The electron gun

The electron gun is the starting section of the accelerator system and provides electrons for the accelerating structure. It comprised two main parts: an emission electrode (cathode) and an extraction electrode (anode). The cathode is a source of electrons for accelerator systems and is typically composed of low-work-function materials to obtain a high electron yield. The cathode used in our system released electrons via thermionic emission. An impregnated dispenser tungsten cathode (Model 532; HeatWave Labs, CA, USA) was used. The temperature-dependent work function (W) of this cathode, as quoted by the manufacturer, was 1.67+(3.17×e^-4)T eV, where T is the absolute temperature [31]. The cathode had a circular flat surface with a diameter of 4.86 mm. It was housed in a cathode assembly connected to an electron gun, as shown in Fig. 1. The estimated heating condition was quoted at a voltage of 2.7 VAC and current of 16 A [30]. As the electrical power increased, the temperature of the cathode surface increased, emitting both electrons and photons. The important properties of the cathode are described in Sect. 3.1.

The electron gun in our system was a Pierce-type DC gun with copper electrodes (cathode and anode) and using stainless steel as the gun housing. The anode, which also acted as a focusing electrode, was located 9 mm away from the cathode surface (Fig. 1). It was originally designed to achieve a maximum DC extraction voltage of 17 kV [30]. This value was used throughout the study, unless stated otherwise. The vacuum duct was connected to the sidewall of the gun and directed to an ion pump to maintain high vacuum inside the gun. The gun emission current was determined by the vacuum pressure, heating power of the cathode, and extraction voltage of the anode.

The accelerating structure

A LINAC is an accelerating structure wherein an electron beam gains kinetic energy through acceleration in an electric field. The LINAC structure is illustrated in Part iii of Fig. 1. The entire piece was made of copper with five ${\text{TM}}_{\text{010}}$-mode standing-wave resonant cavities and side-coupling cavities. It was originally designed to accelerate electrons in the π/2 mode with a final average electron kinetic energy of 4 MeV [30]. In our reengineered system, an adjustable variac transformer was added to vary the high voltage of the RF system. Consequently, the electron beam energy could be adjusted according to the RF power [30]. The RF field in accelerator cavities was a standing-wave electric field formed by the superposition of forward and backward waves. The RF phase inside the consecutive cavities differed by π, whereas that inside the side cavities differed by π/2 with respect to the main accelerating cavities. These side cavities produced a node of the standing wave and maintained a zero electric field. The RF wave was generated from a 2-MW magnetron (Model M5125), which was powered by a high-voltage power supply through a variac transformer and a pulse-forming network. By adjusting the variac, the RF peak power could be varied between 0.6 and 1.6 MW. This high-power RF wave was then fed to the LINAC through a WR-284 rectangular copper waveguide (Part iv of Fig. 1), which was filled with sulfur hexafluoride (${\text{SF}}_{\text{6}}$) gas to prevent arcing. This pressurized section was separated from the vacuum of the LINAC using a ceramic RF window. Inside the LINAC, the RF wave was coupled between the resonant cavities through side-coupling cavities. The forward and reflected RF powers were measured using a directional coupler located in front of the ceramic window.

Beam characterization section and experimental station

This accelerator was originally been designed by the manufacturer to produce X-rays for medical purposes [30]. Therefore, the original LINAC end was enclosed by a tungsten target and a lead equalizer. To utilize an energetic electron beam, this end section must be modified such that the accelerated electrons can exit the ambient environment. Thus, we replaced the X-ray extraction section at the end of the LINAC with an extension tube of length 55 mm and a 6-way stainless steel cross vacuum component (Fig. 1 (v)), whose inner diameter was 38.1 mm for each pipe. Along the beam axis, the total cross length was 130 mm; therefore, this additional section extended the beam drift space from the end of the LINAC, with an overall distance of 185 mm. At the final end, a 50 μm-thick titanium window was installed. This window facilitated the electron beam in penetrating the external atmospheric pressure while maintaining internal vacuum conditions (~10^-7-10^-8 Torr).

Perpendicular pipes were used as part of the electron beam characterization unit, or the diagnostic chamber. Two pneumatic linear motion feedthrough actuators (MDC P/N. 662006, USA) were fitted to allow installation and movement of the phosphor screen used for beam size measurement and the in-house Faraday cup for charge measurement. The actuators were moved in and out via pressurized air. The screen was composed of a 0.5 mm-thick aluminum plate coated on one side with a phosphor material (${\text{Gd}}_{\text{2}}{\text{O}}_{\text{2}}\text{S}$). The screen dimensions were 28 mm × 40 mm. The beam size was observed through a glass window using the CCD camera (Basler, acA 640-120 gm with lens M7528-MP). The CCD sensor of the camera contained 659 × 659 pixels with a resolution of 5.6 μm/pixel.

Additional modifications were made to this section by installing two beam-steering magnets close to the LINAC end. The magnets were air coils composed of copper wires. Each coil had 255 turns and could operate without overheating in an ambient environment at maximum current and voltage of 3 A and 14 V, respectively. The magnetic field strength at 3 A was approximately 12 mT. This magnet set played an important role in beam energy measurement. The customized sample conveyer was placed a few centimeters below the titanium window. It was designed such that the sample could be placed on the conveyer and the electron dose could be varied by moving the sample passing the beam at various conveyer speeds. The details of conveyer design and study are beyond the scope of this study and will be reported elsewhere.

Electron current density and dynamics in the gun

3.1.1

Cathode emission and expected current density

The current density of electrons emitted from a given body via thermionic emission depends on the surface temperature, as explained by Richardson's law [32-34]. This current density is enhanced in the presence of an external electric field because this field lowers the work function of the materials by Δ W. This is known as the Schottky effect and the current density can be determined using the following equation [32, 35, 31]: $J_{\text{R}}=A_0{\lambda }_{\text{R}}{T}^2{e}^{-\left(W-\text{Δ}W\right)/k_{\text{B}}T}\mathrm{,}$ (1) where $A_0=1.20173\times {10}^6\text{A}{\text{m}}^{-\text{2}}{\text{K}}^{-\text{2}}$ is the universal constant, ${\lambda }_{\text{R}}\approx 0.5$ is the correction factor for metals[36], W is the temperature-dependent work function, T is the absolute emission temperature, and k_B is the Boltzmann constant. In this expression, the field-enhanced effect $\text{Δ}W=\sqrt{e^{3}E/4\pi {ϵ}_0}$, where e is the elementary charge, E is the electric field strength (in $\text{[V/m]}$), and ϵ₀ is the permittivity of free space. This thermionic electron current is then extracted using an electron gun with a potential gradient between the cathode and anode. If all emitted electrons leave the volume in front of the cathode under the influence of the applied extraction gradient, the gun is considered to be in the temperature limit regime, and the gun's current density is equal to J_R. However, if the cathode temperature is excessively high, such that an electron space charge accumulates in front of the cathode, the gun is in the space-charge-limit state. In this region, the current density plateaus regardless of the heating temperature, indicating that its lifetime is shortened without producing any higher current density. Consequently, the gun's current density is limited by J_C, that is, the voltage-dependent current density, as explained by the Child-Langmuir law [32-34]: $J_{\text{C}}=\frac{4{ϵ}_0}{9}\sqrt{\frac{2e}{m_e}}\frac{V_a^{3/2}}{d^2}\mathrm{,}$ (2) where Va is the potential difference between the two electrodes, d is the cathode-anode effective separation (9.02 mm in this study), and ϵ₀, e, and me are the permittivity of free space, elementary charge, and electron mass, respectively. The empirical form of the total current density J is $J^{-1}=J_{\text{R}}^{-1}+J_{\text{C}}^{-1}$[34].

Equation (1) shows that for a given material, measuring the emitted electron current density requires the determination of the absolute emission temperature, T, of the surface. A standard method involves observing the wavelength and brightness of the emitting body, and the absolute brightness temperature $T_{\lambda }$ is determined by using a pyrometer. However, the brightness temperature is always lower than the true emission temperature, and conversion must be performed in accordance with the relation[31] $\frac{1}{T}=\frac{1}{T_{\lambda }}+\frac{\lambda \ln \left({ϵ}_{\lambda }\right)}{C}\mathrm{,}$ (3) where λ is the observed optical wavelength according to the pyrometer and C=1.433 cm·deg. Note that $\lambda =650$ nm in this study.

The cathode manufacturer (HeatWave Labs, Inc.) measured cathode temperature at various heating powers using an optical pyrometer. The variation in the brightness temperature of the cathode used in our system with applied electrical heating power is shown in Fig. 2(a). By increasing the cathode heating power from approximately 15 W to 50 W, the brightness temperature obtained from the pyrometer increased from ~1120 K to ~1480 K. This measured brightness temperature was then converted to the emission temperature using Eq. (3), and exhibited slightly higher values. The expected temperature-dependent electron current density from the cathode can be calculated using Eq. (1). The results are presented in Fig. 2(b) together with the theoretical prediction line when the potential difference is $V_a=17$ kV, which is the upper limit of the gun's power supply. Based on this theory, the maximum emission current calculated from our cathode temperature measurements was estimated to be approximately 885 mA, corresponding to a cathode heating power of approximately 50 W. The data also indicate that the current density was still below the space-charge-limit region (plateau).

Fig. 2Full-screen View

(a) Measured cathode brightness temperature, $T_{\lambda }$, and calculated emission temperature, T, at varied heating power. (b) Calculated emission current as a function of cathode heating power. The data clearly show that the experimental current density range is still below the space-charge limit (at $V_a=17\text{kV}$)

3.1.2

Electron beam dynamics in the gun

To construct the electron beam for the simulation throughout the system, the emission current obtained in the previous section was used as the input for the simulation of the electron acceleration in the gun. In this study, CST Studio Suite^® version 2023 [37] was used to construct the electric field inside the gun and trace the emitted electrons through the field. The electric field inside the gun structure was generated based on the potential difference between the cathode and anode of 17 keV.

Two sets of simulations were performed in the study described in this section. First, CST EM Studio software was used to create the three-dimensional (3D) model of the electron gun. The vertical cross section of the model is shown in Fig. 1. In this model, the cathode diameter was 4.96 mm, focusing electrode aperture was 4.10 mm, anode aperture was 2.10 mm, and accelerating gap was 9.02 mm. The 3D electric field distribution inside the gun structure was achieved by applying a potential difference of 17 keV between the cathode and anode. The electric-field vector plot and intensity distribution are shown in Fig. 3(a). A uniform electric field in the region between the cathode and anode was observed, whereas the field was stronger at a diameter greater than the anode aperture. The electric field vectors in this region were not parallel to the beam axis at the anode, which resulted in a focusing field experienced by the electron beam as it entered the anode aperture.

Fig. 3Full-screen View

(Color online) (a) Simulated electric field vectors and intensity distribution (colourbar range: 0-9.2×10⁶ V/m). (b) Longitudinal cross section of the gun and electron beam travelling from the cathode to the entrance of the LINAC structure (colorbar range: 0-17 keV). (c) RMS transverse size and the average kinetic energy of the electron beam from the cathode surface to the LINAC structure

Second, the electron beam dynamics in the gun were simulated using CST Particle Studio software. In this simulation, electrons were tracked using the electric field distribution obtained from the simulation described in the previous paragraph. An input electron current of 885 mA was applied, which is equivalent to a current density of 4.7×10⁴ A/m² at the cathode surface. The longitudinal cross-section of the electron beam traveling from the cathode to the anode aperture is illustrated in Fig. 3(b). As evident, the anode entrance is very close to the cathode and there is no focusing electrode in this DC electron gun, as in the modern design of medical LINACs. Consequently, not all electrons were properly focused on the anode entrance aperture. Certain electrons hit this area, causing a dark burned area around the anode entrance, which was observed in the actual setup. The beam collision with the anode caused a significant current loss. The evolution of the corresponding RMS transverse beam size from the cathode to the LINAC entrance is shown in Fig. 3(c). As evident, the electron beam was focused and had a minimum transverse size at the position of the LINAC entrance owing to the nonuniform electric field lines at the anode aperture. Beyond this position, the beam size increased slightly. The evolution of the average kinetic energy of the electron beam inside the gun is shown in Fig. 3(c). An increase in the average beam energy from 0.07 keV at the cathode surface to a maximum energy of 16.7 keV at a position of 5 mm behind the anode entrance was observed. After this position, the average kinetic energy decreased slightly, and a beam with a kinetic energy of 16.0 keV was injected into the LINAC. The decrease in kinetic energy can be caused by the longitudinal space charge field in the low electric field region between the anode exit and the LINAC entrance.

The output electron beam at the gun exit was a continuous beam containing 2,112,232 macroparticles, each with an average charge of (3.9±0.3)×10^-8 nC. Over a period of 333.6 ps (one RF cycle at a resonant frequency of 2996.82 MHz [27]), this resulted in a total charge of 82±6 pC, corresponding to a current of 245±20 mA. The transverse distribution of the electron beam was circular, with an RMS radius of 0.4±0.1 mm. The beam kinetic energy calculated from the momentum of all the particles in the simulation was found to be 17.51±0.01 keV. The distribution was then used as an input particle to study the electron beam dynamics in the LINAC. This offered an advantage over previous studies [27, 29] in that the simulated electron beam injected into the LINAC structure had properties and a distribution closer to the expected beam in actual operation.

Electron beam dynamics in the linac

After exiting the gun, the electron beam entered the LINAC section and was accelerated by the RF field. To understand the dynamics of the electron beam inside the LINAC, the ASTRA simulation code (DESY, Hamburg, Germany) was applied to track the trajectory of the electrons, including the space-charge interaction. To perform the simulation, all the necessary parameters associated with the real system, such as the electric field profile, electron beam distribution, and physical geometry of the beamline, must be provided.

In our system, the longitudinal electric field profile along the LINAC axis was measured using the bead-pull technique, as presented in our published articles [27, 29]. In this study, the same normalized field profile was applied with the maximum field gradient adjusted to 37.5 MV/m to obtain a final average beam kinetic energy of approximately 4 MeV. This value matched the optimal design of the original system. The electron beam distribution obtained from simulations using the CST Studio Suite^® software in the previous section was used as the input. The distribution included the dimensional position, 3D momentum, time, charge, type, and status of each macroparticle. As the beam was symmetric in cylindrical coordinates, a cylindrical symmetric space-charge grid was chosen. The beam direction was set along z-axis, and the beam cross section was in the $x-y$ plane. The numbers of radial and longitudinal grid rings were 50 and 100, respectively. The field plot subprogram was used in the grid verification and optimization steps. The overall simulation comprised a LINAC (field area) and a downstream vacuum (drift space). The limit of the field area was $z=0-222.0\text{mm}$ and the downstream vacuum drift space distance was $z=222.0-466.5\text{mm}$, where z=0 mm was the LINAC entrance. The titanium window was set at $z=466.5\text{mm}$ and the screen station for monitoring the beam profile was at the center of the 6-way duct, which was located at $z=401.5\text{mm}$.

As the beam traveled through the simulation system, the dynamic properties of the beam at the specified z-positions were observed. Because the accelerating field was a standing-wave RF field, over one cycle, approximately half of the particles traveled in the forward direction and approximately half moved backward. This depended on the phase of the field when entering the field region. Consequently, the continuous electron beam from the gun became a train of electron bunches. The evolution of the dynamic properties of the bunch is shown in Fig. 4(a–b). As evident, the electron bunch gained kinetic energy along the LINAC z-axis, as shown by the increasing graph in Fig. 4(a), reaching a final kinetic energy of approximately 4 MeV at the end of the field position. The electron bunch maintained this kinetic energy through the vacuum duct downstream until it reached the titanium window at $z=401.5\text{mm}$. The ladder-like steps in the field region represent the travel of the bunch across the field boundary between the adjacent cavities. The energy spread of the bunch also increased as the bunch gained higher energy, with the final energy spread on the order of ~700 keV as shown in Fig. 4(a). The transverse properties of the bunch along z-axis are shown in Fig. 4(b). As evident, the bunch had larger transverse size as it traveled down the beamline and the size still increased in the drift space region owing to the transverse momentum and the space-charge effect. The final RMS size was on the order of ~ 1 mm. in contrast to the transverse size, the RMS emittance of the bunch tended to remain unchanged after the end of the field position.

Fig. 4Full-screen View

(Color online) (a–b) Dynamic properties of the electron bunch along the z-axis of the simulation system including the kinetic energy, energy spread, transverse RMS size, and RMS emittance. (c–d) Distribution of the electron bunch at the titanium window on the $x-y$ transverse plane and its 3D distribution. (e–f) x and y phase spaces. (g) Energy spectrum of the electron bunch at the titanium window. (h) Longitudinal phase space of the same bunch. Note that the red histogram represents number of electrons (macroparticles) and the dark blue dots show the kinetic energy associated with each macroparticle

To acquire a complete picture of the bunch at the final position, the bunch distribution in 3D space was plotted along with the bunch's x and y phase spaces. The transverse bunch profile at the titanium window position is shown in Fig. 4(c). The RMS transverse size, calculated from all the electrons in the bunch, was 1.5 mm.

The three 3D shape of the bunch is shown in Fig. 4(d). As evident, the distribution of the electrons in the bunch was more dispersed than in our previous study, wherein the electron beam was generated from the sub-program generator and did not fully represent the actual bunch [29]. The corresponding phase spaces of this electron bunch were similar in both x and y directions, as shown in Fig. 4(e and f). At the bunch profile monitoring position (center of the 6-way duct), the characteristic properties of the bunch were similar to those of the final bunch with an RMS beam size of 0.8±0.3 mm. This value was expected when the measurement was performed under these simulated conditions.

To gain a better understanding of the bunch of electrons, the energy spectrum was plotted as shown in Fig. 4(g). As evident, the majority of particles in the bunch were captured in the ‘RF bucket’ shown as two large energy peaks at ~3.92 MeV and ~4.12 MeV. Thus, they experience two stable but separate phase of the field. The particles injected into the field at different phases experience a lower field or even a reverse field and consequently gain lower energy when traveling through the cavities or, in drastic cases, may travel in the reverse direction and are lost in the LINAC. These minority particles appear as long low-energy tails in the energy spectrum [38]. Consequently, the energy representation of such a bunch can be determined by ignoring low-energy minorities. In our case, the majority of electrons (~78%) had a kinetic energy $\ge 3.9\text{MeV}$. According to the explanation above, the bunch energy was calculated as 4.01±0.07 MeV. Note that this energy is slightly greater than the value shown in Fig. 4(a), where the values were calculated for all particles in the bunch. Figure 4(h) illustrates the longitudinal phase space of the bunch. It is clear that most of the particles in the bunch exhibited bunching with a bunch time of ~120 ps. In a typical standing-wave LINAC, the first cell is normally a half-cell structure with the maximum electric field amplitude at the rear wall of the cell. This results in an electron bunch length of approximately one-fourth the wavelength (~λ/4). In this study, we adopted the longitudinal electric field profile measured using the bead-pull technique, which showed that the field distribution in the first cell was not a half-cell resonant cavity structure. Instead, it appears to be a full-cell resonant cavity structure but with a shorter length than the other four downstream cells, as reported in [27] and [29]. However, we could not confirm this hypothesis because we could not observe the actual inner shape or dimensions of the LINAC cell cavities. Using this longitudinally measured electric field profile as an input in the ASTRA simulation, the continuous electron beam from the DC gun was bunched with a longitudinal beam distribution, owing to the energy distribution of the RF electric field in the linac cavities. As shown in Fig. 7 of [29], the electron bunch length increased while accelerating through the first cell (with a bunch length of ~λ/4) to the third cell (with a bunch length of ~λ/3-λ/2), and was almost constant thereafter until the fifth cell. Subsequently, the electron bunch further elongated after exiting the LINAC's last cavity and travelled in the drift space with a large difference in the energies of the electrons between the head and tail regions, resulting in a bunch length of approximately 120 ps in the titanium window (244.5 mm after the linac exit). The total number of macroparticles in the bunch was 909, 557 (corresponding to a total charge of 36±3 pC). This resulted in a peak current of 300±25 mA. However, the average macropulse current is more appropriate in practice, and the value estimated based on this calculation was 106±8 mA. Based on our beam dynamics simulation, we obtained important parameters and properties of the electron beam, as summarized in Table 1. These values are for operation under optimal machine conditions and will be an important guideline for future measurement and operation.

Electron beam energy measurements were performed both in the diagnostic chamber (in vacuum) and at a position of 5 cm after the titanium window (in air) using a phosphor screen and a steering magnet installed outside the chamber upstream the diagnostic chamber. The magnetic field distribution of the steering magnet and the calibration curve between the applied electric current and magnetic field amplitude were included in the image processing analysis of the spatial and energy distributions of the electron beam on the phosphor screen using a MATLAB script. When the screen was placed in air at a larger distance, a better energy resolution was achieved. In our preliminary observations, the RF peak power was varied up to 1.4 MW for a complete beam energy measurement at both positions (Table 2). It can be observed from Table 2 that the measured average beam energy in air (5 cm after the titanium window) was in line with the simulated beam energy of the entire bunch, with a slightly smaller value. A small difference of 0.4 MeV was consistent for all RF powers and was attributed to energy loss as the beam travelled through the window and ambient air. However, the average energy measured in vacuum had a larger difference owing to the insufficient magnetic field strength (5 mT) of the steering magnet, which resulted in a poorer energy resolution of the diagnostic system at shorter distances. Although the full performance of the machine was limited by certain technical issues, the data in Table 2 can still provide a good understanding of the beam energy measurement. The electron beam current could not be determined because the beam size was larger than the collection area of the Faraday cup installed in the diagnostic chamber. Further improvements to the beam diagnostic system will be made in the future.