EXCITADO 8 ATURDIDO 14 SATISFECHO 2 AGOBIADO 9 TENSO 15 CELOSO

The trap significantly improves the beam’s energy spread, typically achieving FWHM energy spreads of ∼40-60 meV. The trap stage makes use of the buffer gases, nitrogen (N2) and tetrafluromethane (CF4), to trap and cool the positrons

before ejecting them an energy up to 200 eV. The trap cycle consists of three stages: load, cool and dump, where the potentials for each stage are depicted in figure 4.2.2. It is important to note that the trap is constantly loading positrons during the cool and dump phases, improving the trap efficiency, and the cycle rate is usually around 50-70 Hz (i.e. there are 50-70 trap cycles every second).

E1 E2 E3 E4 E5 E6 E7 E8 E9 Potent ial Electrodes Potent ial Electrodes Potent ial Electrodes cooling positrons D um p Tr an sp or tE ne rg y Moderated Positrons Moderated Positrons Moderated Positrons Load Cool Dump TrapCElectrodes 8.6eV N2 CF4 N2 CF4 N2 CF4 Positron Beam electronicCexcitation 8.6eV

Figure 4.2.2: Trap cycle showing load, cool and dump stages. Electrodes are numbered E1-E9

4.2. Experimental and Analysis Methods 59

Load

Loading is the longest phase, typically lasting 10-15 ms. The first electrode potential must be low enough to admit the moderated positron beam, which has an energy defined by the moderator bias. This is not trivial as the change in magnetic field from 88 G in the source stage to 530 G in the trap stage affects the distribution of the positron energy into the parallel (Ek) and perpendicular (E⊥) energy components. The moderated positron beam typically has ∆Ek ∼ 1.5− 2 eV FWHM in source stage, but this is increased fivefold in the trap stage asM ≈5 (a detailed explanation of parallel and perpedicular energies, and their significance to the experiment is give in section 4.1). Therefore, the first electrode is set to∼7 V below the moderated beam energy allowing the majority of moderated positrons to enter the trap. Some positrons are lost at this point as the energy spread is asymmetric, demonstrated in Jones (2010).

The positrons are trapped through electronic excitation of the buffer gas, N2.

N2 is unusual as the electronic excitation of the a1Π state has a threshold of

8.59 eV, lower than the positronium (Ps) formation threshold at 8.78 eV (Marler and Surko (2005a)). Ps formation results in a loss of positron beam intensity as it is not confined by the magnetic field and drifts off the beam axis and self- annihilates. To some extent, loss of positrons through through this process is inevitable. However, it can be mitigated by tuning the positron-N2 impact en-

ergy, using the difference between the moderator potential and electrodes two and three, to ∼ 10 eV. At this energy the electronic excitation cross section is signif- icantly larger than the Ps formation cross section (see figure 4.2.3) and trapping efficiency is maximised.

The N2 pressure is set so that positrons are trapped during a single transit of

the trap. Gas is admitted at electrode two and stepped potentials on later elec- trodes allow the positrons to become trapped through the same collision process in areas where the buffer gas pressure is lower, reducing annihilation. Some colli- sions withCF4 also occur in this region as the two buffer gases mix. Annihilation

due to collision with trap gases is another loss process that must be considered carefully, although the cross section is several orders of magnitude lower than the other scattering cross sections. Annihilation of trapped positrons is minimised by ensuring that they do not spend an excessive amount of time in the trap.

Figure 4.2.3: Energy dependence for N2 electronic excitation and Ps formation

cross sections, reproduced from Danielson and Dubin (2015). _Oelectronic excita- tion, original data from Sullivan et al. (2001b) and • Ps formation, original data from Marler and Surko (2005a).

Cool

During the cooling phase, the electrode seven potential is raised to prevent loading of more positrons into the final section of the trap, as shown in figure 4.2.2. The potential on electrode eight is also raised as this will affect the dump stage, dis- cussed later. The positrons are thus trapped in the potential well formed between electrodes seven and nine and undergo collisions with N2 and CF4. Vibrational

and rotational excitation ofN2 plays an important role in cooling the positrons at

this stage, but CF4 is much more efficient. A comparison of the scattering cross

sections in figure 4.2.4, indicates that CF4 has a significantly larger vibrational

excitation cross section thanN2, especially for the antisymmetricν3stretch mode.

As the energy loss for each vibration is similar, CF4 could be expected to cool

positrons ∼100 times faster than N2. Cooling positrons quickly is important to

reduce annihilation in the trap. Positrons typically cool for 2-3 ms in this stage until they have reached room temperature, with an energyE = 3/2kT ∼40meV, corresponding to Ek ∼25meV.

4.2. Experimental and Analysis Methods 61

Figure 4.2.4: Comparison of N2 and CF4 vibrational cross sections. • ν3 anti-

symmetric stretch mode ofCF4, measured by Marler and Surko (2005b). — Close

coupling calculation of the integral N2 vibrational cross section from Gianturco

and Mukherjee (1997). Diagram reproduced from Jones (2010).

Dump

The dump phase is relatively short, taking around 0.5 ms, and consists of rais- ing the electrode eight potential as a function of time as shown in figure 4.2.5. Positrons are ejected from the trap in a pulse with a beam energy defined by the potential applied to electrode nine, often referred to as the transport energy. The speed at which the electrode eight potential is increased affects the tempo- ral and energy resolution of the beam, where the energy resolution is of greater importance in the single scattering experiments. If the potential is increased too rapidly it can result in unintentional heating of the beam, degrading the energy resolution. The final result of this cycle is a pulsed beam with thousands of positrons per pulse.

In addition to the loss processes already discussed, cross field transport due to misalignment of the trap solenoid with the trap electrodes, or scattering from the buffer gases can further reduce the trap efficiency. Cross field transport causes the positrons to hit the electrodes and annihilate and can, to some extent, be reduced by aligning the trap solenoid for maximum beam intensity. When

Time Electro de 8 Potentia l _Vdump Vcool Dump Time

Figure 4.2.5: The typical change in voltage of electrode eight as a function of time is logarithmic, rising from Vcool, the electrode eight potential during the cool

phase, to Vdump, the final electrode eight potential in the dump phase, over a

specified dump time.

positrons scatter from the buffer gases, they do not necessarily remain on-axis making them susceptible to cross-field transport. However, since the presence of buffer gases is essential for operation, cross field transport due to scattering is impossible to remove completely. The overall efficiency of the trap is∼10%, based on measurements made by Jones (2010). Loss of positron intensity is mostly due to

• Ps formation

• Cross field transport

• Transfer of energy from Ek to E⊥ due to magnetic field changes moving from the source stage to the trap