# Presentation: 504465

## f

**Y. Alexahin**

-     	 **FERMI  NATIONAL  ACCELERATOR  LABORATORY**
**	****	****                           ****US  DEPARTMENT  OF  ENERGY**

**FNAL Accelerator Advisory Committee meeting****	****	****       December 5, 2006**

## Plan of the talk

**   ****low emittance MC**
**   ****6D ionization cooling**
**   ****PIC and REMEX**
**Ongoing work**
**Questions to answer**
**FY07 plan**
**FY08 plan and beyond**
**Summary**

**Muon Collider & Ionization Cooling Issues  - Y. Alexahin, FNAL                        ****December 5, 2006**

**Plan of the talk**

## 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**

## Low emittance option for MC

**Low emittance option for MC**

**Low emittance**** ****pros****:**
** ****smaller ******** ****→ smaller total number of particles n****b****N******** ****→ **
**	****	**** ******** ****relaxed coherent stability requirements**
** ****	****	**** ******** ****low proton driver power**
**	****	**** ******** ****low neutrino radiation **
**Low emittance**** ****cons****:**
** ****bb-effect limits ****N******** ****→ larger ****n****b**** is required ****→ ****electrostatic separation or crossing angle**
** ****smaller ******** ****→ strong IR chromaticity**
**                     ****→  ****smaller ********z**** is required →**
**                                     ******** ****small ********c**** → strong arc cell chromaticity**
**                                     ******** ****higher ********p****/p for the same long. ****emittance **

**problems with momentum acceptance**

## The roadmap to low emittance

**The roadmap to low emittance**

**Ionization cooling**:
**very similar to SR cooling in e-damping rings**
**The** ***longitudinal damping partition****** number*** **is** **naturally negative at p ******** <300MeV/c:**

**How to make it positive – see next slide**.
**The***** ******normalized equilibrium emittance*** **(r.m.s.)**

**so that to achieve ************=2********m**** ************<0.2mm is required (for ********1). Is it feasible?**
**Another possibility (D.Neuffer): decelerate muons to very low ********.**

**With Z=4 (Be) and the natural value of g****||****<0 (the final cooling stage)**

**(overestimation for H and He)**

## Basic 6D Cooling

**Basic 6D Cooling**

**Two ways to get ****g****||****>0:**
**generate large dispersion and use wedge absorbers;**
**generate large momentum compaction ********c**** >0 in a homogeneous absorber**
**The first method is realized in two schemes:**
**"Guggenheimed" RFOFO channel (helical or spiral with reducing radius), estimated emittances ************N****~5********10****2**** ********m**** ****, ********|| N****~1mm**
**straight FOFO channel with tilted solenoids, ************N****~5********10****2**** ********m**** ****, ********|| N****~0.5mm**
**The second method in:**
**Helical Cooling Channel (HCC) ,   ************N****~2********10****2**** ********m**** ****, ********|| N**** ~0.3mm;**
**HCC is the most attractive scheme, however, it has inherent difficulties**

## PIC & REMEX

**PIC & REMEX**

**Basic idea of the ****P****arametric resonance ****I****onization ****C****ooling (Y. Derbenev):**
**  ****form a structure with ~180******** phase advance/cell**
**  ****resonantly excite beta-beating with special lenses to obtain very small ************ at absorber plates **

**R****everse ****EM****ittance ****EX****change:**
**  ****obtain very small ************ as described above**
**  ****enhance transverse damping by making g****||**** <0 as large by the absolute value as possible by reversing the wedge angle and generating maximum dispersion at the wedges**

- Lattice magnets and RF cavities not shown

## “Guggenheim” RFOFO structure (R.Palmer)

**“****Guggenheim” RFOFO structure (R.Palmer)**

**- modification of the initially proposed by V.Balbekov RFOFO ring**

## “Guggenheim” RFOFO cooling simulations (R.Palmer, A.Klier)

**“****Guggenheim” RFOFO cooling simulations (R.Palmer, A.Klier)**

**Adding 804 MHz section would allow to achieve ************N****~7.5********10****2**** ********m**** , but:**
**  ****no matching section designed yet (may further increase losses surpassing 50% already)**
**  ****high magnetic field may drastically limit RF voltage (would GH****2**** filling help?)**
**  ****shown reduction in emittances include both cooling and initial shaving**
**  ****the merit factor of the 2-stage RFOFO channel is just (****N******** ****/********6D****)****fin****/ (****N******** ****/********6D****)****ini**** = 800**

## HCC Simulations (K.Yonehara)

**HCC Simulations (K.Yonehara)**

**6D cooling factor in the series of HCC is ~50,000 **

**Initial proposal: **
**  ****RF cavities packed inside solenoid **
**  ****additional helical coils create rotating dipole and quadrupole fields**
**As R.Palmer noted the transverse field on the coils would exceed 10****3****T at the last stage!**** **

## HCC issues

**HCC issues**

**Vladimir Kashikhin found a brilliant solution: ****helical solenoid!**
**Magically, the dipole and quadrupole components have the right values,  while the orbit goes through the centers of the coils!**

**Still a number of problems to be solved:**
**  ****how far down ****this helix can be scaled? Is helix period of  ~ 20cm (with Bs~15T) technically feasible?**
**  ****a principal solution for the RF structure which can fit inside the HCC has yet to be found;**
**  ****segmented HCC with RF cavities between solenoid sections was proposed but not demonstrated to provide adequate cooling**

## REMEX with HTS solenoids (R.Palmer)

**REMEX with HTS solenoids (R.Palmer)**

**It is possible to obtain ************N****~10 ********m**** in a solenoidal focusing channel with LH****2 ****absorber:**

**Simulations of cooling in a channel with 6 solenoids (no RF yet) gave ************N****=25 ********m**** .**
**To achieve emittances for the low emittance MC option this channel must be followed by a stronger focusing channel with short solid absorbers.**

## Mixed Lattice for PIC/REMEX channels (A.Bogacz)

**Mixed Lattice for PIC/REMEX channels (A.Bogacz)**

**10T solenoid**

**quads**

**dipoles**

**absorber**

**This mixed quadrupole-solenoid focusing lattice provides ************ =1.4cm at the absorber center.**
**Large dispersion function gives the possibility of chromatic correction (not demonstrated yet).**
**By reducing dimensions and increasing field strength one may hope to get ************ in the mm range. **

## Questions to answer

**Questions to answer**

**Collider ring:**
-   **correction of chromatic perturbations (chromatic beta-beating, nonlinear chromaticity and momentum compaction factor);**
**  ****radiation shielding necessary to protect the superconducting magnets and detectors at specific for the particular design beam intensity and sizes ;**
**  ****field quality of the magnets which have the required aperture and field strength (magnets being developed for the LHC luminosity upgrade is a good first approximation);**
**  ****dynamic aperture with realistic field and alignment errors;**
**  ****beam-beam effects;**
**  ****suppression of coherent instabilities at given bunch intensity, length, momentum compaction and lattice functions.**
**6D cooling channel:**
-   **scalability of the proposed by V.Kashikhin HCC technical solution to the helix period of ~ 20cm (with Bs~15T);**
**  ****principal solution for the RF structure which can fit inside the HCC;**

## Questions to answer

**Questions to answer**

**6D cooling channel (continued)**
-   **ability of gas-filled cavities to support high-gradient RF field in the presence of ionizing beam;**
**  ****end-to-end simulation of the "Guggenheimed" RFOFO channel to prove its competitiveness;**
**  ****proof-of-principle study of the FOFO channel with tilted solenoids followed by cooling simulations.**
**PIC / REMEX**
-   **optics design for different stages (solenoidal vs quadrupole and mixed focusing)**
**  ****compensation of chromatic and spherical aberrations;**
**  ****space charge effects**
**Proton driver, Pion production, Muon RF capture, Bunch coalescing, Acceleration**
**There is little doubt in feasibility of these elements of the complex, **
**there are a number of options for each of them which should be studied and compared, **
**but only after the principal solution for the collider ring and the cooling channel is chosen.**

## FY07 plan

**FY07 plan**

-   **Physics analysis and computer simulations of different schemes for the basic 6D cooling channel and PIC/REMEX channel.**
**  ****Side-by-side comparison of the obtained results with the aim of choosing the 6D cooling channel baseline scheme compatible with the chosen collider option.**
**  ****Analysis of implications of different options for the muon collider (low emittance vs. high emittance, electrostatic separation in one ring vs. double ring) resulting in a presumably optimal choice of parameters.**
**  ****Collider ring optics design for the chosen option.**
**  ****Preliminary analysis of the technical feasibility and physical validity of the proposed design (momentum acceptance, medium-term dynamic aperture, coherent stability).**
**  ****Formulating requirements to the proton driver and other systems of the complex.**
**  ****Consistent scheme(s) of the muon collider complex.**

## FY08 plan and beyond

**FY08 plan and beyond**

-   **Upgrade of the muon production and RF capture systems design **
**  ****Analysis, selection and preliminary design of muon acceleration systems  (RLA vs. FFAG for the first stage, RLA vs. fast ramping synchrotrons for subsequent stages)**
**  ****Extensive simulation studies and design optimization of all essential systems of the collider complex.**** **
**  ****Analysis of radiological issues for appropriate choice of the collider orientation and depth**
**  ****Cost  estimates**
**  ****Draft conceptual design report**
**Optimistically, the conceptual design will be finished in 2009 **

## Summary

**Summary**

** ****The Muon Collider for c.o.m. energy 1.5-2TeV seems doable with present day technology and can be accomodated on the Fermilab site**
** ****Extensive design and simulation work is necessary for all parts of the complex with the 1999 PRSTAB Muon Collider Collaboration report being a good first approximation**

** ****The requested funding for this work seems adequate taking into account heavy contribution from other labs especially BNL, JLab and MuonsInc.**

## Backup slides – Emittance diagram 

**Backup slides – Emittance diagram **

**Emittance evolution in R.Palmer’s muon cooling scheme**

## Backup slides – straight FOFO channel (Y.Alexahin)

**Backup slides – straight FOFO channel (Y.Alexahin)**

- straight solenoids

- tilted solenoids

- RF cavities

- Closed orbit at  = 0.01
-  (dispersion follows the same pattern)

- y/L

- z/L

- x/L

-   **Phase advance over the 4-solenoid period is above 2******** ****→ resonant dispersion generation**
**  ****Cooling by combination of ****GH****2**** and Li wedges in high-dispersion locations for damping repartition**
**  ****The scheme requires RF cavities operation in high magnetic field (hopefully ****GH****2**** will help)**

## Backup slides – collider ring optics

**Backup slides – collider ring optics**

**Two optics designs so far:**** **
**  ****prepared for ****1999 PRSTAB Muon Collider Collaboration report  by Carol Johnstone et al.:  ********* = 3mm, peak ********max****=1.5 ********10****5****m, ********c**** ****= - 9.2********10****-5****. Requires further work on chromatic correction, the momentum acceptance is just (- 1.2********10****-4****, 1.6********10****-4****).**
**  ****more conventional design by A.Bogacz: ********* = 1cm, peak ********max****=4.8 ********10****3****m (but with the distance from IP to the first quad just ~2m), ********c**** ****= 2********10****-4**

**IR and a few arc cells in the ****design by A.Bogacz**** **