Channel using Lithium Lens Simulation Study of Final Cooling · BNL Muon Collider Design Workshop...

BNL Muon Collider Design Workshop December 1-3, 2009

Simulation Study of Final Cooling Channel using Lithium Lens

UCLAK. Lee, D. Cline, A. Garren

December 01, 2009


Previous Studies with Lithium lens

• Curved Li lens (~2004-current) by Y. Fukui• Cooling Ring studies (~2002-2004) using Li lens by A.

Garren and Y. Fukui• Initial engineering considerations for a liq. Li lens (2008)

with some inputs from J.P. Morgan and T. Leveling at Fermilab and BINP papers


Li Lens Cooling Ring in ~2004

A. Garren


Results for Cooling Ring w/ Straight Lens

Y. Fukui et. al, Proceedings of 2005 Particle Accelerator Conference, Knoxville, Tennessee,

IEEE01591401


Curved Lithium Lens Cooling Ring

Y. Fukui

f0 = 278.3 MHz for 250 MeV/c


Results for Cooling Ring w/ Curved Lens

Y. Fukui et. al, Proceedings of 2005 Particle Accelerator Conference, Knoxville, Tennessee,

IEEE01591401


•Previous work shows transverse emitt. cooling especially by the curved Li lens

•Objective is to find a channel that can cool the transverse emittance to below 0.1 mm-rad from about 0.5 to 1 mm-rad

•The channel must be mechanically feasible and likely as liquid lithium lens

Current Simulation Study for the Final Cooling Stage


Final Cooling Stages


Li Lens Properties•Strongly focusing

•Low Z material for ionization cooling

οο IπrµBmaxmax 2=

kAI ο 500=sec500 mt =∆

B field ~ 10 T at surface

low β region


Cooling in an ideal Li Lens

maxBmaxpr

eGpβ

3=

=

maxBmaxpr.ˆ.eq 005000850 ≈≈ βε

(cm, MeV/c, T)

V. Balbekov, Aug. 2006

maxBmaxr.eqˆ

eqr30≈= βγ

εβ

Beam focusing parameter in the azimuthal B field

(cm, MeV/c, T)

(cm, T)

Iο≈ 500 kAmps

azimuth. B

Equilibrium beam parameters


Idealized multi-lens cooling channel

In an optimized multi-lens cooling channel, the lens field should increase, and the lens length should decrease by the same factor step by step.

If all the lenses have the same length, a constant increase/decrease factor has to be applied.Exponential transverse cooling is achieved by this, in spite of scattering.Transverse decrement in the lens is about 0.66 / β4γ per meter.Longitudinal increment in the lens is about 1.3 / β4γ3 per meter.

V.Balbekov, August 2006


Example: 7 x 154 cm Li lens channel

The lens field increases, and the radius decreases by factor 1.6 / cell.

Muon momentum drops from 317 MeV/c to 211 MeV/c in any lens.

Beta function, equilibrium transverse emittance and beam radius are given at 211 MeV/c.

---------------------------------------------------------------------------------------------------------------

V.Balbekov, August 2006


ICOOL Simulation Parameters• Li lens 10 cm radii × 60 cm length• Beam input parameters

– (σx, σy, σz)=(1 cm,1 cm, 2 cm)– (σPx, σPy, σPz)= (0.00025, 0.00025, 0.00025 GeV/c)

• Bmax=15 to 150 T or G ~ 10 T/cm• Physics interactions

– dElev=2; straglev=4; scatlev=4


Ionization Cooling with Very Large Beam

Sol0.0T, Li0.1T/cm, Chan10 O5-Sol25-Cell-O5-Li10-O5-RF15-O5-Li10-O5-RF15-O5-

0.000

0.005

0.010

0.015

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

z (m)

e_perp e_long

Sol0.0T, Li0.1T/cm, Chan10 O5-Sol25-Cell-O5-Li10-O5-RF15-O5-Li10-O5-RF15-O5-

0.00

0.05

0.10

0.15

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

z (m)

avgR

•ICOOL simulations show beam cooling in the straight channel Li lens w/o solenoids

•The Li lens channel show trend of cooling out to 6 m for a parrallel beam of 10 cm radius.

•strag=on; scatt=on

Sol18.0T__Li1.36T_cm__Chan10_O5-Sol25-Cell2-O5-Li10-O5-RF10-O5-Li10-O5-Sol25-

0.0000.0050.0100.0150.0200.0250.030

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

z (m)

e_perp e_long

Sol18.0T__Li1.36T_cm__Chan10_O5-Sol25-Cell2-O5-Li10-O5-RF10-O5-Li10-O5-Sol25-

0.00

0.05

0.10

0.15

0.20

0.25

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

z (m)

avgR

Li lens channel w/o solenoid

Li lens channel w/ solenoids


ICOOL Simulation DiagnosticsSol0.0T__Li1.94T_cm__Chan1_O01-Sol25-

03Cell-O05-Li20-O05-RF10-

400.00420.00440.00460.00480.00500.00520.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60

z (m)

total #

•Channel –Li Lens 10 cm × 20 cm length and RF 10 cm cavities

–03Cell-O05-Li20-O05-RF10-

–strag=on; scatt=on; –(σx, σy, σz)=(1 cm,1 cm, 2 cm); (σPx, σPy, σPz)= (0.00025, 0.00025, 0.00025 GeV/c)

•Almost no particle lost

•Pz restored by 185 keV/cm RF to 0.25 GeV/c

Sol0.0T__Li1.94T_cm__Chan1_O01-Sol25-03Cell-O05-Li20-O05-RF10-

0.22

0.23

0.24

0.25

0.26

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60

z (m)

<Pz>


ICOOL Simulation ResultsSol0.0T__Li1.94T_cm__Chan1_O01-Sol25-

03Cell-O05-Li20-O05-RF10-

0.005.00

10.0015.0020.0025.00

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60

z (m)

avgR avgPt


0.00E+00

5.00E-03

1.00E-02

1.50E-02

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60

z (m)

stra_1_scat_1 stra_0_scat_1 stra_0_scat_0


0.00E+002.00E-044.00E-046.00E-048.00E-041.00E-03

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60

z (m)

e_perp e_long

•Beam gets a large kick at entrance; avg P_tswings to maximum and down to minimal level.

•avg R is flat or almost flat at exit of each lens

•Beam emitt. almost zero for parallel beam at entrance and increasing. Scattering appears to increase the avg P_t gradually.

avg Pt to be normalized by 500


Li1.8T_cm__Chan1_O01-Sol25-04Cell-O05-Li60-O05-RF30-

0.0000.0050.0100.0150.0200.0250.030

0.00 1.00 2.00 3.00 4.00 5.00

z (m)

avg

R (m

)

stra_0_scat_1 stra_0_scat_0


0.00

0.02

0.04

0.06

0.08

0.00 1.00 2.00 3.00 4.00 5.00

z (m)

avg

Pt (G

eV/c

)

stra_0_scat_1 stra_0_scat_0

Channel with Four 10 cm x 60 cm LensComparison for Scattering On and Off

emit001b:

(σσσσx, σσσσy, σσσσz)=(1 cm,1 cm, 2 cm)

(σσσσPx, σσσσPy, σσσσPz)= (0.00025, 0.00025, 0.00025 GeV/c)


Channel with Four 10 cm x 60 cm LensComparison for different beam profiles

Both: (σσσσx, σσσσy, σσσσz)=(1 cm,1 cm, 2 cm)

emit001b: (σσσσPx, σσσσPy, σσσσPz)= (0.00025, 0.00025, 0.00025 GeV/c)

emit003b: (σσσσPx, σσσσPy, σσσσPz)= (0.025, 0.025, 0.025 GeV/c)


0.0000.0200.0400.0600.0800.100

0.00 1.00 2.00 3.00 4.00 5.00

z (m)

avg

R (m

)

stra_0_scat_1 emit001b stra_0_scat_1 emit003b


0.00

0.05

0.10

0.15

0.00 1.00 2.00 3.00 4.00 5.00

z (m)

avg

Pt (G

eV/c

)

stra_0_scat_1 emit001b stra_0_scat_1 emit003b


Channel with One 10 cm x 135 cm LensRF (only as gradient)SolenoidLi Lens

135 cm170 cm

Li Lens:10 cm 1.79 T/cm

20 cm 7.60 T/cm

20 cm 15.0 T/cm

75 cm 15.0 T/cm

10 cm 15.0 T/cm

RF: 185 keV/cmLi15.0T_cm_Chan1_O06-Li125-Cell-Sol170(-

Li10-O10-RF150)-

0.000.100.200.300.400.50

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

z (m)

<Pz>

Li15.0T_cm_Chan1_O06-Li125-Cell-Sol170(-Li10-O10-RF150)-

0.00

200.00

400.00

600.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

z (m)

Total # (10 T) Total # (20 T + emit003b)Total # (20 T + emit003b + decay)

stopping µs


List of beam parameters

(1.0,1.0,20.0)×10–3

(1.0,1.0,2.0)×10–2

(1.0,1.0,2.0)×10–1

(1.0,1.0,1.0)×10–3

(1.0,1.0,1.0)×10–2

(1.0,1.0,1.0)×10–1

(σσσσx, σσσσy, σσσσz) [m]

(5.0,5.0,5.0) ×10–2004c(2.5,2.5,2.5) ×10–1(1.0,1.0,2.0)×10–3002c

(5.0,5.0,5.0) ×10–2004b(2.5,2.5,2.5) ×10–1(1.0,1.0,2.0)×10–2002b

(5.0,5.0,5.0) ×10–2004a(2.5,2.5,2.5) ×10–1(1.0,1.0,2.0)×10–1002a

(2.5,2.5,2.5) ×10–2003c(2.5,2.5,2.5) ×10–4(1.0,1.0,2.0)×10–3001c

(2.5,2.5,2.5) ×10–2003b(2.5,2.5,2.5) ×10–4(1.0,1.0,2.0)×10–2001b

(2.5,2.5,2.5) ×10–2003a(2.5,2.5,2.5) ×10–4(1.0,1.0,2.0)×10–1001a

(σσσσPx, σσσσPy, σσσσPz) [GeV/c]

(σσσσPx, σσσσPy, σσσσPz) [GeV/c]

(σσσσx, σσσσy, σσσσz) [m]


Channel with One 10 cm x 135 cm LensComparison between 10 T and 20 T exit solenoid


0.0000.0100.0200.0300.0400.050

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

z (m)

avg

Pt (G

eV/c

)

10 T 20 T


0.000

0.005

0.010

0.015

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

z (m)

avg

R (m

)

10 T 20 T


0.00

0.01

0.10

1.00

10.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

z (m)

beta

_per

p (m

)

10 T 20 T


-5.00

0.00

5.00

10.00

15.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

z (m)

alph

a_pe

r

10 T 20 T


Channel with One 10 cm x 135 cm LensComparison between 10 T and 20 T exit solenoid


0.00000.00020.00040.00060.00080.0010

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

z (m)

e_pe

rp (m

*rad

)

(10 T + emit001b) (20 T + emit001b)


0.00000.00020.00040.00060.00080.0010

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

z (m)

e_pe

rp (m

*rad

)

(10 T + emit001b) (20 T + emit001b)


0.00000.00100.00200.00300.00400.0050

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

z (m)

e_lo

ng (m

*rad

)

(10 T + emit001b) (20 T + emit001b)


0.00000.00050.00100.00150.00200.00250.0030

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

z (m)

e_pe

rp (m

*rad

)

(10 T + emit001b) (20 T + emit003b)


0.00000.00050.00100.00150.00200.00250.0030

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

z (m)

e_pe

rp (m

*rad

)

(10 T + emit001b) (20 T + emit003b)


0.00000.00500.01000.01500.02000.02500.0300

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

z (m)

e_lo

ng (m

*rad

)

(10 T + emit001b) (20 T + emit003b)


Series of 9 cm Li lens Channel of 300 cells

Li06.20T_cm_Chan_O06-300Cell-Li3.0-0Li3.0-Li3.0-RF3.0

0.00

0.01

0.02

0.03

0.04

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00

z (m)

rmsR rmsPt

3 cm

3 cm 3 cm

3 cm

3 cm

3 cm 3 cm

3 cm

3 cm

3 cm 3 cm

3 cm

3 cm

3 cm 3 cm

3 cm

RF=54 MV/mG=6.2 T/cm


Series of 9 cm Li lens Channel


0.000.050.100.150.200.250.30

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00

z (m)

<Pz>


0.00100.00200.00300.00400.00500.00600.00

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00

z (m)

total # no decay


0.0000

0.0005

0.0010

0.0015

0.0020

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00

z (m)

e_perp no mscat


0.00

0.01

0.02

0.03

0.04

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00

z (m)

e_long no mscat


Series of 9 cm Li lens Channel


0.0000

0.0005

0.0010

0.0015

0.0020

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00

z (m)

e_perp no mscat e_perp'


Summary

• Parallel beam used for adjusting Li Lens gradient for beam matching between components

• Achieved a cooling factor 1.7 from 2.5 mm*rad down to 1.5 mm*rad in a channel with a single 10 cm x 135 cm Li Lens with field gradient steps from 1.8 T/cm to 15 T/cm.

• With the capture solenoid at 10 T (or 20 T), significant beam loss at the transition into the RF system

• Strong coupling between the transverse and longitudinal motion, revisit the short length lens and cooling to 500 mm⋅mrad; continue to explore this channel using stronger gradients successfully in ICOOL simulations


Liquid Li Lens Development at BINP

• The Li lens work by Dr. Silvestrov et. al at BINP was for use at the Tevatron anti-proton source (accord w/ Fermilab for run II) and at CERN.

• The lens survived < 100k pulses at 7.5 T (design was 10M and 13 T).

• Shock waves in the Li and cracking of the Ti septum.


BINP Li Lens

BINP liquid lithium lens, opened lens lithium vessel and the entire system.

http://www-bdnew.fnal.gov/pbar/Projects/liquidlilens/liquidli.htm


Properties of Lithium Metal

]3[kg/m3103T3.7995102T8.0035T0.02729540.43liquidρ −×⋅+−×⋅−⋅−=

( )( )

⋅Ω−−⋅−×+⋅−×= mT

solid6102.27331046.4121055.8ρ

( )

−⋅−×−⋅= 3kg/m273.2T4101.81533

solidρ

( )( )[ ]mTliquid ⋅Ω−−−×+⋅−×= 6102.2733107.21210884.27ρ

Resistivity [10−−−−6 ΩΩΩΩ-m]

Density [gm/cm3]

BINP Li Lens Technology



Properties of Lithium Metal

BINP Li Lens Technology


Lithium Resistivity

010203040506070

0 100 200 300 400 500

T [C]

10^-

6 O

hm-c

m

Lithium Density

0.480.490.5

0.510.520.530.54

0 100 200 300 400 500

T [C]gm

/cm

^3


Observed Fermilab Li Lens Lifetime

>10,000,000 (19 wk)700

9,000,000 (17 wk)740

3,000,000 (5.7 wk)800

1,000,000 (3.8 wk)900

<500,000 (1.9 wk)1,000

Avg. Life Time (Pulses)

B grad (T/m)

J. Morgan

Lens Upgrade Note


Initial Mechanical Design

•D 2.54cm × L 30cm

•Outer tube for heated oil above 200 C

•Double layered tubes for liquid Li and heated oil


Push-Pull Flow of Liquid Li

U-joint and bottom out for impurity collection

Reservoir

Pipe to reservoir Li lens tube

of 2 cm dia.

Conceptual Design w/ two reservoirs for push-pull thermal cooling action.


Properties of Related Elements

1.27813Li3N

2.011,570Li2O

7.874 [Fe]1,370Steel

4.511,668Ti

1.851,287Be

2.7660.32Al

0.54180.54Li

Density [g/cc]

Melting pt. [C]


Initial Design of Liquid Li Lens

Lens assembly w/ current discs and the primary and secondary coils

Li D = 2.54 cm; L = 30.0 cm


Thermal Cooling w/ static Li in LensLi Lens Parameters: D = 2.54 cm; L = 30.0 cm; Wall Thickness = 1.06 mm (~41mil)

IDC = 64.0 kAmps; BSurface = 1.00 T; DC Heat Load = 1.77 MW; too high

@15 Hz of 10 msec pulses, Heat Load = 70 kW; manageable

Be Tube [k@20C = 190 W/m/K]: Outer T = 200 C; Inner T = 210 C

Ti Tube [k@20C = 22 W/m/K]: Outer T = 200 C; Inner T = 285 C

Oil Sp. Heat Capacity cP@20C ~ 2 kJ/kg/K: Flow ~ 13 L/min


Steady State Heat Transfer

•Current enters in the left disc and exit in the right disc.

•Temperature on tube is maintained at ~200 C.

COMSOL3.4 (trial license)


B Field at the Current Disc

B field map at the disc

COMSOL3.4 (trial license)


Fermilab Solid Li Lens (Recent Design)

J. Morgan

Lens Upgrade Note

Induction Coils

D 2.0 cm x L 15 cm


Summary to the Liquid Lithium Lens

to work on designing the liquid Li lens in 2010, if we receive funding, collaborating with Fermilab people.

Channel using Lithium Lens Simulation Study of Final Cooling · BNL Muon Collider Design Workshop...

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