KATRIN ToF Simulations and Analysis
Alexander Fulst
15th February 2016
Table of Contents
1
KATRIN
2
Idea of ToF measurements
3
SDS II measurements
Measurement plan
Measurement execution
4
Simulations
Prerequisites
Proof of Concept
First Results
5
Summary and Outlook
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
2
KATRIN
KATRIN
KArlsruhe TRItium Neutrino Experiment
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
3
KATRIN
Neutrinos have a finite mass
Figure: Zenith angle distribution of e-like and µ-like events in Super-Kamiokande
with momenta above and below 1.33 GeV with expectation (boxes) and best fit
(lines) [1]
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
4
KATRIN
Neutrinos have a finite mass
Figure: Zenith angle distribution of e-like and µ-like events in Super-Kamiokande
with momenta above and below 1.33 GeV with expectation (boxes) and best fit
(lines) [1]
Nobel Prize in Physics 2015: T. Kajita
and A. McDonald
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
4
KATRIN
Neutrinos have a finite mass
Figure: Zenith angle distribution of e-like and µ-like events in Super-Kamiokande
with momenta above and below 1.33 GeV with expectation (boxes) and best fit
(lines) [1]
Nobel Prize in Physics 2015: T. Kajita
and A. McDonald
Alexander Fulst
KATRIN ToF Simulations and Analysis
only gives ∆m2 , no
absolute scale
15th February 2016
4
KATRIN
Overview over KATRIN
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
5
KATRIN
Overview over KATRIN
direct determination of ν̄e mass (incoherent sum over mass
eigenstates)
endpoint of e − -spectrum from 3 H → 3 He+ + e − + ν̄e decay
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
5
KATRIN
Overview over KATRIN
direct determination of ν̄e mass (incoherent sum over mass
eigenstates)
endpoint of e − -spectrum from 3 H → 3 He+ + e − + ν̄e decay
Figure: β-spectrum of tritium [2]
needed: strong source, high acceptance, low background
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
5
KATRIN
Overview over KATRIN
direct determination of ν̄e mass (incoherent sum over mass
eigenstates)
endpoint of e − -spectrum from 3 H → 3 He+ + e − + ν̄e decay
Figure: β-spectrum of tritium [2]
needed: strong source, high acceptance, low background
upper limit of ≈ 0.2 eV (90% C.L.), mν = 0.35 eV: 5σ
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
5
KATRIN
Figure: schematic setup of KATRIN
(a) Rear Section
(b) WGTS (1011 Bq)
(c) DPS
(d) CPS (total reduction of gas flow by 1012 )
(e) Pre-Spectrometer (f) Main Spectrometer (energy resolution of 0.93 eV)
(g) Detector Section
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
6
KATRIN
Figure: layout and working principle of a Magnetic Adiabatic Collimation
combined with an Electrostatic (MAC-E) filter
adiabatic: magnetic moment µ =
energy resolution:
Alexander Fulst
∆E
E
=
E⊥
B
is constant
Bmin
Bmax
KATRIN ToF Simulations and Analysis
15th February 2016
7
Idea of ToF measurements
Idea of ToF measurements
Time-of-Flight
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
8
Idea of ToF measurements
Simple ToF
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
9
Idea of ToF measurements
Simple ToF
measuring the time-of-flight of particles gives information about their
energy
Figure: differential ( dN
dE (E ), left) and integrated (Ṅ(qU), right) spectrum [4]
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
9
Idea of ToF measurements
Simple ToF
most simple case: non-relativistic non-accelerated motion
v=
q
Alexander Fulst
2Ekin
m
⇒t=
qs
2Ekin
m
KATRIN ToF Simulations and Analysis
15th February 2016
10
Idea of ToF measurements
Simple ToF
most simple case: non-relativistic non-accelerated motion
v=
q
2Ekin
m
⇒t=
qs
2Ekin
m
in KATRIN electrons get slowed down/accelerated in the main
spectrometer
furthermore: electrons have different pitch angles to B-field, cyclotron
motion causes longer ToF
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
10
Idea of ToF measurements
Figure: ToF for simulated electrons with standard KATRIN setup
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
11
Idea of ToF measurements
Figure: ToF for simulated electrons with standard KATRIN setup
Problem
start signal needed to measure ToF
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
11
Idea of ToF measurements
Figure: ToF spectrum for different neutrino masses at 18570 eV retarding
potential and 18574 eV endpoint energy [3]
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
12
Idea of ToF measurements
Time Focusing Time-of-Flight (tfToF)
most simple solution is a gated filter
periodic blocking of continous beam gives small start window
sensitivity of σstat (mν2e ) = 0.021 eV2 compared to standard
σstat (mν2e ) = 0.020 eV2 [3]
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
13
Idea of ToF measurements
Time Focusing Time-of-Flight (tfToF)
most simple solution is a gated filter
periodic blocking of continous beam gives small start window
sensitivity of σstat (mν2e ) = 0.021 eV2 compared to standard
σstat (mν2e ) = 0.020 eV2 [3]
use time-varying potential to accelerate electrons
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
13
Idea of ToF measurements
Time Focusing Time-of-Flight (tfToF)
most simple solution is a gated filter
periodic blocking of continous beam gives small start window
sensitivity of σstat (mν2e ) = 0.021 eV2 compared to standard
σstat (mν2e ) = 0.020 eV2 [3]
use time-varying potential to accelerate electrons
electrons arriving later are accelerated more than electrons arriving
early, comparable to bunching in accelerators
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
13
Idea of ToF measurements
Time Focusing Time-of-Flight (tfToF)
most simple solution is a gated filter
periodic blocking of continous beam gives small start window
sensitivity of σstat (mν2e ) = 0.021 eV2 compared to standard
σstat (mν2e ) = 0.020 eV2 [3]
use time-varying potential to accelerate electrons
electrons arriving later are accelerated more than electrons arriving
early, comparable to bunching in accelerators
periodicity of potential change also gives a start signal
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
13
SDS II measurements
SDS II measurements
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
14
SDS II measurements
Figure: concept of tfToF Main Spectrometer setup
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
15
SDS II measurements
Measurement plan
What does the potential in the spectrometer look like?
one cannot directly measure the real applied voltage on the inner
electrodes
egun needed to analyze the potential
Figure: Kepco input vs output
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
16
SDS II measurements
Central Part
5 rings
connected
ring 7-11
ring 6
Flat Cone
3 rings
wire
layer
wire
layer
ring 5
Outer
Inner
Main
Spectrometer
vessel
ring 4
ring 3
Steep Cone
2 rings
ring 2
390kΩ
2x200V
...
HV
distribution
rack
...
+500V 2x22
Single channel
offset supplies
ISEG EHS 8205
IE common west
-1kV Dipole
supply FuG
HCV 2M-1000
IE common east
Dipol east
Dipole west
e-gun HV cage
IE common
-2kV ISEG
NHQ 122m
External
supplies
IE Global
Offset
North
-35kV FuG
HCN 140M35000
Triode
Protection board
Wire electrode Ring 12 – 16 Inner and Outer Wire Layer
50
4.7nF
E-gun
LED
50
Channel 21
Patch Panel West
Tektronix
function
generator
3102
+
Sync
Out
- +
-
Patch Panel East
Amplifier
Kepco BOP 1000M
Agilent function
generator 33220A
+
Sync
-
+
Out
-
230V Supply
2V
Supply
+
In
-
+
Out
-
Supply
Vessel Potential -18.4kV
Figure: standard (top) and pulsed-cone tfToF (bottom) HV setup
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
17
SDS II measurements
Measurement execution
Measurement execution
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
18
SDS II measurements
Measurement execution
Measurement execution
30
Agilent pulser as master with rate of
1 kHz (provides waveform for Kepco
and trigger for egun pulser)
ra mp ed vo lta g e [V]
20
10
0
−10
−20
−30
0
200
400
600
800
1,000
time [ μs ]
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
18
SDS II measurements
Measurement execution
Measurement execution
30
Agilent pulser as master with rate of
1 kHz (provides waveform for Kepco
and trigger for egun pulser)
ra mp ed vo lta g e [V]
20
10
0
−10
−20
−30
0
200
400
600
800
1,000
time [ μs ]
egun pulser at 24 kHz means 42 µs pulse period and 15 ◦ phase shift
between pulses
24 egun pulses per cycle, electron ToF is expected to be less than 25 µs
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
18
SDS II measurements
Measurement execution
Measurement execution
30
Agilent pulser as master with rate of
1 kHz (provides waveform for Kepco
and trigger for egun pulser)
ra mp ed vo lta g e [V]
20
10
0
−10
−20
−30
0
200
400
600
800
1,000
time [ μs ]
egun pulser at 24 kHz means 42 µs pulse period and 15 ◦ phase shift
between pulses
24 egun pulses per cycle, electron ToF is expected to be less than 25 µs
for finer scanning, measurements are repeated for phase shifts from
0 ◦ to 13.5 ◦ in 1.5 ◦ steps
this results in 240 pulses during a waveform of 1000 µs
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
18
SDS II measurements
Measurement execution
Measurement execution
30
Agilent pulser as master with rate of
1 kHz (provides waveform for Kepco
and trigger for egun pulser)
ra mp ed vo lta g e [V]
20
10
0
−10
−20
−30
0
200
400
600
800
1,000
time [ μs ]
egun pulser at 24 kHz means 42 µs pulse period and 15 ◦ phase shift
between pulses
24 egun pulses per cycle, electron ToF is expected to be less than 25 µs
for finer scanning, measurements are repeated for phase shifts from
0 ◦ to 13.5 ◦ in 1.5 ◦ steps
this results in 240 pulses during a waveform of 1000 µs
whole procedure repeated for different surplus energies from 0 eV to
5 eV in 0.5 eV steps
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
18
SDS II measurements
Measurement execution
tfTOF spectrum
(phase-aligned, shifted AP, 50 V tf amplitude)
300
phase = 0.0°, energy = 1.0
phase = 4.5°, energy = 1.0
electron count
250
200
150
100
50
0
0
200
400
time of arrival [us]
600
800
1000
Figure: 0 ◦ and 4.5 ◦ waveform scanning for surplus energy of 1 eV
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
19
Simulations
Simulations
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
20
Simulations
Prerequisites
Prerequisites
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
21
Simulations
Prerequisites
Prerequisites
Kassiopeia framework brings nearly everything needed for simulation...
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
21
Simulations
Prerequisites
Prerequisites
Kassiopeia framework brings nearly everything needed for simulation...
... but does not support time-varying potentials!
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
21
Simulations
Prerequisites
Prerequisites
Kassiopeia framework brings nearly everything needed for simulation...
... but does not support time-varying potentials!
there was the idea to multiply the calculated field with a
time-dependent factor
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
21
Simulations
Prerequisites
Prerequisites
Kassiopeia framework brings nearly everything needed for simulation...
... but does not support time-varying potentials!
there was the idea to multiply the calculated field with a
time-dependent factor
this idea was picked up and extended to use two different
pre-calculated fields A and B
i.e. α(t) · A + (1 − α(t)) · B
(e.g. α(t) = 0.5 + 0.5 sin (ω · t))
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
21
Simulations
Prerequisites
Prerequisites
Kassiopeia framework brings nearly everything needed for simulation...
... but does not support time-varying potentials!
there was the idea to multiply the calculated field with a
time-dependent factor
this idea was picked up and extended to use two different
pre-calculated fields A and B
i.e. α(t) · A + (1 − α(t)) · B
(e.g. α(t) = 0.5 + 0.5 sin (ω · t))
−40
−50
potential [V]
−60
−70
−80
−90
−100
−110
−200
0
200
400
600
800
1,000
1,200
t i me [ μs]
Figure: concept of using two fields and interpolating between them
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
21
Simulations
Proof of Concept
Proof of Concept
Figure: simple oscillation test setup to show time-dependent fields
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
22
Simulations
Proof of Concept
Figure: simple transmission test setup to show time-dependent fields
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
23
Simulations
Proof of Concept
1.0
transmission probability
0.8
0.6
0.4
0.2
0.0
100
fit: 1.00-0.88*sin(1.00*2pi/1000)
simulated data
0
100
200
300
400
500
600
start time in ms
Figure: transmission probability over time
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
24
Simulations
First Results
0.1 eV surplus energy
70
60
counts
50
40
30
20
10
0
0
200
400
600
800
1000
time of arrival / us
tfTOF spectrum
(phase-aligned, shifted AP, 50 V tf amplitude)
300
phase = 0.0°, energy = 1.0
phase = 4.5°, energy = 1.0
electron count
250
200
150
100
50
0
0
200
400
time of arrival [us]
600
800
1000
Figure: full waveform scanning for surplus energy of 0.1 eV surplus (simulated,
top) and 1 eV (bottom, measured)
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
25
Simulations
First Results
0.5 eV surplus energy
1400
1200
counts
1000
800
600
400
200
0
10
15
20
25
30
35
25
30
35
time of flight / us
2.0 eV surplus energy
3000
2500
counts
2000
1500
1000
500
0
10
15
20
time of flight / us
Figure: ToF spectrum for 0.5 eV (top) and 2.0 eV (bottom) surplus energy
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
26
Simulations
First Results
1.0 eV surplus energy, 0.0° phase shift
800
700
600
counts
500
400
300
200
100
0
10
11
12
13
14
15
time of flight / us
Figure: ToF distribution in dependence of start time for 1.0 eV surplus, blue: first
500 µs, red: 500 − 1000 µs
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
27
Summary and Outlook
Summary and Outlook
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
28
Summary and Outlook
Summary and Outlook
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
29
Summary and Outlook
Summary and Outlook
time-varying fields have been implemented and work as intended
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
29
Summary and Outlook
Summary and Outlook
time-varying fields have been implemented and work as intended
simulations look good at the first glance
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
29
Summary and Outlook
Summary and Outlook
time-varying fields have been implemented and work as intended
simulations look good at the first glance
open questions for measured data (shift and background/phase
effects)
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
29
Summary and Outlook
Summary and Outlook
time-varying fields have been implemented and work as intended
simulations look good at the first glance
open questions for measured data (shift and background/phase
effects)
next steps:
identify peaks in measured data and analyze them
find the waveform best matching the data
optimize waveform to use for real measurements
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
29
Summary and Outlook
Thank you for your attention
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
30
Summary and Outlook
Literatur und Abbildungen
Y. Ashie et al.: ”Measurement of atmospheric neutrino oscillation
parameters by Super-Kamiokande I”, in Phys. Rev. Lett. D71, 112005
(2005)
KATRIN homepage http://www.katrin.kit.edu/79.php as of
10.02.2016
N. Steinbrink et al.: ”Neutrino mass sensitivity by MAC-E Filter based
time-of-flight spectroscopy with the example of KATRIN”, in New
Journal of Physics 15 (2013) 113020
M. Kleesik: ”A Data-Analysis and Sensitivity-Optimization Framework
for the KATRIN Experiment”, PhD thesis (2014)
Alexander Fulst
KATRIN ToF Simulations and Analysis
15th February 2016
31