Transcript MICE pencil beam raster scan simulation study Andreas Jansson Quick recap of study goal • Would like to see if MICE can test details.

MICE
pencil beam raster scan
simulation study
Andreas Jansson
Quick recap of study goal
• Would like to see if MICE can test details of
simulations, such as e.g. energy straggling.
• “Brute force” method would require very fine binning
of initial values (smaller than the features to be
resolved), yielding few events/bin and hence poor
statistics.
• Perhaps this could be overcome by comparing each
measured track to a large number of MC tracks with
identical initial coordinates, and normalize the
measured deviation in final coordinates from the
(simulated) expectation values using the (simulated)
covariance matrix.
• This should reduce the need for fine binning, and
improve statistics…
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MICE analysis meeting
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The MICE model
• Using g4beamline MICE file(s) from Tom Roberts
(minus beamline).
– “TRD CM13 Flip mode, Case 1 Stage VI”
– 8MV/m, 90 degree RF phase (no longitudinal focusing)
• Tracking from last plane in tracker one (z=-4.65m)
to first plane in tracker two (z=+4.65m).
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The method
• Launch zero emittance “beamlet” with
various 6D initial offsets.
– Look at exit distribution mean, as a
function of initial offsets (e.g. in some
input parameter plane).
– Look at transmission vs offset
– Look at beamlet rms emittance at exit as a
function of initial offsets.
– Look at distribution of the beam as a
function of offset in some particular
direction.
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x-y input plane
px x, y
50
50
50
50
0
50
50
0
50
100
0
50
100
100
0
50
100
0
50
100
100 50
100
100
50
0
50 100
100
0
x mm
x mm
x mm
t x, y
pz x, y
N x, y
E x, y
100
100
50
50
50
50
0
0
y mm
100
y mm
100
0
50
50
50
100
100
100
100
50
0
x mm
50
100
100 50
0
50
x mm
100
100
50
0
x mm
50 100
50
100
50
100
0
50
100
50
x mm
y mm
y mm
0
y mm
100
y mm
100
100
•
py x, y
100
50
•
y x, y
100
y mm
y mm
x x, y
100
50
0
x mm
Mean 6D parameters (x,px,y,py,t,pz) values at exit, as well as
transmission (N) and exit beamlet emittance (E).
Color code: White is higher value, blue is low values.
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x-x’ input plane
px x,xp
0.4
0.2
0.2
0.0
0.2
0.0
0.2
0.4
50
0
50
100
xp rad
0.4
0.2
xp rad
0.4
100
0.0
0.2
0.4
100
50
0
50
100
0.0
0.2
0.4
100
50
0
50
100
100
0
x mm
x mm
x mm
t x,xp
pz x,xp
N x,xp
N x,xp
0.4
0.4
0.2
0.2
0.2
0.0
0.2
0.4
0.0
0.2
0.4
50
0
x mm
50
100
xp rad
0.4
0.2
xp rad
0.4
100
50
x mm
xp rad
xp rad
py x,xp
0.2
0.4
•
y x,xp
0.4
xp rad
xp rad
x x,xp
0.0
0.2
0.4
100
50
0
50
x mm
100
50
100
50
100
0.0
0.2
0.4
100
50
0
x mm
50
100
100
50
0
x mm
Mean 6D parameters (x,px,y,py,t,pz) values at exit, as well as
transmission (N) and exit beamlet emittance (E)
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x’-y’ input plane
px y, yp
0.4
0.2
0.2
0.0
0.2
0.0
0.2
0.4
yp rad
0.4
0.2
yp rad
0.4
0.0
0.2
0.4
0.0
0.2
0.4
0.4 0.20.0 0.2 0.4
0.4 0.2 0.0 0.2 0.4
0.4 0.2 0.0 0.2 0.4
0.4 0.2 0.0 0.2 0.4
xp rad
xp rad
xp rad
xp rad
t y, yp
pz y, yp
N y, yp
E y, yp
0.4
0.4
0.2
0.2
0.2
0.0
0.2
0.4
0.0
0.2
0.4
yp rad
0.4
0.2
yp rad
0.4
yp rad
yp rad
py y, yp
0.2
0.4
•
y y, yp
0.4
yp rad
yp rad
x y, yp
0.0
0.2
0.4
0.0
0.2
0.4
0.4 0.20.0 0.2 0.4
0.4 0.2 0.0 0.2 0.4
0.4 0.2 0.0 0.2 0.4
0.4 0.2 0.0 0.2 0.4
xp rad
xp rad
xp rad
xp rad
Mean 6D parameters (x,px,y,py,t,pz) values at exit, as well as
transmission (N) and exit beamlet emittance (E)
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x-y’ input plane
px x, yp
0.4
0.2
0.2
0.0
0.2
0.0
0.2
0.4
50
0
50
100
yp rad
0.4
0.2
yp rad
0.4
100
0.0
0.2
0.4
100
50
0
50
100
0.0
0.2
0.4
100
50
0
50
100
100
0
x mm
x mm
x mm
t x, yp
pz x, yp
N x, yp
E x, yp
0.4
0.4
0.2
0.2
0.2
0.0
0.2
0.4
0.0
0.2
0.4
50
0
x mm
50
100
yp rad
0.4
0.2
yp rad
0.4
100
50
x mm
yp rad
yp rad
py x, yp
0.2
0.4
•
y x, yp
0.4
yp rad
yp rad
x x, yp
0.0
0.2
0.4
100
50
0
50
x mm
100
50
100
50
100
0.0
0.2
0.4
100
50
0
x mm
50
100
100
50
0
x mm
Mean 6D parameters (x,px,y,py,t,pz) values at exit, as well as
transmission (N) and exit beamlet emittance (E)
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Effect of injection position
y
px
0.15
0.15
py
0.15
0.10
0.10
0.10
0.05
0.05
0.05
x
0.15
0.10
0.05
0.05
0.10
0.15
x
0.15
0.10
0.05
0.05
0.10
0.15
0.05
0.05
0.05
0.10
0.10
0.10
0.15
0.15
0.15
0.15
0.15
px
0.15
0.10
0.10
0.10
0.05
0.05
0.05
py
px
0.15 0.10 0.05
0.05 0.10 0.15
0.05
0.10
0.15
0.05
0.10
0.15
x
0.15
0.10
0.05
0.05
0.10
0.15
y
0.15
0.10
0.05
0.05
0.05
0.05
0.10
0.10
0.10
0.15
0.15
0.15
Initial dx=0,20,40,60,80,100 mm
At larger amplitudes, exit distribution curls up and spreads out
azimuthally
–
–
•
0.10
0.05
py
•
•
y
0.15
Distribution is not well described by second moments alone
Large beamlet rms emittance growth at large amplitudes due to nonlinearities
If beam properly matched, azimuthal spread produces randomization
of phases (filamentation), not necessarily emittance (action) increase.
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Pz, exit time and transverse amplitude
pz
pz
180
180
160
160
140
140
120
120
100
100
t
36
37
38
39
40
radius
0.02
•
•
•
0.04
0.06
0.08
0.10
There is no energy balance at large amplitudes
– Longer path length + no longitudinal focussing => less reacceleration
– Larger angles at absorber => more energy loss
This effective energy loss as a function of amplitudes is what causes
phase space to “curl up”.
Can not separate transverse from longitudinal planes!
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Pz versus azimuth
• The spread in azimuth
is due to the spread in
momentum, which in
turn comes from energy
straggling.
– This is a fairly sizeable
effect
– May be a way to measure
energy straggling in
MICE!
– Requires tight binning in
e.g. initial radius
coordinate
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pz
180
160
140
120
100
azimuth
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Effect of injection angle
0.15
y
xp
0.15
yp
0.15
0.10
0.10
0.10
0.05
0.05
0.05
pz
195
x
0.15
0.10
0.05
0.05
0.10
0.15
x
0.15
0.10
0.05
0.05
0.10
0.15
y
0.15
0.10
0.05
0.05
0.10
0.15
190
0.05
0.05
0.05
0.10
0.10
0.10
0.15
0.15
0.15
yp
0.15
yp
0.15
xp
0.15
0.10
0.10
0.10
0.05
0.05
0.05
185
180
175
xp
0.15
0.10
0.05
0.05
0.10
0.15
170
x
0.15
0.10
0.05
0.05
0.10
0.15
y
0.15
0.10
0.05
0.05
0.10
0.15
t
36.0
•
•
0.05
0.05
0.05
0.10
0.10
0.10
0.15
0.15
0.15
36.5
Initial dx’=0,100,200,400 mrad.
Same effect as with position offset, although less pronounced (as
momentum correlation is less pronounced).
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MICE analysis meeting
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Conclusions so far
• Energy imbalance for large transverse amplitude particles
– This ties transverse and longitudinal planes together and
complicates any “longitudinal slice” analysis
– Are these particles “cooled” in any sense? Not clear at this point.
• Normalization of measured deviations by second moments
of MC distribution (covariance matrix) does not work for
large amplitudes
– At least not in cartesian coordinates…
• Perhaps use cylindrical coordinates instead?
– Natural because of cylindrical symmetry.
– Tight binning may only be required in some coordinates.
– E.g. spread in azimuth for large radii may be a way to quantify
energy straggling.
– Obviously, more study (and realistic errors) are needed.
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MICE analysis meeting
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