beam moving on a circular orbit. A corollary of peaks in the spectrum is the presence of pulses in the wakefield of the bunch at well defined spatial intervals. Through experiments and further calculations we elucidate the resonance and wakefield mechanisms in the CLS vacuum chamber, which has a fluted form much different from a smooth torus. The wakefield is observed directly in the 30-110 GHz range by RF diodes, and indirectly by an interferometer in the THz range. The wake pulse sequence found by diodes is less regular than in the toroidal model, and depends on the point of observation, but is accounted for in a simulation of fields in the fluted chamber. Attention is paid to polarization of the observed fields, and possible coherence of fields produced in adjacent bending magnets. Low frequency wakefield production appears to be mainly local in a single bend, but multi-bend effects cannot be excluded entirely, and could play a role in high frequency resonances. New simulation techniques have been developed, which should be invaluable in further work.
Quasiclassical approach and geometric optics allow to describe rather accurately whispering gallery modes in convex axisymmetric bodies. Using this approach we obtain practical formulas for the calculation of eigenfrequencies and radiative Q-factors in dielectrical spheroid and compare them with the known solutions for the particular cases and with numerical calculations. We show how geometrical interpretation allows expansion of the method on arbitrary shaped axisymmetric bodies.
An understanding of collective effects is of fundamental importance for the design and optimisation of the performance of modern accelerators. In particular, the design of an accelerator with strict requirements on the beam quality, such as a free electron laser (FEL), is highly dependent on a correspondence between simulation, theory and experiments in order to correctly account for the effect of coherent synchrotron radiation (CSR), and other collective effects. A traditional approach in accelerator simulation codes is to utilise an analytic one-dimensional approximation to the CSR force. We present an extension of the 1D CSR theory in order to correctly account for the CSR force at the entrance and exit of a bending magnet. A limited range of applicability to this solution, in particular in bunches with a large transverse spot size or offset from the nominal axis, is recognised. More recently developed codes calculate the CSR effect in dispersive regions directly from the Lienard-Wiechert potentials, albeit with approximations to improve the computational time. A new module of the General Particle Tracer (GPT) code was developed for simulating the effects of CSR, and benchmarked against other codes. We experimentally demonstrate departure from the commonly used 1D CSR theory for more extreme bunch length compression scenarios at the FERMI FEL facility. Better agreement is found between experimental data and the codes which account for the transverse extent of the bunch, particularly in more extreme compression scenarios.
Designing high-finesse resonant cavities for electronic waves faces challenges due to short electron coherence lengths in solids. Previous approaches, e.g. the seminal nanometer-sized quantum corrals, depend on careful positioning of adatoms at clean surfaces. Here we demonstrate an entirely different approach, inspired by the peculiar acoustic phenomena in whispering galleries. Taking advantage of graphenes unique properties, namely gate-tunable light-like carriers, we create Whispering Gallery Mode (WGM) resonators defined by circular pn-junctions, induced by a scanning tunneling probe. We can tune the resonator size and the carrier concentration under the probe in a back-gated graphene device over a wide range, independently and in situ. The confined modes, revealed through characteristic resonances in the tunneling spectrum, originate from Klein scattering at pn junction boundaries. The WGM-type confinement and resonances are a new addition to the quantum electron-optics toolbox, paving the way to real-world electronic lenses and resonators.
We develop a general model of coherent synchrotron radiation (CSR) impedance with shielding provided by two parallel conducting plates. This model allows us to easily reproduce all previously known analytical CSR wakes and to expand the analysis to the situations not explored before. It reduces calculations of the impedance to taking integrals along the trajectory of the beam. New analytical results are derived for the radiation impedance with shielding for the following orbits: a kink, a bending magnet, a wiggler of finite length, and an infinitely long wiggler. All our formulas are benchmarked agains numerical simulations with the CSRZ computer code.
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