# Presentation: 196437

## Correction of resonances driven by random errors

**Previously, we successfully demonstrated that we can correct nonlinear resonance for high-intensity operation where space charge effects are important.**
**All previous studies were done using lumped errors:**** **
**Independent correction of sextupole and octupole resonances**
**Correction of skew resonance**
**Dynamic correction of several resonances which allows to reach low losses at high intensity.**
**      ****In June’03 we began to study resonance correction with resonances driven by random errors.**** **

## Lumped errors budget used in studies

**       ****In resonance correction studies we assumed lumped**** b2=30**** units and ****(b3,****  ****a3) = 60**** units which corresponds to **
**5 times stronger random sextupole errors than measured**
**10 times stronger normal & skew octupole errors than measured**
**      ****With the present error budget coming just from arc dipoles and arc quadrupoles the dominant contribution comes from normal sextupole and normal octupole resonances –  good correction.**
**       ****If the budget of skew octupole errors becomes factor of  5 stronger than the present - one will need skew octupole correctors.**

## Correction of sextupole resonances (lumped errors):w.p. (6.36,6.22) - Correction of 3Qx=19 and 2Qy-Qx=6

**Total emittance pi mm mrad**

**% outside**

**N=0.6*10^14**
**blue – no errors**
**red**** – errors, no correction**
**green**** – errors, correction of 3Qx=19**

**N=2*10^14**
**blue – no errors**
**grey**** – errors, no correction**
**green**** – errors, correction of 3Qx=19**
**pink**** – errors, ****simultaneous correction of 3Qx=19 and 2Qy-Qx=6 resonances**

- 3Qx

- 2Qy-Qx

- Qx

- Qy

## Correction of sextupole resonances (lumped errors):w.p. (6.4,6.3) - Correction of sum coupling resonance Qx+2Qy=19 and 3Qx=19 resonance

**N=0.6*10^14**
**blue- no errors**
**red**** – errors, no correction**
**pink ****– errors, correction of Qx+2Qy=19**

**N=2.0*10^14**
**blue- no errors**
**red****- errors, no correction**
**green****- errors, ****simultaneous corrections of **
**Qx+2Qy=19 and 3Qx=19 resonances**
**N=3.0*10^14**
**pink**** – errors, corrections of Qx+2Qy=19 and**
**3Qx=19 resonances**

**Total emittance pi mm mrad**

**% outside**

**% outside**

## Correction  of octupole resonance due to 10 unitsrandom b3 (w.p. 6.4, 6.3)

**We started by correcting octupole**
**resonance 4Qy=25 driven by random ****b3 of**
**10 units rms**** distributed over all magnets.**
**MAD lattices were constructed to have **
**the same notation of magnets in both ****DYNA**
**and**** UAL**** codes.**
**2. Scripts to transfer errors from one code **
**to another were written.**
**3. Benchmarking tests were done to ensure **
**that implementation is correct**

## Initial study

**Initial correction was not very good:**
**    ****At most ****reduction of factor of 2 in emittance growth was achieved.**
**    ****We then switched back to lumped errors and started detailed study of implementation of various multipoles in various elements (comparison of b3 in dipole vs. b3 in quadrupole, etc).  **
**     ****No problems was found.**
**    ****It was then concluded that ****“not perfect” compensation is due the effect of other resonance**** bandwidth of which was big enough to play a role.**
**     ****We then switched to another w.p. to make sure that we have emittance growth only from a single resonance which we are correcting.**

## w.p. (6.36,6.22)

**3****rd**** order resonances**
**excited by sextupole**
**errors**

**Random errors b2=5 units rms in all**
**magnets (dipoles and quads). **
**Total contribution is about factor of 5 **
**bigger than expected based on measurements.**
**Correction of ****3Qx=19****  resonance.**

## Correction of b2=5 units rms

**Red- no correction**

**Green-correction**

## Remaining study

**1. Perform Dynamic correction for all 3 major resonances**
**for this working points: 3Qx=19, 2Qx+2Qy=25 & 4Qx=25 driven by**
**random b2, b3 and a3.**
**2.  Generate realistic loss models without correction based on available measured multipole:**
**As measured             2) factor of 2-5? Safety margin?**
**3.   Produce loss models with corresponding dynamics correction of major resonances for both w.p.**