PG_courses_2005-6.htm

The Cockcroft Institute

Post-graduate Lecture Courses: Academic Year 2005-6

Dates	Location	Session	Tutor(s)	Time
17th October 2005 to 12th December 2005	Room T27	An Introduction to Accelerator Science (lecture notes are available on-line; see below)	Dr R Appleby	10.30am to 11.30pm
		DC Magnets : Design and Construction	Dr N Marks	11.45am to 12.45pm
	DL Boardroom	Tutorial discussions	Dr J Gratus Prof RW Tucker Dr DA Burton AST staff	2pm to 4pm
16th January 2006 to 27th March 2006* (see below)	DL Tower Seminar Room	AC and Pulsed Magnets/Fundamentals of Wakefields and Impedance* (see below)	Dr N Marks/Dr RM Jones* (see below)	10.30am to 11.30pm
		AC and Pulsed Magnets	Dr N Marks	11.45am to 12.45pm
	Daresbury Innovation Centre	Tutorial discussions	Dr J Gratus Prof RW Tucker Dr DA Burton AST staff	2pm to 4pm
24th April 2006 to 29th May 2006** (see below)	DL Tower Seminar Room	Transverse Dynamics	Dr B Holzer (DESY)	10.30am to 11.30am
		Longitudinal Dynamics	Dr J Leduff (Orsay and JUAS)	11.45am to 12.45pm
	DL Tower Seminar Room	Transverse Dynamics	Dr B Holzer (DESY)	1.45pm to 2.45pm
		Longitudinal Dynamics	Dr J Leduff (Orsay and JUAS)	2.45pm to 3.45pm
	DL Tower Seminar Room	Tutorial	Dr B Holzer (DESY) Dr J Leduff (Orsay and JUAS)	4pm to 5pm

Overview and goals of course. The principle of weak and strong focusing. Beam forces, space-charge and magnets

The Lorentz transformations and their consequences. Transformation of energy/momentum and 4-vectors. Relativistic dynamics

Particle motion and derivation of transverse Hills equations. Matrix formulation of transverse beam dynamics. Stability of motion. Emittance and phase space. Off-momentum particle motion. Closed orbit distortion. Chromaticity

The pill-box cavity. The principle of phase stability

The historical development of accelerators. Review of modern machines. Concluding summary

Basic concepts and definitions are introduced. A field function analysis of wakefields is discussed and practical simplifications are introduced. The features of short-range and long-range wakefields are sketched out.

Further general features of wakefields are described. The wakefield issues that are likely to arise in any high current low-emittance accelerator are analysed. In particular, the wakefield in both L-band (superconducting) and X-band (normalconducting) linacs are investigated. Mode coupling issues that are likely to arise in the ILC main superconducting linacs are described. A circuit model of the dipole wakefield is developed for moderate to heavily damped accelerator structures. Interleaving the cell frequencies of adjacent structures is introduced as a means to combat insufficient fall-off in wakefields. Manifold damped structures are modeled with a transmission-line combined with an L-C circuit model and the additional features (built-in BPM and structure alignment thorough monitoring of manifold radiation) of DDS (Damped Detuned Structures) are modelled in detail.

Higher modes of the TESLA accelerator and measurements made at the TTF (TESLA Test Facility). A coaxial wire method, for determining the modes likely to be excited by a particle beam, is described, from its original concept through to the latest research.

Equation of motion (homogeneous): basic concepts; the linear lattice; magnetic multipoles;

Matrix formalism: how trajectories overlap; trajectory and the definition of tune;

The Twiss parameters alpha, beta, gamma and the phase space parameter epsilon: the mathematical definition of these parameters; meaning of epsilon in Phase space; calculation of sigma and sigma' from the phase space area; Liouville's theorem

Matrix expressed as function of alpha, beta, gamma;
Stability of a lattice or cell;
Calculation of lattice parameters: what is a FoDo; how does beta depend on phi; how do we design a storage ring;
Example: a mini beta insertion

Liouville during acceleration: adiabatic shrinking;

Beams with momentum spread; the inhomogeneous equation solution; the dispersion function;

General particle trajectory: x = x_beta + x_d;

Single element dispersion;

Boundary conditions: dispersion in a FoDo; periodic dispersion;

Momentum compaction factor

Sources of magnet errors;

Tolerances; stringent requirements; examples from different machines: dipole lengths, current stability of magnets, multipole contributions;

Dipole error; closed orbit distortion; comparison with periodic dispersion; sensitivity of the beam determined by square root of beta

Recapitulation of 1) and 2);tune and working diagram; resonance denominator as a general problem (from 4);

Tune shift from quadrupole errors;
Beat from quadrupole errors;
Chromaticity; definition and meaning; examples: typical values;
Chromaticity correction using sextupoles;

Simulation; sextupole in a FoDo ring; effect of 6poles in phase space; resonant extraction close to 3rd integer resonance

Floquet transformation;circular diagram; resulting equation of a simple harmonic oscillator;

The effect of a dipole error in phase space;

A random dipole error distribution in a storage ring (numbers from a real machine: SPS or HERA);

Inhomogeneous equation of motion; the driving term of the orbit distortion; the solution from the harmonic oscillator;

The second order stop band:tune shift; stop band width

Specialist courses

Track 2

Spin Dynamics and Polarization

Tutors: Dr DP Barber (DESY and Liverpool), Dr G Moortgat-Pick (Durham)
Location and timing : The Cockcroft Institute (CCLRC Daresbury Laboratory) over 5th June - 9th June 2006
Prerequisites : A solid knowledge of undergraduate-level classical mechanics including Hamiltonians, a solid understanding of undergraduate-level quantum mechanics, a basic understanding of single particle dynamics in accelerators and storage rings including the phenomenology of synchrotron radiation.

Syllabus
1. Introduction and overview

Overview and goals of the course. Some history and an update on the status of the field. The significance of spin polarisation for particle physics.

2. The meaning of "Spin" in accelerator physics

Spin in the rest frame of the particle. Spin motion at rest in a magnetic field: classical and quantum descriptions. The Thomas-Bargmann-Michel-Telegdi (T-BMT) equation of spin motion (and Thomas precession). The simple consequences of the T-BMT equation: the gyromagnetic anomaly and Thomas precession. Linear acceleration. Electrons, muons, protons, deuterons, He^3. Measurement of (g-2)/2 for muons. The concepts: "polarisation", "local polarisation" and "beam polarisation".

3. Basic phenomenology for rings-protons

The vector n_0(theta). Spin tune on the design orbit and the closed orbit. Perturbation to the spin motion by synchro-betatron motion. Fourier analysis and spin-orbit resonances. Resonance strength and its dependence on emittance and energy. The problem with deuterons. The "single resonance model" (SRM) on the closed orbit. Spin tune gaps. Classification of spin-orbit resonances.

4. Polarisation preservation for accelerating protons

The Froissart-Stora formula, NMR. "Imperfection resonances","Intrinsic resonances". Tune jumping, Examples. Siberian Snakes, Examples. Partial Siberian Snakes, Examples. Adiabatic control of "resonance strengths". Spin rotators. The status at RHIC.

5. Practical spin-orbit tracking algorithms

Ignore Stern-Gerlach effects. 3x3 matrices (SO(3)), quarternion algebra (SU(2)). Linearised spin motion: the "SLIM" formalism. The first step beyond linearised spin motion: sideband resonances. Differential algebra.

6. Modern approaches

The invariant spin field (ISF):the vector n(z;theta), local coordinate systems. The amplitude dependent spin tune. Spectral analysis of spin motion. The maximum equilibrium polarisation and the maximum time-averaged polarisation. Beam history and the actual beam: factorisation of the time-averaged polarisation. The ISF in the SRM. Common misconceptions (e.g."spin closed orbit", "perturbed spin tune"). Generalised resonance strength and generalised F-S effects. The adiabatic invariant for spin motion.

7. Calculating the ISF

Perturbative methods. (SMILE, Successive diagonalisation). Non-perturbative methods:-Analytical:SODOM, MILES -Numerical:Stroboscopic averaging, adiabative antidamping. -On orbital resonance (analytical or numerical). The uniqueness of the ISF.

8. Electrons (are not protons)

Overview of the effects of synchrotron radiation on spins. Irreversibility (electrons) vs reversibility (protons). The Sokolov-Ternov effect. The Baier-Katkovformula. The dependence on g. There is no such thing as a free lunch: spin diffusion => depolarisation. The equilibrium polarisation. The SLIM formalism for depolarisation: spin diffusion wrt the vector n^0.

9. Maximising electron polarisation

The 2x6 spin-orbit coupling matrix of the SLIM formalism. The influence of spin rotators and Siberian Snakes. Strong spin matching and spin transparency. Harmonic synchro-betatron spin matching. Harmonic closed orbit spin matching.

10. The Derbenev-Kondratenko (D-K) formula

The D-K formula: spin diffusion wrt thevector n(z;theta). A common misconception. dn/ddelta with linearised spin motion. Kinetic polarisation. The MIT-Bates ring and the AmPs ring. Getting it together: the quantum mechanical approach. More on the classification of spin-orbit resonances: synchrotron
sideband resonances.

11. Really getting it together: the Fokker-Planck equation for spin

The Fokker-Planck equation for orbital motion. The corresponding Fokker-Planck equation for the polarisation density.
Inclusion of spin flip and K-P terms. An educational model:horizontal electron polarisation (c.f.muons). Equation of motion of the spin density matrix of fermions.

12. Pragmatism:spin-orbit Monte-Carlo simulation of spin diffusion

Approximating photon emission. Examples with a model ring. Beam-beam effects. Insights. ILC damping rings:e.g.the effect of wigglers.

13. Electron rings: examples

HERA:27.5GeV. LEP:46-105GeV, energy measurement: gravitation and the TGV. MIT-Bates:900MeV. CEBAF:6GeV. eRHIC5-10GeV

14. Sources and Polarimetry

Protons. Electrons

Further information may be found at http://www.desy.de/~mpybar.

Module title	Venue	Date
Advanced Electromagnetics	Lancaster University	19th to 30th September 2005
Physical Processes	Strathclyde University	7th to 18th November 2005
Passive Components	Strathclyde University	9th to 20th January 2006
Active Components	Lancaster University	13th to 24th February 2006
Power Supplies	Strathclyde University	13th to 24th March 2006
High Power RF Systems	Lancaster University	1st to 12th May 2006

Track 4

RF Structure Design

Tutor : Dr R Seviour
Location : TBA
Duration : TBA

Syllabus
1. RF resonant cavities

Overview
Superconducting / normal cavities

2. Intro to Superconductivity

Type I & II, Meissner effect, penetration depth
BCS theory, Vortex States
Max B field, residual resistance ratio, super heating magnetic
Impurities (Not dirty SC), grain boundaries, mesoscopic transport

3. Design issues

Materials, geometry
Multipactor, Electron Cloud, Wakefields

4. Numerical Techniques

FD, FE, FIT, BI, and Hybrid Techniques
Effects of griding space
Staircasing, dispersion

5. Numerical Package overview

MWS, MAFIA, MAGIC, FEMLAB, Lorentz

6. Possible Future developments

Bandgap engineered resonant structures
Dielectric Loaded structures

Elements of vector spaces, elements of differential geometry, exterior methods, frames and coframes, metric, connections and covariant derivatives, Stokes theorem, the Frenet apparatus, Fermi transport, use of curvilinear coordinates in field systems, the covariant Maxwell equations, gauge covariance, electromagnetic interactions with charged particles, boundary conditions and constitutive relations, applications to RF cavity mode analysis.

Motion of charged particles in regular electromagnetic external fields, radiation from charged particles, charged fluids, radiation reaction and the Lorentz-Dirac equation, multi-pole analysis and electromagnetic scattering from a conducting and dielectric sphere, Eikonal methods for high frequency Maxwell fields.

Elements of distribution theory, applications to Sagnac effect.

Linearisation techniques, applications to analysis of (non-planar) design orbits in cyclic accelerators, machine coordinates based on design orbits with curvature and torsion, multiple resonance phenomena.

Hill's equation and Floquet theory, applications to transverse charged beam oscillation stability, notions of symplectic methods for beam dynamics and phase space.

Elements of stochastic methods and stochastic differential equations, the Fokker-Planck equations and its uses.

Coding techniques in Maple and use of numerical algorithms for integrating non-linear differential systems.

Core syllabus	Further topics
Variations in design and construction for AC magnets. Coil transposition-eddy loss-hysteresis loss. Properties and choice of magnet steel. Vector potential and its practical significance. Inductance- relationship of voltage and magnetic length. Power supplies. Kicker magnets-lumped and distributed power supplies. Septum magnets-active and passive septa.	Slow and fast cycling synchrotrons: Requirements of a power systems for cycling synchrotrons. Alternator/rectifier sets and direct connection (slow cycling). White circuit and modern power converter systems (fast cycling).