Group leaders: F.V. Hartemann, Institute for Laser Science and Applications, LLNL,

Livermore, CA 94550

P. Chen, SLAC, Stanford, CA 94309

At high electromagnetic field strengths, nonlinear effects play a dominant role, yielding a wide variety of interesting phenomena and opening a new area of physics. The proposed Linac Coherent Light Source (LCLS) appears to be a unique tool to probe these new parameter regimes, both in Quantum and Classical Electrodynamics (QED and CED), and offers very exciting new opportunities, such as the experimental study of Hawking-Unruh radiation, which combines three apparently distinct branches of physics into a new field studying the behavior of the QED vacuum in curved space-time: thermodynamics, quantum mechanics, and general relativity. In addition, the coherent nature of the LCLS radiation output directly translates into the possibility of exciting multiphoton QED processes, including nonlinear Compton scattering, nonlinear Delbruck scattering, as well as reaching the deep quantum regime, where the Lorentz-boosted electromagnetic field is well above the Schwinger critical field, and exotic processes such as trident pair production acquire a significant cross-section.

1. Nonlinear QED: Boiling the Vacuum

The physical nature of the vacuum, as exemplified by the QED vacuum, is an extremely important question, deeply connected with high energy physics and cosmology. A number of exotic effects, including the Casimir force, Hawking-Unruh radiation, and the cosmological constant are directly related to the underlying physical structure of the vacuum; therefore, experimental studies of the vacuum under new physical conditions, such as those produced by the LCLS, are expected to play a major role in 21st-century physics.

Because the focused LCLS X-ray beam approaches near-critical values, new experiments are possible, with reaction rates that are sufficient for detection. Within this context, two categories of experiments can be broadly defined. On the one hand the detailed study of processes already observed, directly or indirectly, such as nonlinear (multiphoton) Compton scattering, should be readily conducted with the much improved brightness of the LCLS, as compared to other short wavelength sources, or by taking advantage of the unique LCLS combination of extremely high peak powers and focused intensities, at short wavelengths. On the other hand, the LCLS parameters will also approach new ranges, including the deep quantum regime and the critical field, thus allowing the study of pair production in vacuum and the trident process, for example.

The study of pair production in vacuum using the LCLS X-ray beam is a challenging, but important, basic physics experiment that was discussed at some length. The breakdown of the vacuum by an intense static electric field was first studied by Schwinger in 1951. For slowly-varying fields (at the Compton time-scale), two regimes have been defined, yielding pair production rates per unit space-time 4-volume. For small fields, at non-relativistic intensities, we have

which clearly scales as a multiphoton effect, as indicated by the power law governing the cross-section. For the LCLS, which will reach relativistic intensities, the probability is given by

The salient feature of this second rate, is the exponential dependence on the ratio of the local electric field to the critical field; for the LCLS, this means that the spikes of the output radiation pulse, which are due to the stimulated amplification of the spontaneous emission (SASE) of the 14 GeV beam in the wiggler, can translates into an exponential increase of the pair production rate; a factor of 10 in the peak intensity will yield a gain of 3 orders of magnitude in the reaction rate:

where is the peak intensity in the spike, and is the average field produced by the focused LCLS beam, chosen here to be 10% of the critical field.

Neglecting this strong enhancement process, the pair production rate calculated for LCLS, for different experimental conditions are as follow:

Note that here, a tapered wiggler was used to enhance the LCLS output power; this is a technique used in conventional free-electron lasers (FELs), where the dephasing of the electron beam due to saturation is compensated for by changing the wiggler parameters: the FEL resonance condition is

,

where is the period of the tapered wiggler and is the wiggler strength parameter (normalized vector potential). These are designed to compensate for the energy loss of the radiating electron beam, described by , which has the initial value , corresponding to the 14 GeV beam energy at the linac output. Such a tapered wiggler can be build at a very small fraction of the LCLS projected cost.

Quantum gravity (QG) remains one of the most elusive problems in modern physics. While superstring theories have given the promise of a truly unified physical theory of such processes, the approach taken by Hawking, Unruh, Davies, and others, where quantum electrodynamics (QED) and general relativity (GR) are integrated in a common theoretical framework, has provided striking new insights into QG processes, including the physics of the early Universe, black hole evaporation via the Hawking process, and Unruh radiation for an accelerated detector in the Minkowski vacuum.

Because the energy densities at which QG is expected to play an important role are extremely high — indeed, at the Planck scale — the question of experimentally verifying the models mentioned above appears to be extremely difficult. However, the particular case of Unruh radiation, where the Minkowski-QED vacuum is predicted to acquire a thermal spectrum, with characteristic temperature , as measured by a uniformly accelerated detector, seems to be a very good candidate for experimental verification, as noted by Tajima and Chen, who derived the expected behavior of a point electron subjected to both an ultrahigh intensity laser field and the Unruh radiation induced by the violent acceleration of the charge within the Minkowski vacuum.

Within this context, the extreme acceleration of an electron with the very high field available in the LCLS raises the possibility of observing the scattering of Unruh radiation in the laboratory. For the LCLS parameters, the Unruh radiation temperature has been estimated at

which corresponds to K. The power is 20 GW, produced by a helical wiggler at a wavelength of 1.5 Å. In this case, the electric field is V/m and the electron acceleration within the coherent wave is m/s².

One of the key parameters for a successful detection of Unruh radiation is to optimize the signal-to-noise ration between the Unruh and Larmor radiation processes; the latter being the parasitic channel in this case. The wavelength scaling of this parameter turns out to be quite advantageous for LCLS as compared to a PW optical laser. The signal-to-noise ratio is given by

where is the laser normalized vector potential, and the signal-to-noise ratio scales as , gaining 4 orders of magnitude when comparing LCLS to an optical laser. Indeed, assuming a PW laser capable of producing a normalized potential at 1 mm, one obtains . For LCLS, and taking into account the different radiation patterns of the Unruh and Larmor radiation processes, the signal-to-noise ratio now reaches 1,000, thus making the experiment feasible. In addition, one can further discriminate between the two signals by spectrally filtering the photon energy.

The use of synchrotron radiation to excite low-lying nuclear excitations (Mossbauer levels) has recently proved to be useful for studies of magnetic phase transitions and lattice dynamics. In addition, the long temporal phase coherence of Mossbauer excitations, when combined with the high brightness of a synchrotron beam, has led to a number of interesting studies of the time evolution of quantum wave packets. So far, using 2nd and 3rd generation synchrotron sources, the available brightness has allowed only single-quantum interference experiments. That is, the experiments are limited to having only one nuclear excitation at a time.

The tremendous peak brightness of the LCLS FEL beam would allow these quantum wave packet experiments to be extended into the regime in which many excitations evolve and interfere simultaneously. It is estimated that a single LCLS pulse would excite about 1000 nuclear excitations in a sample of ¹⁶⁹Tm. These states would evolve coherently for several nanoseconds, giving the possibility of performing experiments exploiting the correlations and interference among them.

The coherent photon field produced by the LCLS could also be used to study multiphoton radiation reaction effects. For example, it is well-known that plane waves cannot accelerate free electrons in vacuum via the Lorentz force; however, the situation changes when the photon wavelength approaches the Compton wavelength, and radiative recoil becomes important. This type of effect can be studied within the context of the classical Dirac-Lorentz equation,

,

where s is the Compton time-scale, and where the first term in the bracketed expression corresponds to the Schott term, while the second term is the usual radiation damping 4-force. For an electron interacting with a plane electromagnetic wave, this reduces to

where the Lorentz force is given in terms of the external electromagnetic field by: , . Subtracting the axial component of this equation from the time-like component, we obtain an equation governing the evolution of the light-cone variable,

which we have recast using the phase as the independent variable. Here, is the inverse of the LCLS wavelength measured in units of the classical electron radius. A perturbation analysis in the small parameter yields a simple differential equation for the light-cone variable, which is no longer invariant:

,

where we are considering a circularly polarized pulse with temporal envelope . This equation is easily integrated, and for a Gaussian pulse of width , the net coherent recoil is given by

for electrons starting from rest, at , and for fs. Note that both and scale as the inverse wavelength, while the relativistic regime is reached above 8.72 GW, independent of the wavelength; therefore, coherent recoil scales as , and the proposed LCLS parameters would make an experimental study of this effect feasible.

Subpicosecond Time-resolved X-ray Measurements

Photon Correlation Spectroscopy and Holography

Non-Linear X-Ray Optical Processes

High Field Physics and Non-linear Quantum Electrodynamics with the LCLS

Content Owner: J. Arthur
Page Master: L. Dunn
Last Update: 16 Nov 1999