Beam by design: Laser manipulation of electrons in modern accelerators

Accelerator-based light sources such as storage rings and free-electron lasers use relativistic electron beams to produce intense radiation over a wide spectral range for fundamental research in physics, chemistry, materials science, biology, and medicine. More than a dozen such sources operate worldwide, and new sources are being built to deliver radiation that meets with the ever-increasing sophistication and depth of new research. Even so, conventional accelerator techniques often cannot keep pace with new demands and, thus, new approaches continue to emerge. In this article, a variety of recently developed and promising techniques that rely on lasers to manipulate and rearrange the electron distribution in order to tailor the properties of the radiation are reviewed. Basic theories of electron-laser interactions, techniques to create microstructures and nanostructures in electron beams, and techniques to produce radiation with customizable waveforms are reviewed. An overview of laser-based techniques for the generation of fully coherent x rays, mode-locked x-ray pulse trains, light with orbital angular momentum, and attosecond or even zeptosecond long coherent pulses in free-electron lasers is presented. Several methods to generate femtosecond pulses in storage rings are also discussed. Additionally, various schemes designed to enhance the performance of light sources through precision beam preparation including beam conditioning, laser heating, emittance exchange, and various laser-based diagnostics are described. Together these techniques represent a new emerging concept of “beam by design” in modern accelerators, which is the primary focus of this article.

Figure 1

Local coordinate system $x$, $y$, and $s$ associated with the beam trajectory shown by the black curve. The direction of beam propagation is shown by the arrow.

Figure 2

Gaussian laser beam width $w(z)$ as a function of the axial distance $z$.

Figure 3

Laser pulses containing two oscillation cycles within the full width at half maximum of their intensity profile, with cosine (1) and sine (2) shaped waveforms.

Figure 4

Interaction of a point charge with an electromagnetic field.

Figure 5

Schematic of a planar undulator and a sinelike trajectory of the electron.

Figure 6

Contour plots of function $f$ using $\tau =0.12$, $s=0$ (left panel) and $\nu =0.7$, $s=0$ (right panel) showing the range of function between 2.0 and 2.3 with 15 equidistant grade steps.

Figure 7

Schematic of orbits in a chicane for the reference particle (solid line), for a particle with slightly higher energy (dash-dotted line), and for a particle with slightly lower energy (dashed line). The four dipole magnets are illustrated with shaded blocks.

Figure 8

The beam energy is modulated in an undulator due to the interaction with a laser beam. The beam then passes through a dispersion section to form a density modulation.

Figure 9

Evolution of the longitudinal phase space in the HGHG scheme with $A=3$. (a) Before the modulator; (b) after the modulator; (c) after the chicane; (d) density distribution after the chicane.

Figure 10

Schematic of two HGHG variants to reduce beam energy spread with two modulators and one chicane.

Figure 11

(a) Phase space after passing through the chicane and the corresponding energy modulation (black curve) in the second modulator; (b) phase space after the reverse modulation in the second modulator; (c) energy distribution before (dashed curve) and after (solid curve) the reverse modulation.

Figure 12

Schematic of the EEHG.

Figure 13

Evolution of the longitudinal phase space of the beam through an EEHG system in a 1D model. Top left: initial phase space, top right: phase space after the first modulator, middle left: phase space in the center of the first chicane, middle right: phase space after the first chicane, bottom left: phase space after the second modulation, bottom right: phase space at the exit after the second chicane. The vertical axis is $p$ and the horizontal axis is $s/{\lambda }_L$ (both lasers are assumed of the same frequency). Shown are three laser periods.

Figure 14

Function $F(A_1)$ from Eq. (3.10).

Figure 15

Two-stage IFEL energy output spectrum. From [123].

Figure 16

Phase space in staged adiabatic buncher with three modulator-chicane modules . Phase space evolution in the first modulator-chicane module (top), in the second modulator (middle), and in the third module (bottom). Adapted from [99].

Figure 17

Evolution of the longitudinal phase space in the difference-frequency generation with two modulators and one chicane. (a) After the first modulator, (b) after the second modulator, (c) after the chicane, and (d) final current distribution.

Figure 18

Helically bunched beam for the emission of coherent OAM light. From [97].

Figure 19

OAM light emitted by a 120 MeV electron beam that had been helically microbunched by a Gaussian mode laser at the second harmonic of a helical undulator. The transverse phase structure (right) was reconstructed from intensity images (left) of the far-field undulator emission. From [93].

Figure 20

Optical-scale linearization of the longitudinal phase space performed by two laser modulators at the same frequency, mediated by dispersive chicane. From [99].

Figure 21

Generation of odd-harmonic bunching with amplitudes $b\mathbf{(}(2n-1)k_L\mathbf{)}=b(k_L)/(2n-1)$ for the emission of square wavefrom fields with a double modulator-chicane system. Top: Modified phase space and current distribution with $A_1=10$, $A_2=1.388$, $B_1=0.295$, $B_2=-0.551$, and ${\varphi }_2={\varphi }_3=0$. Bottom: Bunching factors for various harmonics. From [99].

Figure 22

Typical layout of a storage ring light source.

Figure 23

Schematic of the laser slicing method for generating femtosecond x-ray pulses. The three essential components are (a) a modulator, (b) a radiator, and (c) an x-ray beam line. From [203].

Figure 24

Calculated electron density distribution (as a function of time and horizontal displacement normalized to the rms electron beam size) after electron bunch propagation through one and one-half arc sectors at the ALS from the undulator to the bend magnet. Only a short section of the actual electron bunch is shown. Note that the path-length differences caused by time-of-flight properties of the dispersive section give rise to the time skew observed in the distribution, with electrons having $\mathrm{\Delta }\mathcal{E}<0$ moving toward the bunch head and those with $\mathrm{\Delta }\mathcal{E}>0$ toward the bunch tail. From [203].

Figure 25

Schematic layout of a CHG setup to generate ultrashort coherent radiation in synchrotrons. The electron beam is energy modulated by a laser with wavelength ${\lambda }_L$ in a modulator, microbunched by a chicane, and then used to generate intense coherent radiation with wavelength ${\lambda }_L/n$.

Figure 26

Wigner distributions of the radiation pulse before (a) and after (b) the compressor simulated for a proof-of-principle experiment to demonstrate CPA in CHG. The seed laser has a large frequency chirp with central wavelength at 786 nm. From [75].

Figure 27

Characteristic power gain curve for a SASE FEL. Adapted from [119].

Figure 28

Measured FEL intensity and spectrum for 500 consecutive shots at 32.5 nm seeded with a 260 nm laser. From [5].

Figure 29

Schematic of a current-enhanced SASE x-ray FEL. From [274].

Figure 30

The phase space of the beam showing energy modulation of electrons produced in the interaction with a few-cycle, 800-nm-wavelength laser pulse with CEP stabilization interacting with the electron bunch in the wiggler magnet with two periods. (a) A cosinelike form and (b) a sinelike form.

Figure 31

An example of the x-ray power profile produced in the FEL when using a few-cycle modulating laser. Only a small fragment of the entire x-ray pulse cut at $\pm 6\mathrm{fs}$ is shown. The typical FWHM pulse duration of the central spike is 250 as.

Figure 32

Energy modulation of the electron beam at the exit of the modulator undulator (dashed line), and a profile of the radiation pulse at the exit of the FEL (solid line). From [191].

Figure 33

An example of mode locking, where the time domain is shown in (a) and the frequency domain in (b). The single pulse and its spectrum are also shown. Adding another pulse shown in (a) leads to the spectrum in (b) with additional substructure. The spectrum for the four pulses is also shown. From R. Lindberg.

Figure 34

A schematic of an FEL design with mode-locking capabilities. Chicane magnets are placed between each undulator module to generate the desired slippage between the radiation and the electron beam and to create the radiation modes. The schematic includes a short beam energy modulation undulator at the beginning of the FEL. From [230].

Figure 35

The output power of the mode-locked SASE FEL averaged over five simulation results to eliminate a relatively large shot-to-shot fluctuation. Each individual pulse in the pulse train has a subfemtosecond duration. The inset shows the output spectrum averaged over five simulation results. The central photon energy is 200 eV and mode separation is 1.66 eV defined by the modulating laser. From [130].

Figure 36

Generation of a mode-locked soft x-ray pulse train in a self-seeded FEL. From [251].

Figure 37

(a) Time-dependent energy modulation $A(t)$ and (b) bunching distributions $b_8(t)$. The horizontal axis is the longitudinal position normalized to the rms duration of the laser pulse ${\sigma }_L$. Solid, dash-dotted, and dashed lines are for $A_{\max }=6$, $A_{\max }=7.6$, and $A_{\max }=9$, respectively.

Figure 38

Spectral and temporal FEL intensities for different seed laser powers. Left: Experimental spectral splitting; right: simulated spectral and temporal splitting. From [49].

Figure 39

Geometry of the laser interaction with the relativistic beam.

Figure 40

Layout of the LCLS laser heater inside a magnetic chicane. From [107].

Figure 41

Measured longitudinal phase space at 135 MeV with (a) the laser heater off, (b) the IR laser energy at $10\mu \mathrm{J}$, and (c) at $220\mu \mathrm{J}$. The vertical axis shows the beam longitudinal position and the horizontal axis shows the beam energy. From [107].

Figure 42

Representative beam phase space evolution in EEX with a laser. (a) Initial transverse phase space, (b) $x^{\prime }-s$ distribution after interacting with the laser with wavelength at $10.6\mu \mathrm{m}$, (c) final transverse phase space, and (d) $x-s$ distribution after EEX. The particles that have effective EEX are shown with colored dots. From [247].

Figure 43

A schematic of the laser-assisted conditioner. From [273].

Figure 44

Evolution of the longitudinal phase space in a simplified ORS scheme: (a) initial beam phase space, (b) beam phase space after interaction with an optical laser, (c) beam current with (dashed) and without (solid) the laser modulation, and (d) corresponding radiation spectra.

Figure 45

Illustration of the optical streaking method to measure an electron bunch temporal profile. The horizontal axis is the beam longitudinal position normalized to the laser wavelength and the vertical axis is the particle’s energy deviation normalized to the rms slice energy spread of the beam.