Estimation of the Spatial Extent of the Transient Gain Drop in a Microchannel Plate

Abstract

The gain of the microchannel plate temporally drops after an ion initiates an electron avalanche. Electron multiplication was expected to deplete the charge from the microchannel wall and produce the depleted charge (wall charge). Moreover, it was reported that the gain drop occurred not only in the activated channels, where the electrons are multiplied, but also in the surrounding channels. One mechanism of the gain-drop spatial extension has been considered as that the wall charges in the activated channels change the electric field in the surrounding channels. Anacker et al. assumed that the wall charge is a uniform line charge; the gain-drop spatial extent should be proportional to the amount of the wall charges. We considered that the wall charges exponentially increased in the channel toward the exit. In this study, the electric field produced by the wall charges was calculated, considering the distribution of the wall charges. The transverse electric field generated by the wall charges was expected to disturb the electron trajectory near the channel exit and decrease the number of secondary electrons emitted per collision (gain per collision), resulting in a gain drop. The gain per collision was calculated to decrease by 22% for the position where the gain decreased significantly in the presence of the transverse electric field of 3×10⁵ V/m. In our model, the gain-drop spatial extent extended proportionally to the square root of the wall charges when the distance from the activated channel exceeded 50 μm.

1. INTRODUCTION

A microchannel plate (MCP) is widely used to detect ions, particles, and photons because of its high gain and fast time response.^1,2) An MCP is made of lead silicate glass and has micron-sized 10⁴–10⁸ microchannels with electrical conductivity and high secondary electron emission yield. The channels are tilted 2° to 20° with respect to the normal surface of the front. Each channel has a diameter of 2 to 25 μm, a length of 0.1–1.0 mm, and an electrical resistance of approximately 10¹²–10¹⁴ Ω. The channels are electrically connected in parallel by evaporating metal on the surface of the channel array. Generally, a voltage of 500–1,000 V is applied between the surfaces, and each channel works as a continuous dynode. When a particle or a photon hits the wall of the channel, a few secondary electrons are emitted from the wall. The secondary electrons are accelerated along the channel by the electric field and then collide with the wall again and emit further secondary electrons. The repetition of this electron-multiplication process yields approximately 10⁴ electrons per MCP. Two or three MCPs are stacked to accomplish sufficient gain to detect a single particle or a photon. The chevron MCP consists of two MCPs, one of which rotates 180° relative to the other.^1,2)

The “gain drop” phenomenon in which the MCP gain temporarily drops after multiplication processes was reported in the case of a time-of-flight (TOF) mass spectrometer^3,4) and photon counting.^5,6) The mechanism was explained as follows: the multiplication depletes charges from the wall, and the gain drop lasts until the charges are replenished from the voltage supply.^1,4) Gatti et al. reported that the electric field along an MCP channel changes because of the depleted charges (wall charge) on the walls, and the changed electric field affects the gain of the multiplication processes.⁷⁾ The effect lasts until the charges are replenished. They suggested that the recharging time constant is determined by a product of the resistance (R) and capacitance (C) of the channel plate if the MCP is made of an isotropic medium. Furthermore, a gain drop has been reported not only in activated channels, where the electrons are multiplied, but also in surrounding channels.^8,9) Edgar et al.⁸⁾ and Fraser et al.⁹⁾ evaluated the gain-drop spatial extent of the chevron MCP detector under continuous UV photon illumination at a high count rate. Furthermore, in our previous study using a TOF mass spectrometer,¹⁰⁾ the gain was reduced to 47% when 140 ions were entered into a 1-mm diameter corresponding to 4,200 channels.

Pearson et al. suggested that charges in the quiescent channels were transferred to activated channels through lateral capacitances, decreasing the gains in the quiescent channels.¹¹⁾ Eberhardt proposed and discussed the lateral capacitance between channels.¹²⁾ Although Fraser et al. tested the hypothesis of lateral capacitance, they were unable to obtain an indication of the presence of lateral capacitance.⁶⁾ Therefore, the spatial extension of the gain drop was unable to be explained by the lateral capacitance.

In contrast, Gatti et al. suggested that the electric field produced by wall charges in activated channels leaked into the surrounding channels, affecting the gains of the surrounding channels.⁷⁾ They calculated the potential produced by the wall charges in one activated channel on the basis of the Gauss law. The potential of the second neighbor channels was increased by 6 V when the wall charge of 0.1 pC was placed 0.2 mm from the output end of an MCP. Anacker and Erskine calculated the transverse electric field produced by wall charges in the rear MCP of the chevron MCP. They estimated the spatial extent of the gain drop from the magnitude of the transverse electric field.¹³⁾ The wall charges were assumed to be a uniform line charge because the number of electrons (the wall charges) was expected to saturate in the rear MCP. In their model, the gain drop was extended proportionally to the MCP output charge, and the spatial extents of the gain drop were estimated as 106 and 190 μm in radius at the output charge of 0.43 and 0.83 pC, respectively. Although Edgar et al.⁸⁾ and Fraser et al.⁹⁾ evaluated the gain-drop spatial extent under continuous UV photons at a high count rate, the experimental results are not described by their model. It is necessary to find a mechanism of gain-drop spatial extension that can better explain the results.

Although Anacker and Erskine¹³⁾ assumed that the wall charges were saturated, the wall charges in the rear MCP would exponentially increase along the channel axis toward the electron exit. In this study, we calculated the electric field produced by the wall charges, considering the distribution of the wall charges. Subsequently, we investigated the effect of the electric field on the electron multiplication process. Finally, the gain-drop spatial extent was estimated from the calculated electric field.

2. GAIN-DROP SPATIAL EXTENT ASSUMING WALL CHARGES AS AN INFINITE UNIFORM LINE OF CHARGE

Anacker and Erskine¹³⁾ estimated the spatial extent of the gain drop on the basis of the magnitude of the transverse electric field E_T(r) produced by the uniform line charges on the rear MCP of a chevron MCP detector. They derived the transverse electric field E_T(r), assuming that the wall charges equal to the output charges from the MCP are an infinite uniform line charge, as shown in Fig. 1A. In their calculation, the channel bias angle (the angle between the channel axis and the normal to the MCP front surface) was assumed to be zero, and the line charge was distributed on the z-axis corresponding to the channel axis.

  

$$E_T\left(r\right)={\displaystyle \frac{\left({\epsilon }_r+1\right)}{{\epsilon }_{r}r}\rho ,}$$(1)

Fig. 1. Coordination diagram to calculate the electric field generated by the wall charges in the rear MCP of a chevron MCP detector. (A) Wall charges are treated as an infinite line of charge with uniform charge density of Q/l_s along the z-axis. (B) Wall charges exponentially increase along the z-axis, following Eq. (6). MCP, microchannel plate.

where ε_r, ρ, and r are the relative permittivity of the lead glass, the density of the line charge, and the radial distance from the line charge, respectively. The line charge density ρ is expressed as

  

$$\rho ={\displaystyle \frac{Q}{l_s},}$$(2)

where Q and l_s are the wall charges corresponding to the output charges from the MCP and the length of the wall charges. They defined the threshold electric field E_lim, at which the gain drop occurs, as

  

$$E_{lim}={\displaystyle \frac{e{U}_o}{D},}$$(3)

where e, U₀, and D are the elementary charge, the initial average radial energy of the secondary electron, and the diameter of the channel, respectively. The electric field E_lim prevents the secondary electrons from hitting the opposite wall, affecting the gains in the region where E_T(r)≥E_lim. Therefore, the radius of the gain-drop spatial extent r_d is given by

  

$$r_d={\displaystyle \frac{\left({\epsilon }_r+1\right)}{{\epsilon }_r}{\displaystyle \frac{Q}{E_{lim}{l}_s}.}}$$(4)

In their model, the gain drop was extended proportionally to the MCP output charge.

3. ELECTRIC FIELD ASSUMING WALL CHARGES INCREASING EXPONENTIALLY ALONG THE CHANNEL AXIS

Although Anacker and Erskine¹³⁾ assumed the wall charges as an infinite uniform line of charge, the wall charges should increase with the number of electrons even in the rear MCP of the chevron MCP detector toward the channel exit. We assumed that the wall charges in the rear MCP of the chevron MCP detector increases exponentially along the channel axis. The electric field in the rear MCP was calculated under this condition. In this calculation, the model F1551-01 (Hamamatsu Photonics K.K., Hamamatsu, Japan) was assumed. The channel diameter, channel pitch, and bias angle were 12 μm, 15 μm, and 8°, respectively. Figure 1B illustrates the schematic of the coordinate to calculate the electric field produced by wall charges. The input and output ends of the rear MCP were on z=0 μm and z=480 μm, respectively. The wall charges were distributed on the z-axis from z=0 to 480 μm. The channel bias angle was assumed to be zero and the MCP was treated as a uniform dielectric. Based on studies,^12,14) assuming an MCP as a discrete dynode with n dynodes, the gain of the MCP is expressed as

  

$$G={\delta }^n,$$(5)

where δ is the number of secondary electrons emitted per collision (gain per collision). The number of dynodes n corresponds to the number of collisions in an MCP. If the wall charges increase with the number of electrons, then the distribution of the wall charges in the rear MCP can be expressed as

  

$$q\left(z\right)=eN{\delta }^{{\displaystyle \frac{n}{L}z}},$$(6)

where z, e, N, and L are a spatial coordinate along the channel axis, the elementary charge, the number of wall charges at z=0, and the thickness of the MCP (L=480 μm), respectively. Based on previous studies,^12,15) the number of collisions n was assumed to be 20. The gain of a chevron MCP detector was 1.9×10⁶ as described in the Supporting Information (available online). In the chevron MCP detector, the gain of the rear MCP has been considered to be decreased to approximately 10% by the space-charge effect.¹⁾ Assuming that the gain of the rear MCP is 10% of that of the front MCP, the gain of the rear MCP δⁿ was obtained to be 440. Thus, the gain per collision δ was derived as 1.36. The wall charges were placed with a 1-μm pitch from z=0 to z=480 μm. The amount of total wall charges Q can be calculated as

  

$$Q={\displaystyle {\sum }_{z=0}^{z=480\text{μm}}q\left(z\right) \left(z=0, 1, 2\dots 480 \text{μm}\right)}.$$(7)

The total charge Q was defined as 1.0 pC corresponding to the gain of 6.3×10⁶, which is the typical gain of the chevron MCP detector. The number of wall charges N at z=0 was derived as 180. Figure 2 shows the distribution of the wall charges along the z-axis. Half of all wall charges were distributed in the region of z >430 μm. The transverse and longitudinal electric fields E_T(r, z) and E_L(r, z), respectively, produced by the wall charges were calculated using the following equations:

  

$$E_T\left(r,z\right)={\displaystyle {\sum }_{b=0}^{b=480\text{μm}}\left(\frac{q\left(b\right)}{4\text{π}{\epsilon }_0{\epsilon }_r\left(r^2+{\left(z-b\right)}^2\right)}\frac{r}{\sqrt{r^2+{\left(z-b\right)}^2}}\right),(b=0, 1, 2\dots 480\text{μm),}}$$(8)

  

$$E_L\left(r,z\right)={\displaystyle {\sum }_{b=0}^{b=480\text{μm}}\left(\frac{q\left(b\right)}{4\text{π}{\epsilon }_0{\epsilon }_r\left(r^2+{\left(z-b\right)}^2\right)}\frac{\left(z-b\right)}{\sqrt{r^2+{\left(z-b\right)}^2}}\right), (b=0, 1, 2\dots 480 \text{μm}),}$$(9)

Fig. 2. Distribution of wall charge (q) along the channel axis (z) at a total charge Q=1.0 pC.

where b, ε₀, and ε_r are the position (z=0 to 480 μm) on the z-axis, the electric constant, and the relative permittivity of the MCP, respectively. The relative permittivity ε_r was adopted as 4.5, which is the average value of the relative permittivity of vacuum and lead glass (7.8 to 8.3).^1,6) The volumes of channel pores and surrounding lead glass in the MCP are approximately equivalent; this can be attributed to the open area ratio of 0.6 of the MCP. Mathematica Online Version 13.2 (Wolfram Research, Inc., Champaign, IL, USA) was used to calculate the electric fields.

The electric field produced by the wall charges was calculated in the rear MCP at the total wall charge Q=1.0 pC. Figure 3 shows the Coulomb force acting on an electron. Each Coulomb force vector is displayed every 15 μm (corresponding to the channel pitch) in the r direction. In each channel, the transverse Coulomb force increased as z increased and became a maximum at z=~450 μm. In contrast, when the z was greater than 450 μm, the direction of the longitudinal Coulomb force was opposite to that of the electrostatic force produced by the voltage application. The longitudinal electric field was expected to not be a major factor of the gain-drop spatial extension because the longitudinal Coulomb force was relatively smaller than the transverse Coulomb force as the distance r was larger, as shown in Fig. 3. Additionally, the longitudinal Coulomb force was considerably weaker than the Coulomb force by the electric field developed by the voltage application (bias electric field) (2.1×10⁶ V/m).

Fig. 3. Estimated Coulomb force in the rear MCP at Q=1.0 pC. Each vector is displayed every 15 µm in the r direction (channel pitch) and every 10 µm in the z direction. The red arrow on the right top indicates the Coulomb force acting on an electron at the application of 1,000 V. MCP, microchannel plate.

4. EFFECT OF TRANSVERSE FIELD ON ELECTRON TRAJECTORY

The transverse electric field is expected to change the collision energy of the secondary electron and the number of collisions in the MCP, resulting in a decrease in the gain. To investigate the effect of the transverse electric field, we calculated the collision energy and the flight distance of an individual electron trajectory assumed to be near the channel exit, where the transverse electric field became maximum at z=450 μm, as shown in Fig. 3. Figure 4 shows the coordinate used for this calculation. The initial velocity v₀ of the secondary electron is given by

  

$$v_0=\sqrt{{v_{x0}}^2+{v_{y0}}^2+{v_{z0}}^2},$$(10)

Fig. 4. Coordinate system for the estimation of flight distance and collision energy of secondary electron in the rear MCP. MCP, microchannel plate.

where v_x0, v_y0, and v_z0 are the initial velocities in the x, y, and z directions, respectively. Therefore, the initial energy U₀ is expressed as

  

$$U_0={\displaystyle \frac{m}{2e}{v_0}^2,}$$(11)

where m is the electron mass (9.1×10⁻³¹ kg). The direction of electron emission is expressed using the polar coordinate system. Each velocity can be expressed as

  

$$v_{x0}=v_0\mathrm{s}\mathrm{i}\mathrm{n}\left(\theta -{\theta }_B\right)\mathrm{s}\mathrm{i}\mathrm{n}\phi ,$$(12)

  

$$v_{y0}=v_0\mathrm{c}\mathrm{o}\mathrm{s}\left(\theta -{\theta }_B\right),$$(13)

  

$$v_{z0}=v_0\mathrm{s}\mathrm{i}\mathrm{n}\left(\theta -{\theta }_B\right)\mathrm{c}\mathrm{o}\mathrm{s}\phi ,$$(14)

where θ, φ, and θ_B are the polar angle (θ=0° to 90°), azimuth angle (φ=0° to 360°), and MCP bias angle (θ_B=8°), respectively. The trajectory of the secondary electron can be derived as follows, assuming that the transverse electric field produced by the wall charges is static.

  

$$x\left(t\right)=-{\displaystyle \frac{e}{2m}{E}_T{t}^2\pm v_{x0}t}+x_0,$$(15)

  

$$y\left(t\right)=\pm v_{y0}t+y_0,$$(16)

  

$$z\left(t\right)={\displaystyle \frac{e}{2m}{\displaystyle \frac{V}{L}{t}^2}}+v_{z0}t,$$(17)

where t, E_T, and V are the time, transverse electric field produced by the wall charges, and applied voltage to the MCP (V=1,000 V), respectively. In this calculation, the longitudinal electric field E_L (electric field on the z-axis component) produced by the wall charges was neglected because it was relatively weak compared to the bias electric field V/L as shown in Fig. 3. The secondary electron emits at t=0, x=x₀, y=y₀, and z=0. The surface of the channel wall is given by

  

$$x^2+(y-{\left(R+z\mathrm{t}\mathrm{a}\mathrm{n}\left({\theta }_B\right)\right)}^2=R^2,$$(18)

where R is the radius of the channel (R=6 μm). According to Eqs. (15)–(18), the time t₁ until the electron collides with the channel wall was obtained. The flight distance d on the z-axis component was calculated by substituting t₁ for t in Eq. (17). The collision energy U_c of the electron can be calculated as

  

$$U_c={\displaystyle \frac{m}{2e}\left({\left({\displaystyle \frac{dx\left(t_1\right)}{dt}}\right)}^2+{\left({\displaystyle \frac{dy\left(t_1\right)}{dt}}\right)}^2+{\left({\displaystyle \frac{dz\left(t_1\right)}{dt}}\right)}^2\right).}$$(19)

We calculated the flight distance d and collision energy U_c for each initial energy value U₀ ranging from 1 to 20 eV at the transverse electric field E_T=0 while changing the polar angle θ and azimuth angle φ every 2° and 5°, respectively, because the secondary electrons have different initial energies and emission angles. Assuming that electrons are emitted with the cosine distribution at the polar angle and the uniform distribution at the azimuth angle based on the literature,^16,17) we calculated the average values of d and U_c at various U₀ as $\overline{d}$ and $\overline{U_c}$, as shown in Fig. 5. The calculation was performed when the electrons were emitted from the emission positions of A (0, 0, 0), B (0, 2R, 0), C (R, R, 0), and D (–R, R, 0), as shown in Fig. 4. The following equations were used rather than Eqs. (12)–(14) when the emission positions were C and D:

  

$$v_{x0}=v_0\mathrm{c}\mathrm{o}\mathrm{s}\theta ,$$(12’)

  

$$v_{y0}=v_0\mathrm{s}\mathrm{i}\mathrm{n}\theta \mathrm{s}\mathrm{i}\mathrm{n}\phi ,$$(13’)

  

$$v_{z0}=v_0\mathrm{s}\mathrm{i}\mathrm{n}\theta \mathrm{c}\mathrm{o}\mathrm{s}\phi .$$(14’)

Fig. 5. Average flight distance ($\overline{d}$) and collision energy ($\overline{U_c}$) for each initial energy (U₀) of the secondary electron in the absence of a transverse electric field. (1) $\overline{d}$ against U₀ and (2) $\overline{U_c}$ against U₀. The uppers show the schematics of the electron trajectories for the emission positions A, B, C, and D.

The average value $\overline{d}$ became maximum at U₀=3 eV for the emission position A (0,0,0), as shown in Fig. 5. When secondary electrons were emitted from position A, they began to collide with the opposite wall above U₀ of 3 eV, as shown in the upper diagram of Fig. 5. Thus, $\overline{d}$ decreased as U₀ increased. When electrons were emitted from other positions, $\overline{d}$ decreased as U₀ increased because the electrons only collided with the opposite wall with no dependence on U₀. The collision energy U_c was approximately proportional to d because the secondary electrons gained the energy of 2.1 eV when traveling every 1 μm in the z direction because of the bias electric field V/L (2.1×10⁶ V/m).

In contrast, we calculated $\overline{d}$ and $\overline{U_c}$ while changing E_T from 1.0×10⁵ to 4.0×10⁵ V/m. Figures 6 and 7 show $\overline{d}$ and $\overline{U_c}$ for each initial energy U₀ for the four emission positions, respectively. The average collision energy $\overline{U_c}$ was approximately proportional to $\overline{d}$.

Fig. 6. Average flight distance ($\overline{d}$) for each initial energy (U₀) of the secondary electron under five different magnitudes of the transverse electric field (E_T). The flight distance $\overline{d}$ for each initial emission position is summarized below: A (0, 0, 0): The average flight distance $\overline{d}$ decreases as E_T increases. B (0, 2R, 0): The change in $\overline{d}$ is small. Electrons collide with opposite wall immediately with or without the transverse electric field because the channel wall is shifted toward the +y direction. C (R, R, 0): The average flight distance $\overline{d}$ decreases as E_T increases, similar to A (0, 0, 0). D (−R, R, 0): The distributions of $\overline{d}$ have a maximum value for U₀ by applying E_T. The initial energy U₀, where $\overline{d}$ becomes maximum, increases as E_T increases.

Fig. 7. Average collision energy ($\overline{U_c}$) for each initial energy (U₀) of the secondary electron under five different magnitudes of the transverse electric field (E_T).

The relationship between the collision energy U_c and the gain per collision δ was investigated to understand the effect of the variation in the collision energy U_c on the gain. According to the studies,^16,18) δ(U_c) can be expressed as

  

$$\delta \left(U_c\right)={\delta }_{max}{\displaystyle \frac{s\left({\displaystyle \frac{U_c}{U_{max}}}\right)}{s-1+{\left({\displaystyle \frac{U_c}{U_{max}}}\right)}^s},}$$(20)

where δ_max, U_max, and s are the maximum δ, collision energy with δ_max, and material-dependent parameter, respectively. In our estimation, the dependence of the incident angle was neglected. Wu et al.¹⁸⁾ reported that the MCP gain calculated using their Monte Carlo simulation model was in good agreement with their experimental data, when δ_max=4.0, U_max=270 eV, and s=1.3. Therefore, we adopted these values in this study. We calculated the average value $\overline{\delta }$ for each U₀ using Eq. (20), as shown in Fig. 8. The average value of δ was calculated for each E_T, considering the distribution of the initial energies of secondary electrons, as shown in Table 1; the average values were calculated using U₀=1 to 20 eV, θ=0° to 90°, and φ=0° to 360° for the emission positions A, B, C, D as δ_A, δ_B, δ_C, and δ_D, respectively. The distribution of the initial energies of secondary electrons can be expressed using the Maxwell–Boltzmann probability distribution¹⁷⁾ as

  

$$P(U_0)=C\frac{U_0}{U_p}exp(-\frac{U_0}{U_p}),$$(21)

Fig. 8. Average number of secondary electrons emitted per collision ($\overline{\delta }$) for each initial energy (U₀) of the secondary electron under five different magnitudes of the transverse electric field (E_T).

Table 1. Average value of δ for each transverse electric field (E_T) in U₀=1 to 20 eV, θ=0° to 90°, and φ=0° to 360°.

ET [V/m]	δA: A (0, 0, 0)	δB: B (0, 2R, 0)	δC: C (R, R, 0)	δD: D (−R, R, 0)
0	2.9	1.8	2.3	2.4
1.0×105	2.8	1.8	2.0	2.4
2.0×105	2.7	1.8	1.9	2.5
3.0×105	2.6	1.7	1.8	2.5
4.0×105	2.4	1.7	1.8	2.4

where U_p is the most probable energy of the secondary electron and C is the normalization constant. In this calculation, U_p was set to 3 eV following the literature.^17,18) The values δ_A and δ_C decreased as E_T increased, as shown in Table 1. In contrast, no changes in δ_B and δ_D were observed. The values δ_A and δ_C decreased by 10% and 22%, respectively, when E_T =3.0×10⁵ V/m. The decreases in δ_A and δ_C were expected to cause a decrease in the gain. We also calculated δ_A, δ_B, and δ_C when E_T was applied in the y direction, as shown in Tables S2 and S3 (Supporting Information). The average value δ_A decreased by 10% and 17% when E_T=3.0×10⁵ V/m, given that E_T was in the +y and –y directions, respectively.

5. ESTIMATION OF GAIN-DROP SPATIAL EXTENT

The gain-drop spatial extent was estimated using the calculated electric field. As described in the previous section, the gain per collision decreased by a few percent when the transverse electric field E_T was in the order of 10⁵ V/m. The transverse electric field E_T(r, z) was calculated for various values of r and a fixed value of z of 450 μm, as shown in Fig. 9. Figure 9 shows the calculated transverse electric field E_T(r, 450 μm) in the r direction at the total wall charge of Q=0.2, 0.5, 1.0, 2.0, 3.0, and 4.0 pC. The radius r where the transverse electric field E_T(r, 450 μm) is 1.0 ×10⁵, 2.0 ×10⁵, 3.0×10⁵, and 4.0 ×10⁵ V/m was obtained as the gain-drop spatial extent. Figure 10 shows the relationship between the gain-drop spatial extent and the amount of the wall charge Q. The gain-drop spatial extent gradually extended as Q was larger. Anacker and Erskine¹³⁾ expected the gain-drop spatial extent to be proportional to Q, as shown in Eq. (4), assuming that the wall charge was a uniform line charge. The relationship between the spatial extent of the gain drop and Q, as shown in Fig. 10, is not consistent with Eq. (4). In our model described in the section “Electric Field Assuming Wall Charges Increasing Exponentially along the Channel Axis,” the wall charge was assumed to increase exponentially along the channel axis, and half of the wall charges were concentrated within the region of 50 μm from the channel exit. The wall charges behave as a point charge when the radial distance from the activated channel is sufficiently long. Conversely, the wall charges behave as a line charge when the distance is not considerably far. The spatial extent of the gain drop is proportional to Q in the region where the distance from the activated channel is 50 μm or less, as shown in Fig. 10. The distance of 50 μm corresponds to the neighboring third channel. The spatial extent of the gain drop is proportional to the square root of Q in the region where the distance from the activated channel exceeds 50 μm.

Fig. 9. Transverse electric field E_T (r, 450 µm) at Q=0.2, 0.5, 1.0, 2.0, 3.0, and 4.0 pC.

Fig. 10. Variation of the spatial extent of the gain drop with a wall charge.

6. CONCLUSION

Our investigation has delved into the electric field on the gain-drop spatial extension within the rear MCP of the chevron MCP detector using computational simulations. In convention, the spatial extent of the gain drop is assumed to correlate proportionally with the amount of the wall charges, predicated on the presumption of a uniform line charge distribution. When considering the distribution of the wall charges, the electric field was calculated, and the effect on the gain was investigated by calculating the electron trajectory in the channel. The transverse electric field was expected to decrease the collision energy and gain per collision, resulting in a gain drop. The obtained gain per collision was calculated to decrease by 22% for the emission position, where the gain decreased significantly, in the presence of the transverse electric field of 3.0×10⁵ V/m. The wall charges behaved as a line charge when the distance from activated channels was within 50 μm, corresponding to the neighboring third channel. However, beyond this distance, the wall charge behaved as a spot charge. The spatial extent of gain drop estimated from the transverse electric field was proportional to the square root of the amount of wall charges when the distance exceeded 50 μm.

Notes

Mass Spectrom (Tokyo) 2023; 12(1): A0134

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