# Presentation: 162940

## Ideology of the Muon Collider design

**Ideology of the Muon Collider design**

- Y.Alexahin & E.Gianfelice-Wendt

## Muon Collider parameters

**Muon Collider parameters**

**	****	****	*****Low Emitt.****** ******	******	******High Emitt.***
**Energy (TeV)****	****	****             0.75+0.75 (********=7098.4)**
**Average Luminosity (1e34/cm^2/s)****	****2.7****	****	****1**
**Average bending field (T)****	****10****	****	****8.33**
**Mean radius (m)****	****	****361.4****	****	****363.8**
**Number of IPs****	****	****4 (350m/2 each)****	****2 (200m each)**
**P-driver rep.rate (Hz)****	****	****65****	****	****60**
**Beam-beam parameter/IP,  ********	****0.052****	****	****0.1**
****** ****(cm)****	****	****	****0.5****	****	****3**
**Bunch length (cm),  ********z****	****	****0.5****	****	****2**
**Number of bunches/beam,  n****b****	****10****	****	****1**
**Number of muons/bunch (1e11), N********	****1****	****	****12**
**Norm.transverse emittance (********m), ************N****	****2.1****	****	****13**
**Energy spread (%)****	****	****1 ****	****	****0.1**
**Norm.longitudinal emittance (m), ********||N**** ****	****0.35 ****	****	****0.14**
**Total RF voltage (GV) at 800MHz****	****406.6 ********10****3********c**** ****	****0.26********10****3********c**
**RF bucket height (%)****	****	****23.9****	****	****0.6**
**Synchrotron tune****	****	****0.723 ********10****3********c**** ****	****0.02********10****3********c**** **
******+ ********- in collision / proton****	****	****0.15 /2****	****	****0.15**
**8GeV proton beam power (MW)****	****1.1****	****	****0.6**

** ****Low emittance option**** (advanced): owing to ideas by Yaroslav Derbenev (HCC, PIC) much lower 6D emittances seem to be feasible than previously thought of.**
** ****High emittance option**** (baseline):** **conceptually** **follows** **1999 PRSTAB Muon Collider Collaboration report**

## Muon Collider design wishlist

**Muon Collider design wishlist**

** ********x***** = ********y***** < 1cm**
** ****distance from IP to the first quad d1 = 6.5m (for now)**
** ****momentum acceptance > ****±0.5%**
** ****momentum compaction factor | ********c**** | < ****10****-4**
** ****transverse admittance > 16 ********r.m.s.****(max) ****~ 30 nm (dynamic aperture!)**
** ****2 interaction points (let experiments compete!)**
** ****circumference as small as possible (no long drifts)**
** ****quad gradients within the present day technology (~220T/m)**
**Problem: huge chromatic aberrations ( scale ~ d1/ ********* ) must be compensated in a wide momentum range ( >1% )**

## Chromatic aberrations

**Chromatic aberrations**

**Typical values for IR parameters from the wishlist:**

**this means 400% ********- function modulation at ********p=0.001 (!)**

**chromatic functions in IR w/o correction**

**chromatic functions:**

## IR design guidelines

**IR design guidelines**

**But we make a good use of it: it is possible to earn negative contribution to ********c**** while suppressing this huge *****J******x***** so that the rest of the lattice were simple FODO lattice – circumference is very small (FODO has the largest dipole packing factor)**

**The only way to obtain a non-zero momentum acceptance is to cancel *****a******x,y***** before they convert into *****b******x,y***** : **
** ****sextupole correctors ****must**** be in the IR, not in a separate CC section!**
** ****dispersion must be present in IR, it may be generated**
**   ****1) by dipoles in the IR so that *****D******x*****= *****D******x*****‘= 0 at the IP,**
**   ****2) outside the IR so that *****D******x*****= 0 but  *****D******x*****‘******** 0 at the IP.**
**We explore the first possibility (symmetric design) which has an apparent drawback – huge value of the dispersion invariant generated in the IR**

## IR & Negative Dispersion Section

**IR & Negative Dispersion Section**

**Optics and chromatic functions**

- x

- Dx

- DDx/100

- Wx

- Wy

- y

## Momentum acceptance

**Momentum acceptance**

**In the presence of errors the lower boundary will be determined by Qx=40.5:**
******p****(min) ****= - 0.0034, whereas ********p****(max) ****= 0.0043 which is marginally sufficient for ******** ****p****=0.001**
**After matching the momentum compaction occurred ~ 3 times larger than we’d shot for.**

- Qy

- Qx

******c**

**Circumference in the new design C = 3702.2 m**

## Chromatic correction figure of merit

**Chromatic correction figure of merit**

| machine | * (m) | d1 (m) | NIP | p range | c | Y |
| --- | --- | --- | --- | --- | --- | --- |
| Tevatron | 0.3 | 7.6 | 2 | -0.0012 : +0.0023 | 0.0023 | 0.06 |
| MC_1999 | 0.003 | 6 | 1 | -0.0008 : +0.0007 | -0.000025 | 1.4 |
| MC_v1 | 0.01 | 6.5 | 2 | -0.0034 : +0.0043 | 0.00018 | 4.4 |

**The momentum compaction in the new design can be reduced by better balancing the contributions from the NDS and the arcs, but this is not very important for the high-emittance option.**

## Problems & outlook

**Problems & outlook**

**Cross-derivative produces  ********Q=0.4 at 1******** for the high emittance option (********r.m.s.****=1.8nm);    less of a problem for the low emittance option.**
**What to do:**
** ****use existing sextupole families in the arcs (5/plane) to reduce detuning (little hope),**
** ****install octupoles,**
** ****try asymmetric design with dispersion generated outside the IR.**
**- A long battle is still ahead!**

**Delta(p)/p:      0.00000000                M o d e   1                   M o d e   2**
**Fractional tunes:            Q1      =      0.11719380     Q2      =      0.19469246**
**First order chromaticity:    Q1'     =      5.13087495     Q2'     =      3.32561223**
**Second order chromaticity:   Q1''    = 109576.67263357     Q2''    =   1471.53392320**
**Normalized anharmonicities:  dQ1/dE1 =  0.58955239E+08**
**                             ****dQ1/dE2 =  0.22305272E+09     dQ2/dE2 =  0.62807823E+08**

**Sextupoles are still too strong and produce huge nonlinear detuning. According to MAD8**