# Presentation: 719671

## Ring Tune MeasurementPreliminary Design Review

- Peter Cameron
- July 23, 2002

## Outline

- Motivation
- Tune Footprints
- AP Requirements
- Tune Measurement Options
- Simulations
- Conclusions

- Diagnostics Review July 2002

## Motivation

- SNS tune spread is space charge dominated, with smaller contributions from chromaticity and uncompensated fringe fields
- To control beam loss and activation you must control tune footprint
- To control tune footprint it is very helpful to be able to measure it
- Instruction from high-level management - “Think about e-cloud diagnostics”! Postulated e-cloud behavior will produce measurable tune shift along the bunch?

- Diagnostics Review July 2002

## Tune Footprints - blue dot is coherent tune

- Footprints for 3 intensities
- (0.1, 1, and 2x1014) at cycle end

- Footprints after 263, 526, and 1060 turns

- Diagnostics Review July 2002

## AP Requirements for Tune Measurement

- Coherent tune
- accuracy .001
- Resolution .0005
- Incoherent tune
- accuracy .005
- Resolution .0025
- Both measurements will require averaging

- Diagnostics Review July 2002

## Ring Tune Measurement Options

- Coherent Tune - Beam-in-Gap kicker, one or all BPMs
- Incoherent Tune - Modified HEBT electronics on some subset of Ring PUEs, measure tune of 400 MHz microbunches before decoherence
- Incoherent Tune - Schottky
- Incoherent(?) Tune - HF kicker, Specialized Pickup
- Use resonant transverse pickup to improve sensitivity, reduce common-mode dynamic range problem
- Resonate above coherent spectrum to reduce common-mode dynamic range problem
- Premise is kick small subset of the beam distribution
- Incoherent Tune - Quadrupole Oscillations, common-mode dynamic range problem
- Incoherent Tune - resonance crossing

- Diagnostics Review July 2002

## Coherent Tune, BIG Kicker

- Voltage = +/- 7KV     Aperture = 21cm
- Length = 4.5m
-  = 0.6mrad         = 15m
- Amplitude (p-p) = 5mm
- p/p = .01
- Chromatic Tune spread =  p/p = .08
- Decoherence time about 12 turns
- Multiple measurements to measure +/- .001 AP spec
- qcoh is difference between measured tunes at beginning and end of accumulation cycle

- Diagnostics Review July 2002

## Incoherent Tune, Injected microbunches

- Injected microbunches have coherent oscillations with spectral energy at 402.5MHz, and microbunch samples the space charge environment of the bunch, behaving like a big Schottky particle, soooo -
- measure microbunch tune with some number of 402.5MHz modules!
- Longitudinal debunching of 402.5MHz structure due to momentum spread is fast (3-10 turns) - an argument for more than the minimum of 2 locations of 402.5MHz electronics
- Resolution of .0025 will require ~ a few hundred measurements
- Can imagine a machine studies accumulation cycle with ~10 turns between injections at the time of interest, to avoid complication of microbunch time jitter at injection
- Measured incoherent tune can be correlated with measured amplitude of oscillation (play with the painting!), providing information about transverse distribution and tune footprint
**One** map of footprint will require ~ few thousand machine cycles

- Diagnostics Review July 2002

## Schottky Signal Relative to RHIC Au

- Power spectral density ~ Nx2q2fk2g/ndp/p

- Diagnostics Review July 2002

## RHIC LF Schottky at Injection

- Span 78KHz
- 5dB/div
- q = Np/p
-      ~ 2 KHz
- 
- N ~ 3060
- p/p ~ .001

- Diagnostics Review July 2002

##                               Resonant BPM

- M. Kesselman et al - PAC 2001
- Stub-tuned 1/4 wave resonator
- Simulated in Spice
- frequency ~ 240MHz (8.5xRF)
- Qloaded ~ 100 optimal coupling
- In-tunnel hybrid for  and 
- Resonate difference mode -  not sum mode signal at revolution line
- Moveable - minimize difference mode signal at revolution line
- Resonate above coherent spectrum

- Diagnostics Review July 2002

## Incoherent(?) Tune - HF kicker, Specialized Pickup

- Beam Transfer Function Measurement - Drive beam at one selected frequency for an accumulation cycle, change frequency, repeat,...
- Premise is kick small subset of the beam distribution
- Result is similar to what you get from observing injection oscillations - ‘Enhanced’ Schottky Signal
- Incoherent(?)  because space charge tune shift is particularly sensitive to local coherence - chromaticity selects momentum, space charge selects  transverse emittance
- Use resonant transverse pickup to improve sensitivity, reduce common-mode dynamic range problem
- Resonate above coherent spectrum to reduce common-mode dynamic range problem

- Diagnostics Review July 2002

## RHIC LF Schottky at Injection

- Span 78KHz
- 5dB/div
- q = Np/p
-      ~ 2 KHz
- 
- N ~ 3060
- p/p ~ .001

- Diagnostics Review July 2002

## RHIC Beam Transfer Function

- Diagnostics Review July 2002

## UAL Simulation

-         Beam response (without space charge) to narrowband kick continuous thru accumulation cycle. Each peak corresponds to one cycle. Result is reasonable picture of tune spread due to chromaticity

- Diagnostics Review July 2002

## Linewidths, Chromaticity,Space Charge,...

-          Tune spreads at the lower sideband due to chromaticity (f0p/p) and revolution harmonic (f0np/p) cancel at about 50MHz for nominal SNS conditions, leaving only  the space charge contribution. This would be a good frequency for the kicker and resonant pickup

- Diagnostics Review July 2002

## Incoherent Tune - Quadrupole Oscillations

- Method specifically developed (at CERN) to measure incoherent tune shift for high intensity beams. Measure quadrupole oscillations with specialized kicker and pickup
- All of the previous methods of measuring incoherent tune bear some relation to each other, are either Schottky or quasi-Schottky. Quadrupole oscillations are much different, will provide useful alternative measurement.
- This year’s BIW Faraday Cup went to Quadrupole Monitor
- To build a good quadrupole monitor is not trivial

- Diagnostics Review July 2002

## Basic Method - Quadrupole Oscillations

- Incoherent tune shift in x plane is related to measured quadrupole frequency by:
- 	Q2 = 2Q0 - (1.5-0.5ax/(ax+ay))Qinc
- Where
- 	Q2 = measured quadrupole frequency
- 	Q0 = coherent tune
- 	Qinc = incoherent tune shift
- 	ax = horizontal beam dimension
- 	ay = vertical beam dimension

- Diagnostics Review July 2002

## Hardware - Quadrupole Oscillations

- Possibilities for the Pickup
- Collaboration with Jansson et al
- Resonant QMM, extension of the LF Schottky pickup
- IPM
- Of these the IPM is particularly attractive:
- IPM is in the baseline, no new hardware/software
- Need working IPM anyhow for the width measurement
- Quadrupole oscillation measurement already shown in RHIC
- Opens the possibility of measuring variations in incoherent tune shift along the length of the bunch - e cloud diagnostic?
- Kicker - BIG pulser driving BIG kicker in quadrupole mode

- Diagnostics Review July 2002

## QMM BTF

- Diagnostics Review July 2002

## Summary and Conclusions

- Tune control is crucial for low-loss high-intensity operation
- Tune control implies tune measurement
- Tune measurement is fun
- There are 3 basic approaches
- Coherent - big kick
- Schottky and quasi-Schottky - no kick or non-perturbative kick
- Quadrupole oscillations
- All approaches will be investigated, and it is reasonable to hope that all can be implemented with present budget and manpower limits

- Diagnostics Review July 2002