ABSTRACT
CONTENTS 2.1 The Quantitative Aspects of Radionuclide Production . . . . . . . . . . 10
2.1.1 Nuclear Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.2 Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.3 Excitation Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.4 Excitation Function and Radionuclide Production . . . . . . . . 16 2.1.5 Ion Kinetic Energy Degradation in Matter Interaction . . . . . 19 2.1.6 Stopping Power: Bethe’s Formula . . . . . . . . . . . . . . . . . . . . 20 2.1.7 Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.1.8 Straggling: Statistical Fluctuation in Energy Degradation . . . 23 2.1.9 Energy Degradation versus Ionization . . . . . . . . . . . . . . . . . 25 2.1.10 Thick Target Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.1.11 Experimental Measurement of the Excitation Function: The
Stacked Foils Methodology . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2 The Cyclotron: Physics and Acceleration Principles . . . . . . . . . . . . 32
2.2.1 Introduction and Historical Background . . . . . . . . . . . . . . . 33 2.2.2 The Resonance Condition . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.2.3 Magnetic Focusing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.2.3.1 Axial Focusing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.2.3.2 Radial Focusing . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.2.3.3 Stability Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.2.3.4 Free Oscillation Amplitude . . . . . . . . . . . . . . . . . . . 44
2.2.4 Electric Focusing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.2.4.2 Static Focusing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.2.4.3 Dynamic Focusing . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.2.4.4 Combining the Focusing Effects . . . . . . . . . . . . . . . 48
2.2.5 Phase Relations and Maximum Energy . . . . . . . . . . . . . . . . 50 2.2.5.1 Path and Phase in the First Revolutions . . . . . . . . . 50
2.2.6 Maximum Kinetic Energy: The Relativistic Limit . . . . . . . . . 54 2.2.7 The Synchrocyclotron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.2.7.1 Working Principle . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.2.7.2 Phase Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.2.8 The Isochronous Cyclotron . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.2.8.1 Thomas Focusing and Working Principle . . . . . . . . 58
2.2.9 Focusing Reinforcement Using the Alternating Gradient Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.2.10 Aspects of Quantitative Characterization . . . . . . . . . . . . . . . 62 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
The radionuclei that lead to different nuclear medicine techniques are not readily available in nature and need to be produced through nuclear reactions. The main fundamental physics mechanisms used in radionuclide production are fission, neutron activation, and particle irradiation. Fission and neutron activation are performed in nuclear reactors. Exposing Uranium-235 to thermal neutrons produced in a nuclear reactor can induce the fission of the uranium isotope, resulting in low (usually between 30 and 65) atomic number nuclei. Some of the nuclei produced in this way can be chemically separated from other fission fragments and are widely used in biomedical sciences, particularly in nuclear medicine. Fission is used, for instance, in Molybdenum-99 production, through the nuclear reaction
235U + n → 236U → 99Mo + 132Sn + 4n.
