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Accelerator Physics. Basic Formalism Linear Accelerators Circular Accelerators Magnets Beam Optics Our Accelerator. Greg LeBlanc Lead Accelerator Physicist Australian Synchrotron Project. Basic Formalism. Lorentz Force. Only works on charged particles Electric Fields for Acceleration
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Accelerator Physics • Basic Formalism • Linear Accelerators • Circular Accelerators • Magnets • Beam Optics • Our Accelerator Greg LeBlanc Lead Accelerator Physicist Australian Synchrotron Project
Basic Formalism Lorentz Force • Only works on charged particles • Electric Fields for Acceleration • Magnetic Fields for Steering • Magnetic fields act perpendicular to the direction of motion. • For a relativistic particle, the force from a 1 Tessla magnetic field corresponds to an Electric field of 300 MV/m
Basic Formalism Energy • Rest Energy: • Relativistic Parameter: • Velocity: • Relativistic Mass: • Energy in eV: (Electron rest mass 9.1*10-31kg gives a rest energy of 511 keV)
Basic Formalism • Particles Relativistic when b1
Linear Accelerators • Particles Accelerated in Straight Line • Electrostatic or RF Fields • Planar Wave • Static Case • Lorentz Force • Energy Gain
Linear Accelerators Electrostatic Accelerators • Electron Gun • Van de Graaff generator (~20MV)
Linear Accelerators RF Accelerators • Wideroe • Long for low frequency • Losses • Alvarez • Higher frequency • Higher voltages
Linear Accelerators • Travelling Wave • Standing Wave
Synchronicity in a LINAC The length of the ith drift tube is where is the velocity of the particles in the ith drift tube and is the rf period. Australian Synchrotron Example: Electrons at the speed of light (a valid approximation above 5 MeV) in a 3 GHz linac
Circular Accelerators • Circular Motion in a Magnetic Field • Centripetal Force • Lorentz Force • B, r or T constant
Circular Accelerators • Cyclotron • Constant B • Non-relativistic
Circular Accelerators • Microtron • Synchronicity for Dg=integer • DEe=n x 511 keV • DEp=n x 938 MeV • Race Track Microtron
Circular Accelerators • Synchrotron • Constant r and T • Magnets ‘Ramped’ • Storage Ring
Magnets Dipoles for Steering • Magnetic Field
Magnets Quadrupoles for Focusing • Gradient
Magnets • Sextupoles • Chromatic effects • Octupoles • Correcting Magnetic Errors
Beam Optics Coordinate System • Curvilinear System • Motion Relative Ideal Path individual particle trajectory s y S ideal path y x r x
Beam Optics • Particle motion determined by magnetic lattice • Studied using simulation software
Beam Optics • Machine Functions • Beam Motion • Beam Size • Beam Emittance
Beam Optics • Response Matrix • Probe the Machine with the Beam • Calibrate Models