channel using lithium lens simulation study of final cooling · bnl muon collider design workshop...
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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
BNL Muon Collider Design Workshop December 1-3, 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
BNL Muon Collider Design Workshop December 1-3, 2009
Li Lens Cooling Ring in ~2004
A. Garren
BNL Muon Collider Design Workshop December 1-3, 2009
Results for Cooling Ring w/ Straight Lens
Y. Fukui et. al, Proceedings of 2005 Particle Accelerator Conference, Knoxville, Tennessee,
IEEE01591401
BNL Muon Collider Design Workshop December 1-3, 2009
Curved Lithium Lens Cooling Ring
Y. Fukui
f0 = 278.3 MHz for 250 MeV/c
BNL Muon Collider Design Workshop December 1-3, 2009
Results for Cooling Ring w/ Curved Lens
Y. Fukui et. al, Proceedings of 2005 Particle Accelerator Conference, Knoxville, Tennessee,
IEEE01591401
BNL Muon Collider Design Workshop December 1-3, 2009
Results for Cooling Ring w/ Curved Lens
Y. Fukui et. al, Proceedings of 2005 Particle Accelerator Conference, Knoxville, Tennessee,
IEEE01591401
BNL Muon Collider Design Workshop December 1-3, 2009
•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
BNL Muon Collider Design Workshop December 1-3, 2009
Final Cooling Stages
BNL Muon Collider Design Workshop December 1-3, 2009
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
BNL Muon Collider Design Workshop December 1-3, 2009
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
BNL Muon Collider Design Workshop December 1-3, 2009
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
BNL Muon Collider Design Workshop December 1-3, 2009
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
BNL Muon Collider Design Workshop December 1-3, 2009
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
BNL Muon Collider Design Workshop December 1-3, 2009
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
BNL Muon Collider Design Workshop December 1-3, 2009
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>
BNL Muon Collider Design Workshop December 1-3, 2009
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
Sol0.0T__Li1.94T_cm__Chan1_O01-Sol25-03Cell-O05-Li20-O05-RF10-
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
Sol0.0T__Li1.94T_cm__Chan1_O01-Sol25-03Cell-O05-Li20-O05-RF10-
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
BNL Muon Collider Design Workshop December 1-3, 2009
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
Li1.8T_cm__Chan1_O01-Sol25-04Cell-O05-Li60-O05-RF30-
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)
BNL Muon Collider Design Workshop December 1-3, 2009
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)
Li1.8T_cm__Chan1_O01-Sol25-04Cell-O05-Li60-O05-RF30-
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
Li1.8T_cm__Chan1_O01-Sol25-04Cell-O05-Li60-O05-RF30-
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
BNL Muon Collider Design Workshop December 1-3, 2009
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
BNL Muon Collider Design Workshop December 1-3, 2009
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]
BNL Muon Collider Design Workshop December 1-3, 2009
Channel with One 10 cm x 135 cm LensComparison between 10 T and 20 T exit solenoid
Li15.0T_cm_Chan1_O06-Li125-Cell-Sol170(-Li10-O10-RF150)-
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
Li15.0T_cm_Chan1_O06-Li125-Cell-Sol170(-Li10-O10-RF150)-
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
Li15.0T_cm_Chan1_O06-Li125-Cell-Sol170(-Li10-O10-RF150)-
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
Li15.0T_cm_Chan1_O06-Li125-Cell-Sol170(-Li10-O10-RF150)-
-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
BNL Muon Collider Design Workshop December 1-3, 2009
Channel with One 10 cm x 135 cm LensComparison between 10 T and 20 T exit solenoid
Li15.0T_cm_Chan1_O06-Li125-Cell-Sol170(-Li10-O10-RF150)-
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)
Li15.0T_cm_Chan1_O06-Li125-Cell-Sol170(-Li10-O10-RF150)-
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)
Li15.0T_cm_Chan1_O06-Li125-Cell-Sol170(-Li10-O10-RF150)-
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)
Li15.0T_cm_Chan1_O06-Li125-Cell-Sol170(-Li10-O10-RF150)-
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)
Li15.0T_cm_Chan1_O06-Li125-Cell-Sol170(-Li10-O10-RF150)-
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)
Li15.0T_cm_Chan1_O06-Li125-Cell-Sol170(-Li10-O10-RF150)-
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)
BNL Muon Collider Design Workshop December 1-3, 2009
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
BNL Muon Collider Design Workshop December 1-3, 2009
Series of 9 cm Li lens Channel
Li06.20T_cm_Chan_O06-300Cell-Li3.0-0Li3.0-Li3.0-RF3.0
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>
Li06.20T_cm_Chan_O06-300Cell-Li3.0-0Li3.0-Li3.0-RF3.0
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
Li06.20T_cm_Chan_O06-300Cell-Li3.0-0Li3.0-Li3.0-RF3.0
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
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)
e_long no mscat
BNL Muon Collider Design Workshop December 1-3, 2009
Series of 9 cm Li lens Channel
Li06.20T_cm_Chan_O06-300Cell-Li3.0-0Li3.0-Li3.0-RF3.0
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'
BNL Muon Collider Design Workshop December 1-3, 2009
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
BNL Muon Collider Design Workshop December 1-3, 2009
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.
BNL Muon Collider Design Workshop December 1-3, 2009
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
BNL Muon Collider Design Workshop December 1-3, 2009
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
http://www-bdnew.fnal.gov/pbar/Projects/liquidlilens/liquidli.htm
BNL Muon Collider Design Workshop December 1-3, 2009
Properties of Lithium Metal
BINP Li Lens Technology
http://www-bdnew.fnal.gov/pbar/Projects/liquidlilens/liquidli.htm
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
BNL Muon Collider Design Workshop December 1-3, 2009
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
BNL Muon Collider Design Workshop December 1-3, 2009
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
BNL Muon Collider Design Workshop December 1-3, 2009
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.
BNL Muon Collider Design Workshop December 1-3, 2009
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]
BNL Muon Collider Design Workshop December 1-3, 2009
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
BNL Muon Collider Design Workshop December 1-3, 2009
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
BNL Muon Collider Design Workshop December 1-3, 2009
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)
BNL Muon Collider Design Workshop December 1-3, 2009
B Field at the Current Disc
B field map at the disc
COMSOL3.4 (trial license)
BNL Muon Collider Design Workshop December 1-3, 2009
Fermilab Solid Li Lens (Recent Design)
J. Morgan
Lens Upgrade Note
Induction Coils
D 2.0 cm x L 15 cm
BNL Muon Collider Design Workshop December 1-3, 2009
Summary to the Liquid Lithium Lens
to work on designing the liquid Li lens in 2010, if we receive funding, collaborating with Fermilab people.