Dark current simulations

The task for dark current simulations was to prove the reliability of the ASTRA simulations and to quantify the dark current process in the gun.

Figure 4.6: An example of dark current trajectory in the PITZ RF gun cavity from Ref. [51].

The simulations were performed in the CST Particle studio. The RF fields were taken the same as for the coupler kick tracking in section 2.1. The fields were simulated for the model that includes the gun cavity with simplified cathode area and the RF coupler at the end of which one RF port is located. The electric field is presented in Fig. 4.7.

Figure 4.7: An example of the electric RF field in the PITZ RF gun cavity and coupler setup.

The tracking of the dark current was done by the Particle-In-Cell (PIC) solver of the CST studio. The PIC solver was selected due to the capability of continuous particle emission within a predefined time period. The continuous particle emission simplifies the tracking simulation process because particles are emitted not only for a fixed RF field phase but for a range of phases. The emission time for the simulations was set to

800 ps, which is longer than the RF period (769 ps for the case of 1300 MHz), in order to cover the full range of phases for the dark current emission. The space charge calculation option of the PIC solver was switched off in order to accelerate the simulation process.

The full inner model surface was divided into several parts, and each of these parts was selected as a particle source. The surface division was done in order to distinguish and characterize the dark current from the different parts of the gun and RF coupler surface.

For simplicity, the initial particle parameters were chosen identical for all sources:

the initial kinetic particle energy is 0.04 eV ¹, kinetic spread 50 %, angular spread 45^◦ and total charge of 1 pC. In order to generate approximately constant current within the emission time, a Gaussian emission model with a huge sigma and short cut off length was applied. The window with source settings and schematic presentation of the temporal structure is presented in Fig. 4.8. The parts of the inner surface of the model selected as the sources are presented in Fig. 4.9.

(a)

sigma 2 x cut off

2 x cut off

(b)

Figure 4.8: The CST Particle studio window with the particle source settings (a) which were used for simulations and schematic presentation of the temporal structure (b).

The time structure settings are shown at the bottom part of the plot (a).

1defined via temperature as Ekin≈(500·k)eV, where k is the Boltzmann constant ineV /^◦K

(a) Cathode plug and vicinity (b) Half cell and iris

(c) Full cell and output iris (d) Outer conductor of the coax-ial waveguide

(e) RF coupler transition parts (f) Inner conductor of the coaxial waveguide

(g) Rectangular waveguide walls

Figure 4.9: The particle sources for the dark current simulations. The numbers seen in the image are irrelevant in context and can be ignored.

Amount of detected dark current

The results of the simulations proved that only particles emitted from the cathode and the cathode vicinity can be transported to the beamline. These particles can be detected by a charge measurement device like the Faraday Cup which is located at z=0.803 m downstream the cathode. The example of such trajectories is shown in Fig. 4.10.

The number of particles that escape the gun is only 0.6 % of the total emitted particles from the half cell and iris (particle source in Fig. 4.9(b)) and 30.9 % of the total emitted particles from the cathode and cathode vicinity (particle source in Fig. 4.9(a)).

The particles emitted from all other regions of the gun can not escape the gun cavity or RF coupler volume at all.

Figure 4.10: Example of the dark current particle trajectories simulated by the CST Particle studio. The color code indicates the particle energy.

In order to make an estimation of the total amount of dark current particles present in the gun cavity volume, the relation between the number of particles escaping the gun body to the total number of dark current particles in the gun cavity volume was calculated. Only 10.5 % of the totally emitted particles from the gun cavity can be transported downstream the cathode to the beamline for zero magnetostatic solenoid fields.

Energy spectra of dark current

The dark current from the gun can lead to heating of the cavity surface, X-rays generation, and production of secondary electrons (secondaries). Those additional electrons enhance the dark current so that at certain conditions stable (when the number of secondaries constantly increases) or non-stable (when stable trajectories of secondaries exist only for some limited number of RF periods) multipacting processes can occur. To calculate the probability of secondary electron production, which depends on the primaries energy, and to estimate the heat load by dark current, one should know the particle distribution in a cavity volume (including a portion of the particle that can be measured) and the particles energy spectrum at the moment when a particle hit the surface.

Energy spectra of the electrons impacting with the gun parts were obtained by simulations for different parts of the gun and RF coupler. The selected parts are the rectangular waveguide, the coaxial waveguide, the coaxial antenna nose, the gun cavity, and the molybdenum cathode plug. The sum spectrum of all particles hitting the surface is presented in Fig. 4.11. The example shows the combined spectrum for the coaxial waveguide and the gun cavity. The incident electrons energies have values up to 6.4 MeV. The spectrum consists of two energy regions 0 – 3.4 MeV and 5.7 – 6.4 MeV with the most amount of the electrons. The trajectories of the electrons with the highest energies lie in the region near the gun cavity center, where the RF fields provide high energy to the electrons due to the synchronized motion in the alternating fields.

Figure 4.11: Combined energy spectrum of the free electrons hitting the coaxial waveguide and the gun cavity.

The energy spectra simulations can be described by the following results:

• Molybdenum cathode plug

– total energy range is from 0 eV to 2.73 MeV

– most of particles (72 %) have energies in the range from 0 eV to 56 keV – 9 % of the particles have energies in the range between 2.3 MeV and 2.7 MeV

• Rectangular waveguide

– the spectrum consists of exponential decrease toward the lower energies and a flat distribution at a wide range in the high energy part

– the decreasing part of the spectrum can be roughly described by the following dependency: count∼92.68·exp(0.0226 [1/eV]·E [eV]), where the maximum counts value occur at 0.8 eV

– the total energy range is 0 eV to 40 keV

– the main part of all particles (99 %) have energy from 0 eV to 10 keV

• Coaxial waveguide (all parts)

– the total energy range is 0 eV to 6.36 MeV. The highest energies of the spectrum are possible due to the collision of particles with the surface of the inner coaxial conductor. These particles, started from the back wall of the half cell or the cathode surface, accelerate in the RF fields with synchronous phase and travel to the inner conductor of the RF coupler.

– 88 % of particles are in the range 0.3 eV to 57 keV

– and 88 % of particles are in the range 3.18 MeV to 4.678 MeV

• The coaxial antenna (inner conductor) nose (this part is exposed by the dark current particles with the highest energies in the gun)

– the total energy range is 0.3182 eV to 6.36 MeV

– the particle distribution with highest energies 0.137 MeV to 4.678 MeV consist of 19 % of particles

• The gun cavity. The cavity consists of two cells, two irises and back wall of the half cell, where the cathode plug is inserted.

– 98.33 % of all particles are in the range 0.311 eV to 2.733 MeV

– the range from 0.311 eV to 0.3265 keV has the highest concentrations of the particles of the low energy region which non-exponentially decrease toward the higher energy part. The rang consists of 36.54 % of all particles.

These results show that the gun back wall, the cathode plug, and the coaxial antenna nose undergo interaction with high energy electrons (up to 6.4 MeV). Therefore these places most prone to damage in case of high dark current. This demands high accuracy in design, fabrication, installation, and manipulation with these parts.