R. Bartolini, John Adams Institute, 3 May 20131/29 Lecture 6: beam optics in Linacs LINAC overview Acceleration Focussing Compression

R. Bartolini, John Adams Institute, 3 May 2013 1/29

Lecture 6: beam optics in Linacs

LINAC overview

Acceleration

Focussing

Compression

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LINAC overviewA LINAC is an accelerator consisting of several subsystems

Gun (particle source)

Accelerating section (and RF sources)

Magnetic system (focussing and steering)

Diagnostics – Vacuum – etc

Depending on the application a LINAC might have

bunch compression system (radiation sources, FELs, colliders)

beam delivery systems (medical linacs, colliders)

R. Bartolini, John Adams Institute, 3 May 2013

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A 100 MeV LINAC (at Diamond Light Source)


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AccelerationAcceleration is achieved with RF cavities, using e.m. modes with the electric field pointing in the longitudinal direction (direction of motion of the charged particle)

The RF electric field can be provided by travelling wave structure or standing wave structure

Ez

z

c

Travelling wave: the bunch sees a constant electric field

Ez=E0 cos()

Ez

z

c c2

ct

Standing wave: the bunch sees a varying electric field

Ez=E0 cos(t+)sin(kz)


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Travelling wave and standing wave structuresThe wave velocity and the particle velocity have to be equal hence we need a disk loaded structure to slow down the phase velocity of the electric field

To achieve synchronism vp< c

Slow down wave using irises.

In a standing wave structure the electromagnetic field is the sum of two travelling wave structure running in opposite directions.

Only the forward travelling wave takes part in the acceleration process


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Beam dynamics during acceleration (I)

Consider a particle moving in the electric field of a travelling wave

)kztcos(EE 0z k

v fwith a phase velocity

The equations used to describe the motion in the longitudinal plane are

)kztcos(eEdt

dp0

z )kztcos(zeEdt

d0

ss0s cosveE

dt

d

Define the synchronous particle as

For the generic particle, using as coordinates the deviation from the energy and time from the synchronous particle, we have

Ws uzz s

uv

tkzs

s and changing variable to


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Beam dynamics during acceleration (II)

We get the system of equations

s0 coscoseEds

dW

23s

3s mc

W

cds

d

These describe the usual RF bucket in the longitudinal phase space (, W)

We assumed here that the acceleration is adiabatic i.e. ds/ds 0. If this in not true, numerical integration shows that the RF bucket gets distorted into a “golf club”


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RF technology

Usual operating frequencies for RF cavities for Linear accelerators are

Warm cavities gradient repetition rate

S-band (3GHz) 15-25 MV/m 50-300 Hz

C-band (5-6 GHz) 30-40 MV/m <100 Hz

X-band (12 GHz) 100 MV/m <100 Hz

Superconducting cavities

L band (1.3 GHz) < 35 MV/m up to CW

The main RF parameters associated to the RF cavity, such as shunt impedance quality factor will be discussed in the Lecture 10 on RF.


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Particle sources and Gun

Electrons

Thermionic gun

Photocathode guns

Protons and H-

plasma discharge

Penning ion sources


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Thermionic gun (I)Electrons are generated by thermionic emission from the cathode and accelerated across a high voltage gap to the anode. A grid between anode and cathode can be pulsed to generate a train of pulses suitable for RF acceleration

cathode assemblyBaO/CeO-impregnated tungsten disc is heated

and electrons are emitted


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Thermionic gun (II)Electrons are generated by thermionic emission tend to repel therefore an advance e.m. design is envisaged to control the beam dynamics and reduce the emittance of the beam.

This requires solving Laplace equation for the potential of the e.m. field in the given

geometry


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Photocathode guns (I)

One and half cell RF photocathode gunElectrons are generated with a laser field by photoelectric effect

High voltage at the cathode is delivered by the RF structure

50-60 MV/m in L-band100-140 MV/m in S-band

Higher gradients are useful to accelerate the particle fast and reduce the effect of space charge(scales as 1/E2)

Electron pulses can be made short (as the laser pulse - few ps)


Photocathode guns

BNL /SLAC/UCLA RF gun

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Photocathode guns

Photoemission with a pulsed laser


Photocathode guns

.. and RF acceleration


Photocathode guns



Photocathode guns


The emittance and the energy spread are determined by the laser parameters and the properties of the cathode material.

The emittance can be tens of times better than in a thermionic guns (< 1 m)


Photocathode guns

RF signal distribution for an RF photocathode gun (5-cells )


Focussing system in long LINACsIn a long linac we need a magnetic channel to keep the beam focussed in the transverse dimension.

This can be accomplished with a FODO lattice

or with a doublet structure

e.g. SCSS Japan

19/290 20 40 60 80 100 120 140 160 180 200-10

0

10

20

30

40

50

60

70

80

90

S (m)

Am

plitud

e

Twiss Parameters

Beta X (m)

Beta Y (m)Dispersion (cm)


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A doublet channel

10

L1

1f/1

01

10

d1

1f/1

01

10

L1M

In a FODO channel the RF cavities are placed in the drift sections.

To create longer straight section a double (or triplet) channel is envisaged.

A doublet channel is a series of pairs of quadrupoles F and D with long drift sections between the pairs. the RF cavities are placed in the drift sections

short drift dlong drift 2L

We can compute in the usual way the phase advance and the optics function for the basic cell, assuming it is repeated periodically

22211

f

dL1

2

mmcos

1x

2L2

1

sin2

mm 2211x

2

12

xx2

)x2(Ld

sin

m

2f

dLx and putting

The focussing effect of the cavity is usually added in refined calculations

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Beam dynamics issues: wakefieldsThe interaction of the charged beam with the RF cavity and the vacuum chamber in general generate e.m. fields which act back on the bunch itself

Dtb

In the RF cavity these fields can build up resonantly and disrupt the bunch itself in the so called single beam break up or multi bunch break up

More on lecture 8 on instabilities

t0 t1 t2 t3 t4 t5t6


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Bunch Compression (I)

In many applications the length of the bunch generated even by a photo-injector (few ps) is too long. Tens of fs might be required.

The bunch length needs to be shortened. This is usually achieved with a magnetic compression system.

A beam transport line made of four equal dipole with opposite polarity is used to compress the bunch. In this chicane the time of flight (or path length) is different for different energies

This effect can be used to compress the bunch length

blue = low energyred = high energy

The time of flight of the high energy particle is smaller(v c ...but it travel less !)


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Bunch compression (II)To exploit the dependence of the time of flight (or path length) for different energies we need to introduce an energy-time correlation in the bunch.

This is done using the electric field of an RF cavity with as suitable timing


An energy chirp is required for the compression to work

The high energy particle at the tail travels less and catches up the synchronous particle. The net result is a the compression of the bunch

headtail

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Bunch compression (III)Bunch compression can be computed analytically. Inside the RF cavity the energy changes with the position z0 as

0RF0

RF01

01

zk2

cosE

eV

zz

In the linear approximation in (z, )

0

0

651

1 z

1R

01z

RFRF

RF kE

eVR sin

065

In the chicane the coordinate changes as

12

315666

2156615612

UTRzz

In the linear approximation

1

156

2

2

10

1

zRz


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Bunch compression (IV)The full transformation is, as usual, the composition of the matrices of each, element and reads

1

1

65

565665

0

0

2

2

R

RRRzzMM

Since the transformation is symplectic (i.e. area preserving Liouville theorem) the longitudinal emittance is conserved

222 zz

For a given value of R65 (energy chirp induced), the best compression that can be achieved is

C|RR1| 0

02

zz5665z

C is the compression factor. It can be a large number!

The minimum reachable bunch length is limited to the product of the energy spread times R56


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Bunch compression (V)Further limitations to the achievable compression comes from the high current effect that we have neglected in the linear approximations.

These are longitudinal space charge, wakefields and coherent synchrotron radiation (CSR) – more on lecture 7

When taken into account, these effects can produce serious degradation of the beam qualities, e.g in simulations

10 e- bunches with different

compression C superimposed

under compressed

over compressed

Longitudinal phase space of a disrupted beam


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Linear Colliders

ILC (International Linear Collider)

L-band SC cavities

30 MV/m

500 GeV (36 km overall length)

CLIC (Compact Linear Collider)

X-band NC cavities

100 MV/m

3 TeV (48 km overall length)

Linear accelerators are at the heart of the next generation of linear colliders


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Fourth generation light sources

Linear accelerators are at the heart of the next generation of synchrotron radiation sources, e.g. the UK New Light Source project was based on

photoinjector

BC1BC2 BC3

laser heater accelerating modules

collimation

diagnosticsspreader

FELs

IR/THzundulators

experimental stations

High brightness electron gun operating (initially) at 1 kHz

2.25 GeV SC CW linac L- band

to feed 3 FELS covering the photon energy range 50 eV – 1 keV


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Bibliography

M. Conte, W.W. MacKay,

The physics of particle accelerators, World Scientific (1991)

P. Lapostolle

Theorie des Accelerateurs Lineaires, CERN 87-10, (1987)

J. Le Duff

Dynamics and Acceleration in linear structures, CERN 85-19, (1985)

T.P. Wangler

RF Linear Accelerators, Wiley, (2008)


Syllabus and slides

• Lecture 1: Overview and history of Particle accelerators (EW)• Lecture 2: Beam optics I (transverse) (EW)• Lecture 3: Beam optics II (longitudinal) (EW)• Lecture 4: Liouville's theorem and Emittance (RB)• Lecture 5: Beam Optics and Imperfections (RB)• Lecture 6: Beam Optics in linac (Compression) (RB)• Lecture 7: Synchrotron radiation (RB)• Lecture 8: Beam instabilities (RB)• Lecture 9: Space charge (RB)• Lecture 10: RF (ET)• Lecture 11: Beam diagnostics (ET)• Lecture 12: Accelerator Applications (Particle Physics) (ET)• Visit of Diamond Light Source/ ISIS / (some hospital if possible)

The slides of the lectures are available at

http://www.adams-institute.ac.uk/training

Dr. Riccardo Bartolini (DWB room 622) [email protected]

Documents

R. Bartolini, John Adams Institute, 3 May 20131/29 Lecture 6: beam optics in Linacs LINAC overview Acceleration Focussing Compression