2.1

The wave picture – how to shrink an electron storage ring and still generate multi-keV X-rays

To calculate the X-ray wavelength for a permanent magnet undulator, the undulator equation for the fundamental on-axis can be written as³²

where λ_x,1 is the X-ray wavelength of the fundamental, K is the deflection parameter (for undulators, K ≲ 1), γ = E_e/E₀ is the Lorentz factor (e-beam energy E_e in units of electron rest mass energy E₀ = 0.511 MeV) and λ_uis the period of the undulator. For a weak undulator, K ≪ 1 so that

With λ_u = 1 cm and γ = 6850 (electron beam energy E_e = 3.5 GeV), the X-ray wavelength becomes λ_x,1 = 0.11 nm, which corresponds to X-ray energy of E_x = 11.6 keV. Such storage rings typically have a circumference of several hundred meters. Now, how can we shrink the synchrotron storage ring and still generate multi-keV X-rays? Considering that the magnetic field strength of the bending magnets stays the same, the achievable bending radius is proportional to the e-beam energy. To reduce the circumference of the storage ring by a factor of 100 to a few meters, we need to reduce the e-beam energy, or γ, by the same amount to about 35 MeV. Consequently, we would need to reduce the undulator wavelength by 10,000 to maintain the same X-ray energy. This can be achieved by using a laser beam with a wavelength around 1 µm as an undulator – the electromagnetic field of the laser will “undulate” the electron beam in the same way as the periodic arrangement of permanent magnets in a conventional undulator. In fact, the undulator equation for peak photon energy on axis for a laser undulator can be written as³³

The additional factor of 2 in the denominator comes from the fact that the undulator (laser) field is not stationary, but counter-propagates the electron beam at the speed of light. Table 2 below summarizes typical storage ring parameters of synchrotrons and the Lyncean Compact Light Source.

Table 2.

Typical storage ring parameters of synchrotrons and the Lyncean Compact Light Source

*

At a traditional synchrotron, typically both bending magnet and undulator / wiggler emission is used for experiments. At the CLS, only the laser undulator radiation is used.

2.2

The particle picture – inverse Compton scattering

In the particle picture, this process is known as inverse Compton scattering, where photons in the visible range are backscattered from a beam of relativistic electrons (see Figure 2a). The energy of the backscattered photon for arbitrary angles can be calculated as³³

Figure 2.

(a) Schematic of the inverse Compton scattering process. A laser photon collides with a relativistic electron. The backscattered photon has an energy in the X-ray range. (b) Peak X-ray energy (for head-on collision) as a function of electron energy with a laser wavelength of 1064 nm.

where E_x is the X-ray energy of the backscattered photon, E_L is the laser photon energy, β = v/c is the ratio of velocity v of the electron to the speed of light c and θ_i and θ_f are incident and final scattering angles, respectively. For a head-on collision (θ_i = 180°), small scattering angles (θ_f ≪ 1), E_L ≪ E₀ and γ ≫ 1 this simplifies to

The peak X-ray energy for a backscattered photon (θ_f = 0°) becomes

in analogy to Eq (3) above. Figure 2b plots peak X-ray energy as a function of electron energy for a laser wavelength of 1064 nm.

If we consider only on-axis electrons (θ_i = 180°), we can plot the X-ray energy dependence on scattering angle θ_f from Eq. (5) as shown in Figure 3a. This figure shows how the X-ray energy drops as we move off-axis and indicates how the width of the spectrum depends on the beam divergence that is collected. In practice, the divergence is typically restricted to a few milliradians, which keeps the bandwidth to a few percent.

Figure 3.

(a) X-ray energy of the scattered photons as a function of scattering angle θ_f for on-axis electrons (θ_i = 180°), laser wavelength 1064 nm and electron energy 44.3 MeV (maximum X-ray energy 35 keV). In practice, an aperture typically restricts the beam divergence delivered to the experiment to a few milliradians (gray band), so that the resulting beam has a bandwidth of a few percent. (b) Normalized flux density, i.e. probability distribution for the energy (and corresponding scattering angle) of the scattered X-rays.

The case above represents the lowest bandwidth possible in the ideal case of a parallel, monoenergetic electron beam. For an electron beam with finite emittance and energy spread, the spectrum of the X-ray beam is given by the convolution of the scattering angles collected (typically defined by an aperture) and the range of angles of incidence of the electron beam (defined by the e-beam emittance and focusing strength), the energy spread and the flux density³² (Figure 3b). Measured spectra for the Lyncean Compact Light Source, which agree well with calculated spectra obtained from Monte-Carlo simulations, are provided in Figure 6 below.

Figure 6.

(a) Measured X-ray spectra of the CLS at peak energies 15.2 keV, 24.8 keV and 35.0 keV. The two peaks in the 35 keV spectrum at about 25 and 28 keV are detector artifacts and not part of the CLS X-ray spectrum. (b) Image of the CLS X-ray beam at 16.6 m distance from the interaction point. Both figures reproduced from Ref.²⁰ with permission of the International Union of Crystallography.

2.3

Luminosity

The photon flux Ṅ_x that can be generated by the inverse Compton process is given by the luminosity formula:

Where is the Thomson cross-section and 𝓛₀ is the luminosity:

Here, f_coll is the collision frequency, N_L and N_e are the number of laser photons and electrons in each pulse, respectively, and σ_e.l are the transverse spot sizes of the electron and laser beam, respectively, assuming round beams.

The luminosity equation above shows that the X-ray flux in an inverse Compton scattering X-ray source can be optimized by the following:

2.4

LINAC-based vs. storage-ring-based ICS sources

In general, two approaches exist for ICS sources: linear-accelerator (LINAC) based and storage-ring based.

In the LINAC scheme, low emittance electron bunches from a linear accelerator collide directly with a high intensity pulsed laser, which may be recirculated to enhance flux. The interaction frequency is limited by the repetition frequency of the electron source, which is typically in the tens to hundreds of Hz range (although schemes exist to increase this to the kHz range by using pulse trains). To maximize luminosity, the number of electrons per bunch and the laser pulse energy are both increased, and both beams focused to small spots, until practical limits are reached. This approach may be useful for pulse-probe type experiments because they produce low repetition rate X-ray pulses with a large photon count in each pulse and small spot size. LINAC-based approaches are less appropriate for high average intensity applications due to the low repetition rates. Also, since the electron beam is discarded after a single interaction, the power and shielding requirements are substantial, or complex energy-recovery schemes need to be implemented. While several LINAC-based ICS sources have been proposed or are under development,^34–39 to date none is operational as a user facility for X-ray experiments.

Storage-ring-based sources store the electron bunches on a closed orbit and compensate slow charge decay with infrequent charge injection. Unlike a LINAC source, the electrons are recirculated and can interact over many turns, which keeps power consumption low. The interaction frequency is typically around five orders of magnitude higher (65 MHz in the case of the Lyncean Compact Light Source) which makes them quasi-continuous and able to produce much higher average flux and brightness. The cavity-drive laser is matched to the many MHz rate through the use of a CW mode-locked laser which is frequency-locked to a high finesse optical cavity (pulse stacking). This cavity technology provides a demonstrated way to circulate up to hundreds of kW of optical pulse power. Besides the Lyncean Compact Light Source, which is commercially available, several storage-ring-based ICS sources are proposed or under development.^40–42 A general overview of ICS based sources is provided, for example, in References ^43,44.

3.1

System overview and design

A simplified schematic of the Lyncean CLS is shown in Figure 4, and a photograph in Figure 5. An electron pulse is generated using an RF photocathode gun. A linear accelerator of about 5 m in length accelerates the pulse to energies of 25 to 50 MeV. The pulse is then injected into a storage ring of about 4.6 m circumference. Only one electron pulse circulates in the storage ring at a given time. This pulse is dumped and refreshed at a rate of a few tens of Hz.

Figure 4.

Simplified schematic of the Lyncean Compact Light Source. Electron bunches are generated in the RF photocathode gun, accelerated in the linear accelerator and injected into the electron storage ring. A mode-locked IR laser resonantly drives an optical cavity, shown here schematically as a two-mirror cavity. Electrons and laser pulses collide in the interaction region and generate a collimated, quasi-monochromatic X-ray beam.

Figure 5.

Photograph of the Lyncean Compact Light Source.

The storage ring is configured in a “racetrack” configuration (two 180-degree arcs and two straight sections). One straight section is used for the injection and electron beam dump. In the other straight section (called the Interaction Region), which also serves as one section of a bow-tie optical cavity (see below), the electron beam is focused to a small spot and interacts with an optical pulse to generate X-rays via inverse Compton scattering.

A mode-locked IR laser with wavelength 1 µm resonantly drives the optical cavity to build up a high-power laser pulse via pulse-stacking. The enhancement cavity has a gain of about 10,000, so that a 30 W average power laser builds up to about 300 kW of circulating power. The storage ring and the optical cavity share a common leg, where the electron bunch and the laser pulse collide at the interaction point, producing an X-ray pulse directed in a narrow cone in the same direction as the electron beam. The solid angle of the X-ray beam is determined by a limiting aperture at the optical mirror, and the X-rays are coupled out of the vacuum system through a thin membrane.

While the laser wavelength is fixed, the energy of the X-rays produced can be tuned by changing the energy of the electron beam. This is done by changing the magnetic lattice of the storage ring, i.e., by adjusting the magnet currents to provide a closed-orbit solution at a particular energy. The energy of the injected electron beam is tuned to match the ring by adjusting the RF power in the accelerator structures.

3.2

Beam properties and parameters

The X-ray beam parameters of the Lyncean Compact Light Source are as follows and summarized in Table 3.

Table 3.

Lyncean Compact Light Source X-ray beam parameters.

a)

Measured beam parameters at Munich Compact Light Source20,45

b)

Design parameters of next generation CLS currently under development

3.3

Ongoing and future developments

Several developments are currently underway to increase the performance parameters of the next generation Lyncean Compact Light Source (see Table 3). The storage ring will be upgraded to a multi-bend achromat (MBA) design to lower the emittance and increase the current. At the same time, this will allow increasing the electron beam energy to 50 MeV and thereby the X-ray energy to 42 keV. An improved focusing scheme in the optical cavity will reduce the waist of the optical beam. These two improvements combined are expected to increase the brightness by about a factor of 10. Along with an increase in the size of the output aperture of the X-ray beam, which will increase the beam divergence and therefore beam size at the size of the experiment (albeit at broader bandwidth), this will increase the usable X-ray flux by about one order of magnitude as well.

Implementing alternative cavity lasers with 0.5 µm or 2 µm wavelength allows doubling or halving the X-ray energy, shifting the accessible energy range to 16-84 keV or 4-21 keV, respectively. While these are not active developments at the moment, the fundamental technology in terms of suitable drive lasers and optics is available. Longer term development opportunities include further optimization of the

Longer term development opportunities include further optimization of the storage ring lattice and increase in optical cavity power, which provide an avenue to further increase brightness and flux by another order of magnitude in the medium term, and to narrow the bandwidth.

5.1

X-ray Diffraction

Initial demonstration experiments on the Lyncean CLS focused on diffraction applications, specifically macromolecular crystallography⁹ and powder diffraction (unpublished). Opportunities also exist in diffraction for materials science, where the CLS can offer substantially shorter scan times than conventional laboratory systems and enable in situ and some time-resolved experiments. Furthermore, access to higher energies than what is available from the characteristic lines of electron impact sources, along with energy tunability, enables new applications that are not feasible in a lab otherwise.

5.2

X-ray Imaging

Given the biomedical imaging research focus of the TUM group, a large number of application examples has been generated in this area.^{8,10–18,21–26,28–31} While earlier experiments focused on demonstrating different X-ray imaging techniques on the CLS, such as mono-energy X-ray absorption tomography, grating-based multimodal imaging, propagation-based phase contrast and phase contrast tomography, these are now applied to specific biomedical applications and extended to advanced techniques, such as dynamic imaging, K-edge subtraction imaging and others.

There is substantial interest in imaging for materials science using the CLS and extending the resolution to the micron, submicron and nanoscale range. Initial paper studies indicate that imaging speeds can be increased by more than a factor of 10 for micro-CT and nano-CT using the CLS, compared to existing laboratory systems, although some technical developments will be necessary to achieve that. These will be explored in the future.

5.3

X-ray Spectroscopy

The energy tunability of the CLS lends itself particularly well to providing X-ray absorption spectroscopy (XAS) capabilities in a laboratory setting. Both X-ray Absorption Near-Edge Structure (XANES) and Extended X-ray Absorption Fine Structure (EXAFS) spectroscopy can be performed with the same setup. With a bandwidth of a few percent, energy-dispersive spectroscopy (ED-XAS) is the most efficient way of implementing this on the CLS. This will also be explored in the future.

5.4

Small Angle X-ray Scattering (SAXS)

SAXS for Critical Dimension (CD) measurements on semiconductor samples has been demonstrated in collaboration with NIST (unpublished).