\(\bar{\text{H}}^{+}\) Sympathetic Cooling Simulations with a Variable Time Step

Abstract

In this paper we present a new variable time step criterion for the velocity-Verlet algorithm allowing to correctly simulate the dynamics of charged particles exchanging energy via Coulomb collisions while minimising simulation time. We present physical arguments supporting the use of the criterion along with numerical results proving its validity. We numerically show thatH + ions with 18 meV initial energy can be captured and sympathetically cooled by a Coulomb crystal of Be + and HD + in less than 10 ms, an important result for the GBAR project.

Non-destructive detection of large molecules without mass limitation

“…where L = 2.45 mm is the relevant length as given by the fit which behaves like a harmonic potential at its bottom, characterised by ω z /2π = 90.8 kHz for U DC = 1 V, also deduced from the fit. While the SUI is present in the simulation, the time integration concerning the dynamics driven by the Coulomb interaction and the RF trapping is run with a variable time step Velocity-Verlet algorithm adapted to the closest distance between the charged particles, to make sure the interaction is properly described 80 . This variable time step procedure demands extra computations and therefore is limited to step 4.…”

“…The energy exchanged by a cold charged ensemble and a charged projectile has been studied in the frame of the stopping power of a plasma 90 . Simulation runs for the particular case of cold ions in a RF trap 80,91 consider the energy transfer between the projectile and the trapped ion cloud with a detailed analysis of the projectile's energy evolution during its passage through the ion cloud. It has been shown that two different mechanisms contribute to the energy interchange: collective effects and Coulomb binary collisions and that the energy exchange rate depends on the kinetic energy of the projectile.…”

Analysis of the timing of freely falling antihydrogen

“…As already discussed, the principle of the experiment [19] is to produce ultracold H atoms from antihydrogen ions H`s ympathetically cooled in an ion trap [21,22]. The acceleration ḡ of H atoms in the Earth's gravity field, simply called g from now on, is measured by timing the free fall from the photodetachment of the excess positron to the annihilation of antiatoms when they touch the surfaces of the free fall chamber (see Fig.…”

Improving the statistical analysis of anti-hydrogen free fall by using near edge events

“…The source of H atoms is placed at the centre of the cylindrical vacuum chamber (radius R c and free fall height H f ) in which the free fall measurement is performed. This source is surrounded by obstacles such as the electrodes of the trap [19,20]. We define a cleaner geometry by hiding obstacles with two symmetrically positioned disks of radius R d placed above and below the trap at a distance H d .…”

“…In the present paper, we go further in this analysis by taking into account the obstacles surrounding the anti hydrogen source, required for the experiment [19,20]. These obstacles, such as the electrodes of the ion trap, intercept some trajectories of H atoms.…”