title: Towards Ion Stopping Power Experiments with the Laser-Driven LIGHT Beamline
Creators: name: Nazary, Haress
Publisher: name: UNSPECIFIED
Year: 2024

description: The objective of this thesis was to plan and prepare for a stopping power experiment with the Laser Ion Generation Handling and Transport (LIGHT) beamline, which is a laser-driven ion beamline at Helmholtzzentrum für Schwerionenforschung (GSI). To this end, detailed modeling and a demonstration of the feasibility of the experiment were carried out. In the experiment I planned, the LIGHT beamline will be configured to select and transport carbon ion beams (C⁴⁺) and proton beams with an energy-to-mass ratio of 0.6 MeV/u. These ions will be accelerated using the Petawatt High Energy Laser for Ion eXperiments (PHELIX) and transported via two solenoids. The projectile bunches will then be temporally compressed with a radio-frequency (RF) cavity to achieve the shortest possible bunch length, to examine the transient plasma as precisely as possible. The plasma target will be generated using the Nanosecond High Energy Laser for Ion eXperiments (nhelix), which was newly designed and upgraded within the scope of this work. The nhelix laser will irradiate a carbon foil with an areal density of 100 µg/cm² from both sides with an energy of 30 J each. The pulse length is 7 ns and the wavelength is 527 nm . The resulting plasma is designed to have a free electron density of 3 × 10²⁰ cm⁻³ and a temperature of 180 eV , which results in a projectile velocity close to the thermal velocity of the plasma electrons (vₚ ≈ vₜₕ). In this regime, the stopping maximum is located, and the stopping theories show their highest discrepancies. The laser-generated plasma will be diagnosed with an interferometric measurement of the free electron density. The development, construction, and successful testing of the interferometric setup were overseen by me throughout this work.

I modeled the planned stopping power experiment, encompassing the ion beam transport, the simulation of the laser-heated plasma target, and the interaction of the ion beam with the plasma, both in terms of energy loss and charge state. Beamline simulations were conducted to predict the resulting beam characteristics and requisite beamline settings. The final simulated bunches exhibited a temporal bunch width of 300–340 ps and focal spot size of 4.5–5.5 mm at the plasma target. The plasma was modeled using the MULTI2D hydrodynamic code. A maximum temperature of 180 eV and a free electron density in the order of 10²⁰ cm⁻³ is reached after 7.75 ns . Here, the plasma is longitudinally homogeneous. In the innermost region, where the projectile beam passes through the plasma, transverse homogeneity is achieved after 8 ns. The ion beam’s interaction with the plasma target was then modeled based on different theoretical models describing the stopping power. A two-dimensional simulation of the entire experiment was successfully conducted. In the stopping maximum, the stopping power models predict an increased energy loss of 185–230 % for protons and 230–290 % for carbon ions compared to the energy loss in a solid target. In order to differentiate between five different theoretical stopping power models, it was determined that a required energy resolution of 11 % is sufficient to yield meaningful results. The two-dimensional simulations were employed to identify the optimal pinhole size for the projectile beam in the stopping power experiments, resulting in a diameter of 0.5 mm. 

The performance of the beamline was demonstrated experimentally by transporting and temporally compressing carbon ions (C⁴⁺) with an energy of (7.2 ± 0.2) MeV to a bunch duration of (1.23 ± 0.04) ns (full width half maximum). The focal spot size was (4.11 ± 0.02) mm in diameter, and the compressed bunch was estimated to contain (2.0 ± 0.6) × 10⁸ ions . In addition, protons with an energy of (0.63 ± 0.01) MeV were transported and temporally compressed to a bunch duration of (0.76 ± 0.04) ns . The focal spot size was (2.82 ± 0.03) mm in diameter, and the bunch was estimated to contain (5.9 ± 0.4) × 10⁸ protons. The projectile beams utilized in this study are five to seven times shorter than those employed in previous experiments with linear accelerators, resulting in a shorter time averaging over plasma parameters that change in nanoseconds. The estimated particle numbers were two to three orders of magnitude higher than in similar experiments, resulting in a higher possible time of flight (ToF) distance when measuring the energy and therefore a higher energy resolution. The transported beams were used to conduct stopping power experiments in a solid carbon foil, to demonstrate the feasibility of the planned experiment. The measured energy loss for protons was dE = (29 ± 6) keV , while the measured energy loss for carbon ions was dE = (61±10) keV. Both values are in agreement with the predicted values of the SRIM code (Stopping and Range of Ions in Matter). These measurements indicate an uncertainty of 7 % for protons and 6 % for carbon ions in the stopping power experiments with the plasma target. The preparatory experiments demonstrate the feasibility of the planned stopping power experiment, which will yield meaningful data for benchmarking stopping power theories.