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accelerator physics and ion optics

introduction

Sytze Brandenburg

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course literature

• book used as guideline for the course An introduction to particle accelerators Edmund Wilson Oxford University Press, 2001

ISBN 0 19 850829

• selected topics from

• proceedings of CERN accelerator school 1992

General accelator physics course

• proceedings of CERN accelerator school 1994Cyclotrons, linacs and their applications

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additional literature

• alternative book for the course (in German)

Physik der Teilchenbeschleuniger und IonenoptikFrank Hinterberger

Springer Verlag, 1997ISBN 3-540-61238-6

• links and references on http:\\www.kvi.nl\~brandenburg

• search the web

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material on CD-ROM

• proceedings CERN Accelerator School 1992General accelerator physics course

• proceedings CERN Accelerator School 1994

Cyclotrons, linacs and their applications

• Principles of charged particle accelerationStanley Humphries

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prerequisite knowledge

• electricity and magnetism

• Maxwell equations: differential and integral form

• mechanics

• pendulum

• special relativity

• relation velocity vs. energy and momentum

• Lorentz transformation

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course lay-out

• introduction• accelerator applications• accelerator types

• physics & technology• development

• how to keep the particles on track• single particle optics• beam optics – transverse & longitudinal• matching beam to accelerator

• what makes life difficult• imperfections and resonances

• special topics• damping, cooling and synchrotron radiation• cyclotrons

• injection and extraction• ……..

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goals and objectives

• knowledge

• principles of acceleration and guiding

• function of ion optical elements (first and second order)

• behaviour of single particles vs. beam

• phase space; emittance conservation

• orbit stability in circular accelerators

• properties matched beam for an accelerator lattice

• effects of aberrations, imperfections; resonances

• ability

• calculate first order beam optics in a lattice

• design a beamline in first order

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assessment

• home work assignmentscontribute up to 20 % of final grade

• written exam

• exam grade is lower limit for final grade

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outline introduction

• accelerator applications

• physics & technology of accelerators

• historical development

• accelerator types

• DC-accelerators

• RF and pulse accelerators

• linear accelerators

• circular accelerators

• reading:

• Wilson; chapter 1

• CERN accelerator school 1992 (CAS94-01); chapter 1

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accelerator applications

• medicine

• radioactive isotope production (diagnostics and therapy)

• X-ray diagnostics

• X-ray and electron therapy

• charged particle therapy

• industry

• welding

• X-ray diagnostics

• ion implantation (semi-conductors, surface hardening)

• material analysis (structure, composition)

• material modification; micro machining

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accelerator applications

• science

• nuclear physics

• particle physics

• condensed matter physics

• material science

• biochemistry

• archeology

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accelerator types

• isotope production cyclotron

• X-ray diagnostics, welding DC accelerator

• X-ray and electrontherapy linac

• ion implantation DC accelerator

• archeology DC accelerator

• material analysis DC accelerator, linac, cyclotron

• material modification DC accelerator, linac, cyclotron

• ion therapy cyclotron, synchrotron

• nuclear physics cyclotron, linac, synchrotron,

storage ring

• particle physics synchrotron, storage ring, linac

• condensed matter physics

material science synchrotron, storage ring biochemistry for synchrotron radiation

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accelerator market in the EU

• particle physics 3

• synchrotron radiation 10

• nuclear physics 15

• ion therapy 3 + several under construction

• X-ray and electron therapy ~3000 (NL: ~100)

• X-ray diagnostics >100000 (NL: ~1600 in ziekenhuis +~5500 bij tandartsen)

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some accelerator types

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physics of accelerators

• classical electrodynamics (Maxwell)• guiding, focussing and acceleration• space charge effects• beam – wall interaction

• beam – beam interaction

• quantum electrodynamics

• synchrotron radiation (electrons)

• atomic physics• beam – vacuum interaction

• thermodynamics• cooling

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technology of accelerators developments

• superconductivity

• increase in energy (LHC)

• ultra high vacuum (<10-12 mbar = 3 x104 atoms/cm3)

• storage rings

• computation

• detailed understanding: maximize intensity

• optimization mechanical and (electro-)magnetic design

• automated control and supervision

• material engineering

• high precision machining

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“particle” physics around 1900

• charged particles produced in gas discharges• negative: cathode rays � electrons (Thomson)• positive: Kanalstrahlen; ~1700 x heavier than electrons

• elements• atomic number Z � mass, chemical properties• emission spectra

• radioactivity

• α-, β- and γ-radiation: penetration in matter; charge; mass• electromagnetic radiation (radiowaves, light)• X-rays• photo-electric effect (Nobelprize A. Einstein, 1921)

• atoms: no clear picture of structure • heavy positively charged particle(s) • electrons

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“particle” physics around 1900

• Rutherford et al. (1911): scattering α-particles from gold: comparison with Coulomb-scattering between point particles

2

1 2

40 kin,1

Q Qd 2 sin

d 16 Esin

2

σ π ϑ= ϑϑ πε

• conclusions• Q1, Q2 = Z1e, Z2e; -e is electron charge• mass and positive charge in a small nucleus• deviations at small scattering angle screening by electrons � size of atom (~0.1 nm)• deviations at large scattering angle

“hard sphere” collision � size of nucleus (~10 fm)

• Rutherford’s conjecture: nucleus = protons and electronsinconsistent with Heisenberg uncertainty relation for electrons

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• production of energetic particles for nuclear reactions:

use Lorentz force F = q(E + v × B) to accelerate charged particles

“particle” physics around 1900

• Rutherford (1919): nuclear reaction 14N(α, p)17O

prediction of existence neutron

• idea: “hard sphere” collision needed for nuclear reaction

size and charge of nucleus � Coulomb barrier

conclusion: energy of several MeV needed for protons and

α-particles

�acceleration with DC voltage not feasible

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electrostatic accelerator: Cockroft-Walton

Rutherford laboratoryhttp://www.isis.rl.ac.uk/accelerator

• 1928: tunneling hypothesis (Gamow)� lower energy needed� acceleration with DC feasible

• 1932: first nuclear reaction with accelerated protons

7Li + p → 2α

7Li + p → 7Be + n

Ep= 400 keV

discovery neutron

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electromagnetic force

• electric force qE

• component parallel to velocity: acceleration

• component perpendicular to velocity: focussing and

guiding

• E⊥ determines curvature of trajectory2mv

Eq

⊥

γρ =

mvB

q⊥

γρ =

• magnetic force q(v × B) perpendicular to velocity

• does not contribute to acceleration

• can be used for focussing and guiding

• B⊥ determines curvature of trajectory

• production of energetic particles for nuclear reactions:

use Lorentz force F = q(E + v × B) to accelerate charged particles

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acceleration techniques

• linear accelerators

• electrostatic

• radio-frequency (RF) electric field

• induction (pulsed EM field)

• particles focussed by accelerating field or separate

magnetic and electric fields

• circular accelators

• RF electric field

• induction

• particles guided and focussed by magnetic fields

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electrostatic accelerator: principle

• electrons emitted by hot filament

• cathode: negative high voltage (~10 kV)

• anode: grounded

• steering plates

• time base

• signal

simplest example: oscilloscope

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electrostatic accelerator: principle

• electrons emitted by hot filament

• cathode: negative high voltage (~10 kV)

• anode: grounded

• steering plates

• time base

• signal

CRT of J.J. Thompson, 1897

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electrostatic accelerator: Cockroft-Walton

created 13/11/05 18:19 1/1m odified 13/11/05 18:19

• G reinacher cascade

• voltage distributed overm any electrodes to controlfocussing

• h igh current I = 100 m A

• V m ax ≅≅≅≅ 2 M V

• in jector for high energy,high intensity accelerators

• load effects

• voltage drop ∝ n3I/ωC

• voltage ripple ∝ n2I/ωC

• large C ; high U 0 and ω

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electrostatic accelerators: focussing

• acceleration and focussing: static electric field

• V1 > V2: positive particles accelerated from 1 to 2

• first half gap focussing, second half defocussing

• particle more time in first half � net focussing effect

dE0

dt=

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electrostatic accelerator: van de Graaff

• insulating conveyor belt: transport charge to HV-dome

• motor power: V I + friction

• voltage divider column

• potential definition

• focussing

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electrostatic accelerator: van de Graaff

HMI van de Graaffhttp://www.hmi.de/isl/

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electrostatic accelerator: tandem van de Graaff

• accelerate negative ions to HV-dome (OK for many elements)

• pass ions through a foil or high pressure region to remove anumber of electrons: positive ions in chargestate Q+

• accelerate positive ions to ground

• E = (Q + 1) V

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electrostatic accelerator: tandem van de Graaff

Oak Ridge tandemhttp://www.phy.ornl.gov/hribf

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electrostatic accelerator: tandem van de Graaff

• installed at Center for Isotopereseach (CIO) for 14C dating: count the number of 14C-atoms relative to 12C

� age of material

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electrostatic accelerator: limitations

• corona discharge

• is also used to stabilizevoltage

• surface currents oninsulators of accelerationcolumn

• discharge in insulation gas

• discharge on surfaces(surface roughness)

• air insulation : 2 MV

• high pressure N2 and SF6:up to 25 MV

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RF linear accelerator

• RF electric field parallel to velocity

• particles in phase with RF field (polarity): “bunched” beam

• length bunches RFbl

2

λβ�

• spacing bunches b RFd n= λ

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Widerö linear accelerator (1928)

• acceleration in gaps E qV sin∆ = ϕ

• shielding by drift tubes during polarity reversal (1/2 TRF

)

• length of drift tube i RF RFi

iqV sinl

2 c 2m

β λ λ ϕ= = (v <<c)

• phase (axial) focussing by proper choice of ϕ

• additional transverse focussing needed (in drifttubes)

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Widerö linear accelerator (1928)

• acceleration in gaps E qV sin∆ = ϕ

• shielding by drift tubes during polarity reversal (1/2 TRF)

• length of drift tube i RF RFi

iqV sinl

2 c 2m

β λ λ ϕ= = (v <<c)

• phase (axial) focussing by proper choice of ϕ

• additional transverse focussing needed (in drifttubes)

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RF linear accelerator: further developments

• development of accelerating cavities based on waveguide principle• higher energygain,

higher frequency

• superconducting cavities

• also used in large

synchrotrons

• mainly injectors for synchrotrons

• largest linac: 3 km electron LINAC Stanford (USA)

http://www2.slac.stanford.edu/vvc/

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induction linear accelerator

• current pulse in winding around ferromagnetic core

C S

dd d

t dt

∂∇ × = − = −

∂ ∫ ∫B

E E l B si i�

• pulses in phase with beam

• beam pulses typical ∆t = 50 ns I = 2 kA

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circular accelerators

• betatron

• cyclotron

• synchro-cyclotron

• isochronous cyclotron

• synchrotron

• storage ring

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betatron (1923)

• Widerö design “ray transformer”

• beam secondary winding of transformer

• beam guided in circular orbit with separate magnet

• C S

dd d

t dt

∂∇ × = − = −

∂ ∫ ∫B

E E l B si i�

• stable orbit accguide

2

B dad B 1 d

dt 2 dt r=

π

∫

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betatron (1941)

• Kerst : working prototype

• breakthrough: orbit stabilisation with non-homogeneous field

• only used for electrons

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orbit stabilisation

• F = qv×B � Fz = q(vrBθ-vθBr)

• homogeneous field: Br = Bθ = 0 � Fz = 0

�vz ≠ 0 � spiral motion around z-axis, no stability

• azimuthally symmetric field: Bθ = 0

• Bz decreases with radius � Br towards center

Fz towards midplane � particle oscillates around midplane

� vertical stability, “weak” focussing

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betatron

Kerst with first and largest betatron

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cyclotron (1931)

• Lawrence and Livingston

• inspired by Widerö linac: “wound-up” linac

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cyclotron

• vacuum chamber first cyclotron

10 cm

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cyclotron

• accelerate with RF electric field with νRF = νorb

• theory: homogeneous field � no vertical orbit stability

� large beamlosses

• pratice: due to fringefield effects Bz decreases with radius

�marginal vertical orbit stability

• gradual loss of synchronism: energy limit

• homogenous magnetic field isochronous (non-relativistic)2

orb

mv mv BqqvB R

R Bq 2 m= = ν =

π

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• rapid loss of synchronism: energy limit ~ 20 MeV protons

• only useful for ions (mp/me = 1836)

• two solutions

• vary νRF periodically: pulsed acceleration, synchro-cyclotron

requires phase focussing (McMillan, Veksler; 1945)

• restore isochronism Bz(r) = γ(r) Bz(0): isochronous cyclotron

Bz increases with radius � no vertical stabililty

introduce sectors in magnetic field (Thomas; 1938):

“strong” focussing

cyclotron

2

orb

mv mv BqqvB R f(R)

R Bq 2 m

γ γ= = ν = =

πγ• relativistic effects

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cyclotron

• modern isochronous cyclotron at KVI

• superconducting coils �high field, compact machine

• 200 MeV protons

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“particle” physics around 1935

• atomic model complete:

• nucleus consists of protons and neutrons

• electrons bound in Coulomb-field nucleus

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“particle” physics around 1935

• atomic model complete:

• nucleus consists of protons and neutrons

• electrons bound in Coulomb-field nucleus

• basic theory for α-, β- and γ-emission by nuclei

• “strong” nucleon - nucleon interaction established

• quantum physics: interaction via particle exchange

• EM-interaction: infinite range � massless photons

• “strong” interaction: short range � massive particle

Heisenberg uncertainty principle: mc2 ≥ 100 MeV

� high energy accelerator needed for production

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synchrotron (1950)

• higher energy: larger radius

• 200 MeV proton Bρ = 2.2 Tm

• 1000 MeV proton Bρ = 5.7 Tm� for synchro-cyclotron-like accelerators huge magnets

• alternative approach

• acceleration in severalstages

• constant radius orbit

• magnetic field and νRF

vary during acceleration;pulsed operation(cf. synchro-cyclotron)

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synchrotron

• requires phase focussing

• transverse focussing

• “weak” focussing: dipole magnets with radially decreasing Bz

• needs large magnet gaps

• “strong” focussing

• combined function

dipole magnets with alternating strong radial fieldgradient

no possibility for fine-tuning

• separated function

homogeneous dipole magnets for bending

quadrupole magnets for focussing

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storage / collider ring

( )2 2 4

cm beamE 2 E mc +m c=

• development Standard Model: zoo of particles up to Higgs

• very heavy, exotic particles (e.g. mass W±, Z0 ~ 80 - 90 GeV)

• fixed target: energy available for reaction

• investment explodes

• colliding beams Ecm = 2 (Ebeam + mc2)

• low density compared to fixed target � low event rate

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collider ring

• two beams in opposite direction

• electrons + positrons (LEP)

• protons + protons (LHC, under construction at CERN)

• experiment performed in ring

interaction zones with very small beamsize

• colliding protons with Ekin = 100 GeV: Ecm = 200 GeV

fixed target Ecm = 200 GeV: Ekin = 20000 GeV

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storage ring / collider ring

http://hands-on-cern.physto.se

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LHC: largest storage/collider ring

• circumference 27 km

• proton energy 7000 GeV

http://lhc-machine-outreach.web.cern.ch/lhc-machine-outreach/

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Livingston chart: equivalent energy vs. time

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presentations and excercises

• presentations and excercises available in PDF-format on

http:\\www.kvi.nl\~brandenburg

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next lecture

• reading

• Wilson: chapter 2 Transverse motion

• CERN Accelerator School 1992, CERN report 94-01

chapter 2 Basic course on accelerator optics

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Greinacher cascade

combination of two circuits is a voltage doubler + rectifier

stacking n circuits leads voltage multiplication with factor n

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pulse generator

• capacitors charged in parallel

• triggering spark gaps: all capacitors in series Uout = n U in

• state of the art performance

• n = 100

• Uout = 6 MV

• Iout = 500 kA

• pulse duration 40 ns

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orbit stability (Widerö 1928, Steenbeck 1935, Kerst 1941)

• field in vicinity of reference orbit at radius R

• restoring force ( ) ( )2

r y

mvF r qvB r

r

γ= −

• orbit deviation x : x

r R x R 1R

= + = +

• Taylor expansion in first order

• 1 1 x

1r R R

= −

• ( ) ( )( )

( )( )

( )y

y

y

y

y y

B R xB r B R x B R 1

B RR

Bx RR x

∂= + = +

∂ ∂

∂

• ( ) ( )y y nx

B r B R 1R

= +

• ( ) ( )2

r y

mv x xF r 1 qvB R 1 n

R R R

γ = − − −

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orbit stability

• at reference orbit Fr(R) = 0 : ( )2

y

mvevB R

R

γ=

• ( ) ( )2 2

r 2

mv x d xF x 1 n m

R R dt

γ= − − = γ

• particle oscillates around reference orbit with x 0 1 nω = ω −

for n > 1 particle orbit becomes unstable (imaginary ωx)

• nomenclatureoscillation around reference orbit: betatron oscillations

x x x orbQ ,ν = ω ω : betatron frequency, number of betatron

period per turn

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orbit stability

• for vertical stability similar reasoning

• ( )y xF z qvB=

• yx

BB0

y x

∂∂∇ × = =

∂ ∂B

• in first order ( ) ( ) ( )2

x y y

y v yB y nB R F y mn

R R R= − = −γ

• particle oscillates around reference orbit with y 0 nω = ω

for n< 0 particle orbit becomes unstable (imaginary ωy)

• simultaneous radial and axial stability 0 < n < 1:

“weak” focussing