Trapping Particles
2.4 Loading Ions into the Trap
Due to the high trap depth of a Paul trap compared to optical, magnetical, and magneto-optical traps, loading of a Paul trap does not require pre-cooling of the particles. The trap depth of the order of 10000 K is usually much higher than the kinetic energy of the generated ions. However, the strong rf potentials of the trap
2.4 Loading Ions into the Trap 33
electrodes also prevent ions to be introduced into the trap from outside. To load the trap the ions need to be produced in the trapping region via ionization of the corresponding neutral particle species.
On one hand this requires an efficient ionization process in the trap-ping region. This can be provided by electron impact ionization, which is described in section 2.4.1, or by photo-ionization. On the other hand it requires particle sources which provide sufficiently high neutral particle densities in the trapping region. For the inlet of gases (e. g. HD) a leak valve is connected to the chamber as al-ready described in section 2.3. The partial pressure of the gas in the chamber will determine the loading rate. The solid-state particles like beryllium, which are to be laser-cooled and then sympathet-ically cool the molecular ions, need a somewhat more advanced source. This is described in section 2.4.2 and following.
2.4.1 Electron Gun
The ions are generated by electron impact ionization of the neu-tral particles’ species. Therefore an electron gun (Kimball, type Electron-Flood-Gun-8) is attached to the chamber. The electron beam crosses the trap diagonally, orthogonal to the beam of the evaporated beryllium particles which runs along the other diago-nal. A schematic view of this operating plane in the UHV chamber is shown in Fig. 2.16.
Fig. 2.17 shows the power supply that was developed to provide the required voltages for acceleration and shaping of the electron beam.
The gun can produce electrons with energies between 50 and 1500 eV. The typical current of the electron beam is about 100µA with a diameter of a few mm. The functionality of the gun can be checked by watching the fluorescence light of a phosphor plate placed in beam on the opposite side of the trap. More detailed characteristics of the electron beam are found in the manual.
2.4.2 Beryllium Source
A stream of neutral beryllium atoms is produced by evaporation of a beryllium wire. Beryllium has a melting point of 1278◦C and is rather brittle in solid state. It is found by the estimation presented below that temperatures of at least 900◦C are required to achieve a sufficiently high particle flux. Direct heating of a single thin beryllium by electric current failed, since the wire is not robust enough. Therefore an electrically heated tungsten wire is used as
to CCD camera
laser beams for spectroscopy, cooling, etc.
wall of the UHV chamber Be
oven
phosphor plate
lens
electron gun
92 mm trap
140 mm
Figure 2.16: Horizontal cross-section of the experimental UHV set-up.
electron gun power supply
e-cathode
DN40CF control grid anode
120 mm
100W100W
0 .. 2 V 0 .. 2 A
0 .. - 100 V 0 .. 10 mA H.V.
0 .. - 1.5 kV 0 .. 10 mA
emission meter 0..500 Am
+ +
+
-
-Figure 2.17: Wiring diagram of the electron gun and the corresponding power supply.
carrier, around which the beryllium is wrapped [46]. The data of this kind of atom source for beryllium are in Tab. 2.2.
For fabrication, we attach the ends of the beryllium and the tung-sten wire to each other. Then we slowly start rotating the tungtung-sten wire, while the Beryllium wire is heated with a heat gun. The beryllium wire wraps around the tungsten wire with a covering ra-tio of about 50%. Finally, one piece of the wrapped wire of about 5 mm length is clamped to two connectors (for the electrical heat-ing) which in turn are fixed in the backside (MacorTM) of a stainless
2.4 Loading Ions into the Trap 35
Beryllium Source
diameter of the beryllium wire 0.05 mm diameter of the tungsten wire 0.1 mm length of the wrapped tungsten wire 5 mm distance oven – center of trap 50 mm covering ratio of the wire surface 50 %
Table 2.2: Data of the beryllium source.
steel housing. The housing serves as shielding to prevent the evap-orated beryllium from contaminating the whole chamber, and has a small aperture (shaped as a nozzle with a rectangular cross-section) pointing to the trap center. It can be seen in the left-hand part of Fig. 2.18.
Figure 2.18: Left: Final experimental set-up of the UHV inlet, con-taining the trap, with 12 silver wires leading to the electrodes, the beryl-lium source diagonal before the trap and the phosphor plate right diag-onal behind the trap, and a shielded electron multiplier on top of the trap, Right: UHV chamber with the rf trap electronics in a copper shielding on top, a CCD camera on the right of the chamber, and some optics on the table around the chamber.
To estimate the particles’ flux we consider the vapor pressure of beryllium [47]. The equilibrium vapor pressure in a closed cavity at a given temperature is given by
0 = ˙N = ˙Nevaporate−N˙stick (2.31)
=A κ−AN/2 V hvis ,
where κ the number of evaporated particles per surface area and time, N the number of particles, V the volume of the cavity, A the surface of the surrounding walls, s ≈ 0.1 is the probability
that a particle hitting the wall gets stuck again, hvi=q
2kT
πm is the mean velocity of the particles in one direction (Gaussian energy distribution).
Using the ideal gas equation pV =N kT with (2.31) we find κ=p·s·
r 1
2kT mπ. (2.32)
To predict the loading rate into the trap, we have a closer look at the ionization process in the following paragraph
2.4.3 Loading Rate for Be
+The loading rate of beryllium atoms into the trap is calculated as N˙load =NBe(T)·n˙e·σ , (2.33) where NBe(T) is the number of beryllium atoms in the loading region, ˙ne the number of electrons per area and time crossing the region and σ the cross-section of electron impact ionization. The loading region is the volume where conditions for ionization and trapping are present simultaneously, which we estimate to be 18× 1×1 mm.
The cross-section of electron impact ionization of beryllium can Cross-sections of
electron impact be found in [48]. Although the maximum cross-section is given at electron energies of about 50 eV with σ ≈46·10−18 cm2, we work at electron energies of about 1 keV and σ ≈12·10−18 cm2. Lower energy electrons are strongly influenced by the rf field of the trap and mostly do not reach the loading region. However, observation of the electron beam on the phosphor screen shows that even the 1 kV electron beam gets diffused by the rf field after passing the trap. For a safe estimation, from the observation of the fluorescence on a phosphor, we assume that only 1% of the total electron gun’s flux is passing the trap at the correct location.
Taking all the data of the set-up given above, we find the loading rate as plotted in Fig. 2.19.
From the plot we see that temperatures of at least 900 ◦C are required to achieve acceptable loading times for a number of at least 103. . .104 beryllium ions. These temperatures are reached when the wire, watched with a bare eye, glows in a red color. This is achieved at a heating current of about 1.5 A. The switching time of the beryllium source is on a scale of 1 s. The functionality of the source was also proven by “coating” a glass plate in front of the source with beryllium. Under normal operating condition the evaporative consumption of the beryllium wire can be neglected and the set-up seems to be quite robust: there is no experimental data of the wire lifetime yet!