Asymmetric lateral coherence of betatron radiation emitted in laser-driven light sources

Abstract

-We show that the radiation emitted by betatron oscillations of a high-energy electron beam undergoing wake-field acceleration is endowed with peculiar coherence properties which deliver quantitative information about the electron trajectories. Such results are achieved by means of accurate numerical simulations and a simple geometrical model gives a clear physical interpretation. Copyright c EPLA, 2015Introduction. -Radiation sources from relativistic beams are in continuous development due to the increasing demand of shorter wavelengths and higher brightness. Soft and hard X-rays are produced at large-scale facilities as synchrotrons and linacs (by means of wigglers, bending magnets, undulators) and in compact devices as laserdriven light sources. In many experiments, the emission has been optimized, and its properties measured and characterized in view of a wide range of applications [1]. In other cases, the information encoded in the radiation has been used to understand the beam dynamics [2] or to deduce the source parameters [3][4][5]. Useful information can be obtained from the coherence properties. Temporal coherence depends on the strength parameter a β = γr 0 k b , where γ is the Lorentz factor, r 0 is the oscillation amplitude and k b is the oscillation wave number. X-ray produced by sources with a β 1, such as magnetic wigglers or laser wake-field accelerators, are characterized by limited coherence length. Under these conditions, the analysis of the transverse spatial coherence is generally difficult or useless and the broad spectrum must be limited to get information about the bunches [6].In this work we show that the transverse coherence of a broad spectrum radiation can nevertheless be used to characterize the dynamics of the electron beam when the radiation is emitted in a narrow cone by particles moving along trajectories with non-zero

Analogical optical modeling of the asymmetric lateral coherence of betatron radiation

“…Following the optical analogy, we have reproduced the features of a broadband radiation emitted by electrons on a curved trajectory by means of a very simple table top optical setup operating with white light. Coherence measured through a double slit scheme accurately reproduce the expected enlargement effect, thus giving the first experimental confirmation of the effect described in [6]. The feasibility of the experiment is demonstrated also when properly scaled to the radiation wavelength.…”

“…Therefore, for a proper fixed point X 0 a second peak of the coherence factor is expected. The radiation observed simultaneously from the two points is the origin of the asymmetric enlargement discussed in [6]. The second peak of coherence is related to the particles oscillating in the half plane containing the fixed point.…”

“…The point X = (x, y, z) is referred to a Cartesian frame with the z-axis along the average motion of the electron beam, X 0 is an off-axis fixed point on the detection plane, which is the reference position for evaluating the coherence and τ = 0 elsewhere. In [6] we have shown that if the reference point X 0 is properly displaced from the average motion axis, the radiation obtained from the numerical simulations shows a characteristic asymmetry. It depends on the elongation and curvature of the particle trajectories, so that it gives statistical information about the dynamics of electrons undergoing oscillatory motions, with direct applications in particle beams and radiation source diagnostics.…”

“…A simplified geometrical interpretation of the coherence features described in [6] can be obtained by studying a single particle in a half-cycle of a betatron oscillation. The particle trajectory around the maximum x elongation is locally approximated by its osculator circle with radius R. The radiation is instantaneously emitted along the direction of the normalized particle velocity β = v/c, in a cone of width 1/γ.…”

“…More in general the mutual coherence of radiation should be used to take into account both temporal and spatial coherence effects and it should be considered when the radiation has a broad spectrum. Recently, we have devised particular features of the transverse coherence of broad spectrum radiation emitted by ultrarelativistic electrons undergoing betatron oscillations [6]. We have derived such results on the basis of accurate simulations of the betatron motion of electrons undergoing plasma wakefield acceleration in the SPARC LAB source at the National Laboratories of Frascati (LNF) [7].…”