# Presentation: 492514

## Muon Collider ring optics design

**Muon Collider ring optics design**

**Y.Alexahin & E.Gianfelice-Wendt **
**(FNAL)**

## Muon Collider Parameters

**Muon Collider Parameters**

** ****Low emittance option**** - just a beautiful dream so far**
** ****High emittance option**** - cautiously optimistic, reflects the latest results**

**	****	****	*****Low Emitt.****** ******	******	******High Emitt.***
**Energy (TeV)****	****	****             0.75+0.75 (********=7098.4)**
**Average Luminosity (1e34/cm^2/s)****	****2.7****	****	****2**
**Average bending field (T)****	****10****	****	****6**
**Mean radius (m)****	****	****361.4****	****	****500**
**Number of IPs****	****	****4 ****	****	****2**
**P-driver rep.rate (Hz)****	****	****65****	****	****60**
**Beam-beam parameter/IP,  ********	****0.052****	****	****0.1**
****** ****(cm)****	****	****	****0.5****	****	****1**
**Bunch length (cm),  ********z****	****	****0.5****	****	****1**
**Number of bunches/beam,  n****b****	****10****	****	****1**
**Number of muons/bunch (1e11), N********	****1****	****	****11.3**
**Norm.transverse emittance (********m), ************N****	****2.1****	****	****12.3**
**Energy spread (%)****	****	****1 ****	****	****0.2**
**Norm.longitudinal emittance (m), ********||N**** ****	****0.35 ****	****	****0.14**
**Total RF voltage (GV) at 800MHz****	****406.6 ********10****3********c**** ****	****5.6********10****3********c**
**RF bucket height (%)****	****	****23.9****	****	****2.4**
**Synchrotron tune****	****	****0.723 ********10****3********c**** ****	****0.1********10****3********c**** **

## MC Ring Design Challenges

**MC Ring Design Challenges**

** ****Low ******** (******** 1cm) **
** ****Small momentum compaction factor (********c**** ~ ****10****-4****) **
** ****Focal length of LB quads can not be made small: shielding from decay electrons takes 3-5 cm, the first quad had to be far from IP (>6m at E=750GeV)**
****** ****Huge chromatic aberrations ******** ****very strong sextupoles ******** ****higher order effects**

**Chromatic functions with (x, x’) set (not MAD functions!):**

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

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

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

## MC Lattice Design Philosophy

**MC Lattice Design Philosophy**

**But we make a good use of it: **
** ****we can earn a negative contribution to ********c**** while suppressing this huge *****J******x***** **
** ****rest of the lattice can be simple FODO cells which helps to reduce the circumference (FODO has the largest dipole packing factor)**
** ****to maximize the dipole packing factor (and minimize the circumference) we choose a large phase advance per cell, 108******** for now (plan to try 135********)**
** ****Dipoles in IR provide detector protection from decay electrons (whether SR from this electrons presents a danger is the matter of ongoing study)**

**The only way to obtain a non-vanishing 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**

## “Quad First” @6.5m MC Lattice Design

**“****Quad First” @6.5m MC Lattice Design**

- y

- x

- Wx

**IR, negative dispersion and matching sections**

- DDx/100

- Dx

- Wy

## “Quad First” MC Lattice Properties

**“****Quad First” MC Lattice Properties**

**No octupoles**

**Second order chromaticity:**
**Q1''    = 102511.04779854 **
**Q2''    =    366.54867056**
**Normalized anharmonicities:**
**dQ1/dE1 =  0.55557395E+08**
**dQ1/dE2 =  0.20800890E+09**
**dQ2/dE2 =  0.58845415E+08**

**Huge cross-detuning makes dynamic aperture virtually vanishing – octupoles necessary**

******p**

******p**

## “Quad First” MC Lattice Properties

**“****Quad First” MC Lattice Properties**

**With octupoles (shown in green)**

**Second order chromaticity:**
**Q1''    = 102517.98582532**
**Q2''    =   1127.89764247**
**Normalized anharmonicities:**
**dQ1/dE1 =  0.65239168E+08**
**dQ1/dE2 =  0.47761742E+08**
**dQ2/dE2 =  0.37233974E+08**

**Dynamic aperture with ~ optimum octupole strength still is not sufficient for the ****high-emittance option: <1.5******** for ************N****=12.5 ********m**** (marginally O.K. for the low-emittance option)**

****** ****CSIx [********m]**

****** ****CSIy [********m]**

## How to Improve the DA?

**How to Improve the DA?**

** ****Retreat to ******** 2-3cm (not interesting)**
** ****Move quads closer to the IP? – actually does not help**
** ****Increase dispersion @ IR sextupoles!**
**This can be done by placing a dipole between the IP and the first quad. The arguments pro:**
** ****the requirement of 6.5m stay-clear was obtained for twice higher energy and bunch intensity**
** ****the dipole itself will protect the detector from the most dangerous sources of backgrounds: decay electrons and Bethe-Heitler muons **
**The arguments contra:**
** ****250 Gev decay electrons will produce hard synchrotron radiation in the dipole field**
**But first of all let us see what improvement in the DA it promises**

## “Dipole First” MC Lattice Design Option

**“****Dipole First” MC Lattice Design Option**

- y

- x

- Dx

- DDx/100

- Wx

- Wy

**IR, negative dispersion and matching sections, octupoles not shown (there is one more at maximum |Dx| to control 2****nd**** order chromaticity).**

## “Dipole First” MC Lattice Properties

**“****Dipole First” MC Lattice Properties**

- Qy

- Qx

******c**

******p**

******p**

**Owing to ****larger dispersion at IR sextupoles the requires sextupole gradient became lower reducing 2****nd**** order effects.**
**Also, in this version 2****nd**** order dispersion was corrected with sextupoles in the matching section.**

**Second order chromaticity:**
**Q1''    =  67698.83542578**
**Q2''    =   1860.74134081**
**Normalized anharmonicities:**
**dQ1/dE1 =  0.43575747E+08**
**dQ1/dE2 =  0.16659793E+08**
**dQ2/dE2 =  0.14651033E+08**

**Momentum acceptance of ****± 0.7% is O.K. for the high-emittance option (not for the low)**

## “Dipole First” MC Lattice Properties

**“****Dipole First” MC Lattice Properties**

****** ****CSIy [********m]**

****** ****CSIx [********m]**

** ****The “dipole first”**** option gives a hope to obtain the required DA (by further optimization) with ********=1cm **
** ****It is not clear, however, if the synchrotron radiation from a dipole so close to the IP would be tolerable.**
** ****To proceed further to a realistic design a close collaboration with the detector, energy deposition and magnet technology groups is a must.**
** ****Nikolai estimates the time necessary for backgrounds evaluation and shielding design as ~ 0.5 FTE, but does not have a free person to tackle the issue.**

**The 1024 turns DA is only marginally sufficient ****for the high-emittance option: ~3******** for ************N****=12.5 ********m**** (O.K. for the low)**