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The Mu2e Transport Solenoid. J. Miller Boston University for the Mu2e Collaboration 23 January 2009. Mu2e Muon Beamline Requirements. Pulsed beam Deliver high flux m - beam to stopping target At FNAL, high proton flux ~20x10 12 Hz, 8 GeV

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The mu2e transport solenoid
The Mu2e Transport Solenoid

J. Miller

Boston University

for the Mu2e Collaboration

23 January 2009

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Mu2e Muon Beamline Requirements

  • Pulsed beam

  • Deliver high fluxm-beam to stopping target

    • At FNAL, high proton flux ~20x1012 Hz, 8 GeV

    • Mu2e: use solenoidal muon collection and transfer scheme

    • muons ~5 x 1010 Hz , 1018 total needed

  • Muon properties

    • low momentum and narrow momentum spread

      • stop max # muons in thin target

      • avoid ~105 MeV e- from in-flight m- decay (keep pm<75 MeV/c)

  • Background particles from beam line must be minimized

    • especially ~105 MeV e-and high momentum m-

    • a major factor driving design of muon beamline

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Mu2e Muon Beamline- follows MECO design

Muons are collected, transported, and

detected in superconducting solenoidal magnets

Muon

Stopping Target

Calorimeter

Tracker

Proton Beam

Muon Beam

Collimators

Target

Shielding

Proton

Target

B=1 T

B=1 T

Pions

Electrons

B=2 T

Detector

Solenoid

Muons

B=2.5 T

  • Transport

  • Solenoid

  • Selects low momentum m-

  • Avoids straight line from production target to detectors

B=5 T

Production

Solenoid

Delivers 0.0025 stopped

muons per 8 GeV proton

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Transport solenoid
Transport Solenoid

Inner bore radius=25 cm

Length=13.11 m

Toroid bend radius=2.9 m

Curved sections eliminate line of sight transport of n, g.

Radial gradients (dBs/dR) in toroidal sections cause particles to drift vertically; off-center collimator signs and momentum selects beam

dB/dS < 0 in straight sections to avoid slow transiting particles

Collimation designed to greatly suppress transport of e- greater than 100 MeV

Length decreases flux, by decay, of pions arriving at stopping target in measurement period

B=2.5T

B=2.4T

Beam particles

  • Goals:

  • Transport low energy

  • m- to the detector solenoid

  • Minimize transport of positive particles and high energy particles

  • Minimize transport of neutral particles

  • Absorb anti-protons in a thin window

  • Minimize particles with long transit time trajectories

B=2.4T

B=2.1T

B=2.1 T

B=2.0 T

To stopping

target

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Transport solenoid1
Transport Solenoid

Antiproton

absorber

window

B=2.5T

B=2.4T

Inner radius=25 cm

Length=13.11 m

TS1: L=1 m

coll. radius=15 cm

transverse p<110 MeV/c

TS2: R=2.9 m

TS3: L=2 m

coll. radius=20 cm

TS4: R=2.9 m

TS5: L=1 m

coll. radius=15 cm

transverse p<90 MeV/c

TS3 Vertical cut:

+5 cm to -19 cm

TS1

TS2

B=2.4T

B=2.1T

TS3

TS5

TS4

B=2.0 T

B=2.1 T


Toroid field specifications
Toroid Field Specifications

TS1: First straight section. Field grades linearly 2.5 to 2.4T. Axial (Bs) field on axis within 0.5% of expected value. dBs/ds<-0.02T/m for R<15 cm*.

  • TS2: First toroid. Ripple at outer radius <1% of Bs. Field rises from 2.4 T to 2.6 T along inner radius, then returns to 2.4 T. Field on outer radius follows a similar pattern but reduced by 1/R.

  • * dBs/ds<-0.02T/m can be relaxed in transition regions from straight to curved sections whenever |dBs/dr|>0.275 T/m.


Separation of m from m
Separation of m-from m+

m-

m+

7

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Vertical drift motion in a toroid
Vertical Drift Motion in a Toroid

Toroidal Field: Bs=constant x 1/R. This gives a gradient dBs/dR.

Particle spiral drifts vertically (perpendicular to the plane of the toroid bend):

D= vertical drift distance

R = major toroid radius,

s/R = toroid arc angle=900

D[m]= distance, B[T], p[GeV/c]

Bs

R

(Note: particles with small pitch have large D, and particles with opposite sign drift in opposite directions)

B field line in toroid

cm

cm

Production Target

Central Collimator

Stopping Target

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Acceleration in a solenoid with a gradient field
‘Acceleration’ in a Solenoid with a Gradient Field

  • In a magnetic field, low momentum charged particles follow helical paths along the field lines.

  • The magnetic moment of the particle associated with the helical motion is approximately constant. For a relativistic particle, pt2/B=constant,

    • pl is continuously increasing in the direction of decreasing field

      • Particles ‘accelerate’ when spiraling to lower field: pt decreases and pl increases.

      • Particles ‘decelerate’ when spiraling to higher field: pt increases and |pl| decreases.

    • Particles are pushed in the direction of lower field

Note that net

points downstream

regardless of q (if q flips

sign, pt reverses direction)

(Bz points out of page. Field decreases moving out of page, Gz<0. )

Br

pt

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Magnetic mirror
Magnetic Mirror

p

q

  • If a particle spirals in the direction of higher field,

  • pt increases and |pl| decreases:

  • If the field becomes large enough,

  • and the particle is reflected, spiraling back toward lower field

Solenoid axis

(~+B or ~-B)

For a particle born in the middle of the PS, where B~3.5 T, the maximum pitch which can be reflected in the maximum 5T field upstream is (define q = anglebetween momentum and solenoid axis)

If a particle is born near the target where B~3.5 T, then the maximumq (corresponding to minimum pitch) at the downstream end of the PS, where B=2.5 T, will be about 600.

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Long transit time background
Long Transit Time Background

  • Particles with low longitudinal velocity will take a long time to traverse the beam line, arriving at the stopping target during the measurement period

    • Antiprotons and radiative pion capture:

      • Antiprotons are stopped by a thin window in middle of transport

      • Adjust measure start time until most long-transit time pions decay

  • Example of a potential problem

    • Pion decays into a muon early in the transport solenoid

    • Muon can have small pitch and progress very slowly downstream

    • Muon can decay after a long time into an electron

    • Decay electron can be >100 MeV if pm>75 MeV/c

    • Electron could scatter in collimators, arriving at the target late during the measurement period, where it could scatter into the detector acceptance

  • To suppress this…

    • All straight sections of solenoids have <0 gradient, |dBs/ds|>0.02 T/m

      • Greatly reduces number of particles (e.g. p->m) with small pitch

      • Gradient criterion not necessary in curved solenoid sections, low pitch particles are swept away vertically by dBs/dr field gradient.

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


S shape transport solenoid
S-Shape Transport Solenoid

  • Advantages

    • Second, reverse bend re-centers helices (on average) on the solenoid axis

    • Second, reverse bend cancels vertical dispersion due to first bend- could give more uniform stopping distribution on target and more stops on target (latter to be demonstrated)

    • Second bend gives added protection against neutrals scattering down solenoid from PS

  • Disadvantages

    • Gives only half the dispersion of two bends in the same direction

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Collimators
Collimators

  • Off-center collimator at TS midsection

    • Advantages

      • possible to alter geometry to change the distribution of transmitted particles

      • May be possible to get p+ for calibrations by rotating collimator

      • Could be removed to allow + and – to pass: + for calibration, - to give some realistic background to see its effect on resolution

    • Disadvantages

      • Beam offset may require a larger TS diameter compared to dipole centering.

  • Collimators at TS entrance and exit

    • Advantages

      • Can be modified to increase or decrease transmitted transverse momentum

      • Can be enlarge to pass p+ at larger radii, stop them at larger radii, get better geometric coverage of detector from decay electron

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Field gradient in straight sections
Field Gradient in Straight Sections

  • Advantages

    • Substantially reduces late-arriving particles at the stopping target

  • Disadvantages

    • Increased cost

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Antiproton absorber
Antiproton Absorber

  • Advantages

    • Absorbs all antiprotons and effectively suppresses the background

    • Separates ‘dirty’ upstream vacuum from ‘clean’ downstream vacuum

    • Warm bore access is helpful in accessing that portion of the TS for other purposes, e.g. to rotate the collimators

  • Disadvantages

    • Need warm access to the thin absorber in case it breaks

    • Probably need at least one toroid bend downstream to help eliminate the background from seondaries produced by antiproton capture on nuclei.

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


New ideas other issues
New Ideas/Other Issues

  • Add adjustable vertical dipole fields inside the toroids to control the vertical offset of the helices; reversible for positive beam. Need ~ 500 gauss vertical field.

    • Control momentum of transmitted beam

    • Control sign of transmitted beam

    • May be difficult to put into toroid region

  • Two bends in the same direction a la COMET?

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Pions at the stopping target
Pions at the Stopping Target

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Muon time distribution at the stopping target
Muon Time Distribution at the Stopping Target

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


END

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Vertical drift motion in a toroid1
Vertical Drift Motion in a Toroid

Toroidal Field: Axial field Bs=constant x 1/r. This gives a large dBs/dr

Particle spiral drifts vertically (perpendicular to the plane of the toroid bend):

D= vertical drift distance

pl=longitudinal momentum

pt=transverse momentum

R=major toroid radius=2.9 m,

s/R = total toroid bend angle=900

D[m]=distance, B[T], p[GeV/c]

B

Toroid B field line

R

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Cosmic ray background
Cosmic Ray Background

  • Well-studied and controlled by previous muon conversion experiments

  • Reactions which could produce a fake conversion electron:

    • Scattered electrons from cosmic ray muons in target or detectors

    • Muons decaying in-flight in the Detector Solenoid

    • Muon scattering from the target, then mistaken for an electron

    • Muons interacting in shielding, producing hadrons or photons which may not register in a veto counter.

  • MECO design

    • 0.5 m steel, 2 m concrete shielding

    • Active 4p scintillator veto, 2 out of three layers report, 10-4 inefficiency

    • From simulations with ~70x cosmic flux, expect 0.021 events in 2x107 seconds running at FNAL

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Sensitivity of mu2e
Sensitivity of Mu2e

  • For Rμe = 10-15

    • ~40 events / 0.4 bkg (LHC SUSY?)

  • For Rμe = 10-16

  • ~4 events / 0.4 bkg

Rμe < 6 x 10-17 90% CL

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Lfv susy and the lhc

~

LFV, SUSY and the LHC

Access SUSY through loops:

signal at Terascale seen by LHC implies

~40 event signal in this experiment

In some models,

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Radiative pion capture background
Radiative Pion Capture Background

  • p-, like m-, stop in stopping target and form atoms

    • reaction of p- with nucleus is fast: occurs mid-cascade

    • BR 2% for photon > 55 MeV, peak prob ~110 MeV, endpoint~137 MeV

    • g + material (e.g. target) e+e-

      Calculation:

    • BR~0.02

    • (stopped pions) / (proton on primary target) = 3x10-7

    • Probability: e- (101.5<E<105.5 ) produced in target = 3.5x10-5

    • Detector acceptance ~0.8

    • This gives (0.02)(3x10-7)(3.5x10-5)(0.8) = 1.7x10-13/proton

    • For 4x1020 protons, there would be 7x107potential false conversion e’s over the entire measurement.

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Experimental advantage of m e
Experimental Advantage of m e

  • Electron energy, 105 MeV, is far above the bulk of low energy decay electron background. Considerable improvement in the ultimate sensitivity is quite likely.

  • Contrast with m eg:

    • e and g each have energies of 53 MeV, right at the maximum flux of electron energies from ordinary muon decay. This background is believed to limit future improvements in achievable limits on the branching ratio.

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Electrons from production target
Electrons from Production Target

  • Electrons present largest flux of particles during the proton injection

    • Most traverse the beam line quickly compared to muons, pions, etc.

    • Suppression depends on extinction + suppression in the beam line.

  • Beamline and collimators are designed to strongly suppress electrons > 100 MeV from arriving at stopping target

  • Simulation: With 107 electrons starting at the production target, none made it to the stopping target.

  • Electrons >100 MeV entering the Detector Solenoid from the Transport Solenoid will have the wrong (too large) pitch when arriving at the detector compared to a conversion electron, due to gradient field in the stopping target region, except for target scatter.

    • 45<Qmax< 60 degrees for electrons from stopping target

    • Qmax< 45 degrees for electrons from entrance of Detector Solenoid

  • Estimate: 0.04 background events

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Meco simulations
MECO Simulations

  • Full GEANT simulations of all particles traversing muon beam line: e,p,m,g,n,K…

  • Full GEANT tracking of particles in detector region

  • Separate studies of long transit time particles

    • pions,K0, K+,K-,pbars

    • K_L live a long time, ~52 ns

      • Separate simulation, following decays of low energy K_L from production region; number of background electrons at the stopping target was found to be tiny.

    • neutrons: can energetic neutrons survive many bounces down the beam line and be delayed enough in time to arrive in the measurement period? Study needed

  • As part of the process of absorbing the MECO knowledge, Mu2e is seting up a general simulation apparatus and will repeat the MECO calculations

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Neutrino oscillations and m e
Neutrino Oscillations and me

  • n’s have mass! Individual lepton numbers are not conserved

  • Therefore lepton flavor violation also occurs in charged

  • leptons. In the SM:

  • SM: BR(mNeN)<10-52

  • This is way below any experimental sensitivity

  • Other CLFV are similarly suppressed

  • Any observation of CLFV is evidence for new physics

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Power of signal in muon electron conversion

L. Calibbi, A. Faccia, A. Masiero, S. Vempati hep-ph/0605139

neutrino mass via the see--saw mechanism,analysis in SO(10) framework

Neutrino-Matrix Like (PMNS)

Minimal Flavor Violation(CKM)

measurement

can distinguish

between PMNS and MFV

Power of Signal in Muon-Electron Conversion

tan b=10

Current

Mu2e

0

800

1600

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Detector solenoid stopping target and detectors
Detector Solenoid:StoppingTarget and Detectors

Tracker measures energy of electrons to <1MeV FWHM, high-side tail s~300 keV

Calorimeter after the tracker: provides fast trigger, confirms energy and trajectory

2.4-2.9 m long, 0.5 cm diameter straws

Specs: sz~1.5 mm, sr~sj~200 mm

Target

pt=55MeV/c

Uniform B=1 T

Graded B

B=2 T

30

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Detector solenoid stopping target and detectors1
Detector Solenoid:StoppingTarget and Detectors

Tracker measures energy of electrons to <1MeV FWHM, high-side tail s~300 keV

Calorimeter after the tracker: provides fast trigger, confirms energy and trajectory

2.4-2.9 m long, 0.5 cm diameter straws

Specs: sz~1.5 mm, sr~sj~200 mm

Uniform B=1 T

Graded B

B=2 T

31

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Tracking
Tracking

  • Projection of helical track

  • Conversion electron has high momentum (pT) and has R large enough to pass outside octagon and be tracked

  • DIO (pT < 55 MeV/c) does not!

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Lepton flavor violation
Lepton Flavor Violation

BABAR Pub-07057

< 9 x 10-8

Belle and BABAR

J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


Energy calibration
Energy Calibration

  • Mu2e resolution: s~300 keV on high-side tail, FWHM ~ 1 MeV

    • Response function needs to be well established

  • Proposed energy integration region: 103.6-105.1 MeV

  • Proposed absolute energy calibration: s~0.1-0.2 MeV

  • Calibration approaches:

    • Stop p+ in the stopping target

    • Lower solenoid field to improve geometric overlap with detector

    • Gives energy response function and energy calibration but at lower energy

    • Reverse field to transport positive particles, or rotate collimator

  • Use DIO spectrum to monitor calibrations

  • Calibrate with a 100 MeV electrons from a dedicated accelerator

  • J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


    Antiproton induced background
    Antiproton-induced background

    • Cross section for production by 8 GeV protons is small

    • Only very low energy antiprotons are transported.

      • Can move very slowly through beam line.

    • When material is encountered, forms atom, annihilates producing energetic pions, gammas, etc.

    • Potentially dangerous background source.

    • Eliminated by stopping all antiprotons in a very thin window in the middle of the Transport Solenoid

    • Simulation: Secondary particles from antiproton annihilation tracked.

    • Estimate: 0.006 counts

    • Background is fairly continuous in time, unlike muons and pions

    J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009



    Magnetic spectrometer rates vs time
    Magnetic Spectrometer: Jan 23, 2009Rates vs. Time

    • Rates start at 6 MHz/wire but

    • ≲ 180 kHz/wire in live time window

    • Each muon capture produces 2γ, 2n, 0.1p

    J. Miller, BU Berkeley Mu-e Workshop Jan 23, 2009


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