A free-electron laser (FEL) generates coherent light using an electron beam. Unlike conventional lasers, which obtain light from a gain medium, FELs generate light through periodic interactions between an electron beam and an electric or magnetic field.

A FEL is a light source that can emit a wide range of wavelengths, from terahertz to X-rays. This light can be used in various fields, including high-resolution imaging, ultrafast time-resolved spectroscopy, and applications requiring atomic-level fine resolution [1–4].

FEL technology is a complex combination of various technologies (e.g., semiconductor, vacuum, and laser). Conventional tungsten electron tips can be fabricated via electrochemical etching for use as the electron emitter. Recently, research into carbon nano-tube (CNT) tips has been actively pursued. CNT tips are manufactured via arc discharge, laser vaporization, chemical vapor deposition, and pyrolysis procedures. The electrodes used to control the electron beam are typically manufactured using a micro-electro-mechanical system (MEMS) process and a silicon wafer [5–7]. In addition, vacuum technology is required to generate and control electron beams.

In this study, we used simulations to analyze the optimal structure for generating a laser beam from a basic FEL structure. We fabricated existing tungsten and CNT paste tips, investigated their current characteristics, and analyzed their suitability as electron-emission tips for FELs. In addition, we used a CNT tip to simulate the electron beam trajectory in an optimal FEL structure equipped with multiple tips.

A FEL typically consists of several components, including an electronemission tip, source lens, wiggler, and optical system. An electronemission tip is composed of a metallic material that contains free electrons. Electrons are emitted by applying a negative voltage to the tip.

To increase the efficiency of electron emission, the tip is configured with a very pointed shape. This reduces the tunnel barrier, allowing electrons to be emitted even at relatively low voltages. The sharper the tip, the lower the tunnel barrier and the more efficient the electron emission.

Source lenses are a critical component of FELs: they are responsible for accelerating the electron beam or producing a parallel beam that interacts with the wiggler. They are typically fabricated using MEMS technology and consist of three electrodes. The first electrode, known as the extractor, applies a ground or positive (+) voltage to the electron tip, to eject electrons. The second electrode, known as the accelerator, can apply both positive and negative voltages (accelerating and retarding modes, respectively); these modes control the acceleration or deceleration of the electron beam and provide precise control over the electron trajectory in various applications. The third electrode, known as the limiting aperture, selectively allows electrons to pass close to the optical axis whilst blocking those passing at larger angles. By applying a voltage to each electrode, the source lens controls the properties of the electron beam, ensuring that it is optimized for the desired purpose.

Wigglers are another critical component of the FEL; they modulate the electron beam to generate radiation. Two types of wigglers, magnetic and electric, are commonly used. Magnetic wigglers use the magnetic field generated by the current flowing through a coil to control the electron beam. They have a higher field strength than electric wigglers, resulting in more intense radiation and a wider range of adjustability. Magnetic wigglers are ideal for applications that require shorter wavelengths (e.g., X-rays or extreme ultraviolet light). However, they have complex structures, are expensive to manufacture, and require precise alignment, rendering them susceptible to vibrations and other disturbances.

Electric wigglers have a simpler structure than magnetic wigglers. By replacing the coil with an electrode for applying voltage, their size can be reduced at a lower cost. They are less sensitive to vibrations and offer better control over the radiation wavelengths. However, electric wigglers have a lower field strength than magnetic wigglers, resulting in less intense radiation and a narrower range of adjustability. Figure 1 shows a conceptual diagram of an electric wiggler.

Figure 1. Concept of electrostatic FEL.

To generate laser oscillations, the optical system of the FEL collects only radiation that satisfies the resonance conditions of the resonator. In this study, we analyzed the characteristics of an electron beam according to the geometries of the electron tip, source lens, and wiggler. Therefore, the optical system was excluded from the scope of the study.

The field emission phenomenon was first reported by Wood [8] in 1897. In 1928, Fowler and Nordheim [9] published a study on its relationship equation. During the early stages of its research, field emission was actively studied across various fields, including field emission microscopy, field emission displays, and electron beam lithography [6,10,11].

Field emission is a physical phenomenon that occurs when a strong electric field is applied from outside a material, causing the material’s potential barrier to be distorted and electrons to be emitted from the material to the outside via quantum tunneling.

The current emitted by the applied voltage at the field-emission emitter tip typically follows the Fowler-Nordheim equation, expressed as

where a and b are constants that include the work function. Taking the natural logarithm of both sides of Eq. (1) and rearranging the terms, we obtain

3.1. W-tip

For the field emission tip to be effective, it must be sharpened. The sharper the tip, the higher the electric field strength at the tip end (with respect to the applied voltage); this facilitates electron emission. Tungsten (W) is a popular material for field-emission tips because of its high melting point, excellent electrical conductivity, and high mechanical strength.

The tungsten wire is shaped into a pointed tip using an electrochemical etching method, as shown in Fig. 2 [12]. When a negative voltage is applied to the manufactured field emission tip and a positive voltage is applied to the cathode, electrons are emitted from the tip of the element. The diameter of the electron-emitting needle is typically several tens of nanometers.

Figure 2. W-tip fabricated by electro-chemical etching.

3.2. CNT tip

Recently, the use of CNTs as a material for field-emission tips has been actively researched. A single CNT or a paste composed of multiple clustered CNTs is used as the field-emission tip. CNT paste is understood to be more suitable for a FEL tip.

To produce the CNT emitter, a layer of CNTs was created by applying CNT paste onto the cut surface of a Kovar wire (diameter: ~500 micrometers). A scanning electron microscopy (SEM) image of the resulting CNT paste tip is shown in Fig. 3. Upon magnification, numerous individual CNTs were observed to protrude from the paste [13], indicating its suitability as a field emitter tip; this can be achieved via an electron emission stabilization process.

Figure 3. SEM image of CNT paste tip.

The I−V curves for the W-tip (blue and right axis) and CNT paste tip (black and left axis) are presented in Fig. 4. These depict the current flowing between the tip and extractor electrode (which serves as the anode) at various voltage differences. At a voltage difference of ~500 V, the current measured for the CNT paste tip is several hundred microamperes, whereas the current measured for the W-tip is several hundred nanoamperes, ~1,000 times lower than that measured for the CNT paste tip.

Figure 4. I–V curves of W- and CNT-tips.

A source lens is typically composed of three electrodes. The first electrode (Ex: extractor) is close to the electron-emission tip and generates an electric field in the space between the tip and electrode under the application of ground or positive (+) voltage (V_acc > V_tip); this causes electrons to be emitted from the tip. The strength and direction of the electric field affect the current flowing out of the tip. Moreover, because the emitted electrons are comparatively slow, the characteristics of the electron beam are significantly influenced by electric field characteristics (strength and direction).

The second electrode (AC: accelerator) allows positive (+) or negative (-) voltages to be applied as required. The applied voltage causes the electron beam passing through the source lens to diverge, converge, or remain parallel, affecting the current passing through the source lens.

The third electrode (L.A.: limiting aperture) has the greatest impact on the amount of current passing through the source lens, depending on its size and shape. However, the fundamental role of the limiting aperture is to block electrons from passing through the far edges of the central axis; this improves the characteristics of the electron beam.

The extractor and accelerator electrodes are usually fabricated by etching silicon wafers via the MEMS processes; they have thicknesses ranging from a few micrometers to tens of micrometers, and their thickness does not significantly affect the electron beam control. However, the limiting aperture uses an electrode thicker than the previous two to absorb the electrons making contact with the surface when they pass through the limiting aperture tunnel. This blocks the diverging electrons with respect to the central axis and permits only nearly parallel electrons to pass through, thereby enhancing the electron beam.

4.1. Source lens for conventional FEL module

Figure 5(a) shows a typical electrostatic-type FEL module, with numbers denoting positions (in micrometers). In this section, we compare and analyze the characteristics of an electron beam with respect to the geometrical structure of the source lens. As mentioned previously, the source lens is composed of three electrodes, each with a circular aperture. The electron beam emitted from the tip is conical; furthermore, because it is symmetric about the central axis when it passes through the source lens, the beam can be efficiently controlled using electrodes with circular apertures. Figure 5(b) shows the source lens structure as observed from the wiggler side. The small circle in the center denotes the limiting aperture. Figure 5(c) shows the distributions of the x-direction potential (blue open square) and electric field (black solid line) in the space between the facing wiggler electrodes. The voltage applied to the wiggler electrode was 20 V. Because the same voltage was applied to the two facing electrodes, the voltage exhibited a parabolic distribution with a minimum value at the wiggler center (x = 0). However, the electric field Ex became zero and changed direction at the center.

Figure 5. Conventional electrostatic FEL model.

Figure 6(a) illustrates the electron-beam characteristics of a typical source-lens module. After passing through the source lens, the electron beam enters the wiggler section, where radiation is generated by a periodic change in the trajectory (produced by the voltage applied to the wiggler electrode). The wavelength of the FEL is determined by the wiggler period, which is equivalent to the longitudinal period of the electric field generated by the voltage (V = 20 V) applied to the wiggler electrode. More specifically, the wavelength of the FEL can be expressed as follow:

Figure 6. Conventional source lens.

Here, p denotes the wiggler period, and $\gamma =\sqrt{1-{\left(v/c\right)}^2}$ is the relativistic factor of the electrons. This equation shows that the wavelength of the FEL is inversely proportional to the square of the relativistic factor, implying that a higher electron energy produces a shorter wavelength.

Figure 6(b) shows the shape of the source lens and the attachment points of the electron beam, as measured at the front (detector A) and rear (detector B) positions of the wiggler. Detector A detects a circular electron beam because the source lens (including the limiting aperture) is circular. At detector B, the circular electron beam appears to be enlarged, because the beam spreads. The symmetry of the electrostatic force [Fig. 5(c)] applied to the electron beam is disrupted by the geometric mismatch between the circular electron beam and square wiggler. To improve the characteristics of the light emitted by the wiggler, it is necessary to modify the shape of the source-lens electrode.

4.2. Rectangular source lens

Figure 7 shows the square source lens and its electron beam shape. To improve the asymmetry of the electrostatic force in the wiggler section (which occurs under a circular source lens), the shape of the source lens was switched to a rectangle (similar to the wiggler shape), and the electron-beam characteristics were compared. Although the electron beam had a square shape that resembles the shape of the electrode, distortion was observed both in front of (detector A) and behind (detector B) the wiggler. Therefore, in terms of the beam shape, the square-shaped source lens structure had to be improved.

Figure 7. Rectangular source lens.

4.3. Hybrid source lens

Figure 8 depicts a hybrid source lens in which the extractor and accelerator electrodes are circular (to match the shape of the electron beam emitted from the tip) and the limiting aperture electrode is rectangular (to match the wiggler shape). The electron beam shape was measured in front of (detector A) and behind (detector B) the wiggler and was found to be almost square, making it suitable for the FELs. The similarity between the shape of the electron beam passing through the wiggler section and that of the wiggler electrode resulted in a uniform electrostatic force acting upon the electrode. Therefore, the characteristics of the emitted light generated with respect to the electron beam trajectory change in the wiggler section are expected to be improved.

Figure 8. Hybrid source lens.

However, because the electron beam passes through the central axis, the periodic trajectory change is small and insufficient to emit radiation. This is because when the same voltage is applied to the facing wiggler electrodes, the electric field at the central axis is zero, and the electrons passing near the central axis do not oscillate.

4.4. Optimized source lens

To compensate for the disadvantages of the mixed-shape source lens (as shown in Fig. 9), the limiting aperture is designed with two rectangular apertures. Consequently, it is expected that two streams of electron beams with shapes suitable for FELs can efficiently generate radiation whilst passing close to the wiggler electrode. The shape of the electron beam observed behind the wiggler appears somewhat distorted from a rectangular shape because the electron beam is periodically shaken under the force of the wiggler electrode. This occurs because the magnitudes of the attractive and repulsive forces produced by the applied voltage differ depending on the distance from the wiggler electrode. Nevertheless, light with excellent emission characteristics can be generated by passing the electron beam through a wiggler, without producing a significant change in the shape of the electron beam. Therefore, the source lens in Fig. 9 is the most appropriate structure for the FEL.

Figure 9. Optimized source lens with a double rectangular limiting aperture.

Although the technique of processing and using conventional tungsten as a sharp tip for electron emission has been studied, it is often beneficial to use multiple tips (e.g., CNT paste) in FELs. For instance, the FEL wiggler in Fig. 5(a) has a two-line structure. Therefore, as illustrated in Fig. 9, passing the electron beam through a position close to the wiggler and parallel to the central axis in the two strands can increase the radiation intensity. The structure of the multi-electron tip helps generate two parallel electron beams. This is because the electron beams emitted from multiple electron tips tend to moderately diverge compared to those emitted from a single one.

Figure 10(a) depicts the FEL module with multiple electron emission tips, as well as the optimized source lens (as shown in Fig. 9). Two electron beams pass near the wiggler. Figure 10(b) shows a magnified view of multiple electron tips and beams, revealing the periodic change in the electron beam orbit that generates radiation.

Figure 10. Simulation model and trajectory for multi-tip configuration.

Figure 11 illustrates the electron beam cross-section with respect to the number of electron emission tips. The black dots denote electrons passing through the cross-section: the darker the color, the greater the number of electrons. Thus, the electron beam is strengthened when the number of electron tips increases. At the wiggler entrance plane, the shape of the electron beam is rectangular, matching the shape of the limiting aperture. However, on the wiggler output side, it tapers at the top and bottom, and certain parts appear truncated. The shape change occurs because of the various electrostatic forces acting upon the electrons that pass through points close to the electrode and those passing farther away. For the truncated shape, the electrode surface absorbs electrons because it is a conductor, and these electrons do not propagate to the output surface. Adjusting the voltage applied to the wiggler electrode can increase the number of electrons contributing to radiation generation, resulting in an improved FEL efficiency.

Figure 11. Trajectory cross section for multi-tip configurations: (a) single tip, (b) three tips, (c) four tips, and (d) 13 tips.

In FELs, radiation is generated by periodically shaking the trajectory of electrons using a wiggler. This study analyzed the characteristics of an electron beam for various structures of the source lens in the FEL module. Furthermore, it compared and analyzed the characteristics of the electron beam generated by a conventional single tungsten tip and a FEL module equipped with multiple tips using CNT paste.

When using multiple tips, it was confirmed that the intensity of the electron beam current that generated radiation increased significantly compared to the case of a single tip. Therefore, the optimal approach for a FEL is to employ a multi-electron tip using the CNT paste and an appropriate source lens structure to maximize efficiency.

The optimal radiation output for a FEL can be achieved by adjusting the structure of the FEL module and the applied voltage according to the number of electron-emission tips and the electron beam propagation characteristics. The first step was to parallelize the electron beam by adjusting the voltage applied to the accelerator electrode of the source lens. The second step involved adjusting the size and spacing of the rectangular limiting aperture. The aperture size affects the number of output electron beams (i.e., the amount of charge), whereas the spacing between the apertures determines the proximity of the electron beam to the wiggler. Finally, the voltage applied to the wiggler electrode was adjusted. In general, (+) and (-) voltages of the same magnitude are alternately applied to the wiggler electrode in the direction of the electron beam. However, if the electron beam passes through a point close to the wiggler, it can collide with the electrode because of the (+) voltage and reduce the amount of charge, thereby weakening the emitted light. Hence, an independent adjustment of the voltage applied to each electrode of the wiggler is necessary to control the path of the electron beam. It is believed that the independent adjustment of certain electrodes can produce satisfactory results.

Another method for controlling the electron beam is to apply voltages of opposite signs to the opposite wiggler electrodes. When a voltage of the opposite sign is applied, the electric field strength is increased in the lateral direction, causing significant shaking of the electron beam. However, this can result in numerous electrons being absorbed by the electrode surface as they rapidly approach the electrode. In contrast, applying voltages of the same sign to the facing electrodes produces less lateral shaking of the electron beam, making it possible to achieve relatively stable electron beam control.

To summarize, we expect that the advantages of FELs can be maximized by replacing the single-electron emission tip with multiple CNTpaste electron-emission tips, improving the source lens structure, and adjusting the voltage applied to the wiggler electrode. This work will have widespread implications in imaging and spectroscopy.

The authors declare no conflicts of interest.