In order to replace the stepwise detuning of the bunching frequency by a directly detunable laser system, a second laser system complementing the fixed-frequency cooling laser was introduced in the 2006 beam time to better match the laser force acceptance to the ion beam momentum spread, see Fig. 2.2 on page 15.
13see [130] for an overview of X-ray spectroscopy using laser-cooled ion beams at the future
Figure 2.7: Upper Part: Four sets of bunch length measurements at various
detuning values ∆fb of the bunching frequency relative to the laser frequency.
These measurements were performed using a single, fixed-frequency laser system.
Lower Part: In addition to the fixed-frequency laser system, a second scanning
laser is introduced (2∆fl,lab= 400 MHz) to increase the acceptance of the laser
force as explained in the text. The black lines indicate the scaling of the bunch length with the ion current expected for space-charge (dashed) and, respectively, intra-beam scattering (solid) dominated beams, similar to Fig. 2.3 and are solely meant to guide the eye.
As discussed in part 2.2.2, an argon ion laser system is modified to address a scan
range of maximum 2∆fl,lab = 1 GHz in the UV, giving a momentum acceptance
of the laser force of ∆paccept,l paccept,l = 2γ2∆fl,lab 2fl,lab = 2γλl,lab ∆fl,lab c ≈2×10 −6, (2.5)
which is about a tenth of the total bucket momentum acceptance and of the same size as the momentum resolution of the Schottky noise measurement. This simple way to calculate the acceptance is only valid for a frequency scan fast enough to counteract intra-beam scattering. Unfortunately, the typical scan- ning time which allowed for stable scanning was on the order of some hundred
milliseconds, and thus much longer than the plasma periodτp of the ion beam.
Even with a smaller detuning range of about 2∆fl,lab = 400 MHz in the UV,
heating of the beam due to intra-beam scattering can be reduced. For this de- tuning range, Fig. 2.7 shows a comparison of two bunch length measurements. The color-coded data point sets refer to measurements of the bunch length at
various detuning values ∆fb of the bucket frequency relative to the fixed fre-
quency of the first laser. In the upper part of Fig. 2.7 one finds measurements for which only one laser at a fixed frequency was used for cooling. In the lower part, those measurements including a second, scanning laser system are shown. The dashed and solid lines, which indicate the scaling of the bunch length with the ion current for space-charge dominated (dashed) and intra-beam scattering dominated beams (solid), respectively, are meant to guide the eye. The position of the transition between the two regimes was set to the approximate ion current value at which the transition was observed in Fig. 2.3.
While for the first set of data points the bunch length measurements scatter over a large range and by a factor of almost ten, in the second set using an additional scanning laser reduces the deviations of the data points from the expected scal- ing. Such bunch length fluctuations can be induced by intra-beam scattering, which heats up a part of the beam. Hot ions can escape the acceptance of the fixed-frequency laser and are no longer cooled by its laser force. When this hap- pens, the equilibrium of laser cooling and heating due to intra-beam scattering is no longer maintained and the beam consists of a hot and a cold part. The beam becomes unstable, resulting in fluctuations of the bunch length.
The laser force of the scanning laser counteracts these fluctuations and the bunch length at low ion currents smoothly follows the scaling for space-charge domi-
nated beams. This becomes most evident at large detuning ∆fb, for which the
single laser system is not sufficient to reach the space-charge dominated regime at all and the bunch length is drastically increased, as indicated by the red sym- bols in the upper part of Fig. 2.7.
It has to be pointed out that the second laser does not increase the overall strength of the laser force, but only its acceptance range, since the detuning be- tween the two laser frequencies is usually so large that different velocity classes of ions are cooled by the two laser forces, and the cooling transition is already saturated when only one laser is used. Thus, the transition from the intra-beam
scattering to the space-charge dominated regime is assumed to occur at almost the same ion current, regardless of the number of laser systems.
At high currents, an increase in the bunch length is observed when using the combination of a fixed-frequency laser and a scanning laser at small detuning
∆fb. This increase can be attributed to the influence of the scanning laser, which
at small detuning accidentally leads to a heating of the ions due to the increase in the photon scattering rate. Such an additional heating effect becomes important if the laser frequency is close to the cooling transition frequency [MB0301] in the ion rest frame. While the frequency of the first laser is fixed by the detuning
∆fb, the frequency of the scanning laser can fall below this value, increasing the
photon scattering rate. At large ion currents – meaning large ion densities – this small additional heating can lead to a sudden increase of the intra-beam scatter- ing rate and thus of the the bunch length, which can no longer be compensated by the combined laser forces.
3. Stopping and Cooling
Beams of Highly Charged
Ions
3.1
In-trap Preparation of Highly Charged Ions for
Precision Physics
Delivering cold highly-charged ions for precision in-trap measurements is cur- rently investigated by several groups in the world ([92, 95, 97, 98],[MB0703]). It is a vital prerequisite to increase the precision of current mass measurements.
Typically, charge breeding in an EBIS or direct laser ionization deliver ions in
a high charge state. While charge breeding in an EBIS is currently the choice
for very high charge states, laser ionization allows for the production of pure beams of ions of only a single charge state. The typical energy spread of an ion beam after charge breeding of some hundred eV [131] does not match the energy acceptance of a few eV to meV of the precision Penning trap system in which the ion mass is measured. Thus, additional cooling is required, especially for precision experiments investigating fundamental physical effects.
To test the feasibility of the cooling scheme proposed in this thesis, extensive
computer simulations of the complete interaction dynamics ofN = 105 ions in a
three-dimensional harmonic potential have been performed. For this, a massive- parallel code has been developed, which can compute the complete stopping dynamics of the ion assuming realistic experimental conditions.
The results of such a realistic simulation can be directly applied to plan the experimental setup necessary for stopping and sympathetic cooling of highly
charged ions, which is foreseen for the MLLTRAP system [MB0703, MB0706].
The subject is introduced by summarizing the numerical methods which have entered in the simulation, succeeded by a summary of the simulation results.
3.2
Numerical Methods
In the following two sections the numerical methods used in the simulation code are summarized. A more elaborate summary of these methods can be found in [MB0604].
First, the choice of simulation parameters is discussed, with emphasis on the choice for the initial kinetic energy of the ion of interest. Next, the equation of motion is introduced, followed by a section on the numerical aspects relevant for the integration of the equation of motions.
Confining Potential Properties
integration time ∆τstep[s] 10−9
lower plasma density higher plasma density
Φ⊥ [V/m2] 2.5×105 3.5×105
Φk [V/m2] 2.5×103 3.5×103
One-component Plasma Properties
NumberN of Mg+ ions 105
AMg, QMg 24,1
TMg [K] 10−3
Highly Charged Ion Properties
Number of highly charged ions 1
AHCI 100
QHCI 10,20,30,40
Ekin,HCI[meV] 100,200,300,400
Table 3.1: Complete list of simulation input parameters.