Reection of the side-emitted current

The electron beams of the three setups previously discussed were traced into the main solenoid in order to investigate the occurrence of reected current. Tracing simulations with electron beams emitted from the sleeved cathode and the default cathode with applied optimal Wehnelt potential showed a full acceptance by the solenoid. Therefore this section focuses on the electron beam emitted from the de- fault HEC2 _{gun with the potentials used during the commissioning. To investigate}

SEE, the particle microscope, introduced in Section 4.3.3, was applied to multiply the outermost 36 emitted particles with a factor of 100. The time steps were de- creased by a factor of 10 to 5 · 10−15_{sec, reducing the energy discrepancy of the}

traced reected current to a level of ∆E/E < 0.02 %. The simulation results in a reected current of Ire=2.7 mA, which is carried by 296 trajectories. Fig. 6.2.6(a)

shows a zoom into the drift tubes where particular trajectories are reected. These reected trajectories were back-traced to their point of termination at the electron gun. Fig. 6.2.6(b) shows the back-traced reected electrons overlaid on the electron beam propagating towards the solenoid. These reected electrons have the same amplitude and a similar phase as the side-emitted electrons orbiting the primary electron beam in the main solenoid. The axial positions of reection and the corre- sponding local magnetic eld were read out. The evaluation of the trajectories in the dierent sub-volumes results in a distribution of accepted and reected particles and their points of reection, see Fig. 6.2.7. Here the magnetic eld is overlaid to the sketch of the TestEBIS. The red dots indicate the magnetic eld at the axial position of reection. According to the simulations, SEE are reected starting from ≈ 10 cm inside the solenoid where the magnetic eld is B = 1.8 T until they pass the maximal eld strength of B = 3.5 T as shown in detail in Fig. 6.2.8(a). The total reected current as a function of the axial position is shown in Fig. 6.2.8(b). To determine if only SEE contribute to the reected current, the phase space of the electron beam acquired in front of the HEC2 _{gun was resolved to SEE, front-emitted}

and reected electrons. The resultant phase space is shown in Fig. 6.2.9(a). The front-emitted particle ensemble is represented by black squares. The dashed circles guide the eye to distinguish between the core electron beam and the beam halo. The particles that were introduced by the particle microscope are shown as red

squares. They connect the phase space between the primary particles. The reected particles are shown inblue. The reected electrons are traced back from their point of reection to the electron gun volume as shown in Fig. 6.2.9(b). The reected

(a) Position of the reected trajectories, which are indicated by red arrows (upper subgure) or by a red trajectory (lower sub- gure). 0.0 6.0 r [mm] z [mm] -1300 -700

(b) Back-traced electrons drawn inredover- laid on the electron beam in the low mag- netic eld area between electron gun and main solenoid.

Figure 6.2.6: Reection of SEE at the magnetic eld gradient. The position of reection is 10cm inside the main solenoid. The reected electrons have the same orbit as the incoming orbiting electrons. The axial coordinates are here the distances to the center of the solenoid.

B [T] 0.0 4.0 z [mm] -1.6 0.0 HEC2 _gun Superconducting solenoid Area of re ection

Low B-eld area

Figure 6.2.7: Magnetic eld strength at the point of reection, lower gure shows the location of reection at the TestEBIS assembly.

electron beam has a wider radius than the primary beam. 1.5 mA out of the total reected current of 5 mA is directly deposited on the anode. Trajectories able to pass the anode hole are reected in front of the cathode and Wehnelt electrode. In the simulation a current deposition on the cathode of 0.05 mA and on the Wehnelt of 0.1 µA is observed. This deposited current is non-physical and occurs due to numerical energy discrepancy, which can be reduced by smaller tracing time-steps. Therefore the current observed on Wehnelt and cathode is considered to be deposited on the anode. The particles reected from the cathode or Wehnelt either terminate on the anode electrode or pass the anode again and propagate towards the solenoid. The fraction of current reected from the electron gun is ≈ 10 % = 0.2 mA of the current initially reected at the magnetic eld gradient. The remaining 90 % of the

-0.5 -0.4 -0.3 z [m] B [T] 1.5 2.0 2.5 3.0 3.5

(a) Magnetic eld at the positions of reection.

3.0 2.0 1.0 0.0 -0.5 -0.4 -0.3 z [m] P Ire [mA ]

(b) Sum of reected current versus axial posi- tion of reection.

Figure 6.2.8: Simulated particle reection during the TestEBIS-commissioning experiment of the default HEC2 _gun.

Beam halo Core electron beam P α_i Front-emitted e− SEE Reected SEE 0.0 0.1 0.2 0.3 α [rad ] 0.0 0.5 1.0 1.5 2.0 2.5 r [mm]

(a) Resolved phase space of the electron beam recorded after passing the anode at z = 150 mm. The front-emitted particles are black squares, the accepted and reected SEE are red and blue respectively. The right axis shows the projection of the angles.

0 25 r [mm] z [mm] 0 107

(b) Reected SEE in the gun region, every 10th trajectory is plotted.

Figure 6.2.9: Reected SEE shown in the resolved phase space of the electron beam propagating towards the solenoid and as reected particles at the electron gun.

reected current is deposited on the anode. Of the 0.2 mA of re-emitted electrons, 0.1 mA are nally accepted by the solenoid. The reected electrons propagate again towards the electron gun, equally distributed as in the rst iteration. It can be assumed that 90 % of the total current reected at the magnetic eld gradient is deposited at the anode.