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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

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

- Synchronicity for
- Race Track Microtron

Circular Accelerators

- Synchrotron
- Constant r and T
- Magnets ‘Ramped’
- Storage Ring

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

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