Model for the photodissociation of an H+2 ion cloud created by electron impact

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2.2 REMPI State Selective Ionization Process

Resonance-enhanced multiphoton ionization (REMPI) allows the creation of ions in a state selective way [54]. The principle of REMPI, illustrated in the wave function of the state we want the ion to be in with an additional loosely bound electron in a Rydberg state, and then ionizing it with an additional photon (which may be either at the same wavelength as for the excitation step, or at a dierent one). The probability to reach a given ionic state is given in rst approximation by the Franck Condon principle, i.e., is proportional to the squared modulus of the molecule/ion vibrational wave function overlap.
Therefore there is a high probability for the vibrational quantum number of the ionic core to be preserved in this process because the Born-Oppenheimer curves are almost parallel (e.g. Fig. 1 of Ref. [55]). This means that an ion population could in principle be created in any vibrational state simply by tuning the excitation laser to populate the corresponding vibrational state of the Rydberg electronic level. Since REMPI is a multiphoton process (with the rst excitation step, towards an excited molecular state, often being multiphotonic itself), pulsed and strongly focused excitation lasers are usually required.
The REMPI ionization of small molecules has been studied both experimentally and theoretically in the 1970s and 1980s. In the specic case of H+2 it was studied by Pratt et al. [56] and others [57, 55, 58]. O’Halloran et al. showed that four-photon (3+1) REMPI creation of H+2 in 1sg j = 0; L = 2i through the C1u intermediate state with 303nm light followed well the Franck- Condon principle, i.e. ionizing transitions in which the vibrational state of the resonant intermediate state is preserved in the ion are most probable. More specically, in that work a photoelectron spectra of the Q(2) line: H2 X1+g ( = 0; L = 2) ! C1u (0 = 0; L0 = 2).

Ion Source Equilibrium Pressures

In the following we describe the calculation of the equilibrium pressure in the trap chamber and the ion source buer chamber.
For this estimate, we have assumed that the reservoir connected to a H2 bottle, is maintained at a pressure of 1mbar. The reservoir leaks gas into the buer chamber through the pulsed valve shown in Fig. 2.3, which has a nozzle diameter w = 150 μm. Using Eq. 2.3. we nd that the mean free path in the reservoir is = 648 μm, so that the eusive beam condition of Eq. 2.2 is satised. As will be discussed later on, in our experiments we were led to use a much higher pressure, of the order of 1 bar. This has the important consequence that the condition of Eq. 2.2 is no longer satised, so that the molecular beam is in the supersonic regime rather than the eusive one. However, the order-of-magnitude estimates presented here remain a useful guide. { In the eusive beam regime, for a pressure P = 1mbar in the reservoir, using equation 2.1 we calculate a ow of 1:9 1017 s􀀀1 through a 150 μm diameter hole. { The pulsed valve will send 50 μs pulses 20 times per second to match the ring rate of 20 Hz of the REMPI laser. The pulsed valve will therefore be open for 1 ms per second.
{ This leads to a mean ow of 1:9 1014 s􀀀1. { This chamber being pumped by a Leybold Turbovac 450i turbo pump specied at 200 L s􀀀1 we calculate an equilibrium pressure of 4 10􀀀8 mbar in the buer chamber using equation 2.6. This buer chamber then leaks gas into the main vessel through the 150 μm diameter skimmer shown in Fig. 2.2.
{ Using equation 2.1 we calculate a ow of 7:5 109 s􀀀1 through the skimmer into the main vessel.
{ The main vessel is pumped by a Gamma vacuum 75 S ion pump and getter ribbon. Given the specied reachable vacuums for these pumps and the fact that we are combining them, we estimate the pumping rate of H2 to at least 200 L s􀀀1.
{ Given a 200 L s􀀀1 pumping rate for H2 in the vessel, using equation 2.6 we calculate an equilibrium pressure of 1:5 10􀀀12 mbar, well below the observed limit pressure of the chamber 1 10􀀀10 mbar due to outgassing, so the leak from the buer chamber should not limit the main vessel pressure.
{ In the same fashion we can compute the total ow of particles from the H2 beam into the vessel through the skimmer. The 150 μm diameter skimmer at 15 cm from the pulsed valve has a solid angle of 0:14 10􀀀5 sr. Taking into account the duty cycle of the pulsed valve, this leads to a ow of 4:75 107 s􀀀1 which is negligible compared to the 1:9 1010 s􀀀1 ow from the residual pressure in the buer chamber.

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REMPI Laser

A key component of our state-selective H+2 ion source is of course the laser that will excite the 3+1 photon transition at 303 nm. We use a frequency doubled Nd:YAG Quantel Brilliant laser, producing 5 ns pulses of 532nm light, to pump a Sirah Cobra dye laser, producing 606nm light which is frequency-doubled to 303 nm. The Nd:YAG laser has a repetition rate of 20 Hz and an energy of up to 160mJ per pulse. The pulse energy is adjustable by changing the delay between the ash lamps and the Q-switch. The ash lamps are used to create the population inversion in the Nd:YAG rods and the Q-switch triggers the emission of a pulse. The dye laser produces about 16mJ of 606nm which is doubled to about 4mJ of 303 nm. In Fig. 2.6 we show a curve of the dependence between the Q-switch ash lamp delay and the pulse energy at 303 nm.
The dye laser uses a mixture of Rhodamine-610 and Rhodamine-640 which we have empirically optimised to maximise the output energy at 606 nm. We used a total volume of about 1 litre of ethanol with a 0:0733 g L􀀀1 concentration of Rhodamine-610 and a 0:0267 g L􀀀1 concentration of Rhodamine-640. With respect to the mixture used previously in the group [60] we slightly increased the proportion of Rhodamine 640 which we found empirically to shift the peak of the energy curve towards 606 nm. In Fig. 2.7 we show the pulse energy versus wavelength as we added more Rhodamine-640.

Table of contents :

Introduction
H+2
REMPI ion source
Sympathetic cooling Simulations for GBAR
1. The Paul Trap
1.1 Hyperbolic Paul Trap
1.1.1 Theory
1.1.2 Orders of Magnitude
1.2 Linear Paul Trap
1.2.1 Theory
1.2.2 Orders of magnitude
1.3 RF Heating
1.4 Coulomb Crystal
1.5 Theoretical shape for a single-component crystal
1.6 Conclusion
2. Ion Source
2.1 Introduction
2.2 REMPI State Selective Ionization Process
2.3 Design of the Molecular Beam Apparatus
2.3.1 Vacuum Theory Formulas
2.3.2 Ion Source Equilibrium Pressures
2.3.3 Ion Production Rate
2.3.4 Conclusion
2.4 REMPI Laser
2.5 Experimental Realisation and Testing
2.6 Conclusion and Perspectives
3. H+2 Photodissociation
3.1 213nm Laser Source
3.2 Model
3.2.1 Model for the photodissociation of an H+2 ion cloud created by electron impact
3.2.2 Trap losses
3.2.3 Trap Losses due to the 213nm Laser
3.3 Experimental Testing of Pressure and Trap Losses
3.3.1 Pressure evolution without laser
3.3.2 Pressure Evolution with Laser
3.3.3 Trap Losses without Laser
3.4 Electron-Gun H+2 Lifetime with Laser
3.5 Conclusion
4. GPU Numerical Simulations of Sympathetic Cooling
4.1 Introduction
4.2 Numerical Model
4.2.1 Trapping Force
4.2.2 Coulomb Force
4.2.3 Interaction with the Cooling Laser
4.3 Integration Algorithm
4.4 Formation of Crystals
4.5 Example Curves and Denitions
4.6 Timestep Criteria
4.6.1 Radio Frequency Trapping
4.6.2 Coulomb Collision
4.6.3 Interaction with the cooling laser
4.6.4 Energy Conservation Test
4.6.5 Choice of and
4.6.6 Timestep Orders of Magnitude
4.7 Implementation
4.8 Available Hardware
5. Sympathetic Cooling Simulation Results
5.1 Theoretical Model of Sympathetic Cooling
5.1.1 Energy Loss
5.1.2 Cooling time
5.1.3 Coulomb Logarithm Value
5.2 Optimal Shape of the Crystal
5.3 Ineectiveness of single component Be+ crystal
5.4 Impact of RF Heating
5.5 Improvement Using a Two Component Crystal
5.6 Trapping Parameter ax Disfavouring Orbits
5.7 Be+/Auxiliary ion balance
5.8 Capture Time qx Dependence
5.9 Capture Time vs Energy Scaling Law
5.10 Lack of Improvement using a Hot Cloud
5.11 Detection through Fluorescence Signal
5.12 Capture Time vs Ion Number Scaling Law
Conclusion
Appendices
A. Example Parameter File
B. Introduction to GPU programming
B.1 Introduction
B.1.1 What makes the GPU faster than the CPU?
B.1.2 Faster than GPUs
B.1.3 GPU programming languages
B.2 Introduction to C++
B.2.1 Variable declaration
B.2.2 Functions
B.2.3 Pointers and References
B.2.4 Arrays
B.2.5 Passing by reference
B.2.6 Object Oriented Programming
B.2.7 Main
B.3 Introduction to CUDA
B.3.1 Terminology
B.3.2 Programming Syntax
B.3.3 CUDA examples

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