High Average Current Electron Beam Generation Using RF Gated Thermionic Electron Gun

Abstract

High-current electron beams can significantly enhance the productivity of variety of applications including medical radioisotope (RI) production and wastewater purification. High-power superconducting radio frequency (SRF) linacs are capable of producing such high-current electron beams due to the key advantage to operate in continuous wave (CW) mode. However, this requires an injector capable of generating electron bunches with high repetition rate and in CW mode, while minimizing beam losses to avoid damage to SRF cavities due to quenching. RF gating to the grid of a thermionic electron gun is a promising solution, as it ensures CW bunch generation at the repetition rate same as the fundamental or sub-harmonics of the accelerating RF frequency, with minimal beam loss. This paper presents detailed beam dynamics simulations demonstrating that an RF-gated gun operating at 1.3 GHz can generate bunches with 148 ps full width with 8.96 pC charge.

1. Introduction

High power, more specifically high-average-current electron linear accelerators (linacs) have the potential to revolutionize multiple fields, from medical radioisotope production [1,2] to environmental remediation [3,4]. In particular, for wastewater purification with electron linacs, there are many advantages, such as high productivity, reduced operating costs, and environmentally friendly operation with minimal waste [5,6]. To achieve higher average currents in electron linacs, it is more effective to use superconducting RF accelerating (SRF) cavities than normal-conducting ones. Since the heating caused by the RF power input in a normal-conducting RF cavity limits the ability to increase RF duty. On the other hand, if a high frequency superconducting RF cavity such as 1.3 GHz is used, cavity cooling with liquid helium is required which makes the system impractical for most of the industrial applications including wastewater purification.

A promising solution is the integration of conduction cooled Nb₃Sn based SRF [7,8,9] technology which does not require liquid helium for cooling. This technology enhances the performance of e-linac by enabling continuous wave (CW) operation which is a key feature of SRF cavities, without the use of liquid helium. Nevertheless, the full potential of CW operation in SRF e-linacs, particularly for high-average-current operation, can only be realized if the injector system is capable of generating high-quality electron bunches with high repetition rate in CW mode. While significant progress has been made in high-peak-current injectors with pulse-mode operation [10,11], high-average-current injectors with high RF duty remain limited [12,13].

Several injector systems for high-average-current applications have been developed to date. One such system is an injector consisting of a thermionic cathode with a grid driven at high frequency and multi-stage energy booster cavities, which was developed as an electron source for FELs [12]. The grid-controlled cathode was independently developed, and when combined with the booster cavities, the system becomes complex. In addition, continuous-wave (CW) beam generation has been attempted using RF photoinjectors. To reduce the required laser power as much as possible, semiconductor cathodes with high quantum efficiency are employed [13]. In some systems, superconducting RF cavities are used instead of normal-conducting ones. Although such systems are simple and compact, the robustness of the lasers and semiconductor cathodes remains insufficient. Despite significant advances in the materials and geometry of SRF cavities, the development of suitable injectors remains in a relatively early stage. In particular, the development of injector systems that are robust and reliable—and capable of fully exploiting the capabilities of SRF accelerators—remains a major challenge.

Our research aim is to develop a CW, high average current injector system optimized for SRF linacs. For stable operation of the SRF accelerator, the electron injector system should provide properly shaped short bunches without tails and halo [14]. To meet these requirements, as previously mentioned, RF photoinjectors can be used. However, they rely on complex drive lasers, which introduce challenges such as increased cost, system complexity, and maintenance difficulty [15]. In contrast, thermionic emission [16] offers a simpler, cost-effective alternative, providing high current density with benefits such as low maintenance and structural simplicity. However, the inherent challenge with thermionic emission, which is the generation of continuous beam, necessitates precise bunching mechanisms to achieve compatibility with SRF linac operation.

The issue of continuous emission can be addressed using a cathode grid of electron gun, which controls the temporal structure of the electrons emitted from the cathode to produce a bunched beam. Additionally, a carefully designed bunching system is essential to compress the bunches into a suitable time profile for smooth injection and acceleration in the SRF cavities. To meet these requirements, we have designed a compact, CW operable, high-average-current SRF injector using KUCODE [17] that combines a thermionic gridded electron gun with a conduction cooled 1.3 GHz 3-cell SRF buncher [18].

The primary objective of the buncher design was to compress a bunch, achievable from a thermionic gridded gun, into a longitudinal profile suitable for direct injection into SRF accelerating cavities, with zero beam loss. For this buncher design study, we assumed a pre-formed bunch at the cathode of the thermionic gun, with a gaussian distribution in longitudinal, and uniform in the transverse direction. The resulting 3-cell design introduces a novel buncher capable of compressing electron bunches with a full width (FW) ≤ 400 ps. By successfully passing the bunches through the main accelerating cavities, we confirmed that the output bunches from this 3-cell design possess a longitudinal profile well-suited for seamless injection into the main accelerator linac. A key advantage of this configuration is its ability to compress relatively long bunches (full width ≤ 400 ps), thereby relaxing the performance demands on the thermionic electron gun.

Having established this buncher design, our next objective was to identify a suitable grid driving mechanism for the gun, capable of reliably generating the required electron bunches with full width of ≤400 ps at 1.3 GHz repetition rate in CW mode. While alternative electron gating or grid driving approaches exist, using available grid pulsers such as Field-Effect Transistor (FET) [19] and avalanche pulsers [20], they have significant limitations. FET pulsers produce MHz repetition rate but are limited to producing ~170 ps RMS (FW >> 400 ps) bunches, while avalanche pulsers can achieve short bunches of ~60 ps RMS (FW ~ 400 ps) but only at kHz rates. An effective solution to this challenge is applying RF gating to the grid of the thermionic electron gun. Previous studies on RF gating for thermionic guns have demonstrated the feasibility of generating electron bunches with the required parameters [21,22,23]. Additionally, the RF gating approach not only gates the electrons effectively to produce a short bunched beam but also allows the generation at the desired repetition rate of 1.3 GHz with minimal beam loss.

This paper presents the theoretical basis and simulation outcomes validating the RF gating method for the operation at 1.3 GHz. Unlike typical simulation methods that assume pre-formed bunch characteristics such as length and shape, this study demonstrates bunch generation through RF field modulation in the cathode-grid region, enabling more realistic modeling. Additionally, a detailed analysis is provided for bunch behavior from the cathode, to the grid, anode, and further downstream. As a baseline for high-average-current injector, our initial target is to deliver a 10 mA CW beam, which corresponds to approximately 8 pC per bunch at 1.3 GHz [18,24]. This sets the injector requirement of FW ≤ 400 ps and bunch charge of 8 pC. While this meets the design requirement, further optimization was performed to achieve even shorter bunches, as shorter bunch-length improves overall injector performance.

By resolving the limitations of high-average-current injectors and leveraging the benefits of thermionic emission, this work marks a significant step forward in advancing SRF electron linac technology for high-power applications.

2. Thermionic Gridded Electron Gun

Electron gun, for this study, was developed based on the existing thermionic gridded gun at our facility, using a commercially available cathode (Y646B, diameter 8 mm) from CPI Inc. (Plano, TX, USA) [25]. The grid is 0.16 mm downstream of the cathode, with the grid wire specifications as shown in Figure 1a. The Wehnelt electrode has an angle of 60°. The anode, featuring a bore diameter of 9 mm, is positioned 28.5 mm from wehnelt as shown in Figure 1b. The longitudinal and transverse properties of the beam from this gun are detailed in ref. [24]. The system is currently in use at the test bench of our facility. In this paper, simulations performed for RF gating, consider the same geometry and the arrangement of the cathode and anode of the electron gun system.

3. Theoretical Model and Simulation Setup for RF Gating

3.1. RF Gating Mechanism

In the RF gating mechanism [21,22,23], the emitted electron beam is modulated by combination of RF and DC bias voltages for short bunch generation. This is achieved by using electron gun assembly, where DC high voltage (HV) is applied between the anode and cathode with HV power supply (PS). RF waves generated from RF source are fed in between cathode and grid space using coaxial structure. Additionally, a small negative DC bias voltage is applied across the cathode and grid using a bias power supply, as illustrated in Figure 2a. The resultant potential difference between the cathode and grid is described by Equation (1) and shown in Figure 2b:

$$V_{grid}=V_{bias}+V_{rf}\cos \left(2\pi ft-\theta \right)$$

(1)

where $V_{grid}$ is the total grid voltage, $V_{bias}$ is the small DC biasing voltage, $V_{rf}$ and $f$ are the amplitude and the frequency of the RF waves respectively, $t$ is the time variable and $\theta$ $(=2\pi f\tau )$ is the phase angle corresponding to the half bunch-length ($\tau )$ in time. The bunch repetition rate in this mechanism is determined by the RF wave frequency, which in our case is 1.3 GHz.

Since a thermal energy of the electrons is usually of the order of millivolts (mV) and the negative $V_{bias}$ applied to the grid is of the order of volts (V), electrons from the cathode are allowed to emit and move toward grid only when $V_{grid}\ge 0$. The condition satisfies for $t_A\le t\le t_C$. However, due to the leakage of the HV electric field through the grid, a small offset emission voltage $V_{cutoff}$ is introduced. This leakage causes electron emission to occur for a slightly longer duration than the intended emission area, as shown by the red line in Figure 2b. As a result, the emission occurs when $V_{grid}\ge V_{cutoff}$, and leads to the Equation (2) at the extremes of the extended emission area.

$$V_{cutoff}=V_{bias}+V_{rf}\cos \left(\theta \right).$$

(2)

Assuming a linear relationship between the emitted current $I\left(t\right)$ and the applied grid voltage, as supported by prior work [21,23], the emitted current can be expressed as:

$$I\left(t\right)=g_{21}(V_{grid}-V_{cutoff}).$$

(3)

where $g_{21}$ represents the transconductance of the gun i.e., the emission capability of the gun. By integrating the current over the emission area, the total bunch-charge $\left(Q\right)$ can be calculated as given by Equation (4).

$$Q={\int }_0^{2\tau }I\left(t\right)dt={\displaystyle \frac{V_{rf}}{f}}{\displaystyle \frac{g_{21}}{\pi }}\left(\sin \theta -\theta \cos \theta \right)$$

(4)

This equation demonstrates that $Q$ depends on $V_{rf}$, $g_{21}$, and $\theta$. By adjusting the $V_{rf}$ and $V_{bias}$, the emission area ($2\theta$) can be controlled and thereby tuning both the bunch-length (${\tau }_b=\mathrm{f}\mathrm{u}\mathrm{l}\mathrm{l} \mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}$) and bunch-charge ($Q$). Equation (4) holds true, even if the $V_{cutoff}=0$.

The longitudinal properties of the electron bunch in the RF gating mechanism are thus entirely governed by the applied grid voltages. As a result, operating the gun in the space-charge-limited [23] regime is preferred, as it allows for complete manipulation of the beam by adjusting the grid voltages, enabling precise control over the electron emission.

3.2. Simulation Setup for RF Gating in KUCODE

The principle of the RF gating described in the previous section does not account for factors such as space charge effects, the effect due to the emission of electrons from different transverse distances from the axis, and beam dynamics between the grid and anode. To address these aspects, we analysed the performance of the electron gun with RF gating using KUCODE with the simulation setup as shown in Figure 3.

KUCODE being a 2.5-dimensional particle tracking code pose limitations in modelling the grid as a mesh structure. Therefore, we approximated the grid as an imaginary, perfectly conducting plate with a thickness of 20 µm (the same as the actual grid wire thickness shown in Figure 1a, positioned 160 µm from the cathode surface ($\mathrm{z}=0$). While this plate is physically invisible to the electrons, it allows for the application of DC bias voltage in the simulation. With this approximation, two issues arose. The first issue was that, since no electric field exists inside the metal, this region within the grid metal plate of 20 µm acted like a drift space in the simulations. This caused bunch lengthening, as low-energy electrons took longer to traverse this unphysical drift space compared to high-energy electrons. To address this issue, a thin grid metal plate of 1 nm is considered in the simulations. Second, as KUCODE does not model the grid as a mesh structure, which limits its ability to account for leakage fields i.e., cutoff effect due to the high voltage (HV), thus, the effect is ignored ($V_{cutoff}=0$).

To drive the grid with the RF voltage, we modeled a capacitively loaded coaxial cavity resonating at an eigenfrequency of 1.3 GHz. The parameters of this cavity are shown in Figure 4 and given in

Table 1. Parameters of 1.3 GHz coaxial cavity in Figure 4.

L	72.54355 mm
a	4.455 mm
b	7.175 mm
d	160 µm

.

Electron emission from the cathode surface in the simulations is uniform in both radial and longitudinal directions, with an initial monoenergetic energy of 0 eV and current density of 0.2 A/cm². This current density corresponds to a total DC emission current of 100 mA which can be easily achieved using Y-646B cathode with a nominal heater voltage in our experimental setup. Thus, simulation parameter considered for this study is consistent with our experimental setup.

To be compatible with the designed 3-cell buncher in Ref. [18], the generated electron bunch must achieve β = 0.5. Given this requirement, the accelerating voltage between the cathode and the anode in this study is set at 80 kV. To apply RF voltage, we estimated the maximum achievable $V_{rf}$ based on the available RF amplifier in our facility. The amplifier delivers a maximum power ($P$) of 96 W, and with an impedance ($R$) of approximately 45 Ω (measured using a network analyser) between the cathode and the grid in our gun, the maximum $V_{rf}$ is calculated to be approximately 65 V using the relation: $V=\sqrt{P\times R}$. Consequently, in the KUCODE simulations, $V_{rf}$ was fixed at 65 V, while $V_{bias}$ was varied from 0 to −65 V to evaluate the gun’s performance under different operating conditions. The primary objective of the simulations was to estimate ${\tau }_b$ as the function of $V_{bias}$ and $V_{rf}$, and to confirm that the bunch of ${\tau }_b\le 400 \mathrm{p}\mathrm{s}$ and $Q~8 \mathrm{p}\mathrm{C}$ with 1.3 GHz pulse repetition ($1.3 \mathrm{G}\mathrm{H}\mathrm{z}\times 8 \mathrm{p}\mathrm{C}\approx 10 \mathrm{m}\mathrm{A}$), can be produced. Results of this study are discussed in detail in the following section.

4. Results and Discussion

4.1. Performance of the RF Gated Gun (Cathode—Grid Space)

The bunch characteristics resulting from the time varying electric field, with a fixed RF amplitude ($V_{rf}=65 \mathrm{V}$) and varying bias voltage, are analysed at two positions: near cathode (z = 5 µm) and at the grid (z = 160 µm). For this study, specifically the full width (${\tau }_b$) and charge ($Q$) are evaluated. ${\tau }_b$ is calculated with the threshold of 0.01% of the peak value of $Q$. The dependence of these parameters (${\tau }_b \mathrm{a}\mathrm{n}\mathrm{d} Q$) on the absolute value of biasing voltage i.e., $\left|V_{bias}\right|$ with a fixed $V_{rf}$ (65 V) is presented in Figure 5.

Results indicate that for the same $\left|V_{bias}\right|$, both ${\tau }_b$ and $Q$ are smaller at grid (z = 160 µm) compared to near cathode (z = 5 µm). To discuss this calculation outcome, we analyse the longitudinal phase space distribution (kinematic energy of the bunch vs. time, where negative time in the figures correspond to the front of the bunch) as shown by Figure 6. In RF gating, electrons are emitted within $t_A\le t\le t_C$ (Figure 2b), which corresponds to the emission at different phases of the RF field, as illustrated in Figure 6a. Due to the phase difference, electrons emitted within $t_A\le t\le t_B$ i.e., the front part of the bunch, gain energy more than those emitted within $t_B<t\le t_C$ i.e., the tail part of the bunch while moving from cathode to grid. Consequently, at the grid, energy of the front part of the bunch is higher than that of the tail part, as shown in Figure 6b. In this process, the electrons emitted from cathode at time close to $t_C$ do not gain sufficient energy to cross the cathode-grid gap. As a result, these electrons fail to reach the grid, contributing to the reduction in both ${\tau }_b$ and $Q$, which explains why they are smaller at the grid than near the cathode.

Figure 5 further shows that both ${\tau }_b$ and $Q$ continue to decrease with increasing $\left|V_{bias}\right|$, eventually dropping to zero for $\left|V_{bias}\right|>53 \mathrm{V}$. This trend is a fundamental characteristic of the RF gating mechanism, since the emission area represented by $t_C-t_A=2\tau$, reduces with increasing $\left|V_{bias}\right|$, explaining the reason for reduction in both parameters. However, to further understand why $Q$ drops to zero for $\left|V_{bias}\right|>53 \mathrm{V}$, we examined the electron transit time and the electron acceleration time. The electron acceleration time corresponds to the time in which electrons emit from cathode and accelerate toward the grid. The electron acceleration time is therefore same as the emission time $t_C-t_A=2\tau$. The transit time ${(T}_r)$, on the other hand, represents the average time required for an electron to cross the cathode-grid gap ($d$) under the effect of time varying $V_{grid}$. $T_r$ is determined through the Equations (5)–(8) given below. The equations consider the integrated RF field as given in Equation (7), experienced by the emitted electrons over the duration of the emission area, and calculate $T_r$ as follows:

$$F=-e\times E\left(t\right)=e{\displaystyle \frac{V_{grid}\left(t\right)}{d}}$$

(5)

$$\begin{gathered} F={\displaystyle \frac{dp}{dt}}={\displaystyle \frac{d\left(m\right(t\left)v\right(t\left)\right)}{dt}}=m_0{\gamma }^3{\displaystyle \frac{dv}{dt}} \\ \mathrm{W}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e} m(t)=m_0\gamma \left(t\right) \end{gathered}$$

(6)

$${\int }_{v_i}^{v_f}{\gamma }^{3}dv={\int }_{t_i}^{t_f}{\displaystyle \frac{e}{m_0}}{\displaystyle \frac{V_{grid}\left(t\right)}{d}}$$

(7)

$$T_r={\displaystyle \frac{d}{v_f}}$$

(8)

where $m_0$: rest mass of electron, $\gamma$: Lorentz factor, and $v$: velocity of electron. The results of transit time and acceleration time calculations are presented in Figure 7. For $\left|V_{bias}\right|>53 \mathrm{V}$, $T_r$ exceeds the acceleration time $\left(2\tau \right)$, indicating insufficient energy imparted to emitted electrons to cross the cathode-grid gap within the available acceleration time. Consequently, electrons fail to reach the grid and return to the cathode, causing ${\tau }_b$ and $Q$ to drop to zero. The longitudinal phase space distribution for $\left|V_{bias}\right|=60 \mathrm{V}$ in Figure 6 confirms this behavior. Figure 6a shows electron emission, while Figure 6b demonstrates that no electrons reach the grid.

Lastly, Figure 5a,b showing $Q$ and ${\tau }_b$ at grid, help to determine the optimal ${|V}_{bias}|$ for achieving the required $Q$ (~8 pC) and the smallest achievable ${\tau }_b$. This is because electrons reaching the grid are not lost further downstream. Furthermore, the discussion on transit time and acceleration time suggests that the smallest achievable ${\tau }_b$ occurs at $\left|V_{bias}\right|=50 \mathrm{V}$, since beyond this $\left|V_{bias}\right|$, electrons could not reach the grid to form bunch. However, the corresponding $Q$ is only ~5 pC as seen in Figure 5b. This can be resolved by increasing the emission current density from cathode. $Q$ with higher emission current density is shown in Figure 8. It indicates that with $\left|V_{bias}\right|=50 \mathrm{V}$, $Q$ ≥ 8 pC can be achieved, if the current density is increased from 0.2 A/cm² (earlier setting) to 0.4 A/cm². This higher current density can also be achieved easily by slightly increasing the heater voltage. Thus, both conditions of minimum ${\tau }_b$ and required $Q$ are satisfied. As expected, there is no significant difference in ${\tau }_b$ obtained with these two current densities at the grid, as illustrated by Figure 8.

Therefore, a detailed analysis of the bunch evolution, including its behavior within the cathode-grid gap and further downstream to the buncher position, is performed for $\left|V_{bias}\right|=50 \mathrm{V}$ and current density of 0.4 A/cm² in the following sections. For this analysis, the longitudinal phase space distribution is presented as Δ$E_k$ vs. time where $\Delta E_k{={(E}_k)}_i-{{(E}_k)}_{mean}$ with ${{(E}_k)}_i$: kinematic energy of individual electron and ${{(E}_k)}_{mean}:$ mean kinematic energy of the bunch.

While analyzing the evolution of the longitudinal phase space distribution of the bunch from cathode to grid for $\left|V_{bias}\right|=50 \mathrm{V}$ (Figure 9), we observed that the density of the bunch head is higher than the tail. Careful analysis suggests that this comes from the interplay between time-dependent electron emission and $V_{grid}$. At $t=t_A$ (Figure 2b), electron emission begins and gradually experiences the high accelerating field. Subsequently, the electrons accelerated by the high accelerating field can catch up with the emitted electrons ahead of them. This causes longitudinal compression of the electrons emitted in this region, giving higher density at the bunch head. Electrons emitted in the later region can no longer catch up with the earlier emitted electrons. This leads to a more uniform density distribution in the remaining part of the bunch until $V_{grid}$ falls below the emission threshold and the density drops to zero, as depicted by Figure 9a. This asymmetric electron distribution from the initial emission time plays a crucial role in shaping the bunch evolution downstream of the grid. As shown in Figure 9b, the distribution remains unchanged at the grid i.e., high current density at bunch head. The further evolution downstream of the grid is discussed in the following sections.

4.2. Performance of the RF Gated Gun (Grid—Anode Space)

${\tau }_b$ and $Q$ obtained for different $\left|V_{bias}\right|$ at z = 40 mm i.e., 2 mm downstream of the anode are as shown in Figure 10a,b, respectively. As expected, $Q$ downstream of the anode (z = 40 mm) remains the same as at grid (z = 160 µm), indicating no loss of $Q$ between the grid and the anode. However, ${\tau }_b$ increases as bunch moves from grid to anode for the same $\left|V_{bias}\right|$.

To understand the increase of ${\tau }_b$ and the evolution of bunch downstream of the grid up to the anode, the longitudinal phase space distribution is analysed for $\left|V_{bias}\right|=50 \mathrm{V}$ as shown in Figure 11. The result reveals an energy spread within the bunch. To investigate the origin of this spread, simulations were conducted both with and without the space charge effect. The results of the simulation without space charge effects are shown in Figure 12. The comparison of Figure 11c and Figure 12c clearly demonstrates that the high energy of the bunch head is primarily due to the space charge effect. Space charge effect is more pronounced at the bunch head than at the bunch tail. The reason is an asymmetric temporal distribution of the bunch i.e., high density at bunch head whose origin is described in the previous section. As a result, a stronger accelerating force due to space charge on the bunch head compared to the decelerating force on the bunch tail is present. This explains both the higher energy of the bunch head and the longitudinal expansion of the bunch giving longer ${\tau }_b$ at z = 40 mm than at z = 160 µm. However, the energy spread observed after the grid i.e., at z = 0.5 mm, as visible in Figure 11a and Figure 12a, is not attributable to the space charge effect. A detailed analysis revealed that this spread arises from the difference in the HV field experienced by electrons at different transverse positions. Figure 13 illustrates the HV field along the axis i.e., at r = 0 mm and at r = 4 mm. As a result, electrons along the axis gain higher energy compared to those at the outer positions, resulting in an energy spread within the bunch at this position of z = 0.5 mm.

4.3. Performance of the RF Gated Gun (Anode—Buncher Space)

${\tau }_b$ obtained for different $\left|V_{bias}\right|$ at the buncher position (z = 500 mm) is shown in Figure 14a. The optimal case of $\left|V_{bias}\right|=50 \mathrm{V}$ produces the smallest ${\tau }_b$ of approximately 148 ps and $Q$ = 8.96 pC. The corresponding longitudinal phase space distribution for this optimal configuration is presented in Figure 14b. The transverse slice emittance of the electron bunch is illustrated in Figure 15. While the calculated emittance remains below 20 mm-mrad, this parameter is not the primary concern for our target application of wastewater purification.

This overall analysis demonstrates that the design requirement of ${\tau }_b$ ≤ 400 ps can be achieved using RF gating. Since the calculations do not account for cutoff effects, a safety margin is necessary. Nevertheless, the smallest achievable ${\tau }_b$ with the required $Q$ obtained at $\left|V_{bias}\right|=50 \mathrm{V}$ is significantly shorter than the 400 ps requirement. We anticipate this will remain within acceptable limits even when accounting for cutoff effects [21]. Additionally, the energy spread for the bunch at buncher position is approximately 6%; however, our 3-cell buncher design is not sensitive to energy spread. To verify this, we propagated this bunch through our 3-cell buncher using KUCODE, and the result is as shown in Figure 16. ${\tau }_b$ obtained after 3-cell is suitable to pass through the main accelerator cavity with ${\tau }_b$ = 10 ps and mean kinematic energy 1.2 MeV.

4.4. Other Ways to Reduce the Bunch-Length Further

For smallest ${\tau }_b$ at the buncher position (z = 500 mm), previous section finalises $\left|V_{bias}\right|=50 \mathrm{V}$ with $V_{rf}=65 \mathrm{V}$ which gives $V_g=15 \mathrm{V}$, where $V_g=V_{rf}+V_{bias}$, shown in Figure 2b. However, $V_g=15 \mathrm{V}$ can also be achieved with other combinations of $V_{bias}$ and $V_{rf}$. We therefore investigated the effect of other combinations as shown in Figure 17. While the current RF amplifier at our facility restricts us to $V_{rf}=65 \mathrm{V}$, future improvements may allow for higher $V_{rf}$ values. In this study, we therefore considered the combination of $V_{bias}$ with higher $V_{rf}$ also.

Our analysis reveals that combinations with higher $\left|V_{bias}\right|$ values produce shorter bunch-lengths. This relation can be understood from Figure 18, which demonstrates how the emission area for different $\left|V_{bias}\right|$ and $V_{rf}$ combinations (all yielding $V_g=15 \mathrm{V}$) becomes sharper with increasing $\left|V_{bias}\right|$ and $V_{rf}$, resulting in shorter ${\tau }_b$. However, Figure 17 also demonstrates that increasing voltages lead to significant reduction in $Q$. This creates a critical trade-off between achieving shorter ${\tau }_b$ and maintaining sufficient $Q$. The simulations performed in this section indicate that $\left|V_{bias}\right|>50 \mathrm{V}$ with $V_{rf}>65 \mathrm{V}$ would yield the required $Q$ and ${\tau }_b$ < 148 ps, but would require $J>0.4 \mathrm{A}/{\mathrm{c}\mathrm{m}}^2$ and RF power more than 100 W.

The test bench to validate the simulation study is currently under development at our facility. Simulations suggest that our current setup, with available 1.3 GHz RF amplifier (100 W giving $V_{rf}=65 \mathrm{V}$), satisfies the requirement adequately (${\tau }_b$ $\le$ 400 ps). Therefore, the immediate investment in higher-capacity RF amplifiers is not considered necessary for our test bench.

5. Conclusions

This study presents a comprehensive analysis of an RF-gated electron gun system, demonstrating its capability to produce electron bunches with characteristics suitable for our experimental requirements. Through detailed simulations using KUCODE, we established that the optimal operating parameters of $V_{bias}=-50 V$ with $V_{rf}=65 V$ yield a bunch-length of approximately 148 ps with bunch-charge of 8.96 pC, comfortably meeting our design requirements of ≤400 ps and ≥8 pC. The analysis reveals the fundamental physical mechanisms governing bunch formation, including space charge effects and field interactions. While further performance improvements are theoretically possible with higher $V_{rf}$ values, the current configuration provides an effective balance between performance and practical implementation constraints. These findings establish a solid foundation for the operational deployment of the RF-gated electron gun in our experimental setup.