# Presentation: 517952

## LARP AC Dipole Task

- M. Bai,1 R. Calaga,1 W. Fischer,1 A. Jansson,2
- S. Kopp,3 R. Miyamoto,3 P. Oddo,1 M. Syphers2
- 1*Brookhaven National Laboratory*
- 2*Fermi National Accelerator Laboratory*
- 3*University of Texas at Austin*

## Test of the Nonlinear Optics Measurements Using an AC Dipole in the Tevatron 

** ****TBT data of a BPM**
**  **** ****in the arc**
** *****σ***** ~ 1.3 [mm]**
** *****β***** ~ 100 [m]***** ***

-  At the injection energy (150 GeV), a (skew) sextupoloe and an
-   octupole family are set to various values.
-  Large amplitude oscillations are produced by a vertical AC dipole
-   and the turn-by-turn data and its Fourier spectrum are observed.

## An Example of Nonlinear System

**HO with ****a ****Cubic Potential**

- Equation of Motion:

-  Consider 1st order of *k*
-  Expansion: *x *= *x*0 + *x*1 +...
- Leading order:

- 1st order:

- A sextupole
- 1. shifts the central orbit.
- 2. produces a higher order mode (2*ν*).

## Shifts of the Closed Orbit by a Sextupole

-  A skew sextupole is changed
-   from 0 [A] to -30 [A].
-  The closed orbit changes
-   more for a larger kick.

- The phase of the orbit flips
- if the sign of the sextupole
- current is flipped.

## Higher Order Modes

-  Higher frequency modes appear for a larger oscillation.
-  The frequencies of the higher order modes change
-   with the driving frequency.

## Detuning

_**Detuning**_

**Amplitude of the driven motion**
**when the tune depends on the action**** **

***ν*****d**** ****<**** *****ν***

***ν*****d**** ****>**** *****ν***

## What do we measure?

- The closed orbit formula:

- If we know *β** *and* **ψ*, from information of two BPM’s 1 and 2,we can construct

***s***

**Behavior of***** w***** ****or**** *****W***

## Generating Function of the 1st Order Mode

-  A fixed sextupole current, different AC dipole current.
-  The strength of the sextupole is determined from the step size.
-  The kick strength depends on the action.
-  The action is not factored out, here.
-  The BPM nonlinearity will be considered in future analyses.

## Generating Function of the 3rd Order Mode

-  A similar analysis is possible for the 3rd order mode (Two same condition).
-  Two generating functions for resonances of 2*ν*d−*ν* and 2*ν*d+*ν*.

## AC dipole based nonlinear optics measurements are tested with intentional sources in the Tevatron.
Sextupole driving terms are measured by observing the change of the closed orbit and the 3rd order mode (Accuracy 5~10%? BPM effect should be considered.).
The detuning effect caused by octupole elements is also measured.

- Sextupole driving terms are measured by observing the change of the closed orbit and the 3rd order mode (Accuracy 5~10%? BPM effect should be considered.).
- The detuning effect caused by octupole elements is also measured.

_**Summary**_

## LARP Accelerator Instrumentation: AC Dipole Task Status

- Achieved deliverables:
-  LHC ac dipole constructed based on FNAL model. Resonate a kicker magnet
-  BNL’s binary weighted cap bank tuning circuit developed for the LHC ac dipole circuit.
-  The dynamic tuning technique development at
-      BNL. This will allow one to stay with the high Q
-      ac dipole design
-  Beam optics measurement at BNL and FNAL

## Current Status of LHC AC Dipole

- Two Lab.Gruppen FP13000 amps and 4:1 transformers
-  2000Apk magnet current achieved
-  The 7σ (1800Apk) goal is reached with comfortable margin
-  plan to upgrade the current copper claps of the capacitor banks to MOSFET switches

- the FNAL solution of audio amps(Lab-Gruppen Class-H amp) driving pinger(MKQs)
- Spec: 1800 A in MKQ for 7 @ 7 TeV.

## Current LHC AC-Dipole Tunning Schemedesigned by P. Oddo (BNL)

- Current LHC AC-Dipole Tunning Schemedesigned by P. Oddo (BNL)

- Bit1

- 5-bit binary-weighted capacitor-bank
- 0.255-0.345 (±15%) tune range
- 2.867-3.880kHz
- 0.002-0.005 tune steps
- 22-54 Hz
- Static MOSFET switching
- Can be replaced with mechanical switches or straps
- Conservative design
- Can withstand CW operation
- Peter have been working with Javier Serrano to implement this solution

- Bit0

- Bit2

- Bit3

- Bit4

-  GND Plate

-  MOSFET Module

- Capacitor

-  Coil/Drive Plate

## Effect of secondary driving term:a thin quadrupole error

***ν*****d ****- *****ν***

***β*****d**** [m]**

_**Phase Space @ an **__**IP**_

** ****sensitive to the work point**
** ****For work point close to half integer **
**   ****like Tevatron, this effect can be as **
**   ****big as 12%**
** ****For RHIC and LHC working points, **
**   ****the effect is about 6%**
** ****R. Miyamoto *****et al*****, Submitted to **
**   ****PRST-AB (also arXiv:0709.4192)**

## Dynamic Tuning Development: P. Oddo(BNL)

- A dynamic tuning technique using single switched capacitor with MOSFT was proposed by P. Oddo at BNL
- Simulations shows a tuning range of *** ~ *0.01, should be achievable
- A test setup using a half meter RHIC type ac dipole is under construction.

## Dynamic Tuning Development: P. Oddo(BNL)

- 7.33-9.04kHz (±10%) range
- Basic Topology, 0.56W,  Q=15-19
- Coil current fairly constant ~2.2Apk
- 3rd harmonic –33dBc
- Consistent with simulation

- Low-power Switched-capacitor Results

- Always on

- Always off

- Switching

- 7.33kHz

- 9.04kHz

- 8.67kHz

- Coil current

- Coil voltage

- Drive current

- Switch voltage

## 1kW Dynamic Tuning Test

-  Test RHIC prototype magnet over Spin-
-      Flipper  frequency range:
-  39kHz ±800Hz (±0.01 tune)
-  Magnet current: 145Apk
-  Magnet field: ~92G·m
-  Magnet Q=155, System Q=135-153
-  Estimated MOSFET losses: 86W

## AC dipole task plan in FY09

- A new task under the Accelerator Physics
- Focusing on commissioning
-  LHC ac dipole system to achieve the design goal of delivering 1800 Amps@3kHz, control software
-  Linear optics measurement
- A lot of data have been taken in RHIC and Tevatron
- Help the development of LHC on-line optics measurement/gradient error correction application
-  explore various techniques for gradient error correction using ac dipole
-  dynamic aperture measurement
-  non-linear resonance driving term measurement

## What is needed to enhance AC dipole task in FY09

- To have an experienced person for this task
-  need experience with the FNAL type ac dipole
-      system to help the ac dipole system
-      commissioning
-  need experience with ac dipole based optics
-      measurement
-  Hence we propose to have a joint post doc
-      between LARP AC dipole task and BNL

## Summary

- AC dipole task has achieved its goal as an accelerator instrumentation task
- A new task under the Accelerator Physics to focus on commissioning
- To have an experienced person for this task is very critical

## Backup slides

## A Method to Detect Sources

## Phase Measurement

## FNAL AC dipole Status

- Successfully share the FNAL musical ac dipole technique with LHC ac dipole system
-  transform a kicker to an ac dipole
-  take advantage of commercially available audio power amplifier
-  impedance matching between ac dipole and its power amplifier
- Measured linear optics using its musical ac dipole
-  confirmed the effect of the secondary driving term on the measured optics

*A. Jansson*

## Parameters of RHIC, TeV, and LHC

| machine(GeV) | RHIC(250) | Tev (150) | Tev (980) | LHC(7000) |
| --- | --- | --- | --- | --- |
| frev [kHz] | 78 | 47.7 | 47.7 | 11 |
| ν, 1-ν | 0.71 | 0.58, 0.42 | 0.58, 0.42 | 0.3, 0.7 |
| fm [kHz] | 55 | 20 | 20 | 3 |
| (Bρ) [Tm] | 833.9 | 500 | 3,300 | 23,000 |
| δ | ~ 0.01 | ≥ 0.01 | ≥ 0.01 | ≥ 0.01 |
| β (βm) [m] | 45(11) | 80 (47) | 80 (47) | 180** |
| σ [mm] | 0.75 | 1.3 | 0.5 | 0.3 |
| BmL [Gm] (4σ)  | 142 | 50 | 140 | 190 |
| IFNAL [A] | -- | 100 | 450 | 610 |

*** Serano’s talk @ LTC gives ****m**=258m at location of MKQ kicker*