Schottky Signals�& Diagnostics

Manfred Wendt, CERN

with major contributions for Piotr Kowina, GSI

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U.S. Particle Accelerator School 2024

Design and Engineering of Modern beam Diagnostics

Hampton (VA), U.S.A., January 29 – February 2, 2024

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Longitudinal�Schottky band

Background image:

Schoktty signal spectras taken during a �LHC lead ion run on 3^th Dec. 2015, fill #4690.

frequency

time

Lower transverse�Schottky sideband

Upper transverse�Schottky sideband

Page 1

January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Learning Objectives

• Introduction into Schottky signals
• Noise in electronics and Schottky noise
• Schottky signals from one or many charged particles �circulating in a storage ring
• Fourier series representation of the single particle motion
• Unbunched and bunched beams
• Longitudinal and transverse signals
• Hardware and diagnostics examples
• Momentum spread analysis
• Schottky signals for electron cooling
• Single particle detection
• Engineering challenges of a broadband Schottky monitor system
• …on the example of the LHC Schottky monitor

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Outline

• Introduction into Schottky Signals
• Simplified Theory of Schottky Beam Signals
• Longitudinal, unbunched beam
• A few measurement examples
• Transversal, unbunched beam
• RMS emittance measurement setup for ion beams
• Longitudinal, bunched beam
• Transversal, bunched beam
• Example: The LHC Schottky Pickup
• Overview and some details on the hardware
• Examples of beam measurements

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

To set the Scene: Single Particles

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

To set the Scene: Single Particles

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Walter Schottky

• Emission of electrons in a vacuum tube:
• W. Schottky, “Spontaneous current fluctuations in various electrical conductors”, Ann. Phys. 57 (1918) �[original German title:‘Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern’]
• Observation:
• Crackling noise in the headphone while listening the �DC current on a high-gain vacuum tube amplifier
• Physics reason:
• Carriers of final mass and charge �make up the current signal
• The emission of electrons follows �the laws of statistics ⇒ “white” noise

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• Walter Schottky (1886 – 1976)
• German physicist at Universities Jena,�Würzburg & Rostock, and at Siemens
• Investigated electron and ion emissions from surfaces
• Super-heterodyne method
• E.g. radio, spectrum analyzer
• Solid state electronics
• E.g. metal-semiconductor interface, �known as “Schottky” diode
• Had no connection to particle accelerators

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Page 7

28^th Oct. – 7^th Nov. 2019, JAS 2019, Dubna, Russia – Beam Instrumentation & Diagnostics – M. Wendt

Schottky Signals�of charged particles �in a storage ring

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Schottky Signals

rev. time

T₀ = 1/f₀

injection

extraction

Schottky pickup

Ring�accelerator

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Noise Signals from Electronic Components

noise�free

signal only

S/N=4

sample

Typical challenge for “regular”

beam instrumentation:

• Recover a beam signal�in presence of noise
• Stochastic signal contents has no information

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Schottky Noise in the Frequency Domain

• Have a look at this corn field:
• The straws seem to be perfectly randomly distributed over the field
• Similar to white noise

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• The same corn field from a different perspective:
• You clearly see a macrostructure
• Even with some “harmonics”
• Also, a fine microstructure of single corn rows �are visible
• This is an analogy to the analysis of �Schottky beam signals in the frequency domain

courtesy P. Kowina

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Simulation of a Schottky Beam Signal

Time domain

Sample number

7.17 µS

Frequency domain

(FFT)

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Longitudinal Schottky Signals, unbunched (2)

• 2 particles: (e.g. different momentum ⇒ different revolution time)

1

2

3

4

0

Fourier trans. or

spectrum analyzer

0

1

2

3

4

The entire information �is available around�every revolution harmonic

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Longitudinal Schottky Signals, unbunched (3)

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Longitudinal Schottky Signals, unbunched (4)

For ions the �power scales with:�(larger signal levels!)

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Longitudinal Schottky Signals, unbunched (5)

• Signal detection
• Broadband
• Strip-line Pickup
• Capacitive pickup
• Waveguide pickup
• Narrowband
• Resonant cavity
• Tuned capacitive pickup

h=120

h=121

h=122

500 kHz

f_center = 25.4MHz

100dB

Example: �Schottky pickup at �GSI synchrotron (left)

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Operation from unbunched �to bunched beam (right)

injection

f_rev injection

coasting

beam

adiabatic

bunch formation

start

acceleration

f_rev = h ⋅ f _rf

bunched

beam

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Momentum spread analysis

LINAC bunches at injection:

Δf_h ∝ h⋅Δp

courtesy

P. Forck

P. Kowina

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Schottky Application: Electron Cooling

• Principle of operation:
• Momentum transfer by coulomb scattering
• Cooling force results from energy loss in the cold, co-moving electron beam
• Typical cooling times range 0.1 s for low energy highly charged ions, �up to 1000 s for high energy protons

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e.g.: 220 keV electrons�cool 400 MeV/u ions

electron

temperature

k_BT_⊥ ≈ 0.1 eV

k_BT_║ ≈ 0.1 - 1 meV

Example:

Electron cooler at GSI, U_max = 300 kV

hot beam,

(p-bars, ions, protons)

cold �electron beam

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Monitoring the Cooling Process

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Resonant Cavity as Schottky Pickup

f_res = 244.965 MHz

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Transverse Schottky Signal, unbunched (1)

transverse part�“signal” contribution

observed frequency at a�fixed location, e.g BPM

betatron sidebands

amplitude modulation:

left & right sideband

with

at each

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Transverse Schottky Signal, unbunched (2)

• Betatron motion of 2 particles
• BPM displacement signal:

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• Example:

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• Transverse Schottky bands for�a multi particle distribution
• Amplitude modulation of the �longitudinal carrier signal
• Sidebands at
• Unequal width of the sidebands
• The integrated power is constant

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Transverse Schottky Signal, unbunched (3)

long. part

trans.

chromatic coupling

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Transverse Schottky Signal, unbunched (4)

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

RMS Emittance Measurement

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Longitudinal Schottky Signal, bunched (1)

significant bandwidth

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Longitudinal Schottky Signal, bunched (2)

overlap!

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Transverse Schottky Signals, bunched (1)

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Transverse Schottky Signals, bunched (2)

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Page 29

28^th Oct. – 7^th Nov. 2019, JAS 2019, Dubna, Russia – Beam Instrumentation & Diagnostics – M. Wendt

The LHC Schottky Monitor

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Motivation

Amplitude modulation terms

Time modulation terms

synchrotron�frequency

betatron�frequencies

“chromatic”�frequency

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

LHC Beam Parameter Extraction

• Tune
• Coherent:

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• Incoherent:�
• Momentum spread

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• Chromaticity

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• Emittance

typical LHC Schottky spectrum at h = 427746 (f_rev = 11.245 kHz)�in low-resolution FFT mode

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

LHC Schottky Design Choices

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Principle of Operation

∆

RF-Signal Processing

DAQ

Fast�Gate-Switch

∆-Hybrid

vacuum pipe,

60x60mm cross-section

WR-187 wave-guides,

~1000mm long

2x270 coupling slots,

~20x2mm

WG-to-coaxial

transitions

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

The LHC Schottky monitor

• Two symmetrical arranged, broadband, slot-coupled WG forward �travelling-wave coupler pickup electrodes
• based on Fermilab design ideas
• A broadband RF ∆-hybrid
• Fermilab in-house design
• Fast gate-switch for bunch selection
• CERN in-house design
• Low noise, high dynamic range �RF signal processing system �(3-stage RF down-converter)�followed by a 24-bit digitizer �based on the BBQ system
• CERN/Fermilab �design collaboration

2-of-4 LHC Schottky “tanks” installed�in the straight section near point 4

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Schottky Signals since 2018

• Today (since 2018)
• Rather good Schottky signals for protons and ions
• >10 dB S/N at injection energy
• Gated on single nominals

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• Still visible coherent signals during luminosity runs
• But problems during the energy ramp and at flat top due to long. phase modulation

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Ion Schottky signals

before and after the energy ramp

Proton Schottky signals at injection energy

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Schottky Signals in 2012

• Was not always like this…
• Before 2014 the LHC Schottky systems suffered from �the large common mode revolution harmonics, saturating the low-noise RF amplifiers!

B1H

B1V

B2H

B2V

50 dB

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

LHC Schottky Pickup

• Forward hybrid waveguide coupler
• TEM beam field excites the TE₁₀ WG mode
• Symmetric arrangement of horizontal / vertical couplers
• Any asymmetry will degrade the performance, i.e. limit the common mode suppression!
• Waveguide-to-coaxial couplers: Signal output ports 1 & 3
• Ports 2 & 4 are used for calibration and test signals

Beam pipe 60x60mm

TE₁₀ mode waveguides �type WR187 (WG12)

270 coupling slots in 0.2mm thick CuBe-foil (~20x2mm, 4mm pitch)

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

EM Analysis

transfer impedance�∆-mode Σ-mode

Σ-mode

∆-mode

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Pickup Issue: WG-Coax Coupler

• Waveguide-to-coaxial coupler has large return losses (S11)
• Partially fixed during initial assembly

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• Redesign of the WG-coaxial coupler (Ms.Sc. thesis Matthias Ehret)

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modified pin �extension

blended �through hole

for feedthrough

Metal burr

WG-to coaxial mode launchers: Problems �with tolerances and impedance matching

-20 dB

-30 dB

4.6 GHz

5.2 GHz

WG-to-coaxial �mode launcher

WG-to-coaxial �mode launcher

EM simulation

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Pickup Issue: Warped Coupling Foil

• Construction, but also material related

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• Seems to be caused by elongation of the coupling foil during bake-out:
• Thermal expansion coefficient (μm/m/K)�SS 316L: 16.2 (original design, Fermilab)�AlSi1MgMn: 23.4 (initially used at the LHC)�CuBe foil: 17.0
• (AlSiMgMn – CuBe) x 1.4m x 150 K = 1.3 mm

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• Overhaul of the sandwich construction now based on pure OFHC copper
• Added Au-plated canted-coil springs for better RF contact between the layers

elongated coupling foil�after disassembly

warped foil

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Schottky Pickup Remanufacturing

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Remaining Issue: Beam pipe Coupling

• Beam measurement �in time domain:
• 12 GHz BW, 60 GSPS
• “ringing” indicates reflection effects via beam pipe coupling
• No cure found, yet…
• Current mitigation strategy:
• Apply “precise” bunch signal gating.

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

RF Signal Processing

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

RF Front-end after Overhaul

• Located directly above the Schottky pickup
• To minimize the insertion loss of the signal cables
• Still, ~8 dB losses between pickup and 1^st RF amplifier
• Cables, compensation path, hybrid, gate-switch, isolator, �wide-band Bessel pre-selector band-pass filter

LNA

fast gate

Δ-hybrid

cavity �BPF

Bessel �BPF

isolator

compensation path

RF amplifier

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Compensation Path

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Fast Gate-Switch

LHC proton bunch Schottky signals in the time-domain (acquired with a 20 GHz / 60 GSPS oscilloscope)

Gate-switch performance after resolving numerous problems

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Interdigital Bessel Band-pass Filter

AgAu-plated:�BW ≈ 72 MHz (15 %)�5τ ≈ 25 ns

Insertion loss ≈ 2 dB

TD response of a commercial�Butterworth pre-selector filter

4.8 GHz pre-selector BPF to limit the instantaneous signal level at the 1^st LNA

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Cavity Band-pass Filter

• After fast gate-switch:
• Drastically reduce instantaneous signal level!

TE110

TM111

TE311

Prototype out of brass:�Q₀ ≈ 9300�5τ ≈ 1μs�Q_L ≈ 3700

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�Insertion loss ≈ 2 dB

Features to suppress unwanted modes

Inductive coupling loop

Plunger to fine-adjust fc

Mode-chart for a �cylindrical resonator

with f_TE110 = 4.8 GHz

sweet spot

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

RF Back-end

• Fermilab design (R. Pasquinelli et.al.)
• Includes gate-switch �for noise reduction

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• New LO signal distribution system�(T. Levens, M. Betz)

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Triple stage downconverter

4.8 GHz → 400 MHz → 21.4 MHz → 11 kHz

4 x downconverters

LO distribution

Local-Oscillators (LOs)

VME crate

(control and acq.)

LO signal �distribution system

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Beam Measurements & Studies

Ion Schottky signals before and after the energy ramp

Time domain Schottky pickup signal (12 GHz BW oscilloscope)�indicating beam pipe related reflection effects

Supporting MD1447: Collimator impedance study

with high resolution tune measurements

Background image:

Schoktty signal spectras taken during a �LHC lead ion run on 3^th Dec. 2015, fill #4690.

frequency

time

Longitudinal�Schottky band

Lower transverse�Schottky sideband

Upper transverse�Schottky sideband

Page 50

January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

MD1767: Fun with Fitting

• Different fitting �methods
• Gaussian fit
• Least square
• Robust least �square
• Threshold fit
• With box-car smoothing filter
• ...
• The all need tweaks
• Baseline, noise-reduction, synchrotron lines, coherent signal contribution, etc.

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

LHC MD1767: Beam 1 Results for Chromaticity

Single nominal bunch

Bunch trains

Switching the Schottky measurement�to different bunches

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

LHC MD2408: Chromaticity and Emittance

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Analysis of the longitudinal Spectra

No intra-bunch coherent motion

Single particle spectrum

Synch amp pdf

This is the measured spectrum

This we know how to calculate

These we need to find!

courtesy

K. Lasocha

D. Alves

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

LHC long. SB Spectrum Analysis

Minimize cost function:

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

THANK YOU!

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

https://cas.web.cern.ch/schools/kaunas-2020

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Page 58

28^th Oct. – 7^th Nov. 2019, JAS 2019, Dubna, Russia – Beam Instrumentation & Diagnostics – M. Wendt

Backup Slides

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

MD1767: Chromaticity Study

• Good signals during the shift
• Stayed at injection energy
• Symmetric chroma settings
• Same for B1&B2, h&v

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Shift start

Shift end

Single nominal

Octupoles off

Chroma +5…+20

Trains: 1x12b, 6x96b

Octupoles on

Chroma 0…+20�

Switching �between

bunches

Change of chromaticity

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

More on Schottky Signal Studies

• Challenges:
• High level common mode signals�(long. revolution harmonics)
• Up to 80 dB higher than the incoherent transverse Schottky signals
• ”RF blow-up” on energy ramp
• Distorted/weak Schottky signals on the energy ramp
• Abort-gap cleaning
• 1^st bunch reports a distorted signal on energy ramp and flat top
• Geometric emittance shrinkage
• Weak incoherent Schottky signals at flat top
• Low beam pipe cutoff frequency
• Strong reflection effects, decay time ~800 μs

Effect of the ”RF-blow-up”�during the proton energy ramp

Offline studies on signal

interpolation and fitting

Offline studies to separate coherent �and incoherent signal contents

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Automatic C-Path Tuning w Beam

• Left top:
• Common mode rejection VNA measurement using “balanced” ports
• Left bottom
• Beam orbit effect on the signal level of the coherent revolution harmonic
• Below:
• Automatic tuning of the compensation path of the broadband front-end output via VSA
• With beam signal!

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

RF Front-end Cascade Analysis

• Completely re-designed
• Fast gate-switch, new RF low-noise amplifier �and wide-band, pre-selection bandpass-filter
• Narrow-band cavity BPF before the high gain RF amplifier

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt

Changing LO-Frequencies

• EM analysis of the Schottky pickup indicates a CMR sweet spot around ~4.7 GHz
• 1^st IF BPF is 400±50 MHz
• Beam studies with a fractional PLL source
• Replacing the frequency multiplier (step recovery diode based)
• No improvements in common mode signal contents observed

step-recovery�diode as�frequency�multiplier

low phase noise�fractional PLL�RF source

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January 29^th – February 2^nd , 2024, USPAS Hampton (VA), U.S.A. – Schottky Signals & Diagnostics – M. Wendt