frictional cooling scheme for muon collider: demonstration …€¦ · frictional cooling fcd...

Frictional Cooling FCD Experiment Cooling Simulation

Frictional Cooling Scheme for Muon Collider:Demonstration Experiment Summary

D [email protected]

NuFact’09Chicago

21 July 2009

D Greenwald Frictional Cooling

Frictional Cooling FCD Experiment Cooling Simulation Concept Scheme

Frictional Cooling Concept

A particle is brought to an equilibrium energy by application of a constant electric fieldin a retarding medium where energy loss increases with increasing kinetic energy.

Stopping power for µ+ in Helium:

T / MeV-310 -210 -110 1 10 210 310

-1

g2

Sto

pp

ing

Po

we

r / M

eV

cm

1

10

210

310 Effective dE/dx of E-Field

EquilibriumT

Ionization Peak

High 1ρ

dE/ds around around equilibrium

energy necessitates medium be gas.



Cooling Medium

µ+

charge exchange cross sections for Heliummake it the ideal gas

to reduce loss of muons to formationof Muonium

to reduce changes to equilibriumenergy due to effective charge ofmuon in medium

µ−

capture cross sections for Helium andHydrogen make them the ideal choice.

Energy / eV50 100 150 200 250

2 C

ross

Sec

tion

/ cm

-1810

-1710

-1610

-1510

-1410

Muon Capture in

HeNeArKrXe

Energy / eV1 10 210 310 410 510 610 710 810

2 /

cmσ

-2410

-2310

-2210

-2110

-2010

-1910

-1810

-1710

-1610

-1510

-1410

loss-e capture-e

Energy / eV1 10 210 310 410 510 610 710 810

effe

ctiv

e ch

arge

0

0.2

0.4

0.6

0.8

1



Frictional Cooling Cell



First Simulations

This frictional cooling scheme was simulated with input from a front end scheme asdescribed in Ankenbrandt, 1999 (arXiv: physics/9901022): a muon beam exiting thepion drift region with emittance

ǫ6,N = 2 × 10−4(πm)3

The goal was to acheive a luminosity as prescribed in Ankenbrandt,

L = 7 × 1034cm−2s−1,

which is acheived with an emittance

ǫ6,N = 2 × 10−10(πm)3

The simulation (arXiv: physics/0410017) yielded an emittance

ǫ6,N ≈ 3 × 10−11(πm)3,

and the desired luminosity. (The yield was 0.002 µ+/p.)


Frictional Cooling FCD Experiment Cooling Simulation Construction Simulation Recent Date Status

First Experiment

Motivated by the promising results from the first simulations, an experimentalverification of frictional cooling using a proton beam was undertaken at NevisLaboratories, Columbia University. (arXiv: physics/0311059)

Unfortunately, too-thick exit-windows on the cooling cell prevented cooled protonsfrom exiting the experiment, and frictional cooling was not observed.



FCD Cell

Motivated by the promising results from the first simulations, the FCD experiment atthe MPP aims to verify the principle behind frictional cooling.

Accelerating-grid and gas-cell construction: Detector mounted in gas-cell flange:



Proton Source Mechanism

Protons created by stripping e−from H atoms in Mylar

Silicon Drift Detector (from MPI-HLL)



Experimental Setup

The grid has been operated up to 90 kV, and run stably at 60 kV with the gas-cellfilled with Helium at pressures up to 1.25 Atm.



Ideal Cooling Cell Simulation

Simulation of an ideal cooling cell (uniform fields) was undertaken to investigatevarious aspects of the frictional cooling principle, specifically:

effects of nuclear scattering and multiple scattering

the rate of µ− capture and muonium formation

the role of effective charge

the effects of impurities in the Helium gas

Z [ cm ]0 5 10 15 20 25 30 35 40 45 50

T [

keV

]

0

10

20

30

40

50

60E = 6.0 kV/cm

E = 8.0 kV/cm

E = 10.0 kV/cm

Kinetic Energy [ keV ]2 4 6 8 10 12 14 16 18 20

arbi

trar

y

0

20

40

60

80

100

120

140

160

accepted = 99 % = 0.44 keVσ

<T> = 4.78 keV


<T> = 6.87 keV


<T> = 8.82 keV



FCD Cell Simulation

Using realistic shapes of the fields, these simulations predict acceptance rates andmean proton energy as a function of both the electric field (here represented as a highvoltage placed on the first ring of the accelerating grid) and Helium gas pressure.

P [ mbar ]1 10

HV

[ k

V ]

10

12

14

16

18

20

22

24

26

28

30

Acc

epta

nce

in D

etec

tor

[ %

]

0.2

0.4

0.6

0.8

1

1.2

1.4T = 290.00 K

P [ mbar ]-110 1 10

HV

[ k

V ]

10

12

14

16

18

20

22

24

26

28

30

<T>

[ ke

V ]

2

4

6

8

10

12

T = 290.00 K



Most Recent Spectra

Proton spectra have recently been taken for energies between 5.6 keV and 24 keV in800 eV steps. This allows us to characterize the detector’s response to protons veryaccurately.



Status

The experiment construction has been successfully commissioned:

the accelerating grid runs reliably, without breakdown between rings, at voltagesabove 65 kV (0.65 MV/m).

the gas cell can hold steady pressures of Helium gas from 2 × 10−3 mbar to 1250mbar,

the proton source is constructed and operating (R ≈ 20 kHz)

detector response well understood

Current Issues:

breakdown inside the gas

increases of detector leakage current

Once these are resolved, we will measure proton energy spectra for various strengthsof the electric field and densities of the gas. These spectra will be compared to thosethat have been caclculated from the Monte Carlo simulations.


Frictional Cooling FCD Experiment Cooling Simulation CoolSim Low-E µ Source

CoolSim

We are developing a simulation package based on Geant4 called CoolSim, optimizedfor tracking particles of particles in (gaseous) matter.

CoolSim features

a human-readable macro-command interface

capability to implement geometries quickly and modularly

direct ROOT-tree output

New physics processes:

Charge Exchange / Effective Charge (current):

calculation of particle’s effective charge as function of material and energydiscrete charge changes when transitioning from medium to vacuumplanned expansion to low-density discrete charge changes and nongasseous materials

µ− capture (planned)



Low-Energy µ+ Source

A CoolSim application example: a frictional cooling scheme for a low-energy surfacemuon beam.

The input parameters for the simulation were taken from the Paul Scherrer Institute’smuon beam: 4 MeV beam with large momentum spread and angular spread.

The cooling scheme consists of a thin (≈ 100µm) Tungsten foil, shown in red;followed by a solenoidal magnetic field (1 T), a FODO cell (0.8 T/m), and a weakdipole (5 mT), all shown in green; then a Helium gas cell (0.011mg/cm3) with anaxial electric field (0.8MV/m) aligned towards the dipole, shown in blue.



Low-Energy µ+Source

/CoolSim/AddBox Foil

/CoolSim/Foil/SetX 600 600 0.1 mm

/CoolSim/Foil/SetTranslation 0 0 0.5 cm

/CoolSim/Foil/AddMaterial

/CoolSim/Foil/AddMaterial G4\_W 1.

/CoolSim/Foil/SetDensity 19.3 g/cm3

/CoolSim/AddQuadrupole Q1

/CoolSim/Q1/SetDiameter 100 cm

/CoolSim/Q1/SetLength 10 cm

/CoolSim/Q1/SetTranslation 0 0 18 cm

/CoolSim/Q1/SetMagnitude 3 T/m

/CoolSim/AddBox D1

/CoolSim/D1/SetXYZ 100 100 100 cm

/CoolSim/D1/SetTranslation 0 0 125 cm

/CoolSim/D1/AddEMField

/CoolSim/D1/B/y/SetEquation [0]

/CoolSim/D1/B/y/SetParameter 0 0.005 tesla

/CoolSim/AddCell GasCell

/CoolSim/GasCell/SetLength 600 cm

/CoolSim/GasCell/SetDiameter 100 cm

/CoolSim/GasCell/SetTranslation 0 0 475 cm

/CoolSim/GasCell/AddMaterial G4\_He 1.0

/CoolSim/GasCell/SetDensity 0.011 mg/cm3

/CoolSim/GasCell/E/z/SetEquation [0]

/CoolSim/GasCell/E/z/SetParameter 0 -0.8 megavolt/m

/CoolSim/GasCell/B/z/SetEquation [0]

/CoolSim/GasCell/B/z/SetParameter 0 1 tesla

.

.

.

/CoolSim/AddOutputFile DataFile /mnt/scratch/DataFile.root RECREATE

/CoolSim/DataFile/AddTree DataTree

/CoolSim/DataFile/DataTree/EN/On

/CoolSim/DataFile/DataTree/SN/On

/CoolSim/DataFile/DataTree/R/On

/CoolSim/DataFile/DataTree/Z/On

/CoolSim/DataFile/DataTree/PR/On

/CoolSim/DataFile/DataTree/PZ/On

/CoolSim/DataFile/DataTree/KE/On



Low-Energy µ+ Source

10k muons after the foil:

KE_FoilEntries 6831Mean 2222RMS 864.7

KE0 1000 2000 3000 4000 5000 6000

coun

t

0

20

40

60

80

100

120

KE_FoilEntries 6831Mean 2222RMS 864.7

after the cooling cell + dipole

KE_OutEntries 1231Mean 3.128RMS 0.5441

KE0 2 4 6 8 10 12 14 16 18 20

coun

t

0

20

40

60

80

100

120

140

160

180

200KE_Out

Entries 1231Mean 3.128RMS 0.5441

Ez (keV)0 500 1000 1500 2000 2500 3000 3500 4000 4500

Er

(keV

)

0

100

200

300

400

500

600

700

800

900

1000EzEr_eff

Entries 329Mean x 1896Mean y 60.61RMS x 1078RMS y 37.97

EzEr_effEntries 329Mean x 1896Mean y 60.61RMS x 1078RMS y 37.97

)-2

effic

ienc

y (k

eV0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8-310×


Frictional Cooling FCD Experiment Cooling Simulation Summary

Future

Take FCD data for frictional cooling verification

Implement new physics processes in CoolSim simulation

Investigate using frictional cooling to increase efficiency of low-energy muonbeams

Expand CoolSim simulation to full muon collider front-end

The Muon Group at the Max-Planck-Institute fur Physik:

Allen Caldwell, Daniel Greenwald, Bao Yu, Brodie McKenzie, Andrada Ianus; andDaniel Kollar, Raphael Galea, Christian Blume.


Slowing down of fast muons

x / cm-0.6 -0.4 -0.2 0 0.2 0.4 0.6

y / c

m

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

z / cm0 50 100 150 200 250 300 350 400 450

y / c

m

-2

0

2

4

6

8

10


Frictional Cooling Cell

Muons are guided through gas cell by magnetic field (B⊥E), losing energy until theyare below the ionization peak of the dE/ds curve.


Proton Source Simulation

MC (Geant4) simulation of proton source used to predict spacial distribution ofprotons.


Detector Characteristics

We observe protons with energies between 5 keV and 30 keV. At these energies theydeposite all their energy in the first several hundred nanometers of the detector. Thedetector’s dead layers greatly effect how much energy is measured.

The expected proton energies are used to discover the dead-layer characteristics of theSDD.

Depth / nm0 50 100 150 200 250 300

-1E

nerg

y Lo

ss /

eV n

m

0

10

20

30

40

50

60

70

80

90

100

Cha

rge

Col

lect

ion

Effi

cien

cy

0.2

0.4

0.6

0.8

1

1.2

14.4 keV proton

Deposite Energy

Collected Energy

Charge Collection Efficiency

Energy / keV0 5 10 15 20 25

Cou

nts

/ arb

itrar

y

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Energy / keV0 5 10 15 20 25

Cou

nts

/ arb

itrar

y

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Grid Voltage18 kV16 kV14 kV12 kV10 kV8 kV0 kV

Grid Voltage18 kV16 kV14 kV12 kV10 kV8 kV0 kV

Incoming Energy / keV6 8 10 12 14

Mea

sure

d E

nerg

y / k

eV

3

4

5

6

7

8Measured

Simulated


FCD Cell Simulation

A simulation of the gas cell used in the Fricional Cooling Demonstration experiment isused to predict the energies we will measure when running the experiment.

The electric field calculated from the actual accelerating grid construction is used inthe simulations of the FCD cell.

z [ cm ]0 1 2 3 4 5 6 7 8 9 10

r [

cm ]

-1.5

-1

-0.5

0

0.5

1

1.5 ]-1

E /

HV

[ c

m

0.05

0.1

0.15

0.2

0.25

z [ cm ]0 1 2 3 4 5 6 7 8 9 10

]-1

/ H

V [

cm

zE

-0.15

-0.1

-0.05

0

0.05

0.1

z [ cm ]0 1 2 3 4 5 6 7 8 9 10

/ H

VΦ

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Superconducting Magnet

A superconducting magnet is used to provide a collimating magnetic field, along thecentral axis of the cooling cell. The field strength has been modeled for use insimulations.

Magnet Core Magnetic Field

z /cm-30 -20 -10 0 10 20 30

r /c

m

-20

-15

-10

-5

0

5

10

15

20

100

200

300

400

500

600

700

800

900


FCD Cell Simulation

These simulations have shown the strong effect of the collimating magnetic field.

r [ cm ]0 0.2 0.4 0.6 0.8 1 1.2 1.4

arbi

trar

y

0

10

20

30

40

50

60

70

80

90

100

accepted = 6 % = 0.41 cmσ





frictional cooling scheme for muon collider: demonstration …€¦ · frictional cooling fcd...

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