Beam dynamics studies with a 3 harmonic cavity for the ......OUTLINE • Touschek lifetime for ESRF Extremely Brilliant Source (EBS) • bunch lengthening with 3rd harmonic cavity

Beam dynamics studies with a 3rd harmonic cavity for the ESRF EBS

Nicola Carmignani on behalf of the ESRF Beam dynamics and applications group

XXIII European Synchrotron Light Source Workshop 23-25 November 2015

OUTLINE

•  Touschek lifetime for ESRF Extremely Brilliant Source (EBS) •  bunch lengthening with 3rd harmonic cavity

•  bunch lengthening with impedance and 3rd harmonic cavity •  optimum voltage of harmonic cavity

•  effect of 3rd harmonic cavity on dynamic aperture

Page 2 XXIII European Synchrotron Light Source Workshop l 23-25 November 2015 l Nicola Carmignani

FILLING MODES FOR ESRF EBS

The most critical modes for the Touschek lifetime are the ones with high current per bunch (4B and 16B).


filling mode

Itot (mA) number of bunches

Ib (mA)

εy (pm) delivery time

Multi-bunch 200 868 0.23 5 ~70% 16 bunches 90 16 5.6 5 ~25% 4 bunches 40 4 10 5 ~5%

TOUSCHEK LIFETIME WITHOUT HARMONIC CAVITY

Without harmonic cavity, with impedance of 0.35 Ω, the Touschek lifetime for the three modes are:

MB: 20 h 16B: 1.9 h

4B: 1.3 h


0 5 10 15 20 25 30 35 40 45 50

−0.06

−0.04

−0.02

0

0.02

0.04

0.06

s (m)m

om

entu

m a

ccepta

nce

Momentum acceptance

A possible upgrade of the ESRF EBS will be the installation of a third harmonic cavity to increase LT in few bunch mode.

3RD HARMONIC CAVITY: PHASE AND VOLTAGE


Total RF

main RF

3rd harmonic

- 3 - 2 - 1 1 2 3ct Hrad L

- 5

5

V HMVL

total RF

- 0.20 - 0.15 - 0.10 - 0.05 0.05 0.10 0.15ct Hrad L2.58

2.59

2.60

2.61

2.62

V HMVL

The superconductive harmonic cavity will be passive and almost exactly in phase with the beam. We can simulate it with the Accelerator Toolbox (AT). A small detuning with the beam is used to control the voltage of the cavity.

The phase of the HC is not the optimum one and the second derivative of the RF signal is not 0.

With 6.5 MV, the HC voltage is 1.98 MV

EQUILIBRIUM LONGITUDINAL BUNCH DISTRIBUTION


Tracking is done with radiation damping and quantum fluctuation, for 24000 turns and ~105 particles, using AT. The equilibrium distribution is not gaussian and not symmetric, due to the not optimal phase of the HC. The phase of the HC is set at each turn to the bunch phase.

TOUSCHEK EFFECTIVE BUNCH LENGTH (TEBL)

We need to compute the effective bunch length for the Touschek lifetime when the bunch is not gaussian, assuming no correlation between longitudinal and transverse distribution.

In Piwinski formula:

For a gaussian beam:

If g(z) is an arbitrary f(z):


1τ∝ ρ2 (x, y, z)∫ dxdydz

g(z) = 12πσ z

e−z2

2σ z2

g(z)dz∫ = 1

1τ∝

1

8π32σ xσ yσ z

12 πσ z

⇒ f 2 (z)dz∫

σ zTE =1

2 π f 2 (z)dz∫Courtesy of B. Nash

BUNCH LENGTHENING DUE TO IMPEDANCE

The bunch length with impedance of ESRF-EBS is always shorter than in the present machine, due to smaller impedance and shorter zero-current bunch length.


0 2 4 6 8 10Bunch current [mA]

0

2

4

6

8

10

12

14

16

σs [

mm

]

Current machine - 0.7 ΩNew machine - 0.344 Ω

BUNCH LENGTHENING DUE TO IMPEDANCE: AT PASS METHOD


0 5 10 152

4

6

8

10

12

14

16

18

20

Ib (mA)

Tousc

hek

effect

ive b

unch

length

(m

m)

0.1 Ω tracking

0.1 Ω formula

0.3 Ω

0.5 Ω

0.7 Ω

0.9 Ω

1.1 Ω

We want to simulate the bunch lengthening with both the effect of impedance and the effect of the harmonic cavity. S. White has implemented an inductive impedance element for the Accelerator Toolbox, which agrees with Haissinski equation.

3RD HARMONIC CAVITY AND 0.35 Ω IMPEDANCE


−80 −60 −40 −20 0 20 40 600

500

1000

1500

2000

2500

3000

3500

ct (mm)

cha

rge

de

nsi

ty (

a.u

.)

with 3rd hc: TEBL=16.5074mmwithout 3rd hc: TEBL=3.1044mm

−80 −60 −40 −20 0 20 40 600

200

400

600

800

1000

1200

1400

1600

1800

2000

ct (mm)

charg

e d

ensi

ty (

a.u

.)


−80 −60 −40 −20 0 20 40 600

500

1000

1500

2000

2500

ct (mm)

cha

rge

de

nsi

ty (

a.u

.)


−80 −60 −40 −20 0 20 40 600

500

1000

1500

2000

2500

3000

ct (mm)

cha

rge

de

nsi

ty (

a.u

.)


0 current σHC=5.3 σnoHC

MB current σHC=4.1 σnoHC

16B current σHC=2.5 σnoHC

4B current σHC=2.3 σnoHC

IMPEDANCE AND HARMONIC CAVITY

The gain in Touschek effective bunch length with the harmonic cavity is smaller if there is also bunch lengthening due to impedance.


0 5 10 150

5

10

15

20

25

30

35

40

Ib (mA)

Tousc

hek

effect

ive b

unch

length

(m

m)

0.1 Ω without HC

0.1 Ω with HC

0.3 Ω

0.5 Ω

0.7 Ω

0.9 Ω

1.1 Ω

0 0.2 0.4 0.6 0.8 1 1.2 1.42

4

6

8

10

12

14

16

18

20

Harmonic cavity voltage (fraction of optimal voltage)

Tousc

hek

effect

ive b

unch

length

(m

m)

0 0.2 0.4 0.6 0.8 1 1.2 1.44

6

8

10

12

14

16

18

20


Tousc

hek

effect

ive b

unch

length

(m

m)

0 0.2 0.4 0.6 0.8 1 1.2 1.45

10

15

20

25

30


Tousc

hek

effect

ive b

unch

length

(m

m)

0 0.2 0.4 0.6 0.8 1 1.2 1.410

15

20

25

30

35


Tousc

hek

effect

ive b

unch

length

(m

m)

OPTIMUM VOLTAGE OF THE HARMONIC CAVITY


Ib=0.001mA MB current Ib=0.23mA

16B current Ib=5.6mA

4B current Ib=10mA

The nominal voltage for 6.5 MV in the main cavities is 1.98MV.

LONGITUDINAL BUNCH DISTRIBUTION WITH DIFFERENT HC VOLTAGE 16B CURRENT


−30 −20 −10 0 10 20 300

500

1000

1500

2000

250016 B current, .35hm, without HC. TEBL=9.9142 mm

ct (mm)

Charg

e d

ensi

ty (

a.u

.)

−60 −40 −20 0 20 40 600

500

1000

1500

2000

250016 B current, .35hm, 92% of optimum voltage. TEBL=17.5038 mm

ct (mm)

Charg

e d

ensi

ty (

a.u

.)

−80 −60 −40 −20 0 20 40 600

500

1000

1500

200016 B current, .35hm, optimum voltage. TEBL=24.1313 mm

ct (mm)

Charg

e d

ensi

ty (

a.u

.)

−80 −60 −40 −20 0 20 40 600

500

1000

1500

2000

250016 B current, .35hm, 108% of optimum voltage. TEBL=29.1011 mm

ct (mm)

Charg

e d

ensi

ty (

a.u

.)

without HC TEBL=9.9mm

HC with nominal voltage (1.98MV) TEBL=24.1mm

HC with 92% of nominal voltage TEBL=17.5mm

HC with 108% of nominal voltage TEBL=29.1mm

PATH LENGTHENING WITH AMPLITUDE AND CHROMATICITY

On-energy dynamic aperture is substantially smaller if the RF cavity is on. Particles with large amplitude have a longer trajectory and arrive later to the cavity, so they change their energy. The effect can be reduced changing the chromaticity: high chromaticity is beneficial to reduce the path lengthening with amplitude in ESRF EBS lattice.


−15 −10 −5 0 5 10 150

1

2

3

4

5

6

x (mm)

y (m

m)

without RFwith RF

PATH LENGTHENING AND HARMONIC CAVITY


Total RF

main RF

3rd harmonic

- 3 - 2 - 1 1 2 3ct Hrad L

- 5

5

V HMVL

path length change

ΔE with HC

ΔE without HC

EFFECT OF THE HARMONIC CAVITY ON THE DYNAMIC APERTURE


Harmonic cavity 3rd order

D.A. Injection efficiency (120,5) nm (60,5) nm (30,30) nm

Nominal -8.2 +/- 0.4 63.8 85.6 95.4 + Harmonic Cavity -8.7 +/- 0.6 87.8 98.3 99.6

Courtesy of S. Liuzzo

CONCLUSION

•  Touschek lifetime for ESRF EBS can be increased with a harmonic cavity, that increases the Touschek effective bunch length, by a factor

- 2.3 for 4B mode

- 2.5 for 16B mode

- 4.1 for MB mode

•  the gain could be larger if we accept a doubled peak bunch

•  the harmonic cavity increases the on-energy dynamic aperture and the injection efficiency



MANY THANKS FOR YOUR ATTENTION

Documents

Beam dynamics studies with a 3 harmonic cavity for the ......OUTLINE • Touschek lifetime for ESRF Extremely Brilliant Source (EBS) • bunch lengthening with 3rd harmonic cavity