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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 l.jpg
Accelerator Physics

  • Basic Formalism

  • Linear Accelerators

  • Circular Accelerators

  • Magnets

  • Beam Optics

  • Our Accelerator

Greg LeBlanc

Lead Accelerator Physicist

Australian Synchrotron Project


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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


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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)


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Basic Formalism

  • Particles Relativistic when b1


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Linear Accelerators

  • Particles Accelerated in Straight Line

  • Electrostatic or RF Fields

  • Planar Wave

  • Static Case

  • Lorentz Force

  • Energy Gain


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Linear Accelerators

Electrostatic Accelerators

  • Electron Gun

  • Van de Graaff generator (~20MV)


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Linear Accelerators

RF Accelerators

  • Wideroe

    • Long for low frequency

    • Losses

  • Alvarez

    • Higher frequency

    • Higher voltages


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Linear Accelerators

  • Travelling Wave

  • Standing Wave


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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


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Circular Accelerators

  • Circular Motion in a Magnetic Field

    • Centripetal Force

    • Lorentz Force

    • B, r or T constant


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Circular Accelerators

  • Cyclotron

    • Constant B

    • Non-relativistic


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Circular Accelerators

  • Microtron

    • Synchronicity for

      Dg=integer

    • DEe=n x 511 keV

    • DEp=n x 938 MeV

  • Race Track Microtron


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Circular Accelerators

  • Synchrotron

    • Constant r and T

    • Magnets ‘Ramped’

    • Storage Ring


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Magnets

Dipoles for Steering

  • Magnetic Field


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Magnets

Quadrupoles for Focusing

  • Gradient


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Magnets

  • Sextupoles

    • Chromatic effects

  • Octupoles

    • Correcting Magnetic Errors


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Beam Optics

Coordinate System

  • Curvilinear System

  • Motion Relative Ideal Path

individual particle trajectory

s

y

S

ideal path

y

x

r

x


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Beam Optics

  • Particle motion determined by magnetic lattice

  • Studied using simulation software


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Beam Optics

  • Machine Functions

    • Beam Motion

    • Beam Size

    • Beam Emittance


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Beam Optics

  • Response Matrix

    • Probe the Machine with the Beam

    • Calibrate Models








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