A novel ultra-bright high-intensity source of X-ray and gamma radiation is suggested. It is based on the double Doppler effect, where a relativistic flying mirror reflects a counter-propagating electromagnetic radiation causing its frequency multiplication and intensification, and on the inverse double Doppler effect, where the mirror acquires energy from an ultra-intense co-propagating electromagnetic wave. The role of the flying mirror is played by a high-density thin plasma slab accelerating in the radiation pressure dominant regime. Frequencies of high harmonics generated at the flying mirror by a relativistically strong counter-propagating radiation undergo multiplication with the same factor as the fundamental frequency of the reflected radiation, approximately equal to the quadruple of the square of the mirror Lorentz factor.
Deep Dive into Laser-driven high-power X- and gamma-ray ultra-short pulse source.
A novel ultra-bright high-intensity source of X-ray and gamma radiation is suggested. It is based on the double Doppler effect, where a relativistic flying mirror reflects a counter-propagating electromagnetic radiation causing its frequency multiplication and intensification, and on the inverse double Doppler effect, where the mirror acquires energy from an ultra-intense co-propagating electromagnetic wave. The role of the flying mirror is played by a high-density thin plasma slab accelerating in the radiation pressure dominant regime. Frequencies of high harmonics generated at the flying mirror by a relativistically strong counter-propagating radiation undergo multiplication with the same factor as the fundamental frequency of the reflected radiation, approximately equal to the quadruple of the square of the mirror Lorentz factor.
An electromagnetic wave reflected off a moving mirror undergoes frequency multiplication and corresponding increase in the electric field magnitude. This phenomenon sometimes called the double Doppler effect was discussed by A. Einstein in his seminal paper [1] where the frequency multiplication factor was calculated as an example of the use of Lorentz transformations. The multiplication factor is approximately proportional to the square of the Lorentz factor of the mirror, making this effect an attractive basis for a source of powerful high-frequency radiation. In relativistic plasma, the double Doppler effect manifests itself when a fast change of the electric current density leads to the conversion of an incident light into strongly compressed pulses of high-frequency electromagnetic radiation.
Pulse compression and frequency upshifting can be seen in a broad variety of configurations, [2]. A specular reflection can be afforded by a sufficiently dense relativistic electron cloud as suggested in Refs. [3,4]; a less dense bunch of relativistic electrons causes the backward Thomson scattering as discussed in Refs. [5]. The reflection at the moving ionization fronts was studied in Refs. [6]. Further examples of the manifestation of the double Doppler effect in plasma whose dynamics is governed by the strong collective fields are seen in the concepts of the sliding mirror [7], oscillating mirror [8,9] and flying mirror [10] which can produce ultra-short pulses of XUV radiation and X-ray.
The sliding mirror is formed by a thin foil whose density is so high that the electrons are confined whithin the boundaries of the ion layer. Irradiated by a relativistically strong laser pulse, which is not capable to quickly break the confinement condition, these electrons perform nonlinear motion along the foil, enriching the (partially) reflected radiaiton (as well as transmitted radiation) with high harmonics, [7]. In a less dense foil the electrons can perform collective motion in the direction perpendicular to the foil, thus forming a mirror oscillating with relativistic velocity. A portion of an incident relativistically strong electromagnetic wave, driving the oscillating mirror, is reflected in the form of strongly distorted wave carrying high harmonics, [8,9,11].
In the flying mirror concept [10], the role of the mirror is played by the electron density modulations in a strongly nonlinear Langmuir wave excited by an intense laser pulse (driver) in its wake in underdense plasma. A relatively weak counter-propagating electromagnetic wave (source) is (partially) reflected at these modulations moving with the velocity equal to the group velocity of the driving laser pulse. In addition, due to a finite waist of the driver pulse, the electron density modulations take a paraboloidal shape [12], and hence focus the reflected radiation (signal). The most efficient reflection is afforded by a breaking wake wave, where the caustics of the plasma flow are formed and correspondingly the electron density becomes formally singular. The reflection coefficient is calculated in [13] for a broad class of caustics. For the case of the breaking Langmuir wave, the reflection efficiency is high enough to acess, with present-day technology, the quantum electrodynamics (QED) critical field in the focus of the reflected signal [10].
Here we discuss a novel scheme of the flying mirror, the accelerating double-sided mirror, which can efficiently reflect the counter-propagating relativistically strong electromagnetic radiation. The role of the mirror is played by a high-density plasma slab which is accelerated as a whole by an ultra-intense laser pulse (the driver) in the Radiation Pressure Dominant (RPD) regime (synonymous to the Laser Piston regime), [14]. Such an acceleration can be described as the mirroring effect: it is the reflection that allows the energy transfer from the driver radiation to the co-propagating plasma slab. This effect is inverse with respect to the double Doppler effect. This plasma slab also acts as a mirror for a counter-propagating relativistically strong electromagnetic radiation (the source). As such it exhibits the properties of the sliding and oscillating mirrors, producing high harmonics. As a result, in the spectrum of the reflected radiation both the fundamental frequency of the incident radiation and all the high harmonics are multiplied by the same factor, approximately proportional to the square of the Lorentz factor of the mirror. This concept opens the way towards extremely bright sources of ultrashort energetic bursts of X-ray and gamma-ray, which become realizable with present-day technology.
In the next sections we recall some aspects of the flying mirror concept, then we present the scheme of the accelerating mirror and corresponding computer simulations. Finally, we discuss the prospects of the proposed concept.
The factor by which the frequency of the reflected electromagnetic radiation is m
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