Download ppt - Comparison of single bunch simulations and measurements at the Diamond Light Source

Comparison of single bunch simulations and Comparison of single bunch simulations and measurements at the Diamond Light Sourcemeasurements at the Diamond Light Source

R. Bartolini

Diamond Light Sourceand

John Adams Institute, University of Oxford

Thanks to G. Cinque, I. Martin, J. Puntree, G. Rehm --- (WIP)

TWIICESOLEIL, 17th January 2014

OutlineOutline

• Introduction

• Review of measurements

• Single bunch tracking code – extension to sbtrack (RN)

• Comparison simulations-measurements

• Conclusions and open questions


MotivationsMotivations

Diamond operates

low alpha for X-ray and THz users few weeks – incompatible with normal user operationand single bunch in camshaft modeseveral weeks per year – compatible with normal operation

There is interest in understanding and optimising the performance of the ring for these operating modes

THz users operate above the bursting threshold with negative alpha

THz detector development (P. Karataev, G. Rehm, et al.)

“Academic” understanding the dynamics above thresholds


Low alpha latticeLow alpha lattice


0 10 20 30 40 50 60 70 80 90

0

10

20

30

S (m)

Bet

a F

unct

ion

(m)

x

y

x

0 10 20 30 40 50 60 70 80 90

0

0.2

Dis

pers

ion

(m)

0 10 20 30 40 50 60 70 80 90

0

20

S (m)

Bet

a F

unct

ion

(m)

x

y

x

0 10 20 30 40 50 60 70 80 90

0

0.2

0.4

Dis

pers

ion

(m)

Parameter Standard User Lattice

Low Alpha Lattice

Emittance 2.7nm.rad 4.4nm.rad

α1 1.7×10-4 -1×10-5

α2 (with sext.) few×10-3 few×10-5

Natural bunch length (3MV) 10.0ps 2.4ps

Synchrotron frequency (3MV) 2608Hz 629Hz

DiagnosticsDiagnostics


60-90 GHz 220-300 GHz

Sensitivity 28 V/W 1500 V/W 28 V/W 1500 V/W

Response Time <250 ps ~1 μs <250 ps ~1 μs

Measurement Bandwidth >4 GHz ~1 MHz >4 GHz ~1 MHz

Pre-amp input impedance 50 Ω 100 kΩ 50 Ω 100 kΩ

Pre-amp gain 60 dB 40 dB 60 dB 40 dB

60-90GHz SBD

220-300GHz SBD

•THz Schottky diode detectors from a dedicated dipole beamport

• B22 beamline (FTIR)• Streak camera• Orbit data in dispersive BPMs

B22 beamline (FTIR)B22 beamline (FTIR)


CSR amplification factor for short pulse THz mode (above the bursting threshold)CSR gain > 1000 up to 100 cm–1

CSR gain ~200,000

CSR gain ~1000

Courtesy G. Cinque

Characteristics of THz emissionCharacteristics of THz emission


105

106

100

101

102

bunc

h cu

rren

t (

A)

(fRF

frev

VRF

cos(s)/1/3)3/7

0

measured

shielded CSRfree-space CSR

α1 > 03

7

03

120

2 cos8

sRFrevRFth

thresh

Vff

cZI

856.043456.7 31

thBane, Cai, Stupakov, PRST-AB 13, 104402 (2010)

Wuestefeld et al., IPAC 2010, p. 2504 (2010)

Shielded CSR theory:

Cai, IPAC 2011, p. 3774, (2011)

Ries et al., IPAC 2012, p. 3030 (2012)

30 h

2

2

02.02

25.0exp385.034.05.0

thFrom VFP simulations:

From free-space CSR theory:

Instability thresholds and quadratic dependence with current in good agreement with theory:

Measurement of time structure of THz pulsesMeasurement of time structure of THz pulses


Instability threshold

α1 = +1×10-5 VRF = 3.4MVfs0 = 675HzIbunch = 8.5µA








Positive alpha



α1 = -1×10-5 VRF = 3.4MVfs0 = 675HzIbunch = 8.3µA







Instability threshold

Bursting threshold

Negative alpha

frequency (Hz)

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Many different operating conditions were investigated varying alpha, voltage, fill pattern, detector BW,

showing a dauntingly rich phenomenology

frequency (Hz)

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= -0.6 10–5

= 1.4 10–

5 = -1.410–5

frequency (Hz)

bunc

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frequency (Hz)

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VRF = 3.4 MV VRF = 4 MV

frequency (Hz)

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VRF = 4 MVVRF = 2.2 MV VRF = 2.2 MV

frequency (Hz)

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VRF = 4 MV

frequency (Hz)

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ps)

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= 0.6 10–5

VRF = 4 MV

frequency (Hz)

bunc

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VRF = 3.4 MV

Equation of motion (I)Equation of motion (I)

Particles move in the focussing fields of

quads (transverse motion)cavities (longitudinal motion)

The one turn map for each single particle reads

sn

RFs

RFn1n sinz

csin

E

V

1n0cn1n cTzz

nj

j

0

ny0

1nj

j

'y

y)

E1(QM

'y

y

Transverse

Longitudinal

Includes RF nonlinear potential, chromaticity (and simplecticity)


Equation of motion (II)Equation of motion (II)

Radiation damping and diffusion for electrons

Transverse

Longitudinal

RT2

'yT2

'y'yy

00'y1n

y

01n1n

RT

2T2

s

001n

s

01n1n

These terms guarantee that when tracking a distribution of macroparticles the equilibrium distribution is has the correct equilibrium emittances, beam sizes, divergences, bunch length and energy spread.


Equation of motion (III)Equation of motion (III)

Wakefields are generated via the interaction of the beam with the vacuum pipe, by synchrotron radiation and by direct space charge

Transverse

Longitudinal

iz

||0

1n1n )'zz(W)'z('dzC

Nr

iz

p0

1n1n )'zz(W)'z(D)'z('dzC

Nr'y'y

The effect of the wakefield on the single particle motion is lumped in a kick added to the one turn map (both transverse and longitudinal)The kick is computed binning the longitudinal distribution of the electrons and computing W and W|| from analytical formula or numerical codes


Wakefields implementedWakefields implemented

- CSR impedance with shielding

Simulating the THz pulses as detected by the SBDSimulating the THz pulses as detected by the SBD

The code is capable of

• reproducing the THz pulse as detected by the SBD within the BW of the detector• producing the spectrogrammes (FT of the time signals) vs current as measured

It has been used to replicate

• bunch lengthening curve• centre of charge shift• THz spectrum

mainly by using

• CSR wake• BBR impedance fit (single resonance, R,L,C)• purely inductive impedance L


α1=-1.0x10-5 / VRF = 3.4 MV

The CSR wake was defined using the machine parameter for bending radius and height of the pipe – no fit


CSR only• generates a fine structure in the THz spectrum• missing transition with current in THz spectrum• bunch lengthening off

frequency (Hz)

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measurements

simulations

α1=-1.0x10-5 / VRF = 3.4 MV

Adding a BBI with parameter fitted to achieve the best agreement with the data:e.g. Q = 2; r = 310 GHz; Rs = 41 kOhm


CSR + BBI• generates a fine structure in the THz spectrum• transition with current in THz spectrum present albeit at higher current• bunch lengthening well reproduced

simulations

frequency (Hz)

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measurements

α1=-1.0x10-5 / VRF = 3.4MV

Adding a BBI with parameter fitted to achieve the best agreement with the data:e.g. Q = 1; r = 260 GHz; Rs = 36 kOhm


CSR + BBI• generates a fine structure in the THz spectrum• transition with current in THz spectrum present albeit at higher current• bunch lengthening well reproduced

simulations

frequency (Hz)

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measurements

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Same CSR+BBI, different machine conditionssimulationsMeasurements = -1.410–5 V = 4 MV

frequency (Hz)

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Measurements = 1.010–5 V = 3.4 MV

simulations

2*s= 2 * 677.94 Hz

Bunch current = 50 Amp nturrn = 100,000 / analysed last 80,000 turns

Time signals from SBD

Simulations

spectrum of SBD signal

Measurements = -1.010–5 V = 3.4 MV

No evidence of microbunching – bursting entirely described by the form factorcurrent = 50 microAmps in conditions of stable bursting

Longitudinal dynamics above threshold for negative alpha

Simulations = -1.010–5 V = 3.4 MV 50 uA - bursting

s= 677.94 Hz

FFT of horizontal motion

Time signals from SBD and orbit dataSimulations = -1.010–5 V = 3.4

MV

spectrum of SBD signal

H Orbit PSD (α = -4.5×10-6) above burstingH Orbit PSD (α = -1.0×10-5) below bursting

Conclusions and ongoing workConclusions and ongoing work

Numerical tracking seems to be capable of reproducing the phenomenology of the single bunch dynamics above threshold and the THz emission

Qualitative agreement even with a simple BBR resonator but the results are very sensitive to the details of the impedance model used

Investigation of dynamics above the bursting threshold shows

• numerical evidence that bursting with negative alpha is not due to microbunching• numerical evidence (TBC) that different bursting modes (and transition between bursting mode within the same machine conditions) might be generated by different wakefields becoming unstable

• Code development: real lattice tracking, more macroparticles, ….
