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6. Injection into and ejection from circular machines

PREACCELERATOR

ACCUMULATORRING

PARTICLESOURCE

INJECTION 1EJECTION

INJE

CTI

ON

2

SYNCHROTRON

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The main problem for beam injection : Liouville

22 daAinj

ppzyyxxV

Injected beam

Beam after first circulation

Vaccum chamber

d

Deflection magnet (dipole)Injected beam

Acceptanced

At the entrance of the beam into the Vaccum chamber the distance a of the injected beam is larger than the aperture d of the Vaccuum chamber. Therefore the lower limit of the acceptance has to be:

It is impossible to inject particles into an already occupied phase space volumewithout loosing the old or new ones:

22 daAinj

ppzyyxxV

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Longitudinal phase space stacking

Free phase space volume

Circulating beam

z

Injected beam

z z

z

z

The number of available phase space cells is then given by :vL

LLn

z

The stacking of several beam bunches into the longitudinal phase space of the circular machine is typically used for protons and heavy ions.

The kicker then has to produce rectangular pulses of z length and a rise time much faster than the gap between the bunches in the ring.

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Transversal phase space stacking

Injected beamSeptum

Kicker 1 Kicker 2Accumulated beam

2. Injection 3. Injection

4. Injection 5. Injection 6. Injection

1. Injection

For short rings a longitudinal stacking is problematic and therefore a transversal stacking in phase space is used. This is possible because usually the beam emittance delivered by the accelerator is much smaller than the acceptance of the ring. A system of 3 dipole magnets (septum and kicker) is used together with the movement of the centre of gravity of the beam due to betatron oscillations to “paint” the phase space.

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Non Liouvillian stacking – charge exchange injection

Circulating beam

Stripping foil

Deflecting dipole

Injected beam

Deflecting dipole

To avoid the problems at injection point and to increase the availble current in the ring a charge exchange injection is used. Therefore Liouville is not valid and no

longer a limiting factor. This scheme is usually used with proton drivers accelerating H- and stripping it to H+ using foils or lasers.

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Electron stacking using radiation damping

Injected beamSeptum Accumulated beam

Kicker 1 Kicker 2

Accumulated beam

Acceptance7

Injected beam

x

For light particles like electrons radiation damping can be used to avoid problems with Liouville. The setup is similar to normal transverse phase space stacking. With a kicker the accumulated beam is shifted in phase space in a way that the injected beam is within the acceptance. The acceptance is shifted back then and the injected beam is captured. Due to radiation damping the amplitude of the betatron oszillation is reduced and the new injected particles move towards the center of the acceptance.

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Fast dipole magnets (kicker) for beam injection

0)(

4

221

220

0

22

x

y

B

IbabB

BrrdBI

bar

0)(

4

221

220

0

22

x

y

B

IbabB

BrrdBI

bar

Fast switch

(Thyratron, MOS-FET)

R

Kicker dipole

C

I(t)

U0Beam

0)(

4

221

220

0

22

x

y

B

IbabB

BrrdBI

bar

.max0

22

208

LIU

LC

balb

I

fdBn

IUL

kick

A

To create the required pulsed (typ. 1 s) magnetic dipole fields a low inductivity dipole (no iron) is aroused by the discharge current of a capacity trough a fast switch.

Typical values are B~0.05-0.1 T, I ~1-5 kA , L ~ 1-10 H , C ~ 10-100 nF , U ~10-50 kV

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Shielding of fringe field to reduce influence on circulating beam

Injected beam

Current bar

Coil

(DC&pulsedCoil (pulsed)

Eddy current shield

pulsed current

Circulating beam

To prevent or reduce the influence of the magnetic dipole field on the circulating beam two main techniques are used. One is the use of current bars at the edge of the dipole. The current intensity is chosen to reduce the fringe fields at orbit to zero. This is suitable for DC and pulsed operation. Often only a eddy current shield is used to reduce the influence of the fringe fields (pulsed mode operation only). Those shielded dipole magnets are then called septum.