Muon Collider Lattice Design Status Muon Collider Workshop, Telluride CO, June 27 – July 1 2011 Y. Alexahin (FNAL APC) Lattice design - 1.5 TeV c.o.m

Muon Collider Lattice Design Status

Muon Collider Workshop, Telluride CO, June 27 – July 1 2011

Y. Alexahin (FNAL APC)

Lattice design - 1.5 TeV c.o.m Lattice - New 3 TeV c.o.m Lattice

Fringe Field and Multipole Errors Strong-Strong Beam-Beam Simulations Plans

Ring Lattice Requirements2

What we would like to achieve compared to other machines:

MC Tevatron LHC

Beam energy (TeV) 0.75 0.98 7

* (cm) 1 28 55

Momentum spread (%) 0.1 <0.01 0.0113

Bunch length (cm) 1 50 15

Momentum compaction factor (10^-3) 0.01 2.3 0.322

Geometric r.m.s. emittance (nm) 3.5 3 0.5

Particles / bunch (10^11) 20 2.7 1.15

Beam-beam parameter , 0.1 0.0250.01

Muon collider is by far more challenging:

much larger momentum acceptance with much smaller *

~ as large Dynamic Aperture (DA) with much stronger beam-beam effect

very small momentum compaction factor

- New ideas for IR magnets chromaticity correction needed!

MC Design Status- Y. Alexahin MC workshop 06/30/2011

Chromatic Correction Basics3

,

,1,

22xxx

xpx

xxpx

xx

px

BAW

BA

Montague chromatic functions :

Ax,y are created first, and then converted into Bx,y as phase advances x,y grow

K1 , K2 are normalized quadrupole and sextupole gradients, Dx is dispersion function: Dx = dxc.o./dp

The mantra:

Kill A’s before they transform into B’s !

- difficult to achieve in both planes

- horizontal correction requires 2 sextupoles 180 apart to cancel spherical aberrations

Bx,y are most important since they determine modulation of phase advance x,y

xxx

xxxxx

ABKDKBA

2),(2 21

s

pxppx s

sds0 ),(1

1),(

x,y = -x,y /2 , x,y are Twiss lattice functions, p is relative momentum deviation.

Equations for chromatic functions


Magnet Requirements4


Distance from IP to the 1st quad = 6 m Bending field in the arcs = 10T, in large aperture IR dipoles

8T Aperture diameter > 10 max + 30 mm Quad gradient < 10T/ (/2) Quad length < 2 m, dipole length < 6 m Interconnects > (1 + 2)/2 + 16 cm (typically + 2 cm

added) FF quads horizontally displaced (if possible) to provide a

dipole component that: - generates additional dispersion for chromaticity

correction - sweeps aside decay electrons

*=1cm 1.5 TeV c.o.m. MC IR Optics


5

50 100 150 200 1000

0

1000

2000

3000

4000

5000

6000

xW

xDD

)(

)(,

cmDD

mW

x

yx

yW

)(ms

50 100 150 200

50

100

150

200

250

x

y)(

)(,

cmD

m

x

yx2S

)(ms

2/xD

3S 4S1S

essentially a focusing doublet

chromaticity correction sextupoles

6*=1cm 1.5 TeV MC FF Quads

5 10 15 20 25

2

4

6

8

Q3 Q4 Q5 B1 Q6

Q2Q1

s(m)

a(cm)

5x

5y

Parameter Unit Q1 Q2 Q3

Coil aperture mm 80 110 160

Nominal gradient T/m 250 187 -130

Nominal current kA 16.61 15.3 14.2

Quench gradient @ 4.5 K T/m 281.5 209.0 146.0

Quench gradient @ 1.9 K T/m 307.6 228.4 159.5

Coil quench field @ 4.5 K T 12.8 13.2 13.4Coil quench field @ 1.9 K T 14.0 14.4 14.8Magnetic length m 1.5 1.7 1.7

Quads displaced horizontally by 0.1 aperture to create ~2T bending field


7*=1cm 1.5 TeV MC Lattice Performance

Qx Qy

p

p

c

DA ()

p

“Diagonal” Dynamic Aperture (Ax=Ay) vs. (constant) momentum deviation in the presence of beam-beam effect ( = 0.09/IP) for normalised emittance N=25 m

Only muons at bunch center tracked !Fractional parts of the tunes and momentum compaction factor vs. momentum deviation

beam extent


8Design Pros & Contras


Pros: Achieves all stated goals (momentum acceptance, DA, etc.) Robust chromaticity correction scheme Small horizontal beam size allows for close shielding to intercept secondaries FF quads can be displaced horizontally to create a dipole field

Contras: Large y_max high sensitivity to magnet errors Difficult to upgrade to higher energies: it may not be possible to retain 10T pole tip field in quads with apertures > 16 cm due to mechanical problems

Triplet vs Doublet FF9

A simplified problem considered: Point-to-parallel focusing *=5mm, N=25()mmmrad, 1.5TeV/beam First quad starts at 6m from IP Continuously varying quad gradient G=8T / R_bore, R_bore= 5*Sqrt(max*N/)+15 mm

8 10 12 14 16 18 20

50 000

100 000

150 000

200 000

250 000

15 20

20 000

40 000

60 000

80 000

s s

In the case of triplet focusing max is 3 times smaller! - effect of the gradient dependence on aperture


10

Q3Q4 Q5 B1Q7

Q2Q1

s(m)

a(cm)

5x5y

Q8Q6

*=5mm 3 TeV c.o.m. MC FF Quads (Preliminary!)

Q1 Q2 Q3 Q4-Q6 Q7 Q8

aperture (mm) 80 104 130 146 146 160

gradient (T/m) -250 -192.3 153.9 136.5 -136.7 -121.4

length (m) 1.85 1.75 1.95 2.05 1.75 2.6

Aperture requirement >10 max +30 mm as in 1.5 TeV case The number of different apertures increased to 5 to follow more

closely the beam sizes Length limit < 2 m not fulfilled for Q8, it can be cut in two

pieces if necessary No horizontal displacement due to large horizontal beam size

M1


11*=5mm 3 TeV c.o.m. MC IR Optics (Preliminary!)

y (m)

x (m)

10*DDx (m)

20*Dx (m)

s (m)

Wy

chromaticity correction sextupoles

M2

s (m)

Wx

M1


12*=5mm 3 TeV MC Lattice Performance (w/o Arcs)

Large Qx= -1.65105 octupole (and decapole) correctors at M2 DA < 4 compensating octupole at M1 DA > 5

*(cm)

y*

p

x*

Qx

Qy

p

Static momentum acceptance 0.5% and Dynamic Aperture ~ 5 seem feasible – the arc sextupoles are too weak to have any effect

CSIy [m]

CSIx [m]

5

1024 turns DAFractional parts of the tunes


133 TeV MC Arc Cell

SY

DDx(m)/2

Dx (m)

SX SX

SASY

dsDDDCd

d

dsDC

C

xx

p

c

Cx

c

0

2

0

)(211

,1

x (m)y (m)

Central quad and sextupole SA control the momentum compaction factor and its derivative (via Dx and DDx) w/o significant effect on chromaticity Large -functions ratios at SX and SY sextupole locations simplify chromaticity correction Phase advance 300/ cell spherical aberrations cancelled in groups of 6 cells Large dipole packing factor small circumference (C~4.5 km with 10T dipole field)MC Design Status- Y. Alexahin MC workshop 06/30/2011

14Parameters of the Two Designs

s (TeV) 1.5 3* (cm) (bare lattice) 1 0.5_max (km) 48 94Av. Luminosity / IP (1034/cm2/s) 1.25 4.4Max. bending field (T) 10 10Av. bending field in arcs (T) 8.3 8.4Circumference (km) 2.5 (2.7) 4.5No. of IPs 2 2Repetition Rate (Hz) 15 12Beam-beam parameter / IP 0.087 0.087Beam size @ IP (m) 6 3Bunch length (cm) 1 0.5No. bunches / beam 1 1No. muons/bunch (1012) 2 2Norm. Trans. Emit. (m) 25 25Energy spread (%) 0.1 0.1Norm. long. Emit. (m) 0.07 0.07Total RF voltage (MV) at 800MHz 20 250

hCP

fhNn

f repb

~21

4

2

0L

P – average muon beam power (~ )

4Nr

C – collider circumference (~ if B=const)

– muon lifetime (~ )

* – beta-function at IP

– beam-beam parameter

0.5 1 1.5 2

0.6

0.7

0.8

0.9

h

z /

“Hour-glass factor”


What’s Next? 15


Triplet FF solves the problem with large y_max, but lacks some nice features of the doublet FF associated with small x With triplet FF the major concern is horizontal beam stability, whereas with doublet FF it is for the vertical plane Is a compromise possible? For 3 TeV we must know what gradients can be realistically achieved in large aperture quads, G(A) curve is needed from magnet designers For 1.5 TeV case we may try to optimize y_max/ x_max ratio and reduce * Optimization should be performed with account of systematic and random magnet errors and their correction strategy - a lot of work to do! Extra manpower is needed!

Fringe Field in IR quads (V.Kapin)16

1024 turns DA for 1.5TeV lattice in units of initial coordinates at IP without (left) and with quadrupole fringe fields: center - embedded in MAD-X PTC hard-edge approximation, right - maps produced by COSY. Only vertical motion suffers due to y_max>> x_max PTC underestimates the effect

y0 (m)

x0 (m)


y0 (m)

x0 (m)

IR Open-Midplane Dipole Nonlinearities (V.Kapin)17


Rref=40mm

b1=10000

b3=-5.875

b5=-18.320

b7=-17.105

IR dipole coil cross-section and good field region

Effect of multipole components on DA in 1.5TeV case: decapole is most detrimental

18


DA in the plane of initial particle coordinates:. left - no multipole errors, center -sextupole error added, right - sextupole corrector placed at the 1st y maximum. Effect of the sextupole error can also be compensated with octupole (Netepenko) Sextupole error affects both x- and y-motion

Correction of IR Dipole Nonlinearities (V.Kapin)

50 100 150 200

50

100

150

200

250

x

y)(

)(,

cmD

m

x

yx2S

)(ms

2/xD

3S 4S1S

SC1

Strong-Strong BB Simulations (K.Ohmi) 19


Very fast luminosity degradation (by 15%) observed, most likely due to initial mismatch Dr. Ohmi will come at Fermilab in October to do more studies.

Plans20

Lattice design: - complete 1.5TeV design with new tuning & collimation sections - finish the 3TeV design

Fringe fields & Multipoles: - include realistic long. profile (Enge function) in MAD-X (F.Schmidt, CERN) or borrow from COSY-Infinity (V.Kapin) - nonlinear corrector arrangement for fringe field and multipole error correction (V.Kapin, F.Schmidt)

Strong-Strong Beam-Beam Simulations: - K.Ohmi (KEK) will come at Fermilab in October - A.Valishev and E.Stern (FNAL) also promised to look

Self-Consistent Longitudinal Dynamics: - V.Balbekov & L.Vorobiev (FNAL GS) can address it (using ORBIT?)


Documents

Muon Collider Lattice Design Status Muon Collider Workshop, Telluride CO, June 27 – July 1 2011 Y. Alexahin (FNAL APC) Lattice design - 1.5 TeV c.o.m