Quantum Free-electron Laser Research Articles

Quantum description of free electron laser radiation and nonlinear amplitude equations

A relativistic quantum mechanical model to describe the quantum free electron laser dynamics has been developed. Neglecting the spin of electrons in the impacting beam, this model is based on the Klein–Gordon equation coupled to the Poisson equation for the space-charge potential and the wave equation for the transverse components of the radiation field. Furthermore, a system of coupled nonlinear envelope equations for the slowly varying amplitudes of the electron beam distribution and the radiation field has been derived. The fundamental system of basic equations has been cast into a suitable hydrodynamic formulation. In the framework of the hydrodynamic representation, a new dispersion relation has been derived and analyzed in both the quantum and the quasi-classical regimes, where the space-charge oscillations of the electron beam are taken into account.

A Raman quantum free-electron laser model

Operation of a Quantum Free Electron Laser (QFEL) could provide a compact and fully coherent source of X- and γ-rays. Imperative to experimental realization is allowing for decoherence effects of either spontaneous emission or space-charge to take place, having opposing constraints. Here, for the first time, we present a one-dimensional QFEL Wigner model that includes longitudinal space-charge effects by quantizing the periodic potential derived from the Fourier components of the longitudinal electron beam density. The model is used to investigate steady-state QFEL gain and momentum state dynamics for a variety of space-charge regimes. We find increased saturation lengths and lower saturation intensity as a result of attenuated transitions in the two-level quantum system. In addition, we characterize a space-charge regime where specific transitions outside the QFEL bandwidth are targeted, such that the conventional description breaks down. These findings serve as a consistent theoretical extension of existing QFEL models.

High-gain quantum free-electron laser: Long-time dynamics and requirements

We solve the long-time dynamics of a high-gain free-electron laser in the quantum regime. In this regime each electron emits at most one photon on average, independently of the initial field. In contrast, the variance of the photon statistics shows a qualitatively different behavior for different initial states of the field. We find that the realization of a seeded Quantum FEL is more feasible than self-amplified spontaneous emission.

Beyond Fermi’s golden rule in free-electron quantum electrodynamics: acceleration/radiation correspondence

In this article, we present a unified reciprocal quantum electrodynamics (QED) formulation of free-electron and quantum–light interaction. For electron–light interactions, we bridge the underlying theories of photon-induced near-field electron microscopy, laser-induced particle accelerators, and radiation sources, such as quantum free electron laser, transition radiation and Smith-Purcell effect. We demonstrate an electron–photon spectral reciprocity relation between the electron energy loss/gain and the radiation spectra. This ‘acceleration/radiation correspondence’ (ARC) conserves the electron energy, and photon number exchanged, that is, ΔE/ℏω + Δν q = 0, and in the representation of a quantum electron wavepacket, displays explicit dependence on the history-dependent phase and shape of the wavepacket configuration. It originates from an interaction-induced quantum interference term that is usually ignored in Fermi’s golden rule analyses, but is kept in our combined quantum free electron–photon state formulation. We apply this formulation to both stimulated interaction and spontaneous emission of classical and quantum light by the quantum-featured electrons. The ‘spontaneous’ emissions of coherent states (‘classical’ light) are remarked and squeezed states of quantum light is shown to be enhanced with squeezing. This reciprocal QED formulation has promise for extensions to other fundamental research issues in quantum light and quantum matter interactions.

High-gain quantum free-electron laser: Emergence and exponential gain

We derive an effective Dicke model in momentum space to describe collective effects in the quantum regime of a free-electron laser (FEL). The resulting exponential gain from a single passage of electrons allows the operation of a Quantum FEL in the high-gain mode and avoids the experimental challenges of an X-ray FEL oscillator. Moreover, we study the intensity fluctuations of the emitted radiation which turn out to be super-Poissonian.

Realizing quantum free-electron lasers: a critical analysis of experimental challenges and theoretical limits

We examine the experimental requirements for realizing a high-gain quantum free-electron laser (QFEL). Beyond fundamental constraints on electron beam and undulator, we discuss optimized interaction geometries, include coherence properties along with the impact of diffraction, space-charge and spontaneous emission. Based on desired QFEL properties, as well as current experimental capabilities, we provide a procedure for determining a corresponding set of experimental parameters. Even for an idealized situation, the combined constraints on space-charge and spontaneous emission put strong limits on sustaining the quantum regime over several gain lengths. Guided by these results we propose to shift the focus towards seeded QFELs instead of continuing to aim for self-amplified spontaneous emission. Moreover, we point out the necessity of a rigorous quantum theory for spontaneous emission as well as for space-charge in order to identify possible loopholes in our line of argument.

The Gaussian integration method of the Schrödinger equation and quantum 1-D theory of low gain free electron laser

We study the time-dependent solutions of Schrödinger equations ruled by different non-singular potentials. We employ a recently proposed integration procedure, assuming a time-dependent Gaussian shape for the wave function. The method is independent of the specific form of the potential and allows a straightforward separation of the time and spatial variables. Here, we reconsider the integration method by the use of the formalism of two-variable Hermite polynomials providing a very simple derivation of the relevant physical quantities. This method is eventually exploited to study different problems including anharmonic oscillators and pendulum-like potentials. Regarding the case of periodic potentials, we touch on the application of the method to the quantum free-electron laser dynamics. Finally, we comment on future developments of this line of research regarding the relevant comparison with other exact and approximate integration schemes.

Density matrix approach for quantum free-electron lasers

The density matrix in the Lindblad form is used to describe the behavior of the Free-Electron Laser (FEL) operating in a quantum regime. The detrimental effects of the spontaneous emission on coherent FEL operation are taken into account. It is shown that the density matrix formalism provides a simple method to describe the dynamics of electrons and radiation field in the quantum FEL process. In this work, further insights on the key dynamic parameters (e.g., electron populations, bunching factor, radiation power) are presented. We also derive a simple differential equation that describes the evolution of the radiated power in the linear regime. It is confirmed that the essential results of this work agree with those predicted by a discrete Wigner approach at practical conditions for efficient operation of quantum FELs.

An extended model of the quantum free-electron laser

Previous models of the quantum regime of operation of the Free Electron Laser (QFEL) have performed an averaging and the application of periodic boundary conditions to the coupled Maxwell - Schrodinger equations over short, resonant wavelength intervals of the interaction. Here, an extended, one-dimensional model of the QFEL interaction is presented in the absence of any such averaging or application of periodic boundary conditions, the absence of the latter allowing electron diffusion processes to be modeled throughout the pulse. The model is used to investigate how both the steady-state (CW) and pulsed regimes of QFEL operation are affected. In the steady-state regime it is found that the electrons are confined to evolve as a 2-level system, similar to the previous QFEL models. In the pulsed regime Coherent Spontaneous Emission (CSE) due to the shape of the electron pulse current distribution is shown to be present in the QFEL regime for the first time. However, unlike the classical case, CSE in the QFEL is damped by the effects of quantum diffusion of the electron wavefunction. Electron recoil from the QFEL interaction can also cause a diffusive drift between the recoiled and non-recoiled parts of the electron pulse wavefunction, effectively removing the recoiled part from the primary electron-radiation interaction.

Design of sub-Angstrom compact free-electron laser source

In this paper, we propose for first time practical parameters to construct a compact sub-Angstrom Free Electron Laser (FEL) based on Compton backscattering. Our recipe is based on using picocoulomb electron bunch, enabling very low emittance and ultracold electron beam. We assume the FEL is operating in a quantum regime of Self Amplified Spontaneous Emission (SASE). The fundamental quantum feature is a significantly narrower spectrum of the emitted radiation relative to classical SASE. The quantum regime of the SASE FEL is reached when the momentum spread of the electron beam is smaller than the photon recoil momentum. Following the formulae describing SASE FEL operation, realistic designs for quantum FEL experiments are proposed. We discuss the practical constraints that influence the experimental parameters. Numerical simulations of power spectra and intensities are presented and attractive radiation characteristics such as high flux, narrow linewidth, and short pulse structure are demonstrated.

Quantum dust magnetosonic waves with spin and exchange correlation effects

Dust magnetosonic waves are studied in degenerate dusty plasmas with spin and exchange correlation effects. Using the fluid equations of magnetoplasma with quantum corrections due to the Bohm potential, temperature degeneracy, spin magnetization energy, and exchange correlation, a generalized dispersion relation is derived. Spin effects are incorporated via spin force and macroscopic spin magnetization current. The exchange-correlation potentials are used, based on the adiabatic local-density approximation, and can be described as a function of the electron density. For three different values of angle, the dispersion relation is reduced to three different modes under the low frequency magnetohydrodynamic assumptions. It is found that the effects of quantum corrections in the presence of dust concentration significantly modify the dispersive properties of these modes. The results are useful for understanding numerous collective phenomena in quantum plasmas, such as those in compact astrophysical objects (e.g., the cores of white dwarf stars and giant planets) and in plasma-assisted nanotechnology (e.g., quantum diodes, quantum free-electron lasers, etc.).

What defines the quantum regime of the free-electron laser?

The quantum regime of the free-electron laser (FEL) emerges when the discreteness of the momentum of the electron plays a dominant role in the interaction with the laser and the wiggler field. Motivated by a heuristic phase space approach we pursue two different routes to define the transition from the classical FEL to the quantum domain: (i) standard perturbation theory and (ii) the method of averaging. Moreover, we discuss the experimental requirements for realizing a Quantum FEL and connect them to today's capabilities.

An ultracold electron source as an injector for a compact SASE-FEL

Ultracold electron sources based on near-threshold photoionization of laser-cooled atomic gases can produce ultrashort electron pulses with a brightness potentially exceeding conventional pulsed electron sources. They are presently being developed for single shot ultrafast electron diffraction, where a bunch charge of 100 fC is sufficient. For application as an injector for x-ray free electron lasers (FEL) a larger bunch charge is generally required. Here we present preliminary calculations of an ultracold electron source operating at bunch charges up to 1 pC. We discuss the relevant bunch degradation processes that occur when the charge is increased. Using general particle tracer tracking simulations we show that bunches can be produced of sufficient quality for driving a 1 Å self amplified spontaneous emission free electron laser (SASE-FEL) at 1.3 GeV electron energy. In addition we speculate on the possibility of using the ultracold source for driving a 15 MeV SASE-FEL in Compton backscatter configuration into the quantum FEL regime.

Comment on “Competition between coherent emission and broadband spontaneous emission in the quantum free electron laser” [Phys. Plasmas 20, 033106 (2013)

We point out that in the equation for the electron distribution evolution during Thomson/Compton or undulator radiation used in the paper: “Competition between coherent emission and broadband spontaneous emission in the quantum free electron laser” by G. R. M. Robb and R. Bonifacio [Phys. Plasmas 20, 033106 (2013)], the weight function should be the distribution of the number of emitted photons and not the photon energy distribution. Nevertheless, the considerations expressed in this comment do not alter the conclusions drawn in the paper in object.

Response to “Comment on ‘Competition between coherent emission and broadband spontaneous emission in the quantum free electron laser’” [Phys. Plasmas 20, 124701 (2013)

We reply to the Comment of Petrillo et al. and show that the main result of our paper is unchanged.

Competition between coherent emission and broadband spontaneous emission in the quantum free electron laser

We extend previous analyses of spontaneous emission in a quantum free electron laser (QFEL) and competition between spontaneous and coherent QFEL emission to include a broad distribution of photon frequencies and momenta appropriate for spontaneous undulator radiation. We show that although the predictions of monochromatic and broadband models predict different electron momentum distributions for the quantum regime due to spontaneous emission alone after many photon emissions, the inclusion of broadband spontaneous emission has a negligible effect on the competition between spontaneous and coherent emission in the QFEL. Numerical results from both models are well described by the same condition for the threshold/critical value of spontaneous emission rate.

Relativistic x-ray quantum free-electron lasers: a collective Klein–Gordon model

We present a quantum-relativistic model for the nonlinear interaction between large-amplitude electromagnetic (EM) waves and a quantum plasma. The model is based on a collective Klein–Gordon equation for the relativistic electrons, which is coupled with the Maxwell equations for the EM and electrostatic fields. The model is used to derive a nonlinear dispersion relation for the EM scattering instabilities in a relativistic quantum plasma. With application to the quantum free-electron laser (FEL), a relativistic electron beam is passing through an intense EM wave used as a wiggler to produce coherent tunable radiation. The frequency upshift of the radiation is tuned by the energy of the electron beam. The nonlinear dispersion relation reveals the importance of quantum recoil effects and oblique scattering of the radiation on the gain of the quantum FEL.

Coherent and spontaneous emission in the quantum free electron laser

We present an analysis of quantum free electron laser (QFEL) dynamics including the effects of spontaneous emission. The effects of spontaneous emission are undesirable for coherent short-wave generation using FELs and have been shown in previous studies to limit the capabilities of classical self amplified spontaneous emission (SASE)-FELs at short wavelengths ∼1 Å due to growth of electron beam energy spread. As one of the attractive features of the QFEL is its potential as a relatively compact coherent x-ray source, it is important to understand the role of spontaneous emission, but to date there has not been a model which is capable of consistently describing the dynamics of both coherent FEL emission and incoherent spontaneous emission. In this paper, we present such a model, and use it to show that the limitations imposed by spontaneous emission on coherent FEL operation are significantly different in the quantum regime to those in the classical regime. An example set of parameters constituting a QFEL using electron and laser parameters which satisfy the condition for neglect of spontaneous emission during coherent QFEL emission is presented.

Quantum statistical properties of free-electron laser with ion-channel guiding

AbstractThe operation of the quantum free-electron lasers (QFELs) with a helical wiggler and in the presence of ion-channel guiding is considered. The quantum Hamiltonian of single particle has been derived in the Bambini-Renieri (BR) frame. Time dependent wave function and three constants of motion are obtained. The Raman-Nath equation (RNE) and its approximation solution have been calculated, and then the resulted solution has been employed to obtain the quantum gain, photon statistics parameter and squeezing parameter. A quantum approach has been used to get quantum statistical properties of the FEL and the photon gain formula for the small signal gain limit. It is found that the ion-channel guiding decreases the squeezing. Also, the conditions for positive (bunching) and negative (antibunching) gain have been studied numerically.

The Solution of the Spherical Raman–Nath Equation for Free-Electron Laser in the Presence of Ion-Channel Guiding

In this paper, the Wei–Norman Lie algebraic approach has been employed to solve the spherical Raman–Nath equation for free electron laser in the presence of ion channel guiding and helical wiggler exactly. The result can be applied to discuss quantum free electron laser.