3.1. Determination of Electron Beam Spectrum using the Current Oscillograms

Figure 2 shows the characteristic oscillograms of the accelerating voltage, the total current of the diode assembly, and the electron beam current.

Figure 2:

Oscillograms of the accelerating voltage (1), diode assembly total current (2), and electron beam current (3) (using graphite cathode).

When calculating the integrated electron beam energy spectrum, at first in the program OriginPro 9.0 [21], a spreadsheet of the dependence of electron current on accelerating voltage was built. Then, in the spreadsheet, the values of accelerating voltage and current were sorted synchronously in the order of voltage increase (“sort columns/ascending”). Next, the electron current was integrated over time, which allowed the summation of the electrons with the same energy which are generated during the front and rear edges of the pulse. The charge of the electrons was then recalculated on their number, and the integral dependence of the number of electrons on their energy (which is equal to the product of the electron charge on the accelerating voltage) was built. Figure 3 shows the calculation results.

Figure 3:

The integrated electron beam spectrum calculated using the electron current (1), using the total current in the diode assembly (2), and using the 1D CL (3). The error in calculating the electron beam spectrum using the total current (4). Graphite cathode (a) and carbon fabric cathode (b).

With a total electron beam charge per pulse of 0.5–0.8 mC, the total number of electrons in the beam was (3–5) · 10¹⁵. At the same time, 80% of the electrons had an energy of more than 200 keV.

The approximation of the integrated electron beam energy spectrum by the polynomial and subsequent differentiation enables the distribution of electrons by the energy in the beam (electron beam energy spectrum) to be obtained, as shown in Figure 4.

Figure 4:

An electron beam energy spectrum calculated using the total current in the diode assembly (1) and using the electron current (2). The error of calculation of electron beam spectrum (3) (using graphite cathode).

The electron beam energy spectrum calculated using the electron current was further used to evaluate the correctness of electron spectrum measurements by other methods—using the total current of the diode or one-dimensional Child–Langmuir ratio.

Figures 3 and 4 show also the electron beam energy spectrum calculated using the total current of the diode unit. The calculation was made according to the algorithm, which was used to calculate the electron beam spectrum using the electron current oscillograms. Figure 3 shows the error in calculating the integrated electron beam spectrum. Error was calculated from the following equation:

(1) $\begin{array}{}E{r}_1\left(E\right)=\frac{100\left(N_{\text{RC}}\left(E\right)-N_{\text{FC}}\left(E\right)\right)}{N_{\text{FC}}\left(E\right)},\%,\end{array}$

where N _RC (E) is the number of electrons with energy from 0 to E, calculated from the total current of the diode, and N _FC (E) is the number of electrons with energy from 0 to E, calculated from the electron current.

Figure 4 shows the error in calculating the electron beam energy spectrum. Error was calculated from the following equation:

(2) $\begin{array}{}E{r}_2\left(E\right)=\frac{100\left(n_{\text{RC}}\left(E\right)-n_{\text{FC}}\left(E\right)\right)}{n_{\text{FC}}\left(E\right)},\%,\end{array}$

where n _RC (E) is the number of electrons with energy E, calculated from the total current of the diode, and n _FC (E) is the number of electrons with energy E, calculated from the electron current.

The developed algorithm allows us to determine the change in the spectrum of electrons in the beam when exiting the diode chamber. Figure 5 shows the integrated electron beam spectrum of the original electron beam and the extracted beam.

Figure 5:

Integrated electron beam spectrum calculated using the total current in the diode unit (1), using the electron current measured behind anode (2), and using the electron current measured behind anode and aluminium foil (3). Absolute (a) and normalised (b) values (using carbon fabric cathode).

In this series of experiments, a stainless-steel lattice with a transparency of 70% was used as the anode. The FC collector was 5 mm behind the lattice. Studies show that the anode array only weakens the electron beam without changing its energy spectrum. After passing the 0.13 mm thick aluminium foil, the beam spectrum varies significantly in the low energy region.

3.2. Determination of Electron Beam Energy Spectrum Using the 1D CL

Studies have shown that when operating a vacuum electron diode in the space-charge-limited current mode, the calculation of the electron beam spectrum by CL 1D also produces correct results (see Figure 3). The calculation of the integrated electron beam energy spectrum is made according to the algorithm of spectrum calculation in Figure 3, but instead of the electron current, the calculated current by 1D CL is used. Considering that the A-K gap reduction and cathode area increase at emission surface expansion, the electron current is equal to [Reference Pushkarev, Isakova and Khailov18]

(3) $\begin{array}{}{I}_{CL}\left(t\right)=\frac{2.33\cdot {10}^{-6}\pi F\cdot U{\left(t\right)}^{3/2}{\left(r_0+vt\right)}^2}{{\left(d_0-vt\right)}^2},\end{array}$

where U is the accelerating voltage, d ₀ is the initial A-K gap, r ₀ is the initial radius of the cathode, v is the cathode plasma expansion velocity, and F is the form factor.

In contrast to a smooth emitting surface for which the 1D CL formula was obtained, the cathode surface may have microirregularities. If the cathode‐surface roughness exceeds the thickness of the space charge layer, the emission area of the cathode increases and it is necessary to introduce a form factor F > 1 [Reference Pushkarev, Isakova and Khailov18].

The performed studies showed that the difference in the integrated electron beam energy spectrum, when measured using the total current in the diode and using the electron beam current, does not exceed 15% for 80–95% of the beam electrons and for 95% of the beam energy. The error of electron beam spectrum calculation using the total current in the diode is most significant in the field of low electron energies. The electron beam spectrum calculation by 1D CL also allows for correct results, but the error is higher.

3.3. Thermal Imaging Diagnostics of an Electron Beam Spectrum

The distribution of the absorbed dose over the depth of the target depends on the energy spectrum of electrons in the beam, so thermal imaging diagnostics can be used to measure the energy spectrum of the electrons [Reference Pushkarev, Kholodnaya, Sazonov and Ponomarev10]. To measure the distribution of the absorbed electron beam dose by depth, in a cylindrical target from foamed polystyrene, a section by diameter was made. After irradiation of the target with a pulsed electron beam, the cut target was opened and a thermal image of its inner surface was recorded, 2-3 seconds after irradiation. Due to the low thermal conductivity of the target material, its temperature distribution change was no more than 5% during the first 3 seconds [Reference Pushkarev, Kholodnaya, Sazonov and Ponomarev10]. In this series of experiments, the distribution of the absorbed dose over the depth of the target was measured for a beam extracted from the diode chamber into the atmosphere through an aluminum foil.

Figure 6 shows the oscillograms of accelerating voltage generated by the TEU-500 accelerator in this series of experiments and the thermograms of an internal surface of the target (one pulse). The diameter of the target is 85 mm, the thickness is 110 mm, and the direction of electron movement goes left to right (see Figure 1).

Figure 6:

Oscillograms of accelerating voltage (1) and full current (2) in the diode (a) and thermogram of a target (b) (using graphite cathode).

The thermogram was processed according to the program SmartView 4.1 Fluke Corporation [22], and the absorbed dose of the electron beam was calculated from heating of the target:

(4) $\begin{array}{}D\left(x,y\right)=c_v\Delta T\left(x,y\right),Gr,\end{array}$

where c_v is the target specific heat and ΔT is the target heating.

Figure 7 shows the normalised absorbed dose distribution over the depth of the target for three cross sections (see Figure 6) and the results of the simulation of the absorption of a monoenergetic electron beam in foamed polystyrene with a density of 0.018 g/cm³, according to Geant4 program [23]. The simulation is made for an electron beam with a diameter of 5 cm and with a constant electron fluency across the cross section.

Figure 7:

Normalised absorbed dose distribution over the depth of the target for three cross sections in Figure 6(b) (1, points). Results of simulation absorption dose distribution of electrons with energy 250 keV (2), 300 keV (3), and 350 keV (4).

Figure 8 shows the results of the integrated electron beam spectrum calculation for Figure 6(a).

Figure 8:

Integrated electron beam spectrum (1) and electron beam spectrum (2) calculated using the 1D CL.

Studies have shown that the distribution of the electron beam absorbed dose generated by the TEU-500 accelerator over the depth of the foamed polystyrene target corresponds to the electron beam energy spectrum.