*Article* **Sub-THz Waveguide Spectroscopy of Coating Materials for Particle Accelerators**

#### **Andrea Passarelli 1,2, Can Koral 2, Maria Rosaria Masullo 2, Wilhelmus Vollenberg 3, Lucia Lain Amador <sup>3</sup> and Antonello Andreone 1,2,\***


Received: 20 December 2019; Accepted: 15 January 2020; Published: 20 January 2020

**Abstract:** The electromagnetic characterisation of different materials for the inner wall coating of beam pipes is a long-standing problem in accelerator physics, regardless the purpose they are used for, since their presence may affect in an unpredictable way the beam coupling impedance and therefore the machine performance. Moreover, in particle accelerators and storage rings of new generation very short bunches might be required, extending far in frequency the exploration of the beam spectrum and rendering therefore more and more important to assess the coating material response up to hundreds of GHz. This paper describes a time domain method based on THz waveguide spectroscopy to infer the coating properties at very high frequencies. The technique has been tested on Non Evaporable Getter thick films deposited by DC magnetron sputtering on copper plates.

**Keywords:** THz; waveguide spectroscopy; coating materials; particle accelerators

#### **1. Introduction**

An important step towards the development of a new generation of accelerators and light sources is the special treatment of the vacuum chamber surface, in order to avoid electron cloud (e-cloud) effects that may degrade the machine performance and limit its maximum luminosity.

The e-cloud mechanism starts when the synchrotron radiation, emitted by the beam, creates a large number of photoelectrons at the accelerator wall surface. These primary electrons may cause secondary emission or be elastically reflected [1]. If the value of secondary electron yield (SEY) of the surface material is larger than unity, the number of electrons starts growing exponentially and may lead to beam instabilities and other detrimental side effects [2,3]. It is therefore important to keep the value of SEY as low as possible. Moreover, materials with low photoemission would make not necessary any surface conditioning or in situ heating of the beampipe, which translates in a reduction of machine dead time between experiments.

Reduction of the SEY value in specific sections of the accelerator is therefore mandatory, and an extensive search for the best possible candidates for the pipe internal coating has been extensively carried out in the last years. Amongst other materials, amorphous carbon (a-C) have been thoroughly tested [4] and used [5] at different CERN facilities [6] with very effective results. Another interesting class of materials is non-evaporable getter (NEG) alloys [7], that can be deposited on the inner wall of a vacuum chamber in large accelerators, transforming it from a source of gas into an effective pump. In addition to pumping, NEG films lead to reduced induced gas desorption and secondary electron yields. However, the use of a coating material in an accelerator, being it for the SEY reduction or for the vacuum improvement or both, unavoidably changes the overall surface impedance, possibly producing as adverse effect beam instability because of its electromagnetic interaction with

the surroundings. Therefore, before its insertion in the beam pipe, an accurate electromagnetic characterization is required, for building a reliable impedance model and pinpointing possible problems and performance limitations in modern particle accelerators and storage rings [8].

In the last years, the mitigation properties of coatings have been rarely tested under an electromagnetic field and in the microwave region only [9]. Since beam spectrum may extend up to the very high frequency regime, depending on the bunch length, it might be important to perform an in-depth evaluation of the resistive wall impedance up to millimeter waves and beyond.

Recently, the impedance of NEG films has been measured in frequency domain in the sub-THz range, directly depositing 1–2 μm of the material on the lateral walls of a calibrated waveguide [10,11]. This method can be easily extended to the characterisation of other coating in thin film form, however has its own drawbacks, specifically local in-homogeneity with blistering and peel-off, constraints in sample dimensions, and impossibility to re-use the test system (the waveguide) for further measurements.

An alternative approach is time domain waveguide spectroscopy [12], which has been widely used in the past to obtain high resolution absorption spectra of molecular solids [12], or for the characterisation of thin samples [13,14]. This is done by usually resorting to metallic waveguides since, depending on the design, they can provide a long interaction length and a very high confinement of the electromagnetic field [15], resulting in a significant sensitivity enhancement. Besides that, the use of calibrated devices makes possible the development of characterisation techniques that are both precise and reliable.

With this aim, we have developed a tailored waveguide with integrated pyramidal horn antennas and a removable part where the coating is deposited, which can be placed with ease in the optical path of a THz spectrometer. The design allows us to measure in a simple way large area coating deposited on metallic plates as in the case of accelerators, where averaged quantities are needed. This technique has been successfully used to characterize NEG samples deposited on both sides of thin copper slabs inserted in a circular waveguide [16]. In the case of amorphous carbon however, because of the high temperature growth and the demanding sample thickness requirement, two side deposition is not a feasible approach, because the slab will experience mechanical stress followed by sample peel-off.

Moreover, the transition from the horns to the waveguide, because of the different transverse sections, makes the performance of this device very sensitive to mechanical imperfections and deformations. We designed therefore a modified square waveguide where the transition from antenna to the device is ideally removed, since the horn inner aperture and the waveguide transverse section fully overlap. This results in an increased robustness and a better efficiency of the waveguide in the collection of the THz signal. A major drawback is the reduction by more than 50% in cross section when compared with the circular waveguide, and as a consequence a strong decrease of signal transmitted through the device.

Here we present a detailed description of the high resolution waveguide spectroscopy setup and the analytical method developed for the extraction of the sample electromagnetic properties. In order to validate the technique, we measured the sub-THz response of two coating NEG layers about 4 μm thick deposited using DC magnetron sputtering on both sides of copper plates, and evaluate their conductivity.

#### **2. Materials and Methods**

#### *2.1. The Device under Test*

Ti-Zr-V NEG coatings are grown at the CERN deposition facilities [4] on both sides of copper plates by using a DC magnetron sputtering technique with Krypton as process gas at a working pressure of 7 × <sup>10</sup>−<sup>4</sup> mbar (see Figure 1a). An alloyed disc cathode with 33.3% atomic nominal relative composition of Titanium, Zirconium and Vanadium is placed at a distance of 200 mm from the substrate. The applied tension and current are 294 V and 750 mA respectively, for a total power of 220 W. The complete deposition, giving on average 4 μm thickness, lasts about two days at a growth rate of 1.4 nm/s. During the process, in order to prevent thermal induced deformations the plate is held in an aluminum frame, that in turn is placed on a rotating axis to ensure a homogeneous deposition on both sides of the slab (see Figure 1b). Local composition and thickness of the coating have been checked using X-ray fluorescence (XRF) measurements along the median line of the slab (the waveguide longitudinal axis), showing that samples keep the target composition within 10% and a uniform profile ±2% with an average surface roughness of 0.2 μm [10,17].

**Figure 1.** Non-evaporable getter (NEG) deposition setup. (**a**) Drawing of the system; (**b**) detail of the copper slab placed in the aluminum frame. The four holes shown in the picture are used for the alignment in the waveguide during THz measurements.

For the spectroscopy measurements, we use a gold plated brass device (shown in Figure 2) consisting in a parallelepiped of 16 × <sup>12</sup> × 140 mm<sup>3</sup> machined in two identical pieces. A diagonal waveguide is formed by milling a square cross-section channel, rotated by 45◦ and 62 mm long, in both halves. Two symmetrical pyramidal horn antennas are embedded in both sides of the structure in order to enhance the electromagnetic signal collection and radiation. Moreover, their inner aperture coincides with the waveguide section, ensuring a smooth transition to the waveguide itself without abrupt changes in the device impedance [18]. Disassembling the device, the thin copper slab with the NEG material deposited on both sides can be easily inserted for the sample characterization. The slab has the same length as the device (140 mm) and thickness 0.050 mm.

**Figure 2.** Sketch of the device used for the spectroscopy measurements, consisting in a diagonal section waveguide ending with two pyramidal horn antennas. (**a**) Front view of the assembled device; (**b**) open view of the waveguide and the embedded antennas. The overall size of the device is 16 <sup>×</sup> <sup>12</sup> <sup>×</sup> 140 mm3.

The dimensions and the material used for the waveguide fabrication are reported in Table 1. For the pyramidal horns, maximum and minimum apertures along their length are indicated.


**Table 1.** Technical specifications of device under test.

These dimensions have been chosen in order to have a single mode propagation inside the diagonal waveguide and in the two pyramidal transitions. Due to the central slab inserted along the longitudinal direction, the first mode that can propagate through the structure is the sum of the *TE*1,0 and *TE*0,1. The second allowed mode, given the boundary conditions and the waveguide symmetry, is the sum of *TE*2,1 and *TE*1,2 [19]. For an internal side of the diagonal waveguide of 1.1 mm, the usable frequency window for a single mode propagation ranges from 135 GHz to 300 GHz.

#### *2.2. Sub-THz System*

Sub-THz measurements are carried out using a time domain spectrometer (TDS) operating in transmission mode. The setup is based on a commercial THz-TDS system (TERA K15 by Menlo Systems) customized for the waveguide characterization. The system is driven by a femtosecond fiber laser @1560 nm with an optical power <100 mW and a pulse duration <90 fs. Fiber-coupled photoconductive antenna modules are utilized for both electric field signal emission and detection. A fast opto-mechanical line with a maximum scanning range of approximately 300 ps is used to control the time delay between the pump and the probe beam.

TPX (polymethylpentene) lenses are used to collimate the short (1–2 ps) linearly polarized pulse on the waveguide, producing a Gaussian-like beam with a waist of approximately 8 mm in diameter and a quasi-plane wave phase front. This is a standard configuration commonly used to perform transmission measurements on a number of different materials [20]. A sketch of the optical setup is shown in Figure 3.

**Figure 3.** Side view of the opto-mechanical setup utilized for the measurements: (1) emitter, (2) detector, (3) TPX collimating lenses, (4) micrometric alignment system, (5) waveguide with embedded antennas.

For an accurate control of the optical coupling between the free space signal and the input and output horn antennas, the lower part of the waveguide is fixed on a kinematic mount with a micrometric goniometer. Coated slabs are inserted and replaced by removing the upper part only.

The electric field signal as a function of time is recorded for each sample by averaging 1000 pulses for an overall acquisition time of 10 min, in order to minimize the signal-to-noise ratio. Frequency dependent transmission curves are obtained through the application of a standard FFT algorithm. In the experiment, the frequency resolution is set to about 8 GHz, determined by the scanning range of the delay line.

#### *2.3. The Analytical Method*

The conductivity value of the coated material is obtained from the comparison between the signal amplitude transmitted through the waveguide with the coated slab and the one obtained with an uncoated slab used as a reference.

The attenuation both in the diagonal waveguide *A*diag and in the pyramidal transitions *A*pyr, considering the propagation of the sum of two modes TE1,0 and TE0,1, is [21,22]:

$$A\_{\rm diag} = A\_{\rm pyr} = \frac{1}{2} \text{Re}(Z\_S) \frac{\int \left| \mathbf{n} \times (\mathbf{H}\_{1,0} + \mathbf{H}\_{0,1}) \right|^2 dl}{\text{Re}(Z\_{1,0}) \left| I\_{1,0} \right|^2 + \text{Re}(Z\_{0,1}) \left| I\_{0,1} \right|^2} \tag{1}$$

where *Zi*,*<sup>j</sup>* is the *i*, *j* mode impedance and *Ii*,*<sup>j</sup>* is the relevant excitation current. The field components used in Equation (1) are:

$$H\_{\mathbf{x}\_{1,0}} = I\_{1,0} \frac{\sqrt{2}}{a} \cos\left(\frac{\pi}{a}\mathbf{x}\right) \tag{2}$$

$$H\_{y\_{1,0}} = I\_{1,0} \frac{\sqrt{2}}{a} \cos\left(\frac{\pi}{a}y\right),\tag{3}$$

where *a* is the side of the diagonal waveguide. In case of coating material, the expression of *ZS* is:

$$Z\_S = Z\_{\rm coat} \frac{Z\_{\rm Cu} + jZ\_{\rm coat} \tan(k\_{\rm coat} d)}{Z\_{\rm coat} + jZ\_{\rm Cu} \tan(k\_{\rm cost} d)} \,\mathrm{'} \tag{4}$$

where *d* is the coating thickness. When *d* = 0 there is no coating and *ZS* = *Z*cu. The characteristic impedance in the Leontovich approximation for a metallic case (  ) is [21]:

$$Z = (1+j)\sqrt{\frac{\omega\mu}{2\sigma}} = \frac{1+j}{\sigma\delta} \tag{5}$$

where μ is the total permeability, *ω* = 2*π f* , and *σ* the material conductivity.

The propagation constant under the same condition is

$$k = (1 - j)\sqrt{\frac{\sigma \omega \mu}{2}} = \frac{1 - j}{\delta},\tag{6}$$

where *δ* is the skin-depth defined as

$$
\delta = \sqrt{\frac{2}{\sigma \omega \mu}}\tag{7}
$$

The total attenuation on both sides of the slab in the diagonal waveguide is:

$$A\_{\rm diag} = \sqrt{2} \frac{\text{Re}(Z\_S) k\_{z\_{\rm diag}}}{a Z\_0 k\_0} \left[ 1 + \frac{2k\_{l\_{\rm diag}}^2}{k\_{z\_{\rm diag}}^2} \right] l\_{\rm \%} \tag{8}$$

where *lg* is the length of the waveguide, and

$$k\_{t\_{\rm diag}} = \frac{\pi}{a}; \quad k\_{z\_{\rm diag}} = \sqrt{k\_0^2 - k\_{t\_{\rm diag}}^2}$$

We evaluate the relative attenuation in the diagonal waveguide as:

$$RA\_{\rm diag} = A\_{\rm diag}^{\rm coat} - A\_{\rm diag}^{\rm cu} \tag{9}$$

Differently from the contribution in the diagonal section, the attenuation on the slab given by the symmetric input and output transitions is not constant, since the antenna aperture changes along the horn length. The total attenuation in the single pyramidal transition is:

$$\begin{split} A\_{\mathrm{Pyr}} &= \int\_{0}^{l\_{l}} \sqrt{2} \frac{\mathrm{Re}(Z\_{S}) k\_{z\_{\mathrm{prr}}}(z)}{c(z) Z\_{0} k\_{0}} \left[ 1 + \frac{2k\_{l\_{\mathrm{prr}}}^{2}(z)}{k\_{z\_{\mathrm{prr}}}^{2}(z)} \right] dz \\ &= \frac{1}{\sqrt{2}} \frac{\mathrm{Re}(Z\_{s})}{Z\_{0}} \left\{ -\frac{1}{2b\_{1}} \log \left[ \frac{\sqrt{1 - \left(\frac{\pi}{k\_{0}B}\right)^{2}}}{\sqrt{1 - \left(\frac{\pi}{k\_{0}B}\right)^{2}}} + 1 \frac{\sqrt{1 - \left(\frac{\pi}{k\_{0}b}\right)^{2}} + 1}{\sqrt{1 - \left(\frac{\pi}{k\_{0}b}\right)^{2}} - 1} \right] \\ &+ \frac{2}{b\_{1}} \left[ \sqrt{\left(\frac{\pi}{k\_{0}B}\right)^{2}} - \sqrt{\left(\frac{\pi}{k\_{0}b}\right)^{2}} \right] \end{split} \tag{10}$$

where

$$k\_{t\_{\rm{pyr}}}(z) = \frac{\pi}{c(z)}; \quad k\_{z\_{\rm{pyr}}}(z) = \sqrt{k\_0^2 - k\_{t\_{\rm{pyr}}}^2(z)}$$

and

$$c(z) = b + zb\_1 = b + z\frac{B - b}{l\_t}$$

expresses how the side of the horn changes along the transition. *lt* is the longitudinal length of the transition, *B* and *b* are the side dimension at the entrance and exit of the pyramidal horn transition respectively. Since the transitions are connected to the diagonal waveguide, then *b* = *a*.

The relative attenuation in the pyramidal transition is:

$$RA\_{\rm pyr} = A\_{\rm pyr}^{\rm coat} - A\_{\rm pyr}^{\rm cu}.\tag{11}$$

The total relative attenuation is given by the formula:

$$RA\_{\text{Total}} = RA\_{\text{diag}} + 2RA\_{\text{PVr}} \tag{12}$$

resorting to Equations (9) and (11).

#### **3. Results and Discussion**

The electromagnetic characterization of the NEG coatings in the sub-THz region is realized performing time domain (TD) measurements of the electromagnetic wave propagating inside the specifically designed waveguide with a thin central copper slab, where the material under test is deposited on both sides. The THz beam is polarized with its electric field parallel to the waveguide slab. The use of a device having a square cross section marks an improvement in terms of beam collection efficiency with respect to previous measurements [16]. However, compared to the free space signal, the transmitted electric field is in the order of 10% only. Figure 4 shows the difference in the signal transmitted in air and in the squared waveguide, without and with slab.

**Figure 4.** THz time domain averaged signal propagating in air (dashed line), through the waveguide without (orange, continuous line) and with copper (black, continuous line) or NEG coated (green, continuous line) slab.

The TD curves show that the presence of the NEG layer clearly introduces not only a strong attenuation of the signal but also a significant dispersion. When the THz signal passes through the device, the ps-scale input pulse with respect to the case of free space transmission is strongly reshaped by the reflections inside the waveguide and broadened to more than 50 ps. The stretching of the transmitted signal, compared with the free space input pulse, is due to the strongly dispersive character of the waveguide, that acts as a delay line [23]. After the main burst, at around 120 ps interference features (not shown) appear, due to round-trip reflections inside the waveguide, that have been removed in the subsequent frequency analysis.

In frequency domain, the amplitude spectra are obtained using FFT (Fast Fourier Transform) analysis and are presented in Figure 5 for both samples in comparison with the bare copper slab, with the waveguide without the slab, and with air only.

Data are shown up to the frequency where single mode propagation in the waveguide holds. This ensures that there is no interference from higher order modes, which can produce a modification of the field distribution, as discussed in detail in Section 2.3. The cut-off frequency of the first mode propagating inside the waveguide (approximately 150 GHz) can be clearly seen.

In the graph, the NEG coated samples (red and green dots) behave in a similar way, with a marked difference in amplitude (between 4 and 6 dB on average) with respect to copper (black dots) and slightly increasing at higher frequencies. Changing the design of the waveguide from circular to square therefore does imply a better sensitivity to the coating material properties, since the weight of the slab losses relatively to the overall waveguide losses increases, but this is done at the expense of a reduction in the amplitude of the collected signal, raising noise and data fluctuations.

From the comparison with the uncoated slab, the (relative) attenuation given by the losses produced in the device through its overall length (horn antennas and waveguide) by the coating material can be evaluated.

**Figure 5.** Frequency spectrum showing the averaged amplitude transmission data in air (dashed line-to-point curve), through the waveguide without (orange line-to-point curve) and with copper (black line-to-point curve) or 3.8 μm and 4.3 μm NEG coated (red and green line-to-point curves respectively) slabs.

In Figure 6, the measured relative attenuation due to both the 3.8 μm and 4.3 μm NEG coatings with respect to the copper reference are shown (red and green dots respectively). Data below 200 GHz have been discarded to avoid artifacts in the spectrum due to group and phase velocity dispersion, especially pronounced near the cut off frequency. Therefore, results are presented in the range 200–300 GHz.

**Figure 6.** Experimental relative attenuation as a function of frequency on the NEG coated slab of 3.8 μm and 4.3 μm (red and green dots respectively) and best fit curves (blue and magenta lines respectively).

The conductivity value *σ*coat of the coating material is obtained resorting on the analytical tool detailed in Section 2.3. From the best fit of the analytical formula, we yield *<sup>σ</sup>*coat = (7.7 ± 1.1) × <sup>10</sup><sup>5</sup> S/m for the 3.8 <sup>μ</sup>m sample, and *<sup>σ</sup>*coat = (4.2 ± 0.5) × 105 S/m for the 4.3 <sup>μ</sup>m sample. Magenta and blue continuous lines in Figure 6 show the analytically evaluated attenuation for the two estimated conductivities, taken from Equation (12) in Section 2. For both curves the 95% confidence interval on the attenuation due to the conductivity evaluation uncertainties is also displayed as shaded area. The difference observed between the two samples might be an indication of an increased disorder,

that translates in poorer transport properties and therefore lower conductivity, caused by the larger thickness.

Resorting on [24], we can also evaluate the effect of sample roughness on the NEG conductivity. Using the average roughness value for our samples (0.2 μm), we estimate a maximum conductivity reduction of the order of 8%, that lies within the measurement error band in our frequency range.

Results agree fairly well both with previous data obtained on different NEG samples using the circular waveguide [16] and DC (direct current) conductivity values extracted using the frequency domain approach [10]. Nevertheless, differently to these latter measurements, a TD method allows to evaluate the electromagnetic properties of coatings in a reliable and simple way exploiting tailored (and reusable) waveguides. The knowledge of *σcoat* under operating conditions (coating deposited on a metallic slab) is extremely useful for the evaluation of the real part of the surface impedance as a function of frequency, that is currently used for modeling the resistive wall component of the beam impedance in modern accelerators.

**Author Contributions:** A.P. and A.A. conceived the experiment. A.P., M.R.M. and A.A. developed the theory for the electromagnetic characterization of coating material in a waveguide. A.P. and C.K. performed the THz measurements. W.V. and L.L.A. realized the NEG samples. A.P. ad A.A. wrote the manuscript, with contributions from all authors. A.A. supervised the activity. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research has been funded by the CLIC project in the framework of the CERN-INFN Naples collaboration (KN4542/BE Addendum no.13 to Agreement KN3083). Partial support from INFN Projects "TERA" and "MICA" is gratefully acknowledged.

**Acknowledgments:** The authors thank S. Calatroni, P. Costa Pinto, R. Corsini, Y. Papaphilippou, and M. Taborelli from CERN for their support.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Article* **The TeraFERMI Electro-Optic Sampling Set-Up for Fluence-Dependent Spectroscopic Measurements**

**Nidhi Adhlakha 1, Paola Di Pietro 1, Federica Piccirilli 2, Paolo Cinquegrana 1, Simone Di Mitri 1, Paolo Sigalotti 1, Simone Spampinati 1, Marco Veronese 1, Stefano Lupi 2,3 and Andrea Perucchi 1,\***


Received: 10 December 2019; Accepted: 19 January 2020; Published: 20 January 2020

**Abstract:** TeraFERMI is the THz beamline at the FERMI free-electron-laser facility in Trieste (Italy). It uses superradiant Coherent Transition Radiation emission to produce THz pulses of 10 to 100 μJ intensity over a spectral range which can extend up to 12 THz. TeraFERMI can be used to perform non-linear, fluence-dependent THz spectroscopy and THz-pump/IR-probe measurements. We describe in this paper the optical set-up based on electro-optic-sampling, which is presently in use in our facility and discuss the properties of a representative THz electric field profile measured from our source. The measured electric field profile can be understood as the superimposed emission from two electron bunches of different length, as predicted by electron beam dynamics simulations.

**Keywords:** THz spectroscopy; free-electron-lasers; nonlinear optics

#### **1. Introduction**

The interest in high power pulsed THz sources has seen a steady increase during the last decade. This is due to the great potential which is offered by THz control of matter [1,2]. THz light can indeed be used to tune and modify material's properties in several ways, from the strong acceleration of free charge carriers, to anharmonic lattice distortion and even to ultrafast magnetic switching since magnetic fields in the Tesla range can be accompanying strong THz pulses.

While synchrotrons have always represented a significant source of high brightness THz light for spectroscopy, their use in non-linear THz studies is limited by their relatively low electric fields (<kV/cm). On the other hand, single pass accelerators can store high charge in sub-ps bunches. For this reason, their use for THz control of matter is becoming widespread [3–9].

TeraFERMI is the THz facility based on the FERMI free-electron-laser (FEL) located in Trieste (Italy). The electron bunches that are used by the FERMI free-electron-laser to produce UV and soft X-ray radiation [10] are further exploited by TeraFERMI [11] in order to produce THz waves. The THz pulses emitted by TeraFERMI are coherent due to the so-called superradiance phenomenon. This occurs when the separation between the radiation-emitting electrons is shorter than the wavelength of the light.

In the first part of this paper we will review the basic characteristics and figures of merit of the TeraFERMI source, while on the second part we will mainly describe the electro-optic-sampling (EOS)

based experimental set-up that we are routinely exploiting for nonlinear THz spectroscopies at TeraFERMI. In the third section we discuss a typical electro-optic sampling profile measured at TeraFERMI. Interestingly, the measured electric field profile is compatible with the emission from a 100 fs-long current spike in the bunch head of the ps-long entire electron bunch, as previously predicted by electron beam dynamics simulations [12]. The presence of this current spike is due to Coherent Synchrotron Radiation (CSR) wakefields in the dump line and is the origin of the multi-THz emission at TeraFERMI even in the absence of a sub-ps compression of the total electron bunch.

#### **2. The TeraFERMI Beamline**

The FERMI FEL operates alternatively with two different FEL lines called FEL1 and FEL2, operating between 20–100 nm and 4–20 nm respectively. After the FEL process, both electron lines are merging into one unique beamline before the electron dump. The TeraFERMI source intercepts the electrons at this position, thus allowing operation simultaneously with both FERMI FELs. The THz photons emitted by a Coherent Transition Radiation (CTR) source (see Section 2.1) are propagated along the THz beamline into the FERMI experimental hall, where the THz light is delivered to a dedicated laboratory.

The THz pulses from TeraFERMI are then used to induce non-linear changes in matter. To probe the effects of the THz pulse we use either the same THz photons emitted by TeraFERMI or another probe synchronized to the FERMI master-clock. At present the laboratory is equipped with a femtosecond infrared fiber laser (MENLO C-Fiber 780), which can be operated either on the fundamental at 1560 nm or on its second harmonic at 780 nm. As we will see in the following, the laser can also be used to perform electro-optic sampling measurements thereby probing the time-resolved evolution of the THz electric fields, as well as their spectral content.

#### *2.1. Source*

Coherent Transition Radiation is the phenomenon occurring when a relativistic electron crosses the boundary between two media of different refractive index. The emitted THz light is particularly bright and displays cylindrical symmetry and radial polarization. Its energy distribution as a function of frequency (*ω*) and emission angle (*θ*) can be described by the Ginzburg-Frank formula [13]:

$$\frac{d^2ll}{d\omega c d\Omega} = \frac{c^2}{4\pi^3\epsilon\_0 c} \frac{\beta^2 \sin^2\theta}{(1 - \beta^2 \cos^2\theta)^2},\tag{1}$$

where *β* is the relativistic factor *v*/*c*. To get an estimate of the emitted intensity one should multiply the Ginzburg-Frank equation (or its generalized version for the near-field case [14]) by the so-called coherence enhancement factor:

$$N[1+N|\int\_{-\infty}^{+\infty} \rho(t) \exp(-i\omega t)dt]^2 ]. \tag{2}$$

The TeraFERMI source consists in a 1μm-thick Al membrane of 38 mm diameter, oriented at 45◦ with respect to the electron beam. A wedged diamond window with 20 mm clear aperture is located 80 mm far from the source. The Ginzburg Frank equation allows estimating typical TeraFERMI emission energies ranging from 30 to 100 μJ per pulse, in good agreement with experimental findings [12]. A pictorial view of the TeraFERMI CTR extraction scheme is illustrated in Figure 1.

**Figure 1.** Schematics of the TeraFERMI Coherent Transition Radiation (CTR) extraction. The Al membrane intercepts the electron beam at a 45◦ angle, shortly before the electron beam dump. A diamond window separates the ultra-high vacuum of the electron chamber with respect to the low-vacuum of the TeraFERMI beamline transport system (see Section 2.2). A fluorescent Yttrium Aluminium Garnet (YAG) screen can also be inserted instead of the CTR source (forming a 90◦ angle with respect to the Al CTR screen). This allows to image the electron beam profile through an additional viewport located opposite with respect to the diamond window.

Under the present (∼1 GeV) energy conditions, the intensity emitted by CTR is comparable to the one that would be obtained through CSR (see Figure 2 in Reference [11]). The main difference between the two types of emission resides in the polarization properties (linear for CSR, radial for CTR) and in the spatial profile. CSR originates from an extended source in the horizontal direction, which may give rise to optical aberrations, unless the vertical and horizontal source emissions are independently focused, by an optimized set of conical and cylindrical mirrors [15]. On the other hand the cylindrical symmetry of CTR radiation can be more easily transported with a simple set of toroidal mirrors (see next Section).

#### *2.2. Transport System*

The THz beam emitted at the TeraFERMI source needs to be transported along a distance of about 30 m, to reach the dedicated THz laboratory located in the FERMI experimental hall. In order to transport a THz beam over such a considerable length, the beam can not be propagated as a collimated beam but needs to be continuously refocused by a set of 6 toroidal mirrors [16]. The entire beamline, which is separated from the source by an initial diamond window (see Section 2.1), is kept under low vacuum conditions in order to avoid water vapour absorptions. The final window of the beamline is interchangeable so that one can choose the more suitable material (z-cut quartz, sapphire, TPX, etc.) according to the requirements of the experiment. Above 0.3 THz the losses along transport can be totally ascribed to the transmission of the two optical windows. When the TPX window is mounted, the overall beamline transmission is of about 55–60%, which roughly corresponds to the product of the 70% transmission of the initial diamond window and that of the final TPX window (90–95%).

Once reaching the optical table the beam is further refocused through a series of parabolic mirrors finally allowing to steer the THz beam at sample position with the best possible focusing properties. The beam size at focus is 800 μm diameter FWHM, as measured by a pyroelectric camera (Pyrocam IIIHR). This focus was characterised in ambient humidity conditions, when the frequency content at the camera is almost completely restricted below 1 THz.

By inserting a microbolometric camera (i2S TZcam) slightly out of focus it is possible to characterize the typical doughnut shape expected from a CTR source. The left/right asymmetry (see Figure 2), which is also expected from the THzTransport [14] simulation [16], is due to the combination of the 45◦ orientation of the source radiator and of the 90◦ off-axis arrangement of the various optical components.

**Figure 2.** (**a**) Simulated beam profile at 1 THz, at focus position. (**b**) Measured beam profile with a microbolometric camera. The typical CTR doughnut shape and the left/right asymmetry is in good agreement with the simulation. In order to achieve the proper spatial resolution needed to visualize the doughnut shape the measurement was performed out of focus, with a larger beam, so that the present comparison is only qualitative. The measurement in (**b**) can not be used to estimate the real beam dimension which was previously measured with the Pyrocam IIIHR THz camera (see text).

#### *2.3. Beamline Performance*

The overall TeraFERMI performances, were are already summarized in Reference [17]. During standard user operation conditions the beamline produces THz pulses whose energy ranges from 15 to 60 μJ per pulse, with a bunch charge of ∼700 pC and a bunch length of about 1 ps, as measured at the end of the LINAC. This results in energies at sample up to 35 μJ per pulse. The optical spectrum, as measured by a Michelson interferometer, extends up to 4 THz. However, upon optimization of the electron beam compression specific for TeraFERMI, energies at source up to 100 μJ and a spectral extent up to 12 THz were measured [17]. Two characteristic spectra illustrating the performances under standard and THz beamline-dedicated machine conditions are shown in Figure 3.

**Figure 3.** Characteristic TeraFERMI spectra, as measured with a Michelson interferometer in (**a**) standard operation conditions and (**b**) dedicated shifts. Figure adapted from Reference [17].

#### *2.4. Optical Scheme*

The full optical scheme for transmission spectroscopy experiments is depicted in Figure 4. The THz pulse is first polarized and attenuated by a series of three polyethylene grating polarizers. The first and third polarizers select the polarization required for the experiment under study, while the role of the second polarizer is to act as an attenuator, to allow studying the material's fluence dependence.

**Figure 4.** Schematics of the THz and optical beam paths. The three initial polarizers are used to set the polarization and attenuate the beam according to experimental requirements. The beam undergoes a series of expansions and recollimations in order to decrease its final size at sample position. Both THz and laser paths are splitted in two to allow for the simultaneous measurement of a reference spectrum.

After being transmitted by the sample the beam is first re-collimated and then focused by a slotted parabolic mirror on the electro-optic sampling crystal. At this point the THz pulse interacts with an optical pulse coming from an infrared fs laser synchronized to the free-electron-laser, as discussed in the next Section.

The main concept underlying EOS is that the THz electric field of the pulse under investigation induces a birefringence in the EOS crystal through the Pockels effect [18]. Thus, if the incoming laser pulse displays circular polarization, which can easily be achieved through a *λ*/4 waveplate, after the interaction with a crystal (in our case, a 1 mm thick ZnTe crystal) in presence of THz fields, the polarization will be turned into elliptical. This polarization change can be probed with a Wollaston prism (spatially separating the two orthogonal polarization components) and a balanced detector. Under appropriate approximations, the measured difference signal will then be proportional to the incoming THz field.

In order to allow measuring an online reference of the THz emission spectrum for the source, it is possible to split the THz beam as shown in Figure 4, with the help of a pellicle beam splitter. The infrared laser beam is also being splitted in two different components, one of which is delayed by a suitable amount in order to perform EOS on the reference channel.

#### **3. The TeraFERMI Electro-Optic Sampling Set-Up**

#### *3.1. Laser Synchronization*

In order to perform electro-optic sampling measurements (but also to provide time-resolved THz pump-IR probe information), TeraFERMI has been equipped with a commercial mode-locked fiber laser with ultrashort pulses (<100 fs FWHM) and two output wavelength, 780 nm and 1560 nm. A tight synchronization is required to perform time resolved experiments with FERMI THz light. To this purpose the highest performance time reference (LINK) is provided to the beamline optical table, for example, a stabilized optical pulsed signal from the Optical Master Oscillator (OMO) of FERMI.

A Phase Locked Loop (PLL) is used to stabilize the laser phase with respect to the reference. Two error signals feed the loop, one coming from an RF unit (TMU-RF) and one coming from a Balanced Optical Cross-Correlator (BOCC). The RF phase error signal is used for a first, rough synchronization thus making it possible to find the optical phase error signal, with a duration in the order of 1 ps (<0.1% of the pulse period). The optical signal is then used to achieve the final synchronization with few fs RMS jitter in the 10 Hz–10 MHz range.

Inside the BOCC setup we have installed a delay line to provide 6 ns delay (the period of the LINK pulses) with steps of 5 fs. This device is inside the synchronization loop because both the wavelengths of the pump probe laser are derived from the same oscillator, so that when the translation stage is moved the loop corrects the movement by acting on the piezoelectric motor inside the cavity. As a result, the phase of the 1560 nm and 780 nm signals are shifted exactly by the same delay imposed by the delay line. This technique is used to avoid perturbations due to moving elements on the optical path of the beam towards the sample.

The optimization of the LINK dispersion allows to obtain a single clean pulse to be used in the Sum Frequency Generation (SFG) process together with the 1550 nm pump-probe laser pulses inside the BOCC. To this purpose we have developed an optical scheme to measure trough cross-correlation the shape of the LINK pulses. This scheme will be used as BOCC for the synchronization of the laser.

#### *3.2. Fast Pulse Detection System*

Because of the mismatch between the 78.895 MHz repetition rate of the laser and the 50 Hz repetition rate of the FERMI facility, the detection system employed at TeraFERMI should be able to detect separately all the pulses from the infrared laser. To this aim we are employing a balanced photodetector with fast monitor output up to 350 MHz. The reading of the detector is then performed with the help of a 12 bit, 1 GHz digital oscilloscope. The sampling rate of 10 GS/s allows probing the signal from the photodetector with a 100 ps resolution.

At the maximum sampling rate the oscilloscope acquires the detector signal over a time range of 50 ns. This means that, due to the 78.895 MHz rep rate, we can continuously monitor the signal coming from 4 consecutive laser pulses. Obviously, only one out of the 4 pulses which are present on the oscilloscope's display can be affected by THz light. This means that the remaining three can be used for laser diagnostics. Their signal can be averaged and subtracted to the one which is affected by THz light. In this way we can cancel the residual signal due to laser beam fluctuations and non-perfect balancing between the two detector's channels.

#### **4. Electro-Optic Sampling Results**

#### *Measured Electric Field and Spectrum*

An example of EOS measurement during standard beamtime operations is shown in Figure 5. This profile was obtained by scanning the infrared laser with respect to the THz beam at 100 fs steps. For each position of the scanning delay line we have averaged over 10 shots. However, even with a lower (down to 1) number of averages the electric field profile can be clearly reconstructed, thus showing that jitter between THz and laser is not exceeding our step size. We will come back to this point in the following paragraph.

**Figure 5.** (**a**) Representative electro-optic-sampling (EOS) measurement, acquired by averaging 10 shots for each position of the delay line. (**b**) Intensity time profile obtained by evaluating the square of the EOS profile shown in (**a**). The red curve is a Gaussian fit to the main peak. (**c**) Intensity spectrum obtained by calculating the magnitude squared of the Fourier Transform of the spectrum in (**a**).The arrow indicates the dip in the spectrum at about 1 THz which may result from the interference of a long wavelength (∼0.9 THz) and shorter wavelength (∼2 THz) components.

Interestingly, the full energy profile (see Figure 5b) has a duration of about 2 ps, with a main sharp peak containing 60% of the energy of the full pulse. This THz peak is the proof of the presence of a complex electron bunch profile, compatible with the formation of a strong current spike due to the presence of Coherent Synchrotron Radiation (CSR) wakefields, as predicted in Reference [12]. The measured THz peak can be fitted with a gaussian profile, corresponding to a Δ*tFWHM* = 112 fs FWHM.

The power spectrum related to this electric field shape is reported in Figure 5c, in a logarithmic scale. The spectrum extends up to about 4.5 THz, which roughly corresponds to the maximum detectable signal

in a ZnTe EOS crystal, due to the presence of an optical phonon centered at 5.3 THz [18]. The spectrum shows a pronounced dip at about 1 THz.

The electric field intensity can be determined by employing the standard relationship [19]:

$$E[MV/cm] = 0.39 \sqrt{\frac{P[W]}{\pi (r\_0[\mu m])^2}}.\tag{3}$$

The total intensity measured at focus with a calibrated pyroelectric detector in that configuration was *I* = 4.8 μJ. We can then calculate the peak pulse power as *P* = 0.58 ∗ *I*/Δ*tFWHM* = 25 MW. By inserting this value in Equation (3), together with the proper *r*<sup>0</sup> for the measured spatial pulse profile (400 μm FWHM), we end up with an estimate of the THz electric field at 1.65 MV/cm. However it is important to keep in mind that the focus, as measured with the Pyrocam IIHR was characterised in atmospheric humidity conditions, when the presence of spectral components above 1 THz is almost totally absent due to water vapor absorptions. If we assume that the size of the focus scales linearly with the wavelength of the radiation, according to diffraction laws, the spatial profile of the spectral components between 1 and 4 THz may present a radius down to about 100–150 μm FWHM. According to Equation (3), this would imply reaching electric field values as high as 4.5–6 THz. This estimate clearly requires further investigations, for instance by characterising the beam profile under appropriate N2-purging conditions.

The knowledge of the field shape and value is of the highest importance for the interpretation of non-linear phenomena such as saturable absorption or harmonic generation, which depend directly on the electric field, through appropriate scaling laws. Also in pump-probe experiments, the knowledge of the exact shape of the field is important to precisely single out the rise-time and relaxation phenomena occurring as a consequence of the THz excitation.

To achieve a better understanding of the peculiar spectrum and electric field profile of TeraFERMI, we consider two THz single-cycle pulses centered at 0.9 and 2 THz, as depicted in red and blue respectively in Figure 6a. These two pulses mimic the expected composite shape of the bunch profile, being made up of a ∼100 fs high current spike superimposed on a ps-long electron bunch. With a suitable, phenomenological, choice of the relative time delay and phase, the sum of the two pulses yields the electric field profile of Figure 6b, which roughly reminds the EOS result already shown in Figure 5a and reproduced for clarity in Figure 6d. Interestingly the Fourier Transform of this composite pulse displays a remarkable dip at about 1 THz, in agreement with the experimental data, which is due to the interference of the electric fields from the two pulses at distinct frequencies. It is worth emphasizing that the presence of the short current spike is crucial, since it allows extending the TeraFERMI emission in the multi-THz range even when the compression of the electron bunch in the LINAC is not optimized for THz emission, as it is normally the case in parasitic mode operation.

Different machine conditions and in particular different LINAC settings can change the overall bunch compression and the electron energy spread at the entrance of the FEL. This will affect both the duration of the overall electron bunch and the duration and intensity of the current peak. While this can create a different balance in the spectrum between lower and higher frequency components, the presence of a dip at about 1 THz in the TeraFERMI spectra is very common, during normal user operation, thus underlining the validity of the two-component scenario. An EOS characterization of the TeraFERMI emission under optimized conditions would also be of high interest, to provide a better understanding of the spectral structures observed in Figure 3b) with the Michelson interferometer but is unfortunately still missing.

**Figure 6.** (**a**) Simulated THz waveforms centered at 0.9 (**red**) and 2 THz (**blue**), with a Gaussian envelope of width 1 ps and 200 fs respectively. (**b**) Simulated THz waveform resulting from the sum of the two previous contributions (**c**) Intensity spectrum of the 0.9 THz and 2 THz pulses separately and of the sum pulse black. An interference is clearly seen in the black spectra slightly above 1 THz. (**d**) Experimentally measured EOS profile (same as in Figure 5a). (**e**) Experimental spectrum (same as in Figure 5c).

The measured electric field profile as shown above is affected by many broadening effects which are hampering the detection of high frequency components. In particular the laser pulse duration (90 fs RMS) and the jitter in the electron bunch arrival time (<65 fs) are both affecting the measured electric field line-shape. This effect can be mimicked in terms of Gaussian convolutions of the measured electric field profiles. To better quantify the phenomenon we have modelled the electric field shape in terms of discontinuous flat lines, such as their Gaussian convolution provides an electric field profile similar to the one we measured (see Figure 7). The spectrum associated with the modelled electric field provides a much more enhanced signal from 1 to 3 THz. Even though this is obviously an oversimplified model, it may give an idea of the amount of light produced from our source which could still go undetected by our set-up.

Besides the Gaussian broadening effects discussed above other limiting factors could be the velocity mismatch between the THz and optical pulses in the 1 mm thick ZnTe crystal [18] and the already mentioned absorption from ZnTe itself due to the presence of its 5.3 THz optical phonon.

**Figure 7.** (**a**) Experimental EOS profile (black). Model electric field in the form of broken flat lines (red). Convolution of the model field with a 90 fs Gaussian function (green) (**b**) Intensity spectra calculated from the experimental EOS profile (black), from the broken line (red) and from its Gaussian convolution (green). The components at higher frequencies (i.e., from 1 to 4 THz) are clearly suppressed due to the Gaussian convolution which is mimicking the effects of the laser broadening.

#### **5. Conclusions**

We have reviewed in this paper the properties of the TeraFERMI beamline for THz non-linear and pump-probe studies. In particular we have presented the set-up presently in use for electro-optic-sampling measurements. This allowed characterizing in detail the THz electric field emission from TeraFERMI, which is a crucial information for the interpretation of non-linear THz spectroscopy and pump-probe dynamics. We have found that the usual THz emission from TeraFERMI is the combination of two main components originating by the THz emission from the ps-long electron bunch profile summed to the one from a ∼100 fs long high current spike. This finding is in agreement with previous electron beam dynamics studies [12], pointing to the essential role played by CSR induced wakefields in the high frequency emission properties of TeraFERMI.

**Author Contributions:** Conceptualization, S.L. and A.P.; Investigation, N.A., P.D.P., S.D.M. and A.P.; Methodology, P.C., P.S., S.S. and M.V.; Software, F.P.; Writing—original draft, A.P.; Writing—review and editing, S.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** We acknowledge F. Vitucci from Crisel Instruments and i2S for providing the TZcam. We are also indebted with F. Novelli for useful discussions and suggestions in the preparation of the optical set-up.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **References**



© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Novel Schemes for Compact FELs in the THz Region**

#### **Andrea Doria \*, Gian Piero Gallerano and Emilio Giovenale**

ENEA, Fusion Physics Division, C.R. Frascati, via E. Fermi 45, I-00044 Frascati (Roma), Italy; gianpiero.gallerano@enea.it (G.P.G.); emilio.giovenale@enea.it (E.G.)

**\*** Correspondence: andrea.doria@enea.it

Received: 23 October 2019; Accepted: 15 November 2019; Published: 19 November 2019

**Abstract:** The rapid advance of terahertz technologies in terms of radiation generators, systems, and scientific or industrial applications has put a particular focus on compact sources with challenging performances in terms of generated power (peak and/or average), radiation time structure, and frequency band tunability. Free electron laser (FEL)-based sources are probably the best candidates to express such a versatility; there are a number of schemes that have been investigated over the years to generate coherent radiation from free electrons in the mm-wave and terahertz regions of the spectrum, covering a wide frequency range from approximately 100 GHz to 10 THz. This paper proposes novel schemes for exploring the limits in the performance of radio frequency-driven free-electron devices in terms of ultrashort pulse duration, wide bandwidth operation, and energy recovery for near continuous wave (CW) operation. The aim of the present work is to demonstrate the feasibility of an FEL achieving performance comparable to a conventional photoconductive THz source, which is commonly used for time-domain spectroscopy (TDS), in terms of bandwidth and pulse duration. We will also demonstrate that a THz FEL could be very powerful and flexible in terms of tailoring its spectral features.

**Keywords:** terahertz; free electron laser; energy recovery

#### **1. Introduction**

Time domain-based terahertz (THz) sources have gained more and more attention during the past 15 or 20 years [1], and these systems are now commercially available, reliable, and easy to use. Such THz sources are mainly divided in two categories that are both characterized by broadband emission. The first is the Auston switch, which is named after the American researcher that initiated this research field [2]; the device is made up by a coplanar strip antenna deposited on a nonabsorbing photo-conducting substrate. The circuit, biased by an appropriate voltage, can be closed by a focalized powerful short infrared laser pulse on a gap of few microns. The transient current gives rise to a time-dependent electric field, and the consequent polarization vector follows the envelope of the laser pulse. The most important drawback of the Auston switch is its limited bandwidth and the frequency dispersion that results in a rapid lengthening of this pulse before the launching in the vacuum. The limit bandwidth for these devices is of the order of 1 THz. To overcome this limitation, a different approach has been developed. The idea is to use an electro-optic device realized with a nonabsorbing material [3]. The interaction mechanism is now a nonlinear second-order process: the rapidly oscillating electric field of the laser pulse excites in the medium a polarization vector which is proportional to the modulus of the electric field itself. This polarization vector is the source for a Hertzian vector potential that generates a radiation field. This is a rectification process because the rapid oscillation of the electric field of the laser pulse is averaged in the frequency domain and only the envelope of this pulse remains. Being the medium weakly absorbing, the polarization vector can be very fast in following the laser profile; this means that there are a few limits in the bandwidth of the THz pulse that can be generated with such devices. The main drawback is that, since this is

a second-order process, the intensities of the THz radiation are reduced with respect to the Auston switch, but high intensities can be achieved by the more powerful short-pulse infrared laser source now available also commercially. A complementary and alternative approach, based on free electron devices, is discussed in the present paper.

#### **2. The Free Electron Laser**

In order to understand how a free electron laser can perform in a way similar to the time-domain THz sources, let us recall the main elements constituting a free electron laser (FEL). An FEL uses an electron beam generated by a particle accelerator that, due to the interaction with an external element, can emit radiation. To be more explicit, the electrons—which have several MeV of energy, properly aligned, and focused by steering coils and quadrupoles—are transported into the interaction region that in "conventional" FELs it constituted by a permanent magnet device called a magnetic undulator. Here, the electron kinetic energy is transformed in a radiation field by means of the synchrotron emission mechanisms, which can be considered a spontaneous emission process. With the addition of an optical cavity, the radiation is stored into a volume; therefore, the emission mechanism becomes stimulated by the simultaneous presence of the electrons, the magnetic field, and the stored radiation.

$$\begin{cases} \lambda = \frac{\lambda\_u}{2^{\gamma^2}} (1 + K^2) & \text{Resonance Condition} \\ \eta \propto \frac{1}{2\nabla} & \text{Efficiency} \\ G \propto \frac{N^3 I}{\gamma^3} \mathcal{g}(\theta) & \text{Gain} \end{cases} \tag{1}$$

Relevant FEL relations are reported in Equation (1) indicating that the resonant wavelength is inversely proportional to the second power of the electron energy (expressed by the relativistic factor γ) and directly proportional to the undulator period λ*<sup>u</sup>* and the magnetic field strength contained in the undulator parameter *K*. The efficiency is inversely proportional to the number of the undulator period *N*, and lastly, the gain is proportional to the electron beam current *I* and to the undulator length at the third power, but also inversely proportional to the electron energy at the fifth power. Moreover, the gain is proportional the function *g*(θ) of the detuning parameter θ = *2*π*N(*ω − ω0*)*/ω<sup>0</sup> (where ω*<sup>0</sup>* is the spontaneously emitted frequency). It is important to point out that the synchrotron emission is not the exclusive emission mechanism for free electron devices, but is the one for which the interaction between the particle and field is more effective.

Therefore, it is possible to analyze the characteristics that an FEL should satisfy if designed to operate in the THz region. First of all, looking at the first part of Equation (1), the electron beam energy can be quite low, with respect to the visible and UV operations, and this allows the design of a compact FEL layout with small particle accelerators. A broadband emission that is typical of the conventional solid-state THz sources can be obtained by means of short interaction regions, which clearly add compactness to the overall device. This can be acceptable because the high gain is ensured by the low energy beam (see the third part of Equation (1)). To maintain the bandwidth as broad as possible, we must avoid the use of an optical cavity, which certainly reduces the frequency components, and obtain emission in a single electron passage. The lack of the optical cavity allows a straight-line e-beam propagation. In order to extract as much power as possible in a single-pass device, we have to work in the coherent spontaneous emission regime and super-radiant regime.

#### **3. Coherence and Order in FELs**

The previous section discussed the necessity of exploiting all the coherent mechanisms in order to avoid the use of an optical cavity for a THz FEL. The first degree of coherence is obtained when the electron bunch length is comparable to the wavelength of the radiation to be generated by the device. This mechanism was firstly proposed by Schwinger for the analysis of synchrotron radiation [4] and by V.L.Ginzburg to explain strong radiation emissions from astronomic objects [5]. From the *Condens. Matter* **2019**, *4*, 90

classical electromagnetic theory, it can be demonstrated [6] that the emission into a solid angle *d*Ω in the frequency interval *d*ω is

$$\frac{d\mathcal{I}}{d\omega d\Omega} = \left[N + N(N-1)f(\omega)\right] \frac{q^2 \omega^2}{4\pi^2 c} \left| \int\_{-\infty}^{\infty} \hbar \times \left(\hbar \times \overrightarrow{\beta}\right) e^{i\omega \left[t - \frac{\hbar \cdot \overrightarrow{r} \cdot \left(t\right)}{c}\right]} dt \right|^2. \tag{2}$$

The function *f*(ω) in Equation (2) describes the coherence of the emitted radiation; its values range from 0 to 1. The limit *f*(ω) = 0 indicates an incoherent emission from the bunch that means that the power emitted by *N* particles is just the sum of *N* individual contributions. The upper limit *f*(ω) = 1 represents the total coherence, when the power emitted by *N* charged particles is given by *N*<sup>2</sup> times the emission of the single particle. This result is fully equivalent to the emission of a single particle having a charge *Q* = *Nq*, because looking at Equation (2), power is proportional to *Q*<sup>2</sup> = *N*2*q*2. In order to establish a suitable value for *f(*ω*),* we can observe from Equation (2) that coherent effects dominate when *N*<<*N2f*(ω), which implies *f*(ω)*N*>>1; for the typical case of an S-band radio-frequency (RF) accelerator, the number of electrons in a single bunch is about *N~*108; therefore, a suitable value range for the *f*(ω) function that guarantees high coherence in the emission starts from *f*(*w*)>>*~*10−4. This implies that the wavelength of the radiation generated should be longer than a fraction of the bunch length in order to have a coherent enhancement of the emission. Considering again an S-band accelerator, for which the bunch length is of the order of few millimeters, the result is that coherent emission dominates in the THz or at longer wavelengths.

A second degree of coherence can be exploited taking into account the relationship among all the electron bunches. In fact, an RF accelerator generates a train of pulses, and if the correlation among all the consecutive pulses is good, the radiation will be emitted at discrete frequencies that are harmonics of the RF [7]. This can be easily seen by making a Fourier expansion of the current, as shown in Equation (3)

$$
\overrightarrow{J}\_T = \sum\_{l}^{\infty} \overrightarrow{J}\_{Tl} \exp(-i\omega\_l t) \; ; \; \omega\_l = 2\pi \frac{l}{T\_{RF}} \, \tag{3}
$$

where *TRF* is the RF period and *l* is the harmonic number. The spectral width of the single harmonic is related to the overall length of the bunch train, the so-called macropulse, as well as to the amplitude and phase stability of the bunches over the macropulse. Each harmonic component of the current acts as an isolated source that couples with the electric field of the radiation, which is expanded over the free space, or guiding structure modes *E*<sup>λ</sup> [7]

$$A\_{l,\lambda} = -\frac{Z\_0}{2\mathfrak{\beta}\_{\mathcal{S}}} \int\_V \overleftarrow{J}\_{Tl} \cdot \overrightarrow{E}\_{\lambda} \, d^3 \mathbf{x}\_{\prime} \tag{4}$$

where β*<sup>g</sup>* is the group velocity of the radiation pulse and *Z*<sup>0</sup> is the vacuum impedance. The radiated power is calculated by means of the flux of the Poynting vector: *Pl*,0,*<sup>n</sup>* = β*g*/(2*Z*0) - - -*Al*,0,*<sup>n</sup>* - - - 2 .

A further degree of coherence can be added if we treat the bunch as a collection of *N* particles distributed in the longitudinal phase space [8]. Each electron carries its own energy γ*<sup>j</sup>* and a proper position or phase ψ*<sup>j</sup>* equal to the RF times the time *tj* along the bunch. Using the previous expression (4), the total radiated power can be calculated summing over the particle distribution

$$A\_{\rm I,0,n} = -\frac{Z\_0}{\beta\_\mathcal{S}} \frac{q}{T\_{\rm RF}} \frac{\rm KL}{\sqrt{\Sigma}} F \sum\_{j=1}^{N\_\mathcal{E}} \frac{1}{\beta\_{\bar{z}j} \gamma\_j} \frac{\sin(\theta\_{\bar{l}j}/2)}{\theta\_{\bar{l}j}/2} i e^{j(\frac{\theta\_{\bar{l}j}}{2} + l\psi\_j)} \; ; \; \; \theta\_{\bar{l}j} = \left(\frac{\omega\_{\bar{l}}}{c\beta\_{\bar{z}j}} - \frac{2\pi}{\lambda\_u} - k\_{0,n}\right) \tag{5}$$

where Σ is the radiation mode size and *k*0*,n* is the transverse mode momentum. From Equation (5), we see quite explicitly that the presence of a phase factor gives rise to an interference mechanism; the contributions to the total power, given by the sum over all electrons, indicated by the index "j", may result in constructive or destructive interference. To maximize the power extraction, by means of the

Poynting theorem, it is possible to minimize the negative interference. This goal can be achieved when the phase term in Equation (5) is overall constant with respect to the single electron emission and will only depend by the harmonic number *l* influence. In conclusion, the ideal phase-matching distribution, which maximizes the power extraction by means of the minimization of the destructive interference, is obtained by putting the phase term equal to a constant ϕ*<sup>l</sup>* that depends only by the harmonic number. The ideal distribution for the electrons, in the longitudinal phase space, is therefore as follows:

$$
\left(\frac{\partial\_{l\dot{l}}}{2} + l\psi\right) = \phi\_l. \tag{6}
$$

When the electrons in a bunch are distributed in the longitudinal phase space as in Equation (6), the radiation emission due to each particle is added in phase, as indicated by Equation (5), maximizing the power extraction during the interaction process. A different way to understand the meaning of the ideal energy-phase correlation curve is that, during the passage of the electrons inside the magnetic undulator, the combined ballistic and oscillating motion is such that the maximum bunching (and consequently, the maximum energy spread and the minimum temporal width) is obtained when the bunch reaches the center of the interaction region. So, the ideal phase-matching curve is the one for which the distribution realizes the best bunching at the undulator center [8] (see Figure 1).

**Figure 1.** Electron distribution in the longitudinal phase space while traveling along the magnetic undulator. Frame = 1 (**a**) represents the undulator entrance; Frame = 100 (**b**) represents the undulator center; and Frame = 200 (**c**) represents the undulator end.

In the ENEA Research Centre in Frascati, two FEL compact devices have been realized [9,10], in order to test the three described mechanisms for the generation of coherent radiation from free electrons. In particular, the FEL-CATS (Compact Advanced THz Source) [10] has been realized to test the energy-phase correlation mechanism for the emission of coherent radiation, up to saturation levels, without the use of any optical cavities. This FEL present an element called a phase-matching device (PMD) that is capable of manipulating the electron beam in the phase space. The PMD is an RF device located downstream of the Linac accelerator (2.3 MeV) in which the RF field amplitude and phase, relative to the Linac, can be controlled. This control allows the reference electron passing through the center of the PMD with a phase close to zero. The result is that the higher energy electrons, arriving first at the PMD, are decelerated, while the lower energy electrons are accelerated and emerge first from the PMD. This is exactly the required rotation of the electron distribution in the phase space. The FEL-CATS operates from 450 to 800 μm (corresponding to frequencies from 0.4 to 0.7 THz).

#### **4. The Two-Frequency Cavity**

In order to realize FEL sources generating radiation in the THz range with better performance than FEL-CATS, it is necessary to increase the electron energy (see Equation (1)) and to shorten the bunch duration (see Equation (2)). The PMD realized in ENEA for the FEL-CATS experiment is no longer adequate for such a task. A possible solution to this problem is the use of a two-frequency RF device [11,12]. In fact, such cavities offer appealing possibilities to control the bunch length of an electron beam generated by an RF accelerator. The use of a double-frequency cavity requires the second frequency to be a harmonic of the fundamental one, in order to be resonant. The electrons passing through the cavity will see a field that is the result of the sum of the two field components: the fundamental and its harmonic.

$$V(\phi) = V\_0[\sin(\phi + \phi\_s) + k\sin(n\phi + \phi\_n)]\tag{7}$$

There are some design parameters that can be set, such as the harmonic number *n* and the relative amplitude ratio *k* that contributes to the bunch length, but the most relevant is the relative phase *(*ϕ*s-*ϕ*n)* between the fundamental and the harmonic. These parameters establish the slope of the total field in the cavity right where the electron bunch passes. Two different regimes can be in principle realized: one in which the particles gather with respect to the reference electron, and a second in which one can realize a pulse lengthening, whose spread can help dampen coherent instabilities that often cut down the bunch lifetime in recirculated accelerators. In Figure 2, the behavior of the total field in the two-frequency cavity is reported, as indicated by Equation (7), together with the fundamental frequency field and the harmonic frequency field.

**Figure 2.** Electric potential in a two-frequency cavity as a function of the phase ϕ for the fundamental frequency, the third harmonic, and the resultant field given by Equation (7).

The figure reports the ideal conditions to obtain the best bunching close to the reference electron, for a third harmonic field (*n* = 3) and a relative amplitude between the fundamental and harmonic of *k* = 0.6; the phases for the two fields are ϕ*<sup>s</sup>* = 0 and ϕ*<sup>n</sup>* = π. In this case, the total field results in a slope around the reference particle, whose steepness can be controlled by the amplitude of the third harmonic. This is the required solution for the bunching of the electrons up to the ideal phase-matching distribution reported in Equation (6).

From the calculation of the separatrix of the electron distribution in the longitudinal phase space, it can be demonstrated [11] that the bunch profile is given by the following expression.

$$\begin{split} I(\phi, n) = A \exp\Big\{ \frac{1}{a\_{\phi 0} \cos \phi\_S} \Big[ \cos(\phi + \phi\_S) - \cos \phi\_S + \phi \sin \phi\_S - \frac{\mu}{k} (\cos(n\phi) - 1) \Big] \Big\} \approx \\ \approx A \exp\Big[ - \left( 1 - \frac{k n}{\cos \phi s} \right) \frac{\phi^2}{a\_{\phi 0}} \Big] \end{split} \tag{8}$$

The final expression is obtained by a Taylor expansion of the trigonometric functions around the bunch center; the profile, therefore, results in a more simple Gaussian form. With the parameters used for the evaluation of Figure 2 in terms of phase difference and amplitude ratio, we display in Figure 3 the bunch profile for the fundamental harmonic only and for the simultaneous presence of the third or fifth harmonics. It is clear that the higher the harmonics content, the shorter the bunch will be at the cavity exit, due to the increased steepness of the resultant field around the reference electron.

**Figure 3.** Longitudinal electron bunch profile expressed in terms of the phase ϕ, for the fundamental frequency and for the third and fifth added harmonics.

#### **5. FEL as a THz Radiator**

In order to design an FEL operating at THz frequencies, simulation software that is capable of evaluating several of the characteristics of FEL sources has been developed. This code makes use of the electric field generated inside the double-frequency cavity, which is used as a phase-matching device, as described in the previous paragraph. The simulation considers an FEL device based on the main parameters reported in Table 1. The electrons generated and accelerated by a Linac are injected into the two-frequency cavity that is fed with the fundamental (3 GHz) and fifth harmonic and that is set, according to Table 1, in order to distribute the electrons according to Equation (6).

The simulation reported in Figure 4 shows the electron distribution in the longitudinal phase space at the cavity exit. During the transport toward the magnetic undulator, the particles continue to bunch due to ballistic effects; therefore, the peak current continues to increase. We have previously seen that the electron should enter the wiggler with the ideal distribution in the phase space to reduce the negative interference in order to enhance the extraction efficiency during its passage in the interaction region. To do so, a variable free propagation space may be considered a further optimization tool.


**Table 1.** Main parameters of the free electron laser (FEL) simulation.

**Figure 4.** Electron distribution, in the longitudinal phase space, at the two-frequency cavity exit.

To clearly understand the effects of the drift space, we have analyzed the modification of the output power spectrum, averaged over the macropulse, during the propagation in a drift space, between the end of the two-frequency cavity and the undulator entrance, over a range of 36 cm. Analyzing Figure 5 (column (a)), we can observe that degradation occurs starting from about 7–8 cm from the cavity exit, and that at the end of the drift, it is quite significant. This phenomenon can also be observed by analyzing the single radiation peak pulse and the associated electric field burst; a reduction in the power of about 50%, in the worst situation, is expected (see Figure 5 column (b)). An optimization can be performed acting on the parameters of the two-frequency cavity, such as the voltage on the fundamental and its harmonic, or their relative phase, in order to reduce the rotation in the phase space and let the ballistic propagation complete such rotation and realize the ideal phase-matching distribution. After the proper optimization, we obtain a spectrum that ranges from 0.5 to 1.5 THz with an integrated power over the macropulse duration and over the total spectral bandwidth, of about 90 kW (see Figure 6). It is very important to stress that with this device, due to the RF properties of the accelerator, which are expressed also by Equations (3)–(5), it is possible to isolate the single harmonic with an interferometer, for instance, still having an average power for the single frequency of the order of hundreds of watts. This is not possible with conventional THz sources. Moreover, another interesting result is that the single frequency, being a harmonic of the RF, has a temporal structure equal to that of the RF macropulse. In addition, we have to refer to the RF macropulse for its temporal coherence, which for conventional magnetrons and klystrons is usually quite good. On the other hand, if we look at the whole bandwidth, the temporal structure is the well-known train of microbunches separated by the RF period.

**Figure 5.** Simulation of the effect of a drift space in the terahertz (THz)-FEL emission. The three rows refer to three cases: Fr = 2 denotes 0 cm of drift space; Fr = 25 indicates 18 cm of drift space, and Fr = 39 represents 36 cm of drift space. Column (**a**) reports the radiation power spectrum; column (**b**) indicates the radiation peak power time profile, and column (**c**) shows the peak electric field as a function of time.

**Figure 6.** Simulation of the optimized radiation power spectrum emitted as a comb of frequencies related to the harmonics of the fundamental RF (ν*RF* = 3 GHz).

In conclusion, an FEL THz radiator can operate as a natural "frequency-comb" emitter or a single-frequency emitter; therefore, it can be considered as a convenient, flexible, and powerful source for the generation of coherent radiation in the THz spectral region.

#### **6. Energy Recovery**

Another way to improve the performances of broadband THz FELs is related to their efficiency. One of the problems suffered by RF accelerator-based FELs, both normal conducting and superconducting, is their relatively low overall efficiency. Considering the basic generation mechanism, the power extraction from the electron beam in favor of the radiation never exceeds 1/2*N*, where *N* is the number of periods of the undulator for the low-gain regime, and ρ is the Pierce parameter for the high-gain regime (see [6,13]). In both cases, the best expected efficiency is of the order of few percent. A possibility to increase the efficiency of an FEL is to design a scheme for recovering the electron beam kinetic energy remaining after the undulator interaction. The energy recovered can be used to accelerate a new bunch of electrons, thus lowering the accelerator radio-frequency power requirements. The possibility of managing a lower RF power, and at the same time an exhausted electron beam of low energy, is very useful when designing both the thermal load of the device and the beam dump for the electron exhausting. Generally speaking, there are two possibilities for energy recovery (ER). One is to recycle the electron beam after the undulator interaction. The second possibility is to recover only the energy of the electrons before the beam dumps.

This second technique is particularly useful when the accelerator is designed to be a superconductor due to the reduced losses related to the shunt impedance. This is a relevant point because it allows presenting some interesting solutions. Any RF cavity exhibits power loss related to the ohmic dissipation through the shunt impedance. Considering standard cavity geometry, it can be demonstrated [14] that the shunt impedance per unit length times the cell dimension over the Q factor of the cavity is of the order of 150 Ohm ((*rS*/*Q*)· *d* ≈ 150 *ohm*). This leads us to a simplified but reasonable expression for the power loss as a function of frequency and surface resistance, which is again related to the frequency and conductivity of the material:

$$P\_{\rm Loss} = \frac{\pi \mathcal{c}}{\omega} \frac{1}{L \cdot 150 \,\text{ohm}} \frac{V^2 R\_{\rm Surf}}{\mathcal{G}} \; ; \; R\_{\rm Surf} = \sqrt{\frac{\pi \mu \nu}{\sigma}} . \tag{9}$$

Here, *V* is the accelerating voltage, *L* is the accelerator length, *RSurf* is the surface resistance, *G* is a factor, expressed in ohm, that depends on the RF cavity geometry, ν and ω are the frequency and the pulsation, respectively, and σ is the conductivity of the metal with which the Linac is realized.

Let us first analyze the case of a copper Linac operating in a normal conducting regime (σ = 5.8 × 10<sup>7</sup> ohm<sup>−</sup>1m−1) at room temperature, and the cavities' geometry for which *G* = 280 ohm; the results are reported in Table 2 for two different operating RF frequencies.

**Table 2.** Linac power losses, at room temperature, for two radio frequency (RF) values.


For Case 1, at 3 GHz, we have about 1 MW of power loss, due to ohmic losses across the structure, before any power could be delivered for the acceleration of the beam. With the same parameters, but at 8 GHz of RF (Case 2), we get about one-half of the previous value. This means that if we want to accelerate a beam to a certain energy value, we first need to spend such an amount of power to charge the structure; the rest of the power of the RF source is delivered to the e-beam. The power loss scales with the inverse of the square root of the frequency.

If a Linac based on superconducting material, as niobium, is considered, we know that the two models, the Bardeen–Cooper–Schrieffer (BCS) theory and the two-fluid model [15], are well established and report the same results up to frequencies of about 10 GHz. The surface resistance is now expressed by the following relation:

$$R\_{Sup} = A \frac{\alpha^2}{T} e^{-\alpha \frac{T\_0}{T}} + R\_{res}.\tag{10}$$

From the experimental data and simulations reported in [15], the *A* and α parameters can be deduced, and therefore the surface resistance for the two RF regimes can be deduced as well. The power loss formal expression is the same with the only difference that the surface resistance increases more rapidly with the frequency; consequently, the power losses increase with the frequency as well. Table 3 reports the power loss data for the superconducting Linac, with the same gradient, at 4.2 K.

**Table 3.** Linac power losses, at liquid helium temperature, for two RF values. **Case 1:** <sup>ν</sup> <sup>=</sup> 3 GHz *<sup>L</sup>* <sup>=</sup> 1 m *<sup>V</sup>* <sup>=</sup> 7.5 MV *RSurf* <sup>=</sup> 2.50 <sup>×</sup> <sup>10</sup>−<sup>6</sup> ohm *PLoss* <sup>=</sup> **166 W**


RF source point of view, this amount of loss is negligible; all the RF power would be delivered to the beam in this case. The only problem is that this power must be thermodynamically managed at 4.2 K.

A third alternative is the use of normal-conducting metals, such as copper, at cryogenic temperatures. In fact, at low temperatures, the mean free path of electrons in metals increases; consequently, the electrons will not experience a constant electric field in a coherence length, but rather a variable one. These and other complex effects associated with the frequency, going under the name of an anomalous skin effect [16]. The result is that the classic ohm law, as we know it, is no longer valid, and the current must be calculated over the actual electron path. A simulation for a Linac with the previously reported values in Table 2 is displayed in Figure 7 for three frequencies.

**Figure 7.** Linac power loss behavior as a function of temperature and frequencies as follows from the anomalous skin effect theory.

The power losses decrease with the temperature, as expected, but again, higher frequencies exhibit lower losses. At liquid nitrogen temperatures, the power losses amount to about one-third with respect to the room temperature case. This is a quite good improvement for any energy recovery regime.

Once the amount of ohmic losses on the RF cavities that we have to deal with (both for the Linac and for the two-frequency cavity used as PMD) is clear, it is possible to face the problem about which kind of ER schemes might be appropriate for an FEL operating in the THz range. The most used is the so-called "same-cell" scheme in which a single RF structure acts as an accelerator in a first passage and a decelerator in a second passage. This scheme is usually the most favored choice due to economical reasons; in fact, the costs of the RF structure, especially if realized with superconductors, are quite high, and any saving in the RF power should not relapse on the RF structures (see Figure 8a).

**Figure 8.** Energy recovery schemes suitable for THz-FELs. (**a**) "Same-cell" scheme. (**b**) Alternative "same-cell" scheme. (**c**) Two-cavity scheme with Bridge Couplers. (**d**) Two-cavity scheme with PMDs.

An alternative to the same-cell scheme is the one reported in Figure 8b; in this variant, the electrons, after the Linac, follow a symmetric path where the magnetic undulator for the FEL radiation generation is placed in one of the two branches.

A second ER geometry is obtained when the beam, after the FEL interaction, is directed through a different decelerating structure. Generally, this second RF structure is similar to the accelerating Linac to which it must be strongly coupled in order to efficiently transfer the RF energy (see Figure 8 (c)). The "different-structure" scheme appears to be expensive because of the use of a second Linac structure. However, due to what has been discussed in the previous sections, THz generation, by means of free electron devices, requires low energy electron beams; therefore, the costs of the RF structures can still be affordable. For this reason, this scheme is under investigation at Frascati for the FEL-CATS. Moreover, this second scheme offers us the possibility of coupling the power of the exhausted beam directly into the two-frequency RF cavity: the PMD (see Figure 8d). This is a very interesting opportunity because the electrons, after the passage into the cavity and into the undulator, carry a memory of such an interaction by means of the shape of the current. Furthermore, by the use of the presented model of harmonic expansion (see Equations (3)–(5)), the shape of the field generated inside the PMD will be better tailored for the enhancement of the efficiency in the radiation generation mechanism. A semianalytical and numerical model is under study.

#### **7. Conclusions**

Innovative design schemes for the realization of a compact FEL source for operation in the THz spectral region have been discussed in this work. The proposed device, unlike conventional FELs, is not tuned by varying the electron energy or the undulator gap; instead, it is designed to emit several frequencies, which are the harmonics of the accelerator RF, within a broad spectral band. These characteristics are obtained through working on the coherent properties of the electron beam generated in a RF accelerator together with a proper manipulation of the electron distribution. The goal is to get the ideal energy-phase correlation that allows saturation-level emission without the use of an optical cavity. The features obtained are unique: the presence of the RF harmonics, which are spectrally very narrow, and that can be easily extracted make this device suitable for any spectroscopic application that requires a high spectral power density. A significant example is the diagnostic of magnetically confined plasma. Moreover, the presence of many narrow spectral components (related to the fundamental RF that can be as stable as 1 part over 106) allows creating a combination of them in a frequency "comb" that finds many applications in metrology (optical clock) in spectral phase interferometry and spectroscopy. A wide variety of features in a single device represent uniqueness in the laser source scenario.

**Author Contributions:** A.D. and G.P.G. have developed the theory about the coherent emission also in the case of energy-phase correlated electron beam. A.D. realised all the simulation codes for the electron dynamics, radiation emission and power losses in the RF structures. E.G. has controlled and verified the experiment feasibility of the device proposed.

**Funding:** This research received no external founding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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