Uses of Quasi-Isochronous Helical Channels in the Front End of a Muon Collider/Neutrino Factory

3/1/2011 MAP Winter Meeting at JLAB Cary Y. Yoshikawa

1Muons,Inc.

Uses of Quasi-Isochronous Helical Channels in the Front End of a Muon

Collider/Neutrino Factory

Cary Yoshikawa

Chuck Ankenbrandt

Dave Neuffer

Katsuya Yonehara


2Muons,Inc.

• Evolution of the QIHC (2 snapshots)

• Configuration in the Phase II proposal, which was awarded and is funding current studies.

• Current configuration

Outline

• Motivation

• Design upstream of HCC for increased acceptance

• Design downstream of HCC for bunch merging

• Design upstream of HCC for increased acceptance

• Design downstream of HCC for bunch merging

• Summary & Future


3Muons,Inc.

• Upstream of an HCC optimized for cooling:

• Affords a larger RF bucket size when operating near transition for purpose of capture and bunching after the tapered solenoid.

• Having control over both γT and energy of synchronous particle should enlarge phase space available for particles to be captured.

• The Quasi-Isochronous HC should match naturally into an HCC that is maximized for cooling (equal cooling decrements).

The Quasi-Isochronous HC aims to shorten the length of the front end of a muon collider/neutrino factory by exploiting the tunable slip factor:

in the following ways:

Motivation

)sin(1

)sin(1

2

162'

max

s

s

HC

RF

rfbucket

cmeV

wA

223

2

22

2

3

2 1111ˆ1

1

THC D

zcm

Ec HC 2

)(

• Downstream of the HCC optimized for cooling :

• Allows recombination of bunches over a potentially shorter distance compared to other studies by utilizing a large slip factor after inducing different energies across the bunches:


4Muons,Inc.

Configuration in the Phase II Proposal

300 m? 10 m 4.5 m 20 m FE

Tar

get

Solenoid 5 MV/m in vacuum 35 MV/m in H2/Be Match HCC(MB)

20 m 5.5 m 300 m

p πμ

πμ

BCP HCC(SB)

BC

33 m

z(m) Subsystem Purpose

0.0 to 4.5 Capture/Tapered Solenoid Enhance pion/muon capture

4.5 to 24.5 First straight RF Buncher in vacuum 1.Initial capture of π’s & μ’s into RF buckets.2.Allow lower momenta π’s to decay into μ’s.

24.5 to 44.5 Second straight RF Buncher in 100 atm H2 w/ variably thick Be windows.

1.H2 gas allows higher RF gradient.2.Be causes higher momenta π’s to interact, enhancing useful μ’s. 3.Transverse cooling.

44.5 to 50.0 Match into HCC 1.To match between straight solenoid into HCC.2.Enhance μ capture by manipulating RF bucket size.

50.0 to 350 HCC(Multi-Bunch) To cool string of multiple bunches of muons in 6D phase space.

350 to 360 Bunch Combiner Preparation (BCP) To transform string of bunches at same energy into string at different energies with head bunches at higher energies than trailing bunches.

360 to 393 Bunch Combiner (BC) To combine the multiple bunches in a single one via free drift in large |η| channel.

393 to 693 HCC(Single-Bunch) To cool single bunch of muons in 6D phase space.


5Muons,Inc.

The rate of muons created across the transition from vacuum into the Be/H2 has increased by:

~21% (728882)

Birth of Mu-’s 2m before H2/Be 35 MV/m region

P vs. z

Birth of Mu-’s 2m into H2/Be 35 MV/m region

P vs. z

PhaseII Upstream HCC: Justification for adding H2/Be (z=24.5m)


6Muons,Inc.

Bucket Area, Reference Momenta, GammaT, Slip Factor, Pitch (kappa), & Synch Accel Phase in Matching Section

-200

-100

0

100

200

300

400

44.0 45.0 46.0 47.0 48.0 49.0 50.0 51.0

z (m)

Se

e l

eg

en

d f

or

un

its

.

Pmu(reference, MeV/c)10xBucket Area(Chuck's arb)100xGammaT1000xSlip Factor300xKappa1000 x |sin(φs)|φs (degrees)

Initial design was based on a reference with constant momentum (237 MeV/c) and γT extracted in matching section via earliest arrivals over incremental longitudinal sections.

Note that because κ goes from 0 to 1, the reference sees more material as it traverses the matching section and thus |sin(φs)| must increase to compensate energy loss, forcing the bucket area to decrease along z.

Phase II HCC Upstream: Matching Section

)sin(1

)sin(1

2

162'

max

s

s

HC

RF

rfbucket

cmeV

wA


7Muons,Inc.

(204.5, 236.3)

Phase II HCC Upstream: Matching Sectionz = 50.0 m (End of Match)

P (

MeV

/c)

t (nsec)

~9000 μ–/100k POT


8Muons,Inc.

Bucket Area, Reference Momenta, GammaT, HCC Slip Factor, Pitch(kappa), & Synch Accel Phase in Matching Section

-150.00

-50.00

50.00

150.00

250.00

350.00

450.00

550.00

44.00 45.00 46.00 47.00 48.00 49.00 50.00 51.00

z (m)

Se

e l

eg

en

d f

or

un

its

.

Pmu(reference, MeV/c)100xBucket Area(eV-sec)100xGammaT10000xSlip Factor300xKappa1000 x |sin(φs)|φs (degrees)

In principle, it is possible to achieve monotonic RF bucket growth by manipulating the phase φs, γT (via ), and field gradient . b maxV

Phase II HCC Upstream: Matching Section


9Muons,Inc.

Phase II HCC Downstream: Bunch Recombiner Preparation

Before bunches out of the HCC can be combined, the string of mono-energetic bunches must be transformed into one whose head bunches (early arrivals) are at higher energies than the tail (late arrivals), since we operate above transition.

This can be achieved by using an RF at off frequency. In this case, 204.08MHz for bunches with 200 MHz spacing.

εL=0.002m/bunch

cτ(m)

KE(MeV)

-4 -420 20

f=204.08 MHz V’ = 15 MV/m 9.6m in QIHC

η = 0.05

030

0


10Muons,Inc.

Phase II HCC Downstream: Bunch Recombiner

-4 20

0

cτ(m)

KE(MeV)

-4 20

300Drift

32.5 m in

QIHCC w/ η

= 0.43

Note that these simulations are 1-D only. 3-D using g4beamline is shown later.

Total length:9.6+32.5=~43m.

Compare to 340m*

* R. Fernow, “Estimate of Front-End Magnetic Requirements,” NFMCC Tech. Note 529 (2008)

20-4

After synchrotron oscillations within a 200 MHz rf bucket. ~95% of the initial beam is captured within that bucket.

V’ = 12 MV/mη = 0.05


11Muons,Inc.

Current HCC Upstream: End of 2nd Straight Section

1.081E41.061E4

9.159E39.496E3

Pi– & Mu–

Mu–

Pi+ & Mu+

Mu+


12Muons,Inc.

• Emittances out of second straight:εT=11 mm-rad x ε||= 378 mm-rad

• HCC(cooling optimized) acceptance:εT=20 mm-rad x ε||= 40 mm-rad

• Need to transform a cigar shaped εTxε║ (11 x 378) into a football shaped one (20 x 40).

p

t

450 MeV/c

…

Current HCC Upstream: Match

Want a low κ HCC that’ll have large momentum acceptance (150 MeV/c < p <450 MeV/c) that cools longitudinally. Since we will need to operate with a nearly straight solenoid, we will need to operate below transition. Desire a low κ HCC with a ptransition ~≥ 450 MeV/c.

P(MeV/c)

t(nsec)

Pref = 225 MeV/c

free drift for 45.2 m

Bz(on z-axis) = 2.4 T

Bz(on ref) = 2.3 T

Bφ(on z-axis) = 0.62200 T

dbφ/dρ (on z-axis) = -1.33809 T


13Muons,Inc.

• Maxing out use of wedge (60 atm case) increases longitudinal acceptance by 19% over the case without any wedge.

• Perhaps the matching scheme should incorporate ~30m of κ = 0.25 QIHCC with Be wedges in H2 gas at 60 atm, followed by removal of the Be wedges to achieve the lowest equilibrium emittances.

H2:200 atm H2:100 atm H2:60 atm

εlong (m-rad) at z = 0 m 0.13300 0.14810 0.15820

εlong (m-rad) at z = 30 m 0.09619 0.09843 0.09901

εtrans (m-rad) at z = 0 m 0.03513 0.03426 0.03374

εtrans (m-rad) at z = 30 m 0.01787 0.01914 0.01915

ε6D (m^3) at z = 0 m 1.42800E-04 1.50800E-04 1.53100E-04

ε6D (m^3) at z = 30 m 2.30000E-05 2.85800E-05 2.78500E-05

Lowest emittance (~equilibrium) at z=30m. Highest emittance (acceptance) at z=0.

Current HCC Upstream: Wedge in Match

To enhance longitudinal cooling, we studied effect of adding a cylindrical wedge.

1. H2:200 atm: No wedge, only H2 at 200 atm at 293 K.

2. H2:100 atm: Be wedge ~1mm at reference to loose same energy as 100 atm H2.

3. H2: 60 atm: Max Be wedge ~1.48 mm w/ H2 at knee of breakdown.

Emax = 32 MV/m

φs~14º

Pref = 225 MeV/c

f = 201.25 MHz

Bz(z-axis) = 2.4T

Bz(on ref) = 2.3T


14Muons,Inc.

G4beamline simulation of phase rotation of bunches with 200 MHz spacing with off frequency 405 MHz.

t(ns)

p(GeV/c)

14

Current HCC DownstreamKatsuya Yonehara

bunch 1

bunch 7

bunch 13

bunch 1

bunch 7

bunch 13

f=405 MHz V’ = 10 MV/m

2.5 m in QIHC

η = 0.04


15Muons,Inc.

Phase II HCC Downstream: Bunch Recombiner

p(GeV/c

t(ns)

Drift 46.5 m

in Q

IHCC w/ η= 0.72

f=200 MHz V’ = 5 MV/m

in QIHC η = 0.04

5 nsec

• Initial phase rotation in G4BL result in energy spreads that are larger than 1D simulation.

• These large energy spreads translate into large time spreads at the end of the drift region.

bunch 1

bunch 7

bunch 13

t(ns)

p(GeV/c


16Muons,Inc.

Conclusions and Future (upstream of HCC)

• Maxing out use of wedge (60 atm case) increases longitudinal acceptance by 19% over the case without any wedge.

• Perhaps the matching scheme should incorporate ~30m of κ = 0.25 QIHCC with Be wedges in H2 gas at 60 atm, followed by removal of the Be wedges to achieve the lowest equilibrium emittances.

• Consider use of higher RF frequencies upstream of the matching section to lower its εL acceptance requirement. 201.25 325 MHz?

• Perhaps the matching section is better suited to follow one that has the overall longitudinal emittance be spread across several bunches with smaller emittances, ie. Dave’s baseline FE with phase rotation.

• Throughout 0 < κ < 1 match, design for continual RF bucket growth by manipulating the phase φs, γT (via ), and field gradient . b maxV

)sin(1

)sin(1

2

162'

max

s

sRF

rfbucket

cmeV

wA


17Muons,Inc.

• Initial 1D studies show promising results with 95% capture of muons merged into a single bunch over ~43 m.

• Initial 3D studies in G4BL have phase rotation resulting in energy spreads that are larger than 1D simulation, translating into larger time spreads at the end of the drift region.

• Phase rotation parameters to optimize:

• Off frequency, V’max

• Drift parameters to optimize:

• η, λ

• Can also consider effect of adding RF manipulation into both phase rotation (harmonics) and drift regions.

Conclusions and Future (downstream of HCC)


18Muons,Inc.

Back up


19Muons,Inc.

Configuration in the Phase II Proposal

300 m? 10 m 4.5 m 20 m FE

Tar

get

Solenoid 5 MV/m in vacuum 35 MV/m in H2 Match HCC(MB)

20 m 5.5 m 300 m

p πμ

πμ

BC1 HCC(SB)

BC2

33 m

z(m) Subsystem Purpose Physical Dimensions Fields

0.0 to 4.5 Capture/Tapered Solenoid Enhance pion/muon capture L = 4.5 mR = 7.5 cm 35 cm

Bsol = 20 T 4.2 T

4.5 to 24.5 First straight RF Buncher in vacuum

1. Initial capture of π’s & μ’s into RF buckets.2. Allow lower momenta π’s to decay into μ’s.

L = 20 mR = 35 cm

Bsol = 4.2 T160 RF Cavities: V’max = 5 MV/m, f= 162.5 MHz φs=186°: P(μ−)=150162 MeV/c

24.5 to 44.5

Second straight RF Buncher in 100 atm H2 w/ variably thick Be windows.

1. H2 gas allows higher RF gradient.2. Be causes higher momenta π’s to interact, enhancing

useful μ’s. 3. Transverse cooling.

L = 20 mR = 35 cm

Bsol = 4.2 T160 RF Cavities: V’max = 35 MV/m, f= 162.5 MHz φs=208194°, P(μ−)=162237 MeV/c

44.5 to 50.0

Match into HCC 1. To match between straight solenoid into HCC.2. Enhance μ capture due to transition occurring in

match.

L = 5.5 m (5.5 λ’s)R = 35 cm

Bsol = 6.3 T 4.2 T44 RF Cavities: V’max = 35 MV/m, f= 162.5 MHz φs varied to maintain P(μ−)=237 MeV/c

50.0 to 350

HCC(Multi-Bunch) To cool string of multiple bunches of muons in 6D phase space.

L = 300 m λ=1m R = 35 cm

Bsol = 4.2 T V’max = 16 MV/m, f= 200,400,800 MHz

350 to 360 Bunch Combiner Preparation (BCP)

To transform string of bunches at same energy into string at different energies with head bunches at higher energies than trailing bunches.

L = 10 m λ=1m R = 35 cm

Bsol = 4.2 T V’max = 15 MV/m f= 204.08 MHz for 201.25 MHz spacing.

360 to 393 Bunch Combiner (BC) To combine the multiple bunches in a single one via free drift in large |η| channel.

L = 33 m λ=1m R = 35 cm

Bsol = 4.2 T V’max = 0

393 to 693 HCC(Single-Bunch) To cool single bunch of muons in 6D phase space. L = 300 m λ=1m R = 35 cm

Bsol = 4.2 T V’max = 16 MV/m, f= 200,400,800 MHz


20Muons,Inc.

Reference Momenta and Bucket Area

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30 35 40 45 50

z (m)

Mo

me

nta

(M

eV

/c)

or

Bu

ck

et

Are

a (

arb

. u

nit

s)

Pmu(reference)

Bucket Area

5 MV/m Vacuum35 MV/m H2 100 atm @ 273K Σ{variable Be windows} = λI(π)/2


21Muons,Inc.

Mu+P vs t

Pi+P vs t

Mu-P vs t

Pi-P vs t

(204.5, 236.3)

Phase II HCC Upstream: Matching Sectionz = 50.0 m (End of Match)


22Muons,Inc.

Transverse Emittances of Mu- in the 2 Straight Sections

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

0.020

0.022

0 10 20 30 40 50

z (m)

Tra

ns

ve

rse

Em

itta

nc

e (

m-r

ad

)

eperp-3sig (m-rad)

eperp-6sig (m-rad)

H2, 35 MV/mVacuum, 5 MV/m

εT(acceptance) < 20 mm

162.5 MHz

Current HCC Upstream: Two Straights

300 m? 10 m 4.5 m 20 m FE

Tar

get

Solenoid 5 MV/m in vacuum 35 MV/m in H2 Match HCC(MB)

20 m 5.5 m 300 m

p πμ

πμ

BC1 HCC(SB)

BC2

33 m


23Muons,Inc.

Longitudinal Emittances of Mu- in the 2 Straight Sections

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.400

0 10 20 30 40 50

z (m)

Lo

ng

itu

din

al E

mit

tan

ce

(m

-ra

d)

elong-3sig (m-rad)

elong-6sig (m-rad)

H2, 35 MV/mVacuum, 5 MV/m

162.5 MHz

εL(acceptance) < 40 mm

Current HCC Upstream

• Emittances out of second straight are 11 mm-rad transverse by 378 mm-rad longitudinal.

o Transverse is fine.

o Longitudinal is ~10x’s too large.



24Muons,Inc.

• To transform a cigar εTxε║ into a football, we strive to have emittance exchange from longitudinal to transverse at a rate that can be cooled transversely, netting zero emittance growth transversely and cooling longitudinally.

• So, we look into the following for different cooling decrement schemes in the HCC at various kappa, with particular attention to low kappa values.

• Transverse stability

• Transverse equilibrium emittance

• Momentum acceptance

• Linear extrapolation

• Note at low kappa, we expect less transverse/longitudinal coupling, so the hope is that the momentum acceptance mostly applies to the transverse component and the RF holds onto the muons hot longitudinally.



25Muons,Inc.

Linear Approx for Momentum Acceptance in R=35cm HCC

0

200

400

600

800

1000

1200

1400

1600

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Kappa

Del

ta P

ab

ou

t Ref

225

MeV

/c

Δp=Ď-1pΔa/a(Equal)

Δp=Ď-1pΔa/a(Trans)

Δp=Ď-1pΔa/a(Long)

Equilibrium Transverse Emittances

-2

0

2

4

6

8

10

12

14

16

18

20

0 0.2 0.4 0.6 0.8 1

Kappa(pitch)

Eq

uilib

riu

m T

ran

svers

e

Em

itta

nce (

mm

-rad

) ε+(Equal)

ε-(Equal)

ε+(Trans)

ε-(Trans)

Transverse Stability

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Kappa or pitch

G/R

^2

G/R2 (Equal)

G/R2 (Trans)

G/R2 (Long)

pDaa

p

da

dp

p

aD 11 ˆˆ

Transverse stability requires:

0 < G < R2 or equivalently 0 < G/R2 < 1

where

112

2ˆˆ

1

2

DDq

G

2

2

11

2

1

q

R

a

b

pk

qD

2

2/32

2

221 1

1

1ˆ

11 2

pk

Bq z



26Muons,Inc.

Linear Approx for Momentum Acceptance in R=35cm HCC

0

200

400

600

800

1000

1200

1400

1600

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Kappa

Del

ta P

ab

ou

t Ref

225

MeV

/c

Δp=Ď-1pΔa/a(Equal)

Δp=Ď-1pΔa/a(Trans)

Δp=Ď-1pΔa/a(Long)

Equilibrium Transverse Emittances

-2

0

2

4

6

8

10

12

14

16

18

20

0 0.2 0.4 0.6 0.8 1

Kappa(pitch)

Eq

uilib

riu

m T

ran

svers

e

Em

itta

nce (

mm

-rad

) ε+(Equal)

ε-(Equal)

ε+(Trans)

ε-(Trans)

Transverse Stability

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Kappa or pitch

G/R

^2

G/R2 (Equal)

G/R2 (Trans)

G/R2 (Long)

pDaa

p

da

dp

p

aD 11 ˆˆ


• Emittances out of second straight:

εT=11 mm-rad x ε||= 378 mm-rad

• HCC(cooling optimized) acceptance:

εT=20 mm-rad x ε||= 40 mm-rad


• Look into cooling at low κ.

stab

le

unstable


27Muons,Inc.

Equal Coolingκ = 0.1

Transverse Only Coolingκ = 0.1






28Muons,Inc.

Neither equal cooling decrements nor transverse only cooling provides the desired acceptance. Prior experience with Quasi Iso HCC work suggests the following possibilities to increase acceptance.

1. Enlarging Rref as well as Raperture.

• Will use Rref = Raperture = 30 cm (front end baseline). Previously, used Rref = 16 cm & Raperture = 35 cm (HCC baseline).

2. Increasing B fields.

• Equal cooling and transverse only fix B fields, which turn out to be rather low.

• Quasi-Iso allows Bsol to be a degree of freedom.

3. Try to simultaneously design for ptransition ≥ 450 MeV/c and pref = 225 MeV/c.

• This attempt is not totally consistent. The pseudo-ptransition mentioned on slides going forward effectively defines the dispersion for a muon with p=ptransition on the reference orbit. But, only a muon with p=pref will be on the reference orbit. Despite the skewed accounting scheme for the dispersion, the exercise proved useful. Recall:

DT

ˆ1

12

2

2


29Muons,Inc.

P~transition = 750 MeV/c

Bsol = 2 T


Bsol = 2 T


Bsol = 2 T


Bsol = 2.3 TG/R2 = 0.224 G/R2 = 0.322


30Muons,Inc.

Ptransition (MeV/c) κ

Bsol (T) Ď-1 bd (T) bq (T/m) b2 (T) G/R2

Plow – Phigh PEarliest Arrival (MeV/c)

450 0.25 2 1.126 0.19778 0.83897 0.12585 0.412 100-300 271

550 0.25 2 1.653 0.27054 0.36016 0.05402 0.507 100-345 300

650 0.25 2 2.285 0.35786-

0.21441-

0.03216 0.539 100-402 338

750 0.25 2 3.023 0.45972-

0.88475-

0.13271 0.462 100-455 395

850 0.25 2 3.866 0.57613-

1.65084-

0.24763 0.224 100-326 > 326

850 0.25 2.3 3.866 0.58700-

1.26141-

0.18921 0.322 100-504 406

875 0.25 2.4 4.093 0.62200-

1.33809-

0.20071 0.294 100-521 424

900 0.25 2.5 4.327 0.65790-

1.42075-

0.21311 0.269 100-539 445

950 0.25 2.7 4.814 0.73245-

1.60403-

0.24061 0.225 100-572 431

1050 0.25 3.2 5.868 0.89607-

1.91261-

0.28689 0.159 100-600~500; ~isochronous

>400


Bsol = 2.4 T


Bsol = 3.2 T


31Muons,Inc.

To enhance longitudinal cooling, we investigated effect of adding a wedge:

1. Baseline is the 200 atm of H2 at 293 K as studied before. (200 atm)

2. Channel contains 100 atm of H2 at 293 K plus a cylindrical Be wedge 1.051 mm thick at the reference (r=30cm) between RF cavities 10 cm apart. (100 atm)

• Wedge has zero thickness on the z-axis and twice as thick at r=60 cm.

• Energy loss in Be equals that in H2.

3. Channel contains 60 atm of H2 at 293 K plus a cylindrical Be wedge 1.481 mm thick at the reference (r=30cm) between RF cavities 10 cm apart. (60 atm)

• Wedge has zero thickness on the z-axis and twice as thick at r=60 cm.

• Total energy loss is same as in both cases above.

• H2 density is at knee of breakdown curve.



32Muons,Inc.

Longitudinal Emittance of Mu+'s Traversing a Kappa=0.25 QIHCC (2nd pass stoch on)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0 5 10 15 20 25 30 35 40 45 50

z (m)

Lo

ng

. E

mit

tan

ce (

m-r

ad)

H2:200 atm, 3σ

H2:100 atm, 3σ

H2:60 atm, 3σ

HCC



33Muons,Inc.

Transverse Emittance of Mu+'s Traversing a Kappa=0.25 QIHCC (2nd pass stoch on)

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0 5 10 15 20 25 30 35 40 45 50

z (m)

Tra

ns

. Em

itta

nc

e (

m-r

ad

)

H2:200 atm, 3σ

H2:100 atm, 3σ

H2:60 atm, 3σ

HCC



34Muons,Inc.

6-D Emittance of Mu+'s Traversing a Kappa=0.25 QIHCC (2nd pass stoch on)

0.0E+00

2.0E-05

4.0E-05

6.0E-05

8.0E-05

1.0E-04

1.2E-04

1.4E-04

1.6E-04

1.8E-04

0 5 10 15 20 25 30 35 40 45 50z (m)

6-D

Em

itta

nce

(m

^3)

H2:200 atm, 3σ

H2:100 atm, 3σ

H2:60 atm, 3σ



35Muons,Inc.

bunched beam

Phase rotationToF(ns)

P(GeV)

Test with 3 bunches (ToF = -30, 0, 30 ns)ν = 0.405 GHz, E = 10 MV/m¼ synchrotron oscillation at z = 2.5λ

35

Current HCC Downstream

Katsuya Yonehara

bunch 1

bunch 7

bunch 13

bunch 1

bunch 7

bunch 13


36Muons,Inc.

Phase slipping in HS magnet

η = 0.72Particles are aligned in timing at z = 49λNote that Δt is too large to be in 200 MHz RF bucket

36


bunched beam cont.Katsuya Yonehara

bunch 1

bunch 7

bunch 13

bunch 1

bunc

h 1

bunch 7 bunc

h 7

bunch 13

bunc

h 13


37Muons,Inc.

Merging in isochronous HS magnet

ν =0.2 GHz, E=5 MV/mη =0.04

37


bunched beam cont.Katsuya Yonehara

bunc

h 1

bunc

h 7

bunc

h 13

bunc

h 1

bunc

h 1

bu

nch

1

bunc

h 7

bunc

h 7

bu

nch

7

bunc

h 13

bu

nch

13

bunc

h 13

5 nsec


38Muons,Inc.

single particle

ν =0.408 GHz, E=5 MV/mη =0.04¼ of synchrotron oscillation at z=4.2 λ

Phase rotation in HS magnet Phase rotation in Bessel field magnet

η = 0.72Particles are aligned in timing at z = 33λ

8/20/10 38MI, Friday meeting


Katsuya Yonehara

Documents

Uses of Quasi-Isochronous Helical Channels in the Front End of a Muon Collider/Neutrino Factory