Side-emission of the cathode

When performing electron beam tracing, usually only the front surface of the cathode is set as electron emitting. To evaluate side-emission, the emission surface was extended to the lateral surface. Fig. 6.2.2(a) shows the emission surface for the default geometry. A suggested solution considering a sleeved cathode is shown in Fig. 6.2.2(b).

(a) Default geometry with the cathode in

green, Wehnelt electrode in pink and anode in brown. The emission surface is indicated by a dotted line in front of the cathode. The mission area for SEE are indicated by ared

dotted line.

(b) Modied geometry with the cathode in

green, surrounded by a non-emitting sleeve inred.

Figure 6.2.2: Modication of the default geometry after introduction of a sleeved cathode. The Wehnelt hole was extended in order to provide space for the cathode sleeve. The front surface of the sleeve is the geometric extension of the Wehnelt electrode.

For more accurate results, the sharp cathode edge connecting the front and lateral surfaces was smoothed out by an arc with a radius of 0.1 mm. The gun volume at the cathode is meshed with a radial and axial precision of ∆mr = ∆mz = 30 µm,

which is higher than the suggested values stated in Tab. 4.2.1 of ∆mr = 70 µm

and ∆mz = 150 µm. This results in 375 emission nodes on the front and lateral

surfaces of the cathode. Due to the round edge at the cathode tip a clear division into front and side-emitted current at the cathode tip was dicult to establish and therefore imprecise. To evaluate the side-emitted current all current from emission nodes with number > 342, positioned at the end of the round edge connecting to the lateral surface, was counted as side-emitted. The magnetic eld generated by the gun coil was calculated according to operational values with 85 A at 420 turns in the solenoid, which equals a eld strength of 0.215 T in front of the gun. The current of the main solenoid was adjusted to 3.5 T inside the solenoid. The electron gun was operated at an extraction potential of Uex =15.5 kV. These settings were

kept during all simulations in this section unless explicitly stated otherwise. 6.2.1.1 The default geometry

0 15 r [mm] ISEE=44.1 mA z [mm] 0 100

Figure 6.2.3: Calculated trajectories of the elec- tron beam during the gun commissioning test (de- fault geometry).

Calculations of the default geome- try, see Fig. 6.2.3, show that from the total emitted current of Ie =

1.8 A, the side-emitted current is ISEE = 44.1 mA, corresponding to

2.6% of the total current. This fraction of the total emitted cur- rent is located in the beam halo orbiting around the main electron beam. These trajectories are not matched by the matching magnetic eld, which increases the ∆re-value

of the beam envelope of the front- emitted electron beam. To evalu- ate if the Brillouin-like beam will be accepted by the solenoid, the tra- jectories were simulated until they reached a region with a magnetic eld of 3.5 T. The propagation into

the main solenoid will be investigated in detail in Section 6.2.2 with dierent particle tracing resolutions.

6.2.1.2 The sleeved cathode

0 15 r [mm] z [mm] 0 100 ISEE=4.7 mA

Figure 6.2.4: Electron beam with side- emitted electrons in red (sleeved cath- ode).

The rst suggested modication for reducing the side-emitted current is a sleeved cath- ode, shown in Fig. 6.2.4. The gap be- tween the sleeve and cathode is 0.1 mm. The sleeve itself has a thickness of 0.8 mm and the gap between the sleeve and the Wehnelt is 0.3 mm. The sleeve is at the cathode po- tential. Simulations with the sleeved ge- ometry result in a total emission current of

Ie = 1.8 A, where the side-emitted current is ISEE = 4.7 mA corresponding to a re-

duction of 90% compared to the default geometry. The simulation shows that the inserted sleeve suciently suppresses the side-emitted current. No trajectories with exceptionally high transverse momentum could be observed in any simulations using a sleeved geometry.

6.2.1.3 The default geometry with applied Wehnelt potential

0 15 r [mm] z [mm] 0 100 ISEE=5.4 mA

Figure 6.2.5: Generated electron beam with Uw = −20 V (default geometry). The SEE

are shown as red trajectories orbiting the front-emitted electron beam.

Applying a potential on the Wehnelt electrode, lower than the cathode poten- tial, is the second suggested method to suppress side-emitted electrons. A cor- rect ratio between the potentials of the Wehnelt electrode, cathode and anode is important for suppressing SEE as well as improving the beam injection into the magnetic eld. The gun geometry is de- signed so that the applied electric eld between cathode and anode is perpen- dicular with respect to the front surface of the cathode and creates a focus in the anode hole. The correct Wehnelt po- tential suppresses the electron emission only on the lateral surface with minimal distortion of electrons emitted from the front surface close to the cathode edge. The emission of the HEC2_{gun operating}

with optimal Wehnelt potential is shown in Fig. 6.2.5. Here Uw = −20 V results in

an optimal ratio between SEE suppression and non-distorted front emission. 5.4 mA are carried by the remaining SEE trajectories in the halo. This corresponds to a reduction of 92% compared to the default geometry. Beam tracing calculations with varied extraction potentials of the HEC2 _{gun, see Table 6.2.1, show that the op-}

timum Wehnelt potential suppressing SEE with minimum distortion of the main beam should be scaled as Uw[V] = 2.78 − 1.46Uex[kV].

Table 6.2.1: Side-emitted current as function of the extraction potential.

Uex[kV] Uw[V] Ie[A] ISEE[mA] 15.5 -20 1.8 5.4 20 -26 2.6 7.8 25 -33 3.6 10.5 30 -40 4.8 13.5 35 -48 6.0 16.0 40 -55 7.3 19.5

6.2.1.4 Summary of the SEE-reduction methods

Both methods of reducing the loss current resulted in a similar degree of SEE sup- pression. In each case a signicant reduction of side-emitted current from 44 mA down to 5 mA was achieved for an extraction voltage of 15.5 kV. In addition both approaches result in lower transverse momentum of the electrons orbiting the front- emitted electron beam compared to the default geometry. The usage of a sleeved cathode is more dicult to realize compared to a biased Wehnelt. A risk is the possibility of chemical interaction between the sleeve and cathode material, which might counteract the purpose of the sleeve. When considering the standardized us- age of a Wehnelt potential to suppress SEE during the operation it is recommended to reduce the gap between Wehnelt electrode and cathode even more than in the investigated geometry in order to further improve the ratio between suppression and distortion.