Using Geant-4 for Radioactive Ion Release Simulations

1. Using Geant-4 for Radioactive Ion Release Simulations Brahim MUSTAPHA Physics Division Argonne National Laboratory

2. Outline of Presentation Framework & Motivations: Production of Radioactive Beams Description of the Release Process Simulation of Effusion using Geant-4 Simulation of Diffusion Example of Target Simulation Optimizing the Target Geometry Summary & Outlook

3. Production of Radioactive Beams Geant-4 Simulation: Optimize the target geometry for an efficient production and transport of radio-isotopes.

4. The Release Process The important parameter? Time: from production to release Why? Extract as many ions as possible before they decay. How to minimize this delay ? - Choose target material (not always possible) - Optimize target geometry => Object of this work Why use Geant-4? • Possibility of implementing complicated geometries and modify them easily. • Object oriented: Adding new physics processes possible and easy. • 3. Visualization capabilities to test and debug the geometry and the tracking.

5. Simulation of Effusion using Geant-4 Effusion: A new physics process added to Geant-4 • 1. After diffusion particles (atoms or ions) have thermal energies. • 2. A Particle is tracked inside the target until it encounters a surface. • At the surface, a particle could be adsorbed (sticking time) then desorbed. • A random direction obeying the Cosine Law and pointing to the target volume • is assigned to the particle. (Cosine Law: the probability of a given direction • is proportional to the cosine of its angle with the normal to the surface) • 5. Particles are allowed to exit only through the ion source. Output of the Simulation: event by event 1. Total Path Length => Flight time: tf (Maxwell distribution of velocities for given (T,M)) 2. Number of Collisions => Sticking time: ts (Assuming an average sticking time per collision.)

6. Some Difficulties… Partially Solved • Geometry don’t close 100%, Leakage at corners and connections. • Partially solved by reducing thicknesses from mm to microns … • Boolean Geometries didn’t work well. • Seem to work better with recent versions of Geant-4 (5.2) • At some point, problems with defining ions. • Not needed anymore, simulation done for one type (alpha particles) • to obtain Path Lengths and Number of Collisions which are valid for • any type of ion. • At the surface, particle infiltration to the material instead of being • re-emitted to the target volume. • Also reduced by reducing walls thickness.

7. Simulation of Diffusion Can’t easily be done using Geant-4 Done analytically using the solution of the diffusion equation: For thin foils: the distribution of diffusion time is given by: is the characteristic diffusion time given by: d is the foil thickness D is the diffusion coefficient Diffusion time: td, generated randomly according to P(t)  Total delay time: t = td + tf + ts

8. Example of Target Simulation: RIST Geometry: Target: 18 cm long 2cm diameter 3600 – 25 μm discs Con. Tube: 5 cm long 8 mm diameter Ionizer: 3 cm long 3 mm diameter Resultof the effusion simulation: < Number of Collisions > ~ 2.4 million < Total Path Length > ~ 290 m For Li-8 at 1950 C, this corresponds to a < Flight Time > ~ 115 ms Diffusion coefficient and average sticking time obtained by fit to the data.

9. Best Fit to the data Best fit : D <= 10-7 cm2/s ts = 0 ns l = 2 cm Delay times : Effusion ~ 100 ms Diffusion > 5 s Conclusion : Diffusion is dominant, slow compared to Li-8 decay (0.84 s)  Use thinner discs

10. Optimizing the Target Geometry Shorter Ionizer Thinner Discs Disc Thickness d (m) 25 2.5 <N. of Collisions> 1.6 106 1.6 107 <Path Length> (m) 190 190 <Effusion time> (s) 0.075 0.075 <Diffusion time> (s) 52 0.52 Efficiency (%), Li-8 (.84 s) 8.2 67 Ionizer Length l (cm) 3.5 2. 1. <N. of Collisions> 2.5 106 1.6 106 1.6 106 <Path Length> (m) 290 190 120 <Effusion time> (s) 0.115 0.075 0.047 <Diffusion time> (s) 52 52 52 Efficiency (%), Li-8 (.84 s) 7.9 8.2 8.4

11. Summary and Outlook Geant-4 used successfully to simulate the effusion of radio-isotopes from a production target. Will use Geant-4 for future simulations of more complicated geometries, such those filled with fibers or grains.