U.S. Particle Accelerator School

Intense Beam Physics Course Outline

Sponsoring University:

College of William and Mary


Intense Beam Physics: Space Charge, Halos and Related Topics


John Barnard and Steven Lund, LLNL

Course Outline

I. Introduction to the Physics of Beams and Basic Parameters
    1. Particle equations of motion
    2. Perveance, betatron frequence, space charge depression
    3. Plasma physics of beams
    4. Emittance and brightness
    5. Approximations
    6. Machines and applications

II. Focusing methods and current limits
    1. Paraxial Ray Equation
    2. Focusing
        Einzel Lenses
        Electric and Magnetic Quadrupoles
    3. Current limits in accelerators

III. Particle Equations of Motion
    1. Approximate equations of motion
    2. Linear equations of motion without space charge; Hill's equation
    3. Floquet's theorem and the phase-amplitude form of the particle orbit
    4. The Courant Snyder invariant
    5. The betatron formulation of the particle orbit
    6. Resonances in rings
IV. Injectors/Longitudinal Beam Physics I.
    1. Child-Langmuir law
    2. Pierce electrodes
    3. Transients in injectors
    4. Injector choices

V. Transverse Distribution Functions
    1. Vlasov Equation and Vlasov Equilibria
    2. The KV Equilibrium
    3. Continuous focusing limit of the KV distribution
    4. Equilibrium distributions in continuous focusing channels
    5. The thermal equilibrium distribution in continuous focusing channels
    6. Debye screening in a thermal equilibrium beam
    7. The density inversion theorem

VI. Envelope Modes
    1. Continuous focusing
    2. Transverse envelope modes in periodic channels
    3. Longitudinal envelope modes in bunched beams
    4. 3D envelope modes in bunched beams

VII. Transverse Kinetic Stability
    1. Overview - going beyond the envelope model
    2. Linearized Vlasov Equation
    3. Collective modes on a KV equilibrium beam

VIII. Longitudinal Beam Physics II.
    1. Acceleration - introduction
    2. Space-charge of short bunches (rf)
    3. Space-charge of long bunches (g-factor)
    4. Longitudinal space charge waves
    5. Longitudinal rarefaction waves and bunch ends
    6. Bunch compression
    7. Neuffer distribution

IX. Kinetic Stability II.
    1. Global conservation constraints
    2. Kinetic stability theorem

X. Transverse and Longitudinal Halos
    1. Definition and importance
    2. Qualitative picture of halo-formation
    3. Core/particle models
    4. Amplitude/phase analysis

XI. Electron cloud and beam/gas interactions
    1. Processes and cross-sections
    2. Pressure instability
    3. Electron-clouds

XII. Simulation Techniques
    1. Why numerical simulations?
    2. Classes of intense beam simulations
        a. Particle methods
        b. Vlasov distribution methods
        c. Fluid models
        d. Moment methods
    3. Numerical methods
        a. Discretizations
        b. Applications to moment methods
    4. Numerical methods for particle and distribution methods:
        a. Field discretizations
        b. Particle methods:
    1. Leap frog advance
    2. Field solution
    3. Particle weighting
    4. Advance cycle
    5. Iniitializaton
    6. Numerical convergance
    7. Examples
        c. Distribution methods
    1. Similarities with particle methods
    2. Distribution advance
    3. Examples