Longitudinal Phase Space in MICE

1
Longitudinal Phase Space in MICE

• Chris Rogers
• MICE CM
• 2nd March 06

2
Overview

• First look at longitudinal phase space in MICE
• Magnetic lattice
• Momentum acceptance of 200 MeV/c lattice
• Emittance
• Transverse emittance effects
• Longitudinal phase space
• RF bucket
• Longitudinal emittance
• Justification for TOF2 resolution
• TOF2 is required primarily for longitudinal
  emittance measurement
• Tells us where to sit on the dE/dx curve for best
  cooling
• Gives us a comparison with ring coolers etc
• Examine the time reconstruction resolution in
  tracker
• Longitudinal emittance reconstruction resolution
• Can we measure energy straggling

3
MICE VI Momentum Acceptance
MICE VI en12mm sx 52 mm spx 25 MeV
Stop band
Pass band
Pz MeV/c
Pz at start of channel
Pz MeV/c

• Transmission of MICE magnetic lattice vs Pz
• Particles matched for 200 MeV/c
• Red is 10 MICE lattices, blue is 20 lattices, 1
  metre aperture
• Left is histogram of Pz at various points in the
  channel
• Particles seem to diffuse away from 180 MeV/c
  (3p/2)
• Right plot show pz at beginning of the channel of
  particles that survive

4
Comparison with FS2
MICE VI en12mm sx 52 mm spx 25 MeV
Pz MeV/c

• Left is transmission of MICE VI, right is FS2
  (1,1) lattice (Fernow, Muc-241)
• FS2 (1,1) exhibits broader momentum acceptance in
  the 200 MeV/c region
• FS2 (1,1) lattice has b280 mm in the absorbers
• Both use 1 metre apertures
• Not realistic

5
Stop-Bands

• Decompose k2 (B2) into Fourier components qn
  where
• Width of nth stop-band given by
• Gives stop-bands at
• 548 - 559 n1
• 264 - 288 n2
• 184.5 - 184.8 n3
• 135 - 141 n4
• Wider stop-bands comes from larger 2nth order
  Fourier modes
• n1? From matching section?

Wang Kim, Phys Rev E 63 056502
6
Transport Matrix Approach

• Can also get momentum acceptance using transport
  matrix formalism (Fernow, Muc-241)
• Define transport matrix over 1 lattice R
• Require transport matrix over n lattices, Rn, is
  finite for large n
• Gives Dlt2 where Dtrace(R) (textbook result)
• Calculate R(pz) using R P(MDrift(ds/2)MFocus(ds)
  MDrift(ds/2))

FS2 (1,1)
MICE VI
n3?
n1?
n4
n2
7
Comparison with tracking
FS2 (1,1)

• Agreement is questionable
• ICOOL acceptance is in 160/175 - 270/280
• Tr(R) lt 2 between 146 - 253 MeV/c
• Doesnt quite reach 2 at 184 MeV/c
• Cross check using Wang and Kims scheme (141-264
  MeV/c)
• Calculate Tr(R) using Fourier modes of k2
• Better to use matched beams at each momentum?

8
Magnet Issues

• Does the presence of LH2 change the momentum
  acceptance?
• Diffusion into pass-band from energy straggling?
• Change in pz from RF/LH2
• Calculations and plots assumes constant pz
• Other stuff
• Strengthening of the transverse defocusing due to
  msc?
• To what accuracy can we measure this?
• To what accuracy is this desirable
• What does it look like for other MICE settings?
• This is all MICE VI, pz 200 MeV/c, b 420 mm
• What are the effects of the matching section?
• Can the beamline deliver a beam like this?
• I would like a beam that fills the pass-band in
  each MICE case
• Thats a lot of work!

9
Effect of Energy Spread on Cooling
1 MeV 90o
1 MeV/G4MICE
25 MeV 90o
25 MeV/G4MICE
25 MeV/RF 40o
25 MeV/ICOOL

• Beta function for several different beams
• Left hand plot has no RF/Absorbers, RH has full
  cooling
• Energy spread gives a mismatch in the beam
• Define 90o as on-crest

10
Transverse Emittance
25 MeV/RF 40o
25 MeV/G4MICE
25 MeV/ICOOL
25 MeV/RF 90o
1 MeV/G4MICE
1 MeV
1 MeV/RF 90o

• Non-linear effects dominate with a small NuFact
  energy spread
• Typical NuFact dE 25-100 MeV
• Note blue red have same beam but with different
  scaping (1-5)
• In ICOOL I killed particles at rgt250 mm, full
  aperture in G4MICE
• Emittance growth originates from magnetic lattice
• And is strong enough to kill all cooling

11
Emittance Growth vs Energy Spread
eout p mm rad
eout for E0-dE lt E lt E0dE
eout for E0lt E lt E0dE
dE MeV

• Use a distn that is flat in momentum
• Magnets only, ein12 p mm rad, taken over a 5.5 m
  MICE VI lattice
• Clearly higher momentum spreads give more heating
• Even for low momentum spreads eout gt 20 p mm rad
• If we only take E gt E0 then we see no dependence
  on energy spread

12
Emittance Growth vs Energy
de p mm rad
Pz 177
Pz 200
n3
E0 MeV

• Emittance growth is peaked around pz 180 MeV/c
• Emittance growth over a single MICE lattice
  (-2750 to 2750) is 50 p mm rad!
• Input beam has 12 p mm rad
• This corresponds to the n3 resonance
• The presence of this resonance seems a strong
  candidate for the emittance growth
• It should be possible to remedy this by changing
  q0

13
Stop bands (Big)
14
Longitudinal Phase Space

• MICE is scheduled to run on-crest
• RF power too expensive to run off-crest
• FS2 RF runs at 40o (relative to Ez0)
• May be possible to run MICE V off-crest
• Off-crest allows us to look at debunching due to
  Energy straggling
• Longitudinal phase space at the centre of the 8th
  RF cavity

On crest
Off crest
15
Longitudinal Emittance
0.41 p ns rad
Un-normalised Trace Space (t,t), p ns/MeV
Normalised Phase Space (t, E) p ns rad
90 deg
40 deg
Heating associated with long drifts and magnets
Heating associated with magnetic lattice gtgt pz
normalisation
40 deg
90 deg

• See large longitudinal emittance growth
• Highly non-linear effects
• Feeling is heating is mainly caused by the
  magnetic lattice
• Also some particles dropping out of the RF
  bucket, some captured
• Would like to see mainly heating from energy
  straggling
• Why is there such a big difference between trace
  (x10) and phase (x2-4)?
• It is crucial to understand what is going on here

16
Longitudinal Issues

• Cov(E,t) is a free parameter?
• I choose Cov(E,t)0 initially
• Amplitude momentum correlation
• Transverse emittance growth vs pz
• Seems MICE VI baseline does not cool with an
  energy spread
• The 3p/2 resonance is a good candidate for a
  cause
• It would be interesting to look at general
  non-linear beam optics
• We should be able to fix it by changing the
  magnetic lattice
• In particular changing the q0 Fourier mode ltB2gt
• But this needs to be verified
• Longitudinal emittance growth
• Longitudinal phase space is highly non-linear
• Some particles in the RF bucket, some not
• Emittance growth looks like it comes from the
  magnets here too
• I havent gone into enough detail on this yet
• There doesnt seem to be much literature on the
  subject

17
TOF, time and emittance

• We need the timing measurements for certain tasks
  not related to PID
• Longitudinal/6D emittance measurement
• Longitudinal emittance growth tells us where to
  sit on the dE/dx curve for best cooling
• Important for comparison with ring coolers, etc
• Longitudinal-transverse correlations
• As we have seen previously these are also
  important to MICE
• Phasing of RF RF bucket
• For these tasks
• Timing measurement should be considered after any
  detector material
• Timing measurement should be considered in the
  same plane as the other phase space variables
  (position, momentum, energy)
• Think of MICE cooling channel as a black box
• Measure phase space variables at each end of the
  cooling channel
• Seek to understand what happens in between

18
Time at TRP

• Seek to extrapolate TOF2 measurements into the
  tracker
• Malcolm defines a Tracker Reference Plane (TRP)
  at the inside edge of the tracker
• Seek to transport time measurement from TOF using
  energy measurement at SciFi
• Track reconstructed particles from SciFi recon
  plane to TOF using G4MICE
• Calculate time at TRP by t(z TRP) t(z TOF)
  dttracking
• Tracking using reconstructed phase space
  variables from the downstream TRP to TOF2 (using
  G4MICE)
• Expect to introduce an error from tracking s(t)
  s(dt/dz)Dz
• I use standard beam matched to 4 T
• Assume we have selected a beam with s(t) 500 ps
  upstream
• In reality s(t) would grow in MICE but for
  convenience I assume it is 500 ps in the
  downstream tracker as well
• s(E) 25 MeV

19
Detector Resolutions
Emeas - Etrue from SciFi
tmeas -ttrue from TOF
Full tracker
dElt10 MeV

• Crucial variables are energy (dt/dz) resolution
  and time resolution
• No TOF reconstruction yet so I assume a Gaussian
  distribution in t
• No correlations with other phase space variables
• Start with 70 ps resolution from TRD
• Energy resolution looks rather large (rms21 MeV)
• Malcolm informs me this is a bug
• I will also try a cut dE lt 10 MeV gt (rms 5 MeV)

20
Error due to s(E)
dt(ztrp) ttrue - textr
textr (recon flight time from TRP to TOF)
Full tracker s(dt) 181 ps ltdtgt 27 ps
Full tracker
dElt10 MeV
dElt10 MeV s(dt) 93 ps ltdtgt 29 ps

• Reconstructed flight time from TRP to TOF 7 ns
• Track downstream to the TOF
• Take out stochastic effects from the tracking,
  but still include ltdE/dzgt from the tracker
• See 25 ps offset
• Doesnt effect emittance measurement
• Significant effect even without the larger
  momentum spread
• Compare with TOF resolution 70 ps

21
Overall time resolution
dt(ztrp) tmeas - textr
Full tracker s(dt) 192 ps ltdtgt 26 ps
dElt10 MeV s(dt) 114 ps ltdtgt 28 ps

• Time resolution at TRP roughly addition in
  quadrature of time resolution at TOF and time
  resolution from extrapolation
• Calculated s(t) 194, 116 from addition in
  quadrature
• Nb I define the 0 of time at the TRP

22
Time res at TRP vs Tof res
s(ttotal) ns
s(ttotal) ns
Full tracker
dElt10 MeV
s(ttof) ps
s(ttof) ps

• Time resolution at TRP
• Note the axes are different
• 0.4-0.5 vs 0.1-0.2 ns
• Compare with bunch length 500 ps
• This answer is different to the one on the
  previous slide
• I have made a mistake somewhere (ran out of time)

23
Correlations
Erec - Etrue MeV
Erec - Etrue MeV
s(dt,dE) 1.97 ns MeV
s(E,dE) 11.4 MeV2
trec - ttrue ns
dt ns

• As expected, lots of correlations in the
  longitudinal phase space
• Energy and time errors are highly correlated
• E-dE correlation isnt as obvious
• Remember

24
Emittance at TRP vs Tof Res
el ns
el ns
Full tracker
dElt10 MeV
s(ttof) ps
s(ttof) ps

• Emittance resolution at TRP
• Again the axes are different
• Compare with true values
• 0.116 inside cut
• 0.119 outside cut

25
Time measurement issues

• This is still preliminary
• We need to measure time in MICE in order to
  measure longitudinal emittance
• Also transverse-longitudinal correlations
• Also RF bucket RF phase
• A timing resolution of 70 ps is desirable to
  get a decent resolution on emittance
• Timing at the TRP is crucially dependent on
  tracker resolution
• Once the tracker bug is fixed, we should see an
  improvement in the resolution
• With target tracker resolution 5MeV, we see of
  order 932 ps2 contribution to time resolution at
  TRP
• I need to check the mistake in the time
  resolution calculation
• The major hole really is understanding of the
  longitudinal emittance growth

26
Future

• To write a MICE note on TOF II resolution
  requirement I need
• To understand/resolve longitudinal emittance
  growth in MICE
• Feeling is this means moving off the resonance
• Need to check
• Fall back use FS2 lattice (also has a notceable
  resonance)
• To get a working reconstruction of pz
• Fall back cut on pt or use a fitted
  reconstruction
• To check/fix TOF resolution plots
• These issues require input from other people
• The time pressure is becoming more critical
• Can we run on crest at MICE V?
• What is the time scale for a decision if any?
• What is the effect of a realistic RF field?
• Is it reasonable to run without a central
  absorber?