Abstract
This paper sheds light on the time structure of betatron radiation, emitted by electrons that undergo betatron oscillations as they accelerate under the action of plasma wakefields. It is a common practice to assume that the betatron pulses are as short as the electron bunch length, however we show that this is not a general rule. Indeed, the betatron pulse length is affected by the betatron motion, which stretches and modulates the radiation pulses already at the source level. Propagation in a vacuum, therefore, can greatly lengthen the betatron pulses by orders of magnitude. In the wake of the above, the coherent emission of betatron radiation is studied. Coherent betatron radiation has been found to propagate in an underdense region created by ponderomotive forces, thus not suppressed by the overdense plasma absorption. This could be observed experimentally, revealing information on the acceleration process and on key beam parameters.
Highlights
Betatron radiation is the electromagnetic radiation emitted from electrons that undergo transverse oscillations as they accelerate under the action of three-dimensional plasma wakefields [1,2]
The physical explanation of Eq (2) is that the length of any electromagnetic pulse is found by a Pythagorean-like theorem, as if the square of the hypotenuse τr2ms were the sum of the squared lengths of the two sides, the first related to the variations of the spectral amplitude and the second to the variations of the spectral phase
It is extremely remarkable that the pulse length measured at a certain distance from the source can be significantly longer than the electron bunch length at the source
Summary
Betatron radiation is the electromagnetic radiation emitted from electrons that undergo transverse oscillations as they accelerate under the action of three-dimensional plasma wakefields [1,2]. Equation (1) must be understood as the full width at half-maximum (FWHM), and it could overestimate the bunch length by at least a factor of ∼4 [4] if the injected electron beam is high-quality and confined in the accelerating and focusing region of the plasma wave bucket (for example, obtained with a different injection scheme [18–20]) For typical parameters such as ne/nc ∼ 10−3–10−2 and Lacc = 1 mm, and assuming a betatron pulse length τFWHM equal to the electron bunch length, we obtain τFWHM = τb ∼ 5– 50 fs. Coherent betatron radiation would allow for simpler diagnostics of the electron bunch length than time-domain measurements of incoherent x-ray betatron pulses It would broaden the range of wavelengths emitted in plasma acceleration schemes.
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