Periodic Reporting for period 1 - STEFF (Strong-field electrodynamics in Flying Focus pulses)
Reporting period: 2023-05-01 to 2025-04-30
The dynamics of an electron in a strong external electromagnetic field is one of the most fundamental unsolved problems in classical and quantum electrodynamics (QED). In this regime, electron motion is dominated by quantum radiation reaction (RR), which is the loss of energy and momentum of electrons due to their own radiation under acceleration. Aside from the unquestionable fundamental interest, this problem is of practical importance as a laboratory source of gamma rays and because it can explain radiative properties of extreme astrophysical objects, such as quasars and pulsars. In the past decade, ultra-intense laser pulses were established as a powerful tool soon-to-be capable of probing the light-electron interactions in this regime. In fact, the first ultra-intense laser-based RR experiments were conducted in 2018. The results so far had difficulties distinguishing between RR models because of the low event statistics at current laser intensities, problematic laser-electron beam synchronization and issues determining laser beam parameters during the interaction.
This project has a potential to overcome the above mentioned challenges by theoretically investigating particle beam behavior in external laser fields using the recently-described “flying focus” (FF) laser pulses. FF pulses allow precise control of the position and velocity of their peak intensity, which can travel at any velocity, over distances much longer than a Rayleigh range. Specifically, particle beams can propagate with the laser focus, so that the particles stay in the region of peak field intensity orders of magnitude longer than in collisions with stationary focus gaussian (SFG) pulses (see Fig. 1). This has profound implications, because any cumulative effects are amplified by the prolonged interaction times. The objectives of this project were the following:
+ Exploring cumulative aspects of classical electron-laser interactions in FF regime.
+ Developing analytical and numerical tools for studying strong field processes in FF laser pulses.
+ Simulating strong-field processes in FF regime and identifying circumstances in which FF pulses outperform SFG pulses.
Both the theoretical and simulation parts of this project were aimed towards devising experimental scenarios realizable with existing technology which would bridge the current gap in laser capabilities and allow us to probe directly the strong-field QED regime and unlock other useful capabilities.
This project has a potential to overcome the above mentioned challenges by theoretically investigating particle beam behavior in external laser fields using the recently-described “flying focus” (FF) laser pulses. FF pulses allow precise control of the position and velocity of their peak intensity, which can travel at any velocity, over distances much longer than a Rayleigh range. Specifically, particle beams can propagate with the laser focus, so that the particles stay in the region of peak field intensity orders of magnitude longer than in collisions with stationary focus gaussian (SFG) pulses (see Fig. 1). This has profound implications, because any cumulative effects are amplified by the prolonged interaction times. The objectives of this project were the following:
+ Exploring cumulative aspects of classical electron-laser interactions in FF regime.
+ Developing analytical and numerical tools for studying strong field processes in FF laser pulses.
+ Simulating strong-field processes in FF regime and identifying circumstances in which FF pulses outperform SFG pulses.
Both the theoretical and simulation parts of this project were aimed towards devising experimental scenarios realizable with existing technology which would bridge the current gap in laser capabilities and allow us to probe directly the strong-field QED regime and unlock other useful capabilities.
+ A code was developed to propagate a single particle in exact flying focus fields, including those with higher orbital angular momenta. This code employs a classical RR module and a stochastic quantum Monte-Carlo module to describe RR energy loss in different parameter regimes. In the classical regime we proved that charged particles can be confined in FF beams with L=1 angular momentum.
+ A model for collective radiation of electrons in FF undulator was devised. Simulations of microbunching and coherent production of x-rays showed the energy advantage of the FF pulses.
+ A wave-function of an electron with flying focus properties was described and a photon emission probability of such an electron in a laser pulse modelled as a plane wave was calculated.
+ The vacuum polarization effects in co-propagation of a high-energy x-ray probe beam with the peak intensity of a FF laser pulse were described analytically and simulated numerically. It was shown how the vacuum polarization effect accumulates with the interaction time.
+ Finally, the electron beam interaction with a FF pulse using both the Particle-In-Cell code SMILEI and our custom made code was simulated, and parameter regimes where FF pulses outperform SFG pulses were identified.
+ A model for collective radiation of electrons in FF undulator was devised. Simulations of microbunching and coherent production of x-rays showed the energy advantage of the FF pulses.
+ A wave-function of an electron with flying focus properties was described and a photon emission probability of such an electron in a laser pulse modelled as a plane wave was calculated.
+ The vacuum polarization effects in co-propagation of a high-energy x-ray probe beam with the peak intensity of a FF laser pulse were described analytically and simulated numerically. It was shown how the vacuum polarization effect accumulates with the interaction time.
+ Finally, the electron beam interaction with a FF pulse using both the Particle-In-Cell code SMILEI and our custom made code was simulated, and parameter regimes where FF pulses outperform SFG pulses were identified.
This project explored scenarios in which interaction of particles with FF pulses provides an advantage to stationary focus gaussian (SFG) setups. First, we have shown the ability of L=1 orbital angular momentum FF pulses to trap the electrons or positrons close to the beam axis for prolonged interaction lengths (see Fig. 2) using much less laser energy than other approaches. This can be beneficial for future laser-based electron or positron accelerators, by preventing the spreading of particle beams between acceleration stages. An experimental demonstration of this effect is required for further development.
By investigating collective effects in a classical interaction of electrons with laser pulses, we have shown that FF pulses can substantially reduce the energy required to produce coherent, narrowband, high-power X-rays in a laser-driven free-electron laser. In contrast to the static focal point of a conventional laser pulse, the dynamic focal point of a flying-focus pulse travels with the electron beam, ensuring a uniform undulator over the entire interaction length (Fig. 3). Coherent X-rays allow for imaging of molecules, cells, high-energy-density materials, and structural defects, absorption spectroscopy and Thomson scattering to probe the structure of matter, and the exploration of QED processes. If realized, our FF-based setup provides an extremely compact source with much lower laser pulse energy requirements than other optical undulator proposals.
In the interaction of high energy photons with vacuum polarized by a laser pulse the interaction time can be prolonged by many orders of magnitude by employing FF pulses. Figure 1 shows that while in the FF pulse case (a) the blue probe x-ray beam co-propagates with the peak intensity of the FF pulse (red) for the distance of many Rayleigh ranges, in the SFG case (b) the x-ray beam quickly passes through the focal region. We have demonstrated the possibility of measuring vacuum birefringence in low-power flying focus pulses by letting the effect on the probe x-ray beam phase shift accumulate. There is a concerted push to provide the all-optical proof of vacuum birefringence at XFEL facilities including European XFEL. Our proposal uses more accessible laser systems by lowering the requirements on the laser peak power from petawatts to terawatts and thus could prove viable for experimental implementation in the near future.
Similar tradeoff can be achieved in the interaction of a high energy laser pulse with ultra-relativistic electrons in which the electrons lose energy through radiation. With fixed-energy FF pulses we can again substantially lower the laser power and intensity in exchange for extending the interaction time. Moreover, we demonstrated that the electron energy loss in the quantum regime, and the photon yield in general, scale more favorably with the interaction time than the laser intensity. Therefore higher energy loss and photon yields can be achieved by employing a long FF pulse, rather than an equal energy short SFG pulse. In this way FF pulses create a more controllable environment with simpler diagnostics of the interaction field strength, while simultaneously providing an extremely high-brilliance source of gamma radiation. Planned future experiments will demonstrate this method's usefulness for producing gamma rays applicable in cancer treatment, nuclear waste disposal, and medical isotope production.
By investigating collective effects in a classical interaction of electrons with laser pulses, we have shown that FF pulses can substantially reduce the energy required to produce coherent, narrowband, high-power X-rays in a laser-driven free-electron laser. In contrast to the static focal point of a conventional laser pulse, the dynamic focal point of a flying-focus pulse travels with the electron beam, ensuring a uniform undulator over the entire interaction length (Fig. 3). Coherent X-rays allow for imaging of molecules, cells, high-energy-density materials, and structural defects, absorption spectroscopy and Thomson scattering to probe the structure of matter, and the exploration of QED processes. If realized, our FF-based setup provides an extremely compact source with much lower laser pulse energy requirements than other optical undulator proposals.
In the interaction of high energy photons with vacuum polarized by a laser pulse the interaction time can be prolonged by many orders of magnitude by employing FF pulses. Figure 1 shows that while in the FF pulse case (a) the blue probe x-ray beam co-propagates with the peak intensity of the FF pulse (red) for the distance of many Rayleigh ranges, in the SFG case (b) the x-ray beam quickly passes through the focal region. We have demonstrated the possibility of measuring vacuum birefringence in low-power flying focus pulses by letting the effect on the probe x-ray beam phase shift accumulate. There is a concerted push to provide the all-optical proof of vacuum birefringence at XFEL facilities including European XFEL. Our proposal uses more accessible laser systems by lowering the requirements on the laser peak power from petawatts to terawatts and thus could prove viable for experimental implementation in the near future.
Similar tradeoff can be achieved in the interaction of a high energy laser pulse with ultra-relativistic electrons in which the electrons lose energy through radiation. With fixed-energy FF pulses we can again substantially lower the laser power and intensity in exchange for extending the interaction time. Moreover, we demonstrated that the electron energy loss in the quantum regime, and the photon yield in general, scale more favorably with the interaction time than the laser intensity. Therefore higher energy loss and photon yields can be achieved by employing a long FF pulse, rather than an equal energy short SFG pulse. In this way FF pulses create a more controllable environment with simpler diagnostics of the interaction field strength, while simultaneously providing an extremely high-brilliance source of gamma radiation. Planned future experiments will demonstrate this method's usefulness for producing gamma rays applicable in cancer treatment, nuclear waste disposal, and medical isotope production.