AP activity at DIAMOND Light Source. R. Bartolini DIAMOND Light Source

AP activity at DIAMOND Light Source AP activity at DIAMOND Light Source

R. Bartolini

DIAMOND Light Source

DIAMOND Layout DIAMOND Layout

Main parameters:

100 MeV Linac

3 GeV Booster (158.4 m)

3 GeV Storage Ring (561.6 m) 24 cell DBA lattice 2 + 1 SC RF cavities 18 straight for ID (5 m) 6 long straights (8 m)

Commissioning end 2006

DIAMOND AP Team DIAMOND AP Team

Group Leader :

S. Smith (ASTeC, Daresbury) Accelerator Physicists:

R. Bartolini (DLS) D. Holder (ASTeC) J. Jones (ASTeC) I. Martin (DLS) B. Singh (DLS) J. Varley (ASTeC) N. Wyles (ASTeC)

• AP Theory

• Design finalization

• Assist Commissioning

• Numerical Codes management and High Level Software

DIAMOND AP Activity DIAMOND AP Activity

• AP activity:

linear optic

non linear optic (Dynamic Aperture optimization) closed orbit corrections (and feedback system) lifetime studies

collective effects (and feedback systems) effects of the Insertion Devices

Injection (extraction) schemes and transfer lines design High Level Software

• Machine commissioning

define strategies for commissioning (accelerators, IDs, feedbacks) definition of intermediate targets

achieving low emittance in storage ring at desing current (2.7 nm, 500 mA)

Estimate of Linear coupling with expected errors on DIAMOND Estimate of Linear coupling with expected errors on DIAMOND

Error Type RMS

Quadrupole Transverse Displacement 0.1 mm Sextupole Transverse Displacement 0.1 mm Dipole Transverse Displacement 0.05 mm Dipole Longitudinal Displacement 0.05 mm

Dipole Field Error 0.1 %

Quadrupole Roll Error 0.2 mrad

Dipole Roll Error 0.2 mrad

Assumed alignment errors

for the DIAMOND storage ring. Emittance ratio on 50 seeds

x y

ε χ = ε

Emittance ratio (CO corrected)

0 5 10 15 20 25

0.00 0.01 0.02 0.02 0.03 0.04 0.05 0.05 0.06 0.07 Emittance ratio χ

# seeds

χ average = 0.015 χ r.m.s. = 0.013

Computation done with BETA – LNS courtesy by J. Payet – CEA

Linear Coupling correction strategies

• Compensation of sum and difference resonances is not effective for random distributed errors at the working point

Qx = 27.22 Qz = 12.36 Qx ± Qz = p

∫ ^⎜ _⎝ ^{⎛ ⎟} _⎠ ^{⎞ ⎜} _⎝ ^{⎛ ⎟} _⎠ ^⎞

=

R

R ips s W s W z i

x

p a s e ds

h ^{x z}

π

β β

π

2

0

)) ( ) ( 2 (

/ 2 1

/ 1 2

1001

( ) 2 2

2 1

G. Guignard (1976)

∑

−∞

=

+ +

=

p x z

p

p Q

Q

s₁₀₀₁

( 0 )

• Compensation schemes based on cross response matrix

analysis: BETA (LOCO is also currently evaluated).

Linear Coupling Studies (3) Linear Coupling Studies (3)

Emittance ratio χ aver. r.m.s

Uncorrected ^{0.8 1.4}

CO correction ^{0.015 0.013} Skew Quads ^{0.0008 0.0006} V Dispersion ^{0.0002 0.0005}

) (

) (

correction after

correction before

of ratio

χ χ = χ

is a measure of the effectivness of the correction

Emittance ratio correction (with SQ correction)

1 10 100 1000 10000

0.001 0.01 0.1 1

emittance ratio χ (CO corrected) ratio ofχ's

Emittance ratio correction (with DISP. correction)

1 10 100 1000 10000

0.001 0.01 0.1 1

emittance ratio χ (CO corrected) ratio ofχ's

Linear Coupling Studies (4) Linear Coupling Studies (4)

Recently MATLAB-AT and LOCO were considered (A. Terebilo, J. Safranek)

A fully coupled analysis run with LOCO for DIAMOND would

require 2 GByte RAM (168 BPM; 168 Correctors)

Touschek Lifetime Studies (1) Touschek Lifetime Studies (1)

Previous tracking studies with physical aperture gave:

• RF lifetime = 45.0 hr

• Touschek lifetime = 39.4 hr

[for operation with no IDs (1.05 MeV/turn loss), 2.6 MV peak voltage (4

% RF momentum aperture, φ_s = 157 deg ), 300 mA with a 2/3 fill (624 bunches)]

Operation with IDs reduces the momentum aperture to less than 4

%, so a higher voltage of 3.3 MV peak voltage was considered in recent studies:

3.3 MV peak voltage gives:

• 4.9 % RF aperture without IDs (1.05 MeV/turn, φ _s = 161 deg)

• 4.6 % RF aperture with 7 IDs (1.25 MeV/turn, φ _s = 157 deg)

• 3.7 % RF aperture with 22 IDs (1.75 MeV/turn , φ _s = 148 deg)

Touschek Lifetime Studies (2) Touschek Lifetime Studies (2)

Recent tracking studies gave:

• RF + engineering aperture: Touschek lifetime = 47.1 h

• NL dispersion Touschek lifetime = 44.6 h

• optic functions vs δ Touschek lifetime = 42.7 h

• NL synchrotron motion Touschek lifetime = 28.6 h [for operation with 3.3 MV peak voltage, 300 mA with a 2/3 filling]

-10 -8 -6 -4 -2 0 2 4 6 8 10

0 20 40 60 80

(m)

εacc (%) and τ *10-1 (h) Lifetime and

momentum aperture in a superperiod

Tracking studies performed with BETA–LNS (courtesy J. Payet, CEA)

Touschek Lifetime Studies (3) Touschek Lifetime Studies (3)

A 3^rd harmonic RF cavity option is currently analysed:

Tracking studies

show negligible effect of second order momentum compaction

on bunch length

3rd HC bunch lengthening

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

0 0.2 0.4 0.6 0.8 1 1.2

Voltage (MV)

σz /σz0

Collective Effects studies for DIAMOND Collective Effects studies for DIAMOND

• Single bunch longitudinal – MI (BBI)

• Single bunch transverse – TMCI (BBI)

• Multi-bunch transverse – RW

• HOM …

• Impedance estimates

• Analytical estimates of current threshold

• Macroparticle Tracking

• Mode Coupling Analysis

Boussard criterion provides analytical estimates on the current threshold:

) ( 2 2

sin

sin ⁰ ₀ ⁰

1 ind n

e n

e s

n s s

s n

n T T r V z

c z U

qV − + +

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡ ⎟⎟−

⎠

⎜⎜ ⎞

⎝

⎛ −

+

+ = ε σ τ

φ τ β

φ ω ε

ε _ε

n c

n

n z cT

z ₊₁ = −α ₀ ⋅ε A n

n Z

I µ

ω ) (

7 . 43

0

||

0 0 <

∑

−

=

k

k n s

n

ind W z z

U z e

V ( ) ( )

Non-linear 2

synchrotron motion

RLC resonator wakefields Radiation damping

Quantum noise

using a BBI

model:

( ) = 1 Ω

||

0

||

n n

Z ω

mA

operation with a 2/3 fill

one turn map

The analytical estimates were compared with tracking studies with

a BB impedance (RLC resonator with low Q):

BB impedance (RLC resonator):

0 1 2 3 4 5 6 7 8

0 10 20 30 40

BB Resonator Frequency (GHz)

Threshold Current (mA)

⎟⎟ ⎠

⎜⎜ ⎞

⎝

⎛ −

+

=

c

iQ

Z R

ω ω ω

ω ω

1 )

(

to |Z|/ n = 1.8 Ω at the beam pipe cut-off frequency

0.5 0.75 1 1.25 1.5 1.75 2

0 0.5 1 1.5 2 2.5 3 3.5

I (mA) σz/σz0 and

σ

e/σe0

Bunch length

Energy spread

Gives a current threshold (~1 mA) suitable for operation at

300 mA with a 2/3 fill

TMCI studies with MOSES

BBI model Q = 1, Rs = 1 MΩ/m Varying the central frequency f_res

To be included:

betatron frequency spread bunch lenghtening

more general impedance models