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Accelerator Physics* Accelerator Physics Overview: Outline 1 Overview Prof Accelerator Physics* Accelerator Physics Overview: Outline 1 Overview Prof. Steven M. Lund 2 Quadrupole and Dipole Fields and the Lorentz Force Equation Physics and Astronomy Department 3 Dipole Bending and Particle Rigidity Facility for Rare Isotope Beams (FRIB) 4 Quadrupole Focusing and Transfer Matrices Michigan State University (MSU) 5 Combined Focusing and Bending 6 Stability of Particle Orbits in a Periodic Focusing Lattice 7 Phase­Amplitude Form of the Particle Orbit 8 Beam Phase­Space Area / Emittance 9 Effects of Momentum Spread 10 Illustrative Example: Fragment Separator Exotic Beam Summer School 11 Conclusions Michigan State University References National Super Conducting Cyclotron Laboratory (NSCL) 18­19 July, 2016 (Version 20160731) * Research supported by: FRIB/MSU, 2014 onward via: U.S. Department of Energy Office of Science Cooperative Agreement DE­SC0000661and National Science Foundation Grant No. PHY­1102511 SM Lund, EBSS, 2016 Accelerator Physics 1 SM Lund, EBSS, 2016 Accelerator Physics 2 1. Overview In nuclear physics, accelerators are used to produce beams of Accelerators tend to be viewed by specialists in other fields as a “black box” producing important rare isotopes particles with some parameters Accelerator Start with the stable isotopes (black) and make all the others Application r e b m u N But accelerator science and technology is a highly developed field enabling a broad range n of discovery science and industry o r t Discovery Science: u High Energy (Colliders) and Nuclear Physics (Cyclotrons, Rings, Linacs) e N Materials Science (Light Sources) Industrial: Semiconductor Processing, Material Processing, Welding Green – New territory to be Medical: X­Rays, Tumor Therapy, Sterilization explored with next-generation Modern, large­scale accelerator facilities are a monument to modern technology and take a blue – around 3000 rare isotope facilities large number of specialists working effectively together to develop and maintain known isotopes Only briefly survey a small part of linear optics in this lecture …. much much more ! Neutron Number SM Lund, EBSS, 2016 Accelerator Physics 3 SM Lund, EBSS, 2016 Accelerator Physics 4 Accelerators for rare isotope production Cyclotrons • The particle accelerator used for production is called the “driver” Continuous train of particle bunches injected from center and spiral outward on RF acceleration over many laps. Exits machine on last lap to impinge on target. • Types ● Relatively easy to operate – Cyclotron NSCL (USA; MSU), GANIL (France), TRIUMF (proton; Canada), and tune (few parts) HRIBF (proton; USA ORNL), RIKEN RIBF (Japan) • Used for isotope production – Synchroton GSI, FAIR-GSI (Germany); IMP (China) and applications where reliable and reproducible – LINAC (LINear ACcelerator) FRIB (USA; MSU), ATLAS (USA; ANL), operation are important RAON (Korea) (medical) – Others like FFAGs (Fixed-Field Alternating Gradient) • Intensity low (but continuous train of bunches) due to not currently used but considered limited transverse focusing, • Main Parameters acceleration efficiency is – Max Kinetic Energy (e.g. FRIB will have 200 MeV/u uranium ions) high, cost low – Particle Range (TRIUMF cyclotron accelerates hydrogen, used for spallation) • Relativity limits energy gain, – Intensity or Beam Power (e.g. 400 kW = 8x6x1012/s x 50GeV so energy is limited to a few hundred MeV/u. – Power = pμA x Beam Energy (GeV) ( 1pμA = 6x1012 /s) • State of art for heavy ions: http://images.yourdictionary.com/cyclotron RIKEN (Japan) Superconducting Cyclotron 350 MeV/u SM Lund, EBSS, 2016 Accelerator Physics 5 SM Lund, EBSS, 2016 Accelerator Physics 6 Cyclotron example: NSCL’s coupled cyclotron facility Synchrotrons D.J. Morrissey, B.M. Sherrill, Philos. Trans. R. Soc. Lond. Ser. A. Math. Phys. Eng. Sci. A “train” of bunches injected to fill ring and then bunches in ring accelerated 356 (1998) 1985. while bending and focusing rise synchronously. At max energy bunch train is 86 78 K500 Example: Kr → Ni kicked out of ring and impinges on target. Then next cycle is loaded. ion sources • Can achieve high energy at modest cost – tend to be used to coupling 86Kr14+, line 12 MeV/u deliver the highest energies K1200 • Intensity is limited by the Coulomb A1900 focal plane force of particles within bunches (Space Charge) p/p = 5% • production transmission The magnets (bend and focus) 86Kr34+, target stripping of 65% of the must rapidly ramp and this can be foil 140 MeV/u produced 78Ni difficult to do for superconducting wedge magnets • Machine must be refilled for next fragment yield after target fragment yield after wedge fragment yield at focal plane operating cycle giving up average intensity due to overall duty factor • State of the art for heavy ions now under construction: FAIR http://universe-review.ca/R15-20-accelerators.htm (Germany) and IMP/Lanzhou + CERN LHC for p-p (Higgs) SM Lund, EBSS, 2016 Accelerator Physics 7 SM Lund, EBSS, 2016 Accelerator Physics 8 Example synchrotron: Facility for Antiproton and Ion Research LINAC (LINear ACcelerator) (FAIR), GSI Germany A continuous “train” of bunches injected into a straight lattice for acceleration • Beams at 1.5 GeV/u with strong transverse focusing and RF acceleration • 1012/s Uranium • Many types for ions, protons, and DESY LINAC segment • Research electrons and has simpler physics than (XFEL driver) – Rare isotopes rings. Applications from industrial and – Antiproton small medical to discovery science. – Atomic physics • Intensity can be very high since – Compressed matter compatible with strong transverse – Plasma physics focusing and a continuous train of bunches • Under construction with significant delays but front • Retuning for ions can be complex end working/upgraded • Can use superconducting RF cavities for high efficiency but at high cost/complication • Cost can be high (RF cavities one pass: need high gradient) http://www.fair-center.de/index.php?id=1 • Used to provide the highest intensities • State of art for heavy ions: FRIB folded linac (MSU) under construction SM Lund, EBSS, 2016 Accelerator Physics 9 SM Lund, EBSS, 2016 Accelerator Physics 10 Example LINAC: Facility for Rare Isotope Beams (FRIB) 2. Quadrupole and Dipole Fields and the Lorentz Force Equation Consider a long static magnet where we can approximate the fields as 2D transverse within • 200 MeV/u, 400 KW the vacuum aperture: continuous power on- target with heavy ions • Superconducting RF Taylor expand for small x,y about origin and retain only linear terms of “right” symmetry: cavities and solenoid 0 0 0 0 0 focusing • Novel liquid Li stripper to boost charge state and simultaneously Via: symmetry choices and design accelerates several Maxwell equation for a static magnetic field in a vacuum aperture: species to increase power on target • Under construction: front end undergoing early commissioning in 2016 Superconducting RF cavities Giving: 4 types ≈ 344 total E ≈ 30 MV/m peak β = β = β = β = 0.04 0.08 0.2 0.5 SM Lund, EBSS, 2016 Accelerator Physics 11 SM Lund, EBSS, 2016 Accelerator Physics 12 Magnets Elements of accelerator are typically separated by function into Magnet design is a complicated topic … but some examples of elements to produce these a sequence of elements making up a “lattice” static magnetic fields: Example – Linear FODO lattice (symmetric quadrupole doublet) for a LINAC Idealized Structure Laboratory Magnet tpe_lat_fodo.png e l o p i D Example – Synchrotron lattice with quadrupole triplet focusing India: Dept Atomic Eng ring.png e l o p u r d a u Q Canada: TRIUMF SM Lund, EBSS, 2016 Accelerator Physics 13 SM Lund, EBSS, 2016 Accelerator Physics 14 Lorentz force equation for particle of charge q and mass m evolving in magnetic field: 3. Dipole Bending and Particle Rigidity Magnetic field only bends particle without change in energy: Illustrative Case: Particle bent in a uniform magnetic field Particle is bent on a circular arc so Lorentz force equation gives: Simplified Lorentz force equation giving the particle evolution in the field: Putting in the expanded field of our specific form of interest: Beam is directed, so assume particle primarily moving longitudinally with: Dipole bends are used to manipulate “reference” path Rings Transfer Lines and also manipulate focusing properties since bend radius depends on energy Fragment Separators for nuclear physics SM Lund, EBSS, 2016 Accelerator Physics 15 SM Lund, EBSS, 2016 Accelerator Physics 16 Rigidity measures the particle coupling strength to magnetic field For ions take: and kinetic energy per nucleon [MeV/u] fixes Set in terms of: Particle Species: Common measure of energy since determines synchronism with RF fields for Particle Kinetic Energy: acceleration and bunching Units are Tesla­meters and is read as one symbol “B­rho” Electrons Ions (and approx Protons) Heavy ions much more “rigid” than electrons and require higher fields to move: Electron: Ion: Particle kinetic energy sets : ekin_e.png ekin_i.png Electrons are much less “rigid” than ions and are deflected with lower field strength SM Lund, EBSS, 2016 Accelerator Physics 17 SM Lund, EBSS, 2016 Accelerator Physics 18 4. Quadrupole Focusing and Transfer Matrices Transfer Matrix Solutions Illustrative Case: Focused within a quadrupole magnetic field Integrate equation from initial condition: Free drift: Write linear phase­space solutions in 2x2 “Transfer Matrix” form: Let s be the axial coordinate (will later bend on curved path in dipole) and assume beam motion is primarily longitudinally (s) directed + analogous for
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